Satallax---3.5.THM-Prf.s

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEU793^1 : 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 : n011.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 02:50:04 PM UTC 2025

% Result   : Theorem 276.17s 275.97s
% Output   : Proof 277.02s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : SEU793^1 : 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
% 0.12/0.34  % Computer : n011.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Wed Oct  8 21:49:53 EDT 2025
% 0.12/0.34  % CPUTime  : 
% 276.17/275.97  % SZS status Theorem
% 276.17/275.97  % Mode: mode498:USE_SINE=true:SINE_TOLERANCE=1.5:SINE_GENERALITY_THRESHOLD=16:SINE_RANK_LIMIT=2.:SINE_DEPTH=2
% 276.17/275.97  % Inferences: 796
% 276.17/275.97  % SZS output start Proof
% 276.17/275.97  thf(ty_kfst, type, kfst : ($i>$i)).
% 276.17/275.97  thf(ty_binintersect, type, binintersect : ($i>$i>$i)).
% 276.17/275.97  thf(ty_singleton, type, singleton : ($i>$o)).
% 276.17/275.97  thf(ty_if, type, if : ($i>$o>$i>$i>$i)).
% 276.17/275.97  thf(ty_subset, type, subset : ($i>$i>$o)).
% 276.17/275.97  thf(ty_setunion, type, setunion : ($i>$i)).
% 276.17/275.97  thf(ty_iskpair, type, iskpair : ($i>$o)).
% 276.17/275.97  thf(ty_breln1invset, type, breln1invset : ($i>$i>$i)).
% 276.17/275.97  thf(ty_eigen__1, type, eigen__1 : ($i>$i)).
% 276.17/275.97  thf(ty_eigen__0, type, eigen__0 : $i).
% 276.17/275.97  thf(ty_cartprod, type, cartprod : ($i>$i>$i)).
% 276.17/275.97  thf(ty_breln, type, breln : ($i>$i>$i>$o)).
% 276.17/275.97  thf(ty_emptyset, type, emptyset : $i).
% 276.17/275.97  thf(ty_breln1, type, breln1 : ($i>$i>$o)).
% 276.17/275.97  thf(ty_setminus, type, setminus : ($i>$i>$i)).
% 276.17/275.97  thf(ty_kpair, type, kpair : ($i>$i>$i)).
% 276.17/275.97  thf(ty_descr, type, descr : (($i>$o)>$i)).
% 276.17/275.97  thf(ty_reflwellordering, type, reflwellordering : ($i>$i>$o)).
% 276.17/275.97  thf(ty_breln1compset, type, breln1compset : ($i>$i>$i>$i)).
% 276.17/275.97  thf(ty_breln1Set, type, breln1Set : ($i>$i)).
% 276.17/275.97  thf(ty_ap, type, ap : ($i>$i>$i>$i>$i)).
% 276.17/275.97  thf(ty_funcSet, type, funcSet : ($i>$i>$i)).
% 276.17/275.97  thf(ty_symdiff, type, symdiff : ($i>$i>$i)).
% 276.17/275.97  thf(ty_dsetconstr, type, dsetconstr : ($i>($i>$o)>$i)).
% 276.17/275.97  thf(ty_powerset, type, powerset : ($i>$i)).
% 276.17/275.97  thf(ty_omega, type, omega : $i).
% 276.17/275.97  thf(ty_ex1, type, ex1 : ($i>($i>$o)>$o)).
% 276.17/275.97  thf(ty_ksnd, type, ksnd : ($i>$i)).
% 276.17/275.97  thf(ty_prop2set, type, prop2set : ($o>$i)).
% 276.17/275.97  thf(ty_set2prop, type, set2prop : ($i>$o)).
% 276.17/275.97  thf(ty_lam, type, lam : ($i>$i>($i>$i)>$i)).
% 276.17/275.97  thf(ty_in, type, in : ($i>$i>$o)).
% 276.17/275.97  thf(ty_func, type, func : ($i>$i>$i>$o)).
% 276.17/275.97  thf(ty_binunion, type, binunion : ($i>$i>$i)).
% 276.17/275.97  thf(ty_dpsetconstr, type, dpsetconstr : ($i>$i>($i>$i>$o)>$i)).
% 276.17/275.97  thf(ty_setadjoin, type, setadjoin : ($i>$i>$i)).
% 276.17/275.97  thf(def_exu,definition,(exu = (^[X1:$i>$o]:(~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3)))))))))))).
% 276.17/275.97  thf(def_setextAx,definition,(setextAx = (![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) = ((in @ X3) @ X2))) => (X1 = X2)))))).
% 276.17/275.97  thf(def_emptysetAx,definition,(emptysetAx = (![X1:$i]:(~(((in @ X1) @ emptyset)))))).
% 276.17/275.97  thf(def_setadjoinAx,definition,(setadjoinAx = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) = ((~((X3 = X1))) => ((in @ X3) @ X2)))))))).
% 276.17/275.97  thf(def_powersetAx,definition,(powersetAx = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) = (![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1)))))))).
% 276.17/275.97  thf(def_setunionAx,definition,(setunionAx = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) = (~((![X3:$i]:(((in @ X2) @ X3) => (~(((in @ X3) @ X1)))))))))))).
% 276.17/275.97  thf(def_omega0Ax,definition,(omega0Ax = ((in @ emptyset) @ omega))).
% 276.17/275.97  thf(def_omegaSAx,definition,(omegaSAx = (![X1:$i]:(((in @ X1) @ omega) => ((in @ ((setadjoin @ X1) @ X1)) @ omega))))).
% 276.17/275.97  thf(def_omegaIndAx,definition,(omegaIndAx = (![X1:$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))))))).
% 276.17/275.97  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))))))))))))))))))).
% 276.17/275.97  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))))))))))))))).
% 276.17/275.97  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:$i]:(((in @ X7) @ X6) => ((in @ X7) @ X4))))) => ((in @ X5) @ X6)))))))))))))))))))))).
% 276.17/275.97  thf(def_descrp,definition,(descrp = (![X1:$i>$o]:((exu @ X1) => (X1 @ (descr @ X1)))))).
% 276.17/275.97  thf(def_dsetconstrI,definition,(dsetconstrI = (![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((in @ X3) @ ((dsetconstr @ X1) @ X2))))))))).
% 276.17/275.97  thf(def_dsetconstrEL,definition,(dsetconstrEL = (![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ ((dsetconstr @ X1) @ X2)) => ((in @ X3) @ X1))))))).
% 276.17/275.97  thf(def_dsetconstrER,definition,(dsetconstrER = (![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ ((dsetconstr @ X1) @ X2)) => (X2 @ X3))))))).
% 276.17/275.97  thf(def_exuE1,definition,(exuE1 = (![X1:$i>$o]:((exu @ X1) => (~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))))))).
% 276.17/275.97  thf(def_prop2setE,definition,(prop2setE = (![X1:$o]:(![X2:$i]:(((in @ X2) @ (prop2set @ X1)) => X1))))).
% 276.17/275.97  thf(def_emptysetE,definition,(emptysetE = (![X1:$i]:(((in @ X1) @ emptyset) => (![X2:$o]:X2))))).
% 276.17/275.97  thf(def_emptysetimpfalse,definition,(emptysetimpfalse = (![X1:$i]:(~(((in @ X1) @ emptyset)))))).
% 276.17/275.97  thf(def_notinemptyset,definition,(notinemptyset = (![X1:$i]:(~(((in @ X1) @ emptyset)))))).
% 276.17/275.97  thf(def_exuE3e,definition,(exuE3e = (![X1:$i>$o]:((exu @ X1) => (~((![X2:$i]:(~((X1 @ X2)))))))))).
% 276.17/275.97  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))))))).
% 276.17/275.97  thf(def_emptyI,definition,(emptyI = (![X1:$i]:((![X2:$i]:(~(((in @ X2) @ X1)))) => (X1 = emptyset))))).
% 276.17/275.97  thf(def_noeltsimpempty,definition,(noeltsimpempty = (![X1:$i]:((![X2:$i]:(~(((in @ X2) @ X1)))) => (X1 = emptyset))))).
% 276.17/275.97  thf(def_setbeta,definition,(setbeta = (![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ ((dsetconstr @ X1) @ X2)) = (X2 @ X3)))))))).
% 276.17/275.97  thf(def_nonempty,definition,(nonempty = (^[X1:$i]:(~((X1 = emptyset)))))).
% 276.17/275.97  thf(def_nonemptyE1,definition,(nonemptyE1 = (![X1:$i]:((nonempty @ X1) => (~((![X2:$i]:(~(((in @ X2) @ X1)))))))))).
% 276.17/275.97  thf(def_nonemptyI,definition,(nonemptyI = (![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => (nonempty @ ((dsetconstr @ X1) @ X2))))))))).
% 276.17/275.97  thf(def_nonemptyI1,definition,(nonemptyI1 = (![X1:$i]:((~((![X2:$i]:(~(((in @ X2) @ X1)))))) => (nonempty @ X1))))).
% 276.17/275.97  thf(def_setadjoinIL,definition,(setadjoinIL = (![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ X2)))))).
% 276.17/275.97  thf(def_emptyinunitempty,definition,(emptyinunitempty = ((in @ emptyset) @ ((setadjoin @ emptyset) @ emptyset)))).
% 276.17/275.97  thf(def_setadjoinIR,definition,(setadjoinIR = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ ((setadjoin @ X1) @ X2)))))))).
% 276.17/275.97  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))))))))).
% 276.17/275.97  thf(def_setadjoinOr,definition,(setadjoinOr = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) => ((~((X3 = X1))) => ((in @ X3) @ X2)))))))).
% 276.17/275.97  thf(def_setoftrueEq,definition,(setoftrueEq = (![X1:$i]:(((dsetconstr @ X1) @ (^[X2:$i]:(~($false)))) = X1)))).
% 276.17/275.97  thf(def_powersetI,definition,(powersetI = (![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1))) => ((in @ X2) @ (powerset @ X1))))))).
% 276.17/275.97  thf(def_emptyinPowerset,definition,(emptyinPowerset = (![X1:$i]:((in @ emptyset) @ (powerset @ X1))))).
% 276.17/275.97  thf(def_emptyInPowerset,definition,(emptyInPowerset = (![X1:$i]:((in @ emptyset) @ (powerset @ X1))))).
% 276.17/275.97  thf(def_powersetE,definition,(powersetE = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X2) @ (powerset @ X1)) => (((in @ X3) @ X2) => ((in @ X3) @ X1)))))))).
% 276.17/275.97  thf(def_setunionI,definition,(setunionI = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X2) @ X3) => (((in @ X3) @ X1) => ((in @ X2) @ (setunion @ X1))))))))).
% 276.17/275.97  thf(def_setunionE,definition,(setunionE = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) => (![X3:$o]:((![X4:$i]:(((in @ X2) @ X4) => (((in @ X4) @ X1) => X3))) => X3))))))).
% 276.17/275.97  thf(def_subPowSU,definition,(subPowSU = (![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((in @ X2) @ (powerset @ (setunion @ X1)))))))).
% 276.17/275.97  thf(def_exuE2,definition,(exuE2 = (![X1:$i>$o]:((exu @ X1) => (~((![X2:$i]:(~((![X3:$i]:((X1 @ X3) = (X3 = X2)))))))))))).
% 276.17/275.97  thf(def_nonemptyImpWitness,definition,(nonemptyImpWitness = (![X1:$i]:((nonempty @ X1) => (~((![X2:$i]:(~(((in @ X2) @ X1)))))))))).
% 276.17/275.97  thf(def_uniqinunit,definition,(uniqinunit = (![X1:$i]:(![X2:$i]:(((in @ X1) @ ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))))).
% 276.17/275.97  thf(def_notinsingleton,definition,(notinsingleton = (![X1:$i]:(![X2:$i]:((~((X1 = X2))) => (~(((in @ X2) @ ((setadjoin @ X1) @ emptyset))))))))).
% 276.17/275.97  thf(def_eqinunit,definition,(eqinunit = (![X1:$i]:(![X2:$i]:((X1 = X2) => ((in @ X1) @ ((setadjoin @ X2) @ emptyset))))))).
% 276.17/275.97  thf(def_singletonsswitch,definition,(singletonsswitch = (![X1:$i]:(![X2:$i]:(((in @ X1) @ ((setadjoin @ X2) @ emptyset)) => ((in @ X2) @ ((setadjoin @ X1) @ emptyset))))))).
% 276.17/275.97  thf(def_upairsetE,definition,(upairsetE = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) => ((~((X3 = X1))) => (X3 = X2)))))))).
% 276.17/275.97  thf(def_upairsetIL,definition,(upairsetIL = (![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))))).
% 276.17/275.97  thf(def_upairsetIR,definition,(upairsetIR = (![X1:$i]:(![X2:$i]:((in @ X2) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))))).
% 276.17/275.97  thf(def_emptyE1,definition,(emptyE1 = (![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => (~((((dsetconstr @ X1) @ X2) = emptyset)))))))).
% 276.17/275.97  thf(def_vacuousDall,definition,(vacuousDall = (![X1:$i>$o]:(![X2:$i]:(((in @ X2) @ emptyset) => (X1 @ X2)))))).
% 276.17/275.97  thf(def_quantDeMorgan1,definition,(quantDeMorgan1 = (![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3))))) => (~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3)))))))))).
% 276.17/275.97  thf(def_quantDeMorgan2,definition,(quantDeMorgan2 = (![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))) => (![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))))).
% 276.17/275.97  thf(def_quantDeMorgan3,definition,(quantDeMorgan3 = (![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))) => (![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))))).
% 276.17/275.97  thf(def_quantDeMorgan4,definition,(quantDeMorgan4 = (![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3))))) => (~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3)))))))))).
% 276.17/275.97  thf(def_prop2setI,definition,(prop2setI = (![X1:$o]:(X1 => ((in @ emptyset) @ (prop2set @ X1)))))).
% 276.17/275.97  thf(def_prop2set2propI,definition,(prop2set2propI = (![X1:$o]:(X1 => (set2prop @ (prop2set @ X1)))))).
% 276.17/275.97  thf(def_notdexE,definition,(notdexE = (![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))) => (![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))))).
% 276.17/275.97  thf(def_notdallE,definition,(notdallE = (![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3))))) => (~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3)))))))))).
% 276.17/275.97  thf(def_exuI1,definition,(exuI1 = (![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (exu @ X1))))).
% 276.17/275.97  thf(def_exuI3,definition,(exuI3 = (![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => ((![X2:$i]:(![X3:$i]:((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))) => (exu @ X1)))))).
% 276.17/275.97  thf(def_exuI2,definition,(exuI2 = (![X1:$i>$o]:((~((![X2:$i]:(~((![X3:$i]:((X1 @ X3) = (X3 = X2)))))))) => (exu @ X1))))).
% 276.17/275.97  thf(def_inCongP,definition,(inCongP = (![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((in @ X3) @ X1) => ((in @ X4) @ X2)))))))))).
% 276.17/275.97  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)))))))))).
% 276.17/275.97  thf(def_exuE3u,definition,(exuE3u = (![X1:$i>$o]:((exu @ X1) => (![X2:$i]:(![X3:$i]:((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))))))).
% 276.17/275.97  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))))))).
% 276.17/275.97  thf(def_emptyset__Cong,definition,(emptyset__Cong = (emptyset = emptyset))).
% 276.17/275.97  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)))))))))).
% 276.17/275.97  thf(def_powerset__Cong,definition,(powerset__Cong = (![X1:$i]:(![X2:$i]:((X1 = X2) => ((powerset @ X1) = (powerset @ X2))))))).
% 276.17/275.97  thf(def_setunion__Cong,definition,(setunion__Cong = (![X1:$i]:(![X2:$i]:((X1 = X2) => ((setunion @ X1) = (setunion @ X2))))))).
% 276.17/275.97  thf(def_omega__Cong,definition,(omega__Cong = (omega = omega))).
% 276.17/275.97  thf(def_exuEu,definition,(exuEu = (![X1:$i>$o]:((exu @ X1) => (![X2:$i]:(![X3:$i]:((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))))))).
% 276.17/275.97  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))))))))).
% 276.17/275.97  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)))))))))).
% 276.17/275.97  thf(def_subsetI1,definition,(subsetI1 = (![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((subset @ X1) @ X2)))))).
% 276.17/275.97  thf(def_eqimpsubset2,definition,(eqimpsubset2 = (![X1:$i]:(![X2:$i]:((X1 = X2) => ((subset @ X2) @ X1)))))).
% 276.17/275.97  thf(def_eqimpsubset1,definition,(eqimpsubset1 = (![X1:$i]:(![X2:$i]:((X1 = X2) => ((subset @ X1) @ X2)))))).
% 276.17/275.97  thf(def_subsetI2,definition,(subsetI2 = (![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((subset @ X1) @ X2)))))).
% 276.17/275.97  thf(def_emptysetsubset,definition,(emptysetsubset = ((!!) @ (subset @ emptyset)))).
% 276.17/275.97  thf(def_subsetE,definition,(subsetE = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => (((in @ X3) @ X1) => ((in @ X3) @ X2)))))))).
% 276.17/275.97  thf(def_subsetE2,definition,(subsetE2 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ X1)))))))))).
% 276.17/275.97  thf(def_notsubsetI,definition,(notsubsetI = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => (~(((subset @ X1) @ X2)))))))))).
% 276.17/275.97  thf(def_notequalI1,definition,(notequalI1 = (![X1:$i]:(![X2:$i]:((~(((subset @ X1) @ X2))) => (~((X1 = X2)))))))).
% 276.17/275.97  thf(def_notequalI2,definition,(notequalI2 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => (~((X1 = X2)))))))))).
% 276.17/275.97  thf(def_subsetRefl,definition,(subsetRefl = (![X1:$i]:((subset @ X1) @ X1)))).
% 276.17/275.97  thf(def_subsetTrans,definition,(subsetTrans = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => (((subset @ X2) @ X3) => ((subset @ X1) @ X3)))))))).
% 276.17/275.97  thf(def_setadjoinSub,definition,(setadjoinSub = (![X1:$i]:(![X2:$i]:((subset @ X2) @ ((setadjoin @ X1) @ X2)))))).
% 276.17/275.97  thf(def_setadjoinSub2,definition,(setadjoinSub2 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X3) => ((subset @ X1) @ ((setadjoin @ X2) @ X3)))))))).
% 276.17/275.97  thf(def_subset2powerset,definition,(subset2powerset = (![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => ((in @ X1) @ (powerset @ X2))))))).
% 276.17/275.97  thf(def_setextsub,definition,(setextsub = (![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((subset @ X2) @ X1) => (X1 = X2))))))).
% 276.17/275.97  thf(def_subsetemptysetimpeq,definition,(subsetemptysetimpeq = (![X1:$i]:(((subset @ X1) @ emptyset) => (X1 = emptyset))))).
% 276.17/275.97  thf(def_powersetI1,definition,(powersetI1 = (![X1:$i]:(![X2:$i]:(((subset @ X2) @ X1) => ((in @ X2) @ (powerset @ X1))))))).
% 276.17/275.97  thf(def_powersetE1,definition,(powersetE1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ X2) @ X1)))))).
% 276.17/275.97  thf(def_inPowerset,definition,(inPowerset = (![X1:$i]:((in @ X1) @ (powerset @ X1))))).
% 276.17/275.97  thf(def_powersetsubset,definition,(powersetsubset = (![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => ((subset @ (powerset @ X1)) @ (powerset @ X2))))))).
% 276.17/275.97  thf(def_sepInPowerset,definition,(sepInPowerset = (![X1:$i]:(![X2:$i>$o]:((in @ ((dsetconstr @ X1) @ X2)) @ (powerset @ X1)))))).
% 276.17/275.97  thf(def_sepSubset,definition,(sepSubset = (![X1:$i]:(![X2:$i>$o]:((subset @ ((dsetconstr @ X1) @ X2)) @ X1))))).
% 276.17/275.97  thf(def_binunionIL,definition,(binunionIL = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ ((binunion @ X1) @ X2)))))))).
% 276.17/275.97  thf(def_upairset2IR,definition,(upairset2IR = (![X1:$i]:(![X2:$i]:((in @ X2) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))))).
% 276.17/275.97  thf(def_binunionIR,definition,(binunionIR = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ ((binunion @ X1) @ X2)))))))).
% 276.17/275.97  thf(def_binunionEcases,definition,(binunionEcases = (![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$o]:(((in @ X3) @ ((binunion @ X1) @ X2)) => ((((in @ X3) @ X1) => X4) => ((((in @ X3) @ X2) => X4) => X4))))))))).
% 276.17/275.97  thf(def_binunionE,definition,(binunionE = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binunion @ X1) @ X2)) => ((~(((in @ X3) @ X1))) => ((in @ X3) @ X2)))))))).
% 276.17/275.97  thf(def_binunionLsub,definition,(binunionLsub = (![X1:$i]:(![X2:$i]:((subset @ X1) @ ((binunion @ X1) @ X2)))))).
% 276.17/275.97  thf(def_binunionRsub,definition,(binunionRsub = (![X1:$i]:(![X2:$i]:((subset @ X2) @ ((binunion @ X1) @ X2)))))).
% 276.17/275.97  thf(def_binintersectI,definition,(binintersectI = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => ((in @ X3) @ ((binintersect @ X1) @ X2))))))))).
% 276.17/275.97  thf(def_binintersectSubset5,definition,(binintersectSubset5 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X3) @ X1) => (((subset @ X3) @ X2) => ((subset @ X3) @ ((binintersect @ X1) @ X2))))))))).
% 276.17/275.97  thf(def_binintersectEL,definition,(binintersectEL = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binintersect @ X1) @ X2)) => ((in @ X3) @ X1))))))).
% 276.17/275.97  thf(def_binintersectLsub,definition,(binintersectLsub = (![X1:$i]:(![X2:$i]:((subset @ ((binintersect @ X1) @ X2)) @ X1))))).
% 276.17/275.97  thf(def_binintersectSubset2,definition,(binintersectSubset2 = (![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((binintersect @ X1) @ X2) = X1)))))).
% 276.17/275.97  thf(def_binintersectSubset3,definition,(binintersectSubset3 = (![X1:$i]:(![X2:$i]:((((binintersect @ X1) @ X2) = X2) => ((subset @ X2) @ X1)))))).
% 276.17/275.97  thf(def_binintersectER,definition,(binintersectER = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binintersect @ X1) @ X2)) => ((in @ X3) @ X2))))))).
% 276.17/275.97  thf(def_disjointsetsI1,definition,(disjointsetsI1 = (![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => (~(((in @ X3) @ X2))))) => (((binintersect @ X1) @ X2) = emptyset)))))).
% 276.17/275.97  thf(def_binintersectRsub,definition,(binintersectRsub = (![X1:$i]:(![X2:$i]:((subset @ ((binintersect @ X1) @ X2)) @ X2))))).
% 276.17/275.97  thf(def_binintersectSubset4,definition,(binintersectSubset4 = (![X1:$i]:(![X2:$i]:(((subset @ X2) @ X1) => (((binintersect @ X1) @ X2) = X2)))))).
% 276.17/275.97  thf(def_binintersectSubset1,definition,(binintersectSubset1 = (![X1:$i]:(![X2:$i]:((((binintersect @ X1) @ X2) = X1) => ((subset @ X1) @ X2)))))).
% 276.17/275.97  thf(def_bs114d,definition,(bs114d = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((binintersect @ X1) @ ((binunion @ X2) @ X3)) = ((binunion @ ((binintersect @ X1) @ X2)) @ ((binintersect @ X1) @ X3)))))))).
% 276.17/275.97  thf(def_setminusI,definition,(setminusI = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => ((in @ X3) @ ((setminus @ X1) @ X2))))))))).
% 276.17/275.97  thf(def_setminusEL,definition,(setminusEL = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setminus @ X1) @ X2)) => ((in @ X3) @ X1))))))).
% 276.17/275.97  thf(def_setminusER,definition,(setminusER = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setminus @ X1) @ X2)) => (~(((in @ X3) @ X2))))))))).
% 276.17/275.97  thf(def_setminusSubset2,definition,(setminusSubset2 = (![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((setminus @ X1) @ X2) = emptyset)))))).
% 276.17/275.97  thf(def_setminusERneg,definition,(setminusERneg = (![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => (((in @ X3) @ X1) => ((in @ X3) @ X2)))))))).
% 276.17/275.97  thf(def_setminusELneg,definition,(setminusELneg = (![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ X1)))))))))).
% 276.17/275.97  thf(def_setminusILneg,definition,(setminusILneg = (![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))))).
% 276.17/275.97  thf(def_setminusIRneg,definition,(setminusIRneg = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))))).
% 276.17/275.97  thf(def_setminusLsub,definition,(setminusLsub = (![X1:$i]:(![X2:$i]:((subset @ ((setminus @ X1) @ X2)) @ X1))))).
% 276.17/275.97  thf(def_setminusSubset1,definition,(setminusSubset1 = (![X1:$i]:(![X2:$i]:((((setminus @ X1) @ X2) = emptyset) => ((subset @ X1) @ X2)))))).
% 276.17/275.97  thf(def_symdiffE,definition,(symdiffE = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((symdiff @ X1) @ X2)) => (![X4:$o]:((((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => X4)) => (((~(((in @ X3) @ X1))) => (((in @ X3) @ X2) => X4)) => X4))))))))).
% 276.17/275.97  thf(def_symdiffI1,definition,(symdiffI1 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => ((in @ X3) @ ((symdiff @ X1) @ X2))))))))).
% 276.17/275.97  thf(def_symdiffI2,definition,(symdiffI2 = (![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => (((in @ X3) @ X2) => ((in @ X3) @ ((symdiff @ X1) @ X2))))))))).
% 276.17/275.97  thf(def_symdiffIneg1,definition,(symdiffIneg1 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => (~(((in @ X3) @ ((symdiff @ X1) @ X2))))))))))).
% 276.17/275.97  thf(def_symdiffIneg2,definition,(symdiffIneg2 = (![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ ((symdiff @ X1) @ X2))))))))))).
% 276.17/275.97  thf(def_secondinupair,definition,(secondinupair = (![X1:$i]:(![X2:$i]:((in @ X2) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))))).
% 276.17/275.97  thf(def_setukpairIL,definition,(setukpairIL = (![X1:$i]:(![X2:$i]:((in @ X1) @ (setunion @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)))))))).
% 276.17/275.97  thf(def_setukpairIR,definition,(setukpairIR = (![X1:$i]:(![X2:$i]:((in @ X2) @ (setunion @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)))))))).
% 276.17/275.97  thf(def_kpairiskpair,definition,(kpairiskpair = (![X1:$i]:(![X2:$i]:(iskpair @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))))))).
% 276.17/275.97  thf(def_kpairp,definition,(kpairp = (![X1:$i]:(![X2:$i]:(iskpair @ ((kpair @ X1) @ X2)))))).
% 276.17/275.97  thf(def_singletonsubset,definition,(singletonsubset = (![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((subset @ ((setadjoin @ X2) @ emptyset)) @ X1)))))).
% 276.17/275.97  thf(def_singletoninpowerset,definition,(singletoninpowerset = (![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((in @ ((setadjoin @ X2) @ emptyset)) @ (powerset @ X1))))))).
% 276.17/275.97  thf(def_singletoninpowunion,definition,(singletoninpowunion = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((in @ ((setadjoin @ X3) @ emptyset)) @ (powerset @ ((binunion @ X1) @ X2))))))))).
% 276.17/275.97  thf(def_upairset2E,definition,(upairset2E = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) => ((~((X3 = X1))) => (X3 = X2)))))))).
% 276.17/275.97  thf(def_upairsubunion,definition,(upairsubunion = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ ((binunion @ X1) @ X2)))))))))).
% 276.17/275.97  thf(def_upairinpowunion,definition,(upairinpowunion = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))))).
% 276.17/275.97  thf(def_ubforcartprodlem1,definition,(ubforcartprodlem1 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))))).
% 276.17/275.97  thf(def_ubforcartprodlem2,definition,(ubforcartprodlem2 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))))).
% 276.17/275.97  thf(def_ubforcartprodlem3,definition,(ubforcartprodlem3 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))))).
% 276.17/275.97  thf(def_cartprodpairin,definition,(cartprodpairin = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)))))))))).
% 276.17/275.97  thf(def_cartprodmempair1,definition,(cartprodmempair1 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (~((X3 = ((kpair @ X4) @ X5)))))))))))))))).
% 276.17/275.97  thf(def_cartprodmempair,definition,(cartprodmempair = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (iskpair @ X3))))))).
% 276.17/275.97  thf(def_setunionE2,definition,(setunionE2 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) => (~((![X3:$i]:(((in @ X3) @ X1) => (~(((in @ X2) @ X3)))))))))))).
% 276.17/275.97  thf(def_setunionsingleton1,definition,(setunionsingleton1 = (![X1:$i]:((subset @ (setunion @ ((setadjoin @ X1) @ emptyset))) @ X1)))).
% 276.17/275.97  thf(def_setunionsingleton2,definition,(setunionsingleton2 = (![X1:$i]:((subset @ X1) @ (setunion @ ((setadjoin @ X1) @ emptyset)))))).
% 276.17/275.97  thf(def_setunionsingleton,definition,(setunionsingleton = (![X1:$i]:((setunion @ ((setadjoin @ X1) @ emptyset)) = X1)))).
% 276.17/275.97  thf(def_singletonprop,definition,(singletonprop = (![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => (singleton @ ((dsetconstr @ X1) @ X2)))))))).
% 276.17/275.97  thf(def_ex1E1,definition,(ex1E1 = (![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))))))).
% 276.17/275.97  thf(def_ex1I,definition,(ex1I = (![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X4) => (X4 = X3)))) => ((ex1 @ X1) @ X2))))))))).
% 276.17/275.97  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))))))).
% 276.17/275.97  thf(def_singletonsuniq,definition,(singletonsuniq = (![X1:$i]:(![X2:$i]:((((setadjoin @ X1) @ emptyset) = ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))))).
% 276.17/275.97  thf(def_setukpairinjL1,definition,(setukpairinjL1 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))))).
% 276.17/275.97  thf(def_kfstsingleton,definition,(kfstsingleton = (![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:((in @ ((setadjoin @ X2) @ emptyset)) @ X1)))))))).
% 276.17/275.97  thf(def_theprop,definition,(theprop = (![X1:$i]:((singleton @ X1) => ((in @ (setunion @ X1)) @ X1))))).
% 276.17/275.97  thf(def_kfstpairEq,definition,(kfstpairEq = (![X1:$i]:(![X2:$i]:((kfst @ ((kpair @ X1) @ X2)) = X1))))).
% 276.17/275.97  thf(def_cartprodfstin,definition,(cartprodfstin = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (kfst @ X3)) @ X1))))))).
% 276.17/275.97  thf(def_setukpairinjL2,definition,(setukpairinjL2 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X1 = X3)))))))).
% 276.17/275.97  thf(def_setukpairinjL,definition,(setukpairinjL = (![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X1 = X3)))))))).
% 276.17/275.97  thf(def_setukpairinjR11,definition,(setukpairinjR11 = (![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X1) @ emptyset))))))).
% 276.17/275.97  thf(def_setukpairinjR12,definition,(setukpairinjR12 = (![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ emptyset))))))).
% 276.17/275.97  thf(def_setukpairinjR1,definition,(setukpairinjR1 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => ((X3 = X4) => (X2 = X4))))))))).
% 276.17/275.97  thf(def_upairequniteq,definition,(upairequniteq = (![X1:$i]:(![X2:$i]:(![X3:$i]:((((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X3) @ emptyset)) => (X1 = X2))))))).
% 276.17/275.97  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)))))))).
% 276.17/275.97  thf(def_setukpairinjR,definition,(setukpairinjR = (![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X2 = X4)))))))).
% 276.17/275.97  thf(def_ksndsingleton,definition,(ksndsingleton = (![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:(X1 = ((kpair @ (kfst @ X1)) @ X2))))))))).
% 276.17/275.97  thf(def_ksndpairEq,definition,(ksndpairEq = (![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))))).
% 276.17/275.97  thf(def_kpairsurjEq,definition,(kpairsurjEq = (![X1:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))))).
% 276.17/275.97  thf(def_cartprodsndin,definition,(cartprodsndin = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))))).
% 276.17/275.97  thf(def_cartprodpairmemEL,definition,(cartprodpairmemEL = (![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))))).
% 276.17/275.97  thf(def_cartprodpairmemER,definition,(cartprodpairmemER = (![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))))).
% 276.17/275.97  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)))))))))).
% 276.17/275.97  thf(def_cartprodfstpairEq,definition,(cartprodfstpairEq = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))))).
% 276.17/275.97  thf(def_cartprodsndpairEq,definition,(cartprodsndpairEq = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))))).
% 276.17/275.97  thf(def_cartprodpairsurjEq,definition,(cartprodpairsurjEq = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))))).
% 276.17/275.97  thf(def_dpsetconstrI,definition,(dpsetconstrI = (![X1:$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)))))))))))).
% 276.17/275.97  thf(def_dpsetconstrSub,definition,(dpsetconstrSub = (![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))))).
% 276.17/275.97  thf(def_setOfPairsIsBReln,definition,(setOfPairsIsBReln = (![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))))).
% 276.17/275.97  thf(def_dpsetconstrERa,definition,(dpsetconstrERa = (![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))))).
% 276.17/275.97  thf(def_dpsetconstrEL1,definition,(dpsetconstrEL1 = (![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))))).
% 276.17/275.97  thf(def_dpsetconstrEL2,definition,(dpsetconstrEL2 = (![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))))).
% 276.17/275.97  thf(def_dpsetconstrER,definition,(dpsetconstrER = (![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))).
% 276.17/275.97  thf(def_funcImageSingleton,definition,(funcImageSingleton = (![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))).
% 276.17/275.97  thf(def_apProp,definition,(apProp = (![X1:$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))))))))).
% 276.17/275.97  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))))))))).
% 276.17/275.97  thf(def_infuncsetfunc,definition,(infuncsetfunc = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))))).
% 276.17/275.97  thf(def_ap2p,definition,(ap2p = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))))).
% 276.17/275.97  thf(def_funcinfuncset,definition,(funcinfuncset = (![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))))).
% 276.17/275.97  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))))))))))).
% 276.17/275.97  thf(def_lamp,definition,(lamp = (![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))))).
% 276.17/275.97  thf(def_lam2p,definition,(lam2p = (![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))))).
% 276.17/275.97  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))))))))))).
% 276.17/275.97  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))))))))))).
% 276.17/275.97  thf(def_ex1E2,definition,(ex1E2 = (![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))))).
% 276.17/275.97  thf(def_funcGraphProp1,definition,(funcGraphProp1 = (![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))))).
% 276.17/275.97  thf(def_funcGraphProp3,definition,(funcGraphProp3 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))))).
% 276.17/275.97  thf(def_funcGraphProp2,definition,(funcGraphProp2 = (![X1:$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)))))))))))).
% 276.17/275.97  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:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))))).
% 276.17/275.97  thf(def_funcGraphProp4,definition,(funcGraphProp4 = (![X1:$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)))))))))))).
% 276.17/275.97  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)))))))))).
% 276.17/275.97  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))))))))))).
% 276.17/275.97  thf(def_funcext,definition,(funcext = (![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))))).
% 276.17/275.97  thf(def_funcext2,definition,(funcext2 = (![X1:$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)))))))))).
% 276.17/275.97  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)))))))))).
% 276.17/275.97  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)))))))))).
% 276.17/275.97  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)))))))))).
% 276.17/275.97  thf(def_eta1,definition,(eta1 = (![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))))).
% 276.17/275.97  thf(def_lam2lamEq,definition,(lam2lamEq = (![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((((lam @ X1) @ X2) @ X3) = (((lam @ X1) @ X2) @ X3)))))))).
% 276.17/275.97  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)))))))))).
% 276.17/275.97  thf(def_eta2,definition,(eta2 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))))).
% 276.17/275.97  thf(def_iffalseProp1,definition,(iffalseProp1 = (![X1:$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))))))))))))))))))).
% 276.17/275.97  thf(def_iffalseProp2,definition,(iffalseProp2 = (![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X4) @ emptyset))))))))))).
% 276.17/275.97  thf(def_iftrueProp1,definition,(iftrueProp1 = (![X1:$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))))))))))))))))))).
% 276.17/275.97  thf(def_iftrueProp2,definition,(iftrueProp2 = (![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X3) @ emptyset))))))))))).
% 276.17/275.97  thf(def_ifSingleton,definition,(ifSingleton = (![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4)))))))))))))))))).
% 276.17/275.97  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))))))))).
% 276.17/275.97  thf(def_theeq,definition,(theeq = (![X1:$i]:((singleton @ X1) => (![X2:$i]:(((in @ X2) @ X1) => ((setunion @ X1) = X2))))))).
% 276.17/275.97  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)))))))))).
% 276.17/275.97  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)))))))))).
% 276.17/275.97  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))))))))))).
% 276.17/275.97  thf(def_binintersectT_lem,definition,(binintersectT_lem = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))))).
% 276.17/275.97  thf(def_binunionT_lem,definition,(binunionT_lem = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binunion @ X2) @ X3)) @ (powerset @ X1))))))))).
% 276.17/275.97  thf(def_powersetT_lem,definition,(powersetT_lem = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((in @ (powerset @ X2)) @ (powerset @ (powerset @ X1)))))))).
% 276.17/275.97  thf(def_setminusT_lem,definition,(setminusT_lem = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X2) @ X3)) @ (powerset @ X1))))))))).
% 276.17/275.97  thf(def_complementT_lem,definition,(complementT_lem = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ X1))))))).
% 276.17/275.97  thf(def_setextT,definition,(setextT = (![X1:$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)))))))))).
% 276.17/275.97  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))))))))).
% 276.17/275.97  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)))))))))).
% 276.17/275.97  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)))))))))))).
% 276.17/275.97  thf(def_complementTI1,definition,(complementTI1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))))))).
% 276.17/275.97  thf(def_complementTE1,definition,(complementTE1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => ((in @ X3) @ X2))))))))).
% 276.17/275.97  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)))))))))))))).
% 276.17/275.97  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)))))))))))))).
% 276.17/275.97  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)))))))))))))).
% 276.17/275.97  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)))))))))))))).
% 276.17/275.97  thf(def_contrasubsetT2,definition,(contrasubsetT2 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ X3) => ((subset @ ((setminus @ X1) @ X3)) @ ((setminus @ X1) @ X2)))))))))).
% 276.17/275.97  thf(def_contrasubsetT3,definition,(contrasubsetT3 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ ((setminus @ X1) @ X3)) @ ((setminus @ X1) @ X2)) => ((subset @ X2) @ X3))))))))).
% 276.17/275.97  thf(def_doubleComplementI1,definition,(doubleComplementI1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => ((in @ X3) @ ((setminus @ X1) @ ((setminus @ X1) @ X2))))))))))).
% 276.17/275.97  thf(def_doubleComplementE1,definition,(doubleComplementE1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ ((setminus @ X1) @ ((setminus @ X1) @ X2))) => ((in @ X3) @ X2))))))))).
% 276.17/275.97  thf(def_doubleComplementSub1,definition,(doubleComplementSub1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ X2) @ ((setminus @ X1) @ ((setminus @ X1) @ X2)))))))).
% 276.17/275.97  thf(def_doubleComplementSub2,definition,(doubleComplementSub2 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ ((setminus @ X1) @ X2))) @ X2)))))).
% 276.17/275.97  thf(def_doubleComplementEq,definition,(doubleComplementEq = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (X2 = ((setminus @ X1) @ ((setminus @ X1) @ X2)))))))).
% 276.17/275.97  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)))))))))))))).
% 276.17/275.97  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))))))))))))).
% 276.17/275.97  thf(def_complementSubsetComplementIntersect,definition,(complementSubsetComplementIntersect = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))))).
% 276.17/275.97  thf(def_complementInPowersetComplementIntersect,definition,(complementInPowersetComplementIntersect = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))).
% 276.17/275.97  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))))))))))))).
% 276.17/275.97  thf(def_complementTcontraSubset,definition,(complementTcontraSubset = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))))).
% 276.17/275.97  thf(def_binunionTILcontra,definition,(binunionTILcontra = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ ((binunion @ X2) @ X3)))) => (~(((in @ X4) @ X2))))))))))))).
% 276.17/275.97  thf(def_binunionTIRcontra,definition,(binunionTIRcontra = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ ((binunion @ X2) @ X3)))) => (~(((in @ X4) @ X3))))))))))))).
% 276.17/275.97  thf(def_inIntersectImpInUnion,definition,(inIntersectImpInUnion = (![X1:$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)))))))))))))).
% 276.17/275.97  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:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binintersect @ X2) @ X3)) => ((in @ X5) @ ((binunion @ X3) @ X4)))))))))))))).
% 276.17/275.97  thf(def_inIntersectImpInIntersectUnions,definition,(inIntersectImpInIntersectUnions = (![X1:$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))))))))))))))).
% 276.17/275.97  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))))))))))))).
% 276.17/275.97  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))))))))))))).
% 276.17/275.97  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)))))))))))).
% 276.17/275.97  thf(def_binunionTE,definition,(binunionTE = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$o]:(![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binunion @ X2) @ X3)) => ((((in @ X5) @ X2) => X4) => ((((in @ X5) @ X3) => X4) => X4))))))))))))).
% 276.17/275.97  thf(def_binunionTEcontra,definition,(binunionTEcontra = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X2))) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binunion @ X2) @ X3))))))))))))))).
% 276.17/275.97  thf(def_demorgan2a1,definition,(demorgan2a1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))))).
% 276.17/275.97  thf(def_complementUnionInPowersetComplement,definition,(complementUnionInPowersetComplement = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))))).
% 276.17/275.97  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)))))))))))).
% 276.17/275.97  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))))))))))))).
% 276.17/275.97  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))))))))))))).
% 276.17/275.97  thf(def_demorgan1,definition,(demorgan1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))))).
% 276.17/275.97  thf(def_demorgan2a,definition,(demorgan2a = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))))).
% 276.17/275.97  thf(def_demorgan2b2,definition,(demorgan2b2 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))))).
% 276.17/275.97  thf(def_demorgan2b,definition,(demorgan2b = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))))).
% 276.17/275.97  thf(def_demorgan2,definition,(demorgan2 = (![X1:$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)))))))))).
% 276.17/275.97  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)))))))))).
% 276.17/275.97  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))))))))))).
% 276.17/275.97  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))))))))))).
% 276.17/275.97  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))))))))))))).
% 276.17/275.97  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:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))))).
% 276.17/275.97  thf(def_woz1_1,definition,(woz1_1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))).
% 276.17/275.97  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:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))))).
% 276.17/275.97  thf(def_woz1_3,definition,(woz1_3 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))))).
% 276.17/275.97  thf(def_woz1_4,definition,(woz1_4 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))))).
% 276.17/275.97  thf(def_woz1_5,definition,(woz1_5 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))))).
% 276.17/275.97  thf(def_breln1all2,definition,(breln1all2 = (![X1:$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)))))))))).
% 276.17/275.97  thf(def_breln1SetBreln1,definition,(breln1SetBreln1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))))).
% 276.17/275.97  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:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))))).
% 276.17/275.97  thf(def_setOfPairsIsBReln1,definition,(setOfPairsIsBReln1 = (![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))))).
% 276.17/275.97  thf(def_breln1all1,definition,(breln1all1 = (![X1:$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)))))))))).
% 276.17/275.97  thf(def_subbreln1,definition,(subbreln1 = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))))).
% 276.17/275.97  thf(def_eqbreln1,definition,(eqbreln1 = (![X1:$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)))))))))).
% 276.17/275.97  thf(def_breln1invprop,definition,(breln1invprop = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))))).
% 276.17/275.97  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)))))))))))).
% 276.17/275.97  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))))))))))).
% 276.17/275.97  thf(def_breln1compprop,definition,(breln1compprop = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))))).
% 276.17/275.97  thf(def_breln1compI,definition,(breln1compI = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))))).
% 276.17/275.97  thf(def_breln1compE,definition,(breln1compE = (![X1:$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:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))))).
% 276.17/275.97  thf(def_breln1compEex,definition,(breln1compEex = (![X1:$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)))))))))))))).
% 276.17/275.97  thf(def_breln1unionprop,definition,(breln1unionprop = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))))).
% 276.17/275.97  thf(def_breln1unionIL,definition,(breln1unionIL = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))))).
% 276.17/275.97  thf(def_breln1unionIR,definition,(breln1unionIR = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))))).
% 276.17/275.97  thf(def_breln1unionI,definition,(breln1unionI = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))))).
% 276.17/275.97  thf(def_breln1unionE,definition,(breln1unionE = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))))).
% 276.17/275.97  thf(def_breln1unionEcases,definition,(breln1unionEcases = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))))).
% 276.17/275.97  thf(def_breln1unionCommutes,definition,(breln1unionCommutes = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))))).
% 276.17/275.97  thf(def_woz2Ex,definition,(woz2Ex = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))))).
% 276.17/275.97  thf(def_woz2W,definition,(woz2W = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))).
% 276.17/275.97  thf(def_woz2A,definition,(woz2A = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))))).
% 276.17/275.97  thf(def_woz2B,definition,(woz2B = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))))).
% 276.17/275.97  thf(image1Ex,conjecture,((![X1:$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 @ 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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(powerset @ X1)) => ((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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))).
% 276.17/275.97  thf(h0,negated_conjecture,(~(((![X1:$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:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => (~((((dsetconstr @ X1) @ X2) = emptyset)))))) => ((![X1:$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)))))) => 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((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binunion @ X2) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))) => ((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),inference(assume_negation,[status(cth)],[image1Ex])).
% 276.17/275.97  thf(h1,assumption,(![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) = ((in @ X3) @ X2))) => (X1 = X2)))),introduced(assumption,[])).
% 276.17/275.97  thf(h2,assumption,(~(((![X1:$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 @ 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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:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin 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=> (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ 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(![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) 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X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.17/275.98  thf(h3,assumption,(![X1:$i]:(~(((in @ X1) @ emptyset)))),introduced(assumption,[])).
% 276.17/275.98  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) => 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:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))) => 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=> ((subset @ ((setminus @ X1) @ ((setminus @ X1) @ X2))) @ X2)))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ 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(~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.17/275.99  thf(h5,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) = ((~((X3 = X1))) => ((in @ X3) @ X2)))))),introduced(assumption,[])).
% 276.17/275.99  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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ 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((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.17/275.99  thf(h7,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) = (![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1)))))),introduced(assumption,[])).
% 276.17/275.99  thf(h8,assumption,(~(((![X1:$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]:(((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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(![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:$i]:(((in 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X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.17/275.99  thf(h9,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) = (~((![X3:$i]:(((in @ X2) @ X3) => (~(((in @ X3) @ X1)))))))))),introduced(assumption,[])).
% 276.17/275.99  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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) 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((![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)) @ 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((~(((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:$i]:(((in @ X2) @ (powerset @ X1)) => 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@ X2)) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))) => ((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.17/275.99  thf(h11,assumption,((in @ emptyset) @ omega),introduced(assumption,[])).
% 276.17/275.99  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:$i]:(((in @ X3) @ X1) => (~(((in @ X2) @ X3)))))))))) => ((![X1:$i]:((subset @ (setunion @ ((setadjoin @ X1) @ emptyset))) @ X1)) => ((![X1:$i]:((subset @ X1) @ (setunion @ ((setadjoin @ X1) @ emptyset)))) => ((![X1:$i]:((setunion @ ((setadjoin @ X1) @ emptyset)) = X1)) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => (singleton @ ((dsetconstr @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X4) => (X4 = X3)))) => ((ex1 @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => ((ex1 @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:((((setadjoin @ X1) @ emptyset) = ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:((in @ ((setadjoin @ X2) @ emptyset)) @ X1)))))) => ((![X1:$i]:((singleton @ X1) => ((in @ (setunion @ X1)) @ X1))) => ((![X1:$i]:(![X2:$i]:((kfst @ ((kpair @ X1) @ X2)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (kfst @ X3)) @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X1) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => ((X3 = X4) => (X2 = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X3) @ emptyset)) => (X1 = X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X2 = X4)))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:(X1 = ((kpair @ (kfst @ X1)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))) => ((![X1:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => 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((![X1:$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:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ 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((~(((in @ X4) @ X2))) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))) => ((![X1:$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 @ 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X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))) => ((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.25/276.00  thf(h13,assumption,(![X1:$i]:(((in @ X1) @ omega) => ((in @ ((setadjoin @ X1) @ X1)) @ omega))),introduced(assumption,[])).
% 276.25/276.00  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 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=> (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) => 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((![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:$i]:((subset @ (setunion @ ((setadjoin @ X1) @ emptyset))) @ X1)) => ((![X1:$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:$i]:(![X2:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.25/276.00  thf(h15,assumption,(![X1:$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,[])).
% 276.25/276.00  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) @ 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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) @ 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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))))))))))) => 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@ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => 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X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.25/276.00  thf(h17,assumption,(![X1:$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:$i]:(((in @ X5) @ X2) => (~(((X1 @ X5) @ X4))))))))))))))))),introduced(assumption,[])).
% 276.25/276.00  thf(h18,assumption,(~(((![X1:$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:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin 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=> (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ 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((![X1:$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:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) 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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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.25/276.01  thf(h19,assumption,(![X1:$i]:((~((![X2:$i]:(~(((in @ X2) @ X1)))))) => (~((![X2:$i]:(((in @ X2) @ X1) => (~((![X3:$i]:(((in @ X3) @ X2) => (~(((in @ X3) @ X1))))))))))))),introduced(assumption,[])).
% 276.25/276.01  thf(h20,assumption,(~(((![X1:$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)))))))))))))))))))) => ((![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:$i]:((((setadjoin @ ((setadjoin @ 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((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ 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X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.25/276.01  thf(h21,assumption,(![X1:$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,[])).
% 276.25/276.01  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:$i]:((in @ X2) @ (setunion @ ((setadjoin @ ((setadjoin 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((![X1:$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:$i]:(((in @ X4) @ X2) => ((in @ 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((![X1:$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 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=> (((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) => 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(![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((((lam @ X1) @ X2) @ X3) = (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => ((in @ X4) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => ((in @ X3) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X3) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4)))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ X1))))))) => ((![X1:$i]:((singleton @ X1) => (![X2:$i]:(((in @ X2) @ X1) => ((setunion @ X1) = X2))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((((if @ X1) @ X2) @ X3) @ X4) = X3)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((((if @ X1) @ X2) @ X3) @ X4) = X4)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X2) @ (powerset @ X1)) => ((in @ ((setminus @ 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(![X3:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.25/276.01  thf(h23,assumption,(![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (X1 @ (descr @ X1)))),introduced(assumption,[])).
% 276.25/276.01  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:$i]:(((in @ X4) @ 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@ X2))))))) => ((![X1:$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 @ 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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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.25/276.02  thf(h25,assumption,(![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((in @ X3) @ ((dsetconstr @ X1) @ X2))))))),introduced(assumption,[])).
% 276.25/276.02  thf(h26,assumption,(~(((![X1:$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) @ ((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:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => 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@ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ 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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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X3) => ((in @ X4) @ ((setminus @ X1) @ 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(![X4:$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:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.25/276.02  thf(h27,assumption,(![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ ((dsetconstr @ X1) @ X2)) => ((in @ X3) @ X1))))),introduced(assumption,[])).
% 276.25/276.02  thf(h28,assumption,(~(((![X1:$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:$i]:(((in @ X3) @ ((binintersect @ X1) @ X2)) => ((in @ X3) @ X2))))) => ((![X1:$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)) => 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((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => 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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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@ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => 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(![X3:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.25/276.02  thf(h29,assumption,(![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ ((dsetconstr @ X1) @ X2)) => (X2 @ X3))))),introduced(assumption,[])).
% 276.25/276.02  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:$i]:(((in @ X3) 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@ X2)))))) => ((![X1:$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:$i]:(((in @ 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@ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.25/276.03  thf(h31,assumption,(![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))))),introduced(assumption,[])).
% 276.25/276.03  thf(h32,assumption,(~(((![X1:$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:$i]:(((in @ X3) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) => ((~((X3 = X1))) => (X3 = X2)))))) => ((![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:((in @ X2) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))) => ((![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => (~((((dsetconstr @ X1) @ X2) = emptyset)))))) => ((![X1:$i>$o]:(![X2:$i]:(((in @ X2) @ emptyset) => (X1 @ X2)))) => ((![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3))))) => (~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3)))))))) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))) => (![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))) => (![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))) => ((![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3))))) => (~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3)))))))) => ((![X1:$o]:(X1 => ((in @ emptyset) @ (prop2set @ X1)))) => ((![X1:$o]:(X1 => (set2prop @ (prop2set @ X1)))) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))) => (![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))) => ((![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3))))) => (~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3)))))))) => ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))))) => ((![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => ((![X2:$i]:(![X3:$i]:((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))) => (~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3)))))))))))) => ((![X1:$i>$o]:((~((![X2:$i]:(~((![X3:$i]:((X1 @ X3) = (X3 = X2)))))))) => (~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((in @ X3) @ X1) => ((in @ X4) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((in @ X3) @ X1) = ((in @ X4) @ X2)))))))) => ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (![X2:$i]:(![X3:$i]:((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))))) => ((![X1:$i>$o]:(![X2:$i>$o]:((![X3:$i]:(![X4:$i]:((X3 = X4) => ((X1 @ X3) = (X2 @ X4))))) => ((~((![X3:$i]:((X1 @ X3) => (~((![X4:$i]:((X1 @ X4) => (X3 = X4))))))))) = (~((![X3:$i]:((X2 @ X3) => (~((![X4:$i]:((X2 @ X4) => (X3 = X4))))))))))))) => ((emptyset = emptyset) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((setadjoin @ X1) @ X3) = ((setadjoin @ X2) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((powerset @ X1) = (powerset @ X2))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((setunion @ X1) = (setunion @ X2))))) => ((omega = omega) => ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (![X2:$i]:(![X3:$i]:((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))))) => ((![X1:$i>$o]:(![X2:$i>$o]:((![X3:$i]:(![X4:$i]:((X3 = X4) => ((X1 @ X3) = (X2 @ X4))))) => ((~((![X3:$i]:((X1 @ X3) => (~((![X4:$i]:((X1 @ X4) => (X3 = X4))))))))) => ((~((![X3:$i]:((X2 @ X3) => (~((![X4:$i]:((X2 @ X4) => (X3 = X4))))))))) => ((descr @ X1) = (descr @ X2))))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i>$o]:(![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => ((X5 = X6) => ((X3 @ X5) = (X4 @ X6))))))) => (((dsetconstr @ X1) @ X3) = ((dsetconstr @ X2) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((subset @ X2) @ X1)))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((subset @ X1) @ X2)))) => (((!!) @ (subset @ emptyset)) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => (((in @ X3) @ X1) => ((in @ X3) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => (~(((subset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:((~(((subset @ X1) @ X2))) => (~((X1 = X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => (~((X1 = X2)))))))) => ((![X1:$i]:((subset @ X1) @ X1)) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => (((subset @ X2) @ X3) => ((subset @ X1) @ X3)))))) => ((![X1:$i]:(![X2:$i]:((subset @ X2) @ ((setadjoin @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X3) => ((subset @ X1) @ ((setadjoin @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => ((in @ X1) @ (powerset @ X2))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((subset @ X2) @ X1) => (X1 = X2))))) => ((![X1:$i]:(((subset @ X1) @ emptyset) => (X1 = emptyset))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ X1) => ((in @ X2) @ (powerset @ X1))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ X2) @ X1)))) => ((![X1:$i]:((in @ X1) @ (powerset @ X1))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => ((subset @ (powerset @ X1)) @ (powerset @ X2))))) => ((![X1:$i]:(![X2:$i>$o]:((in @ ((dsetconstr @ X1) @ X2)) @ (powerset @ X1)))) => ((![X1:$i]:(![X2:$i>$o]:((subset @ ((dsetconstr @ X1) @ X2)) @ X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ ((binunion @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:((in @ X2) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ ((binunion @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$o]:(((in @ X3) @ ((binunion @ X1) @ X2)) => ((((in @ X3) @ X1) => X4) => ((((in @ X3) @ X2) => X4) => X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binunion @ X1) @ X2)) => ((~(((in @ X3) @ X1))) => ((in @ X3) @ X2)))))) => ((![X1:$i]:(![X2:$i]:((subset @ X1) @ ((binunion @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:((subset @ X2) @ ((binunion @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => ((in @ X3) @ ((binintersect @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X3) @ X1) => (((subset @ X3) @ X2) => ((subset @ X3) @ ((binintersect @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binintersect @ X1) @ X2)) => ((in @ X3) @ X1))))) => ((![X1:$i]:(![X2:$i]:((subset @ ((binintersect @ X1) @ X2)) @ X1))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((binintersect @ X1) @ X2) = X1)))) => ((![X1:$i]:(![X2:$i]:((((binintersect @ X1) @ X2) = X2) => ((subset @ X2) @ X1)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binintersect @ X1) @ X2)) => ((in @ X3) @ X2))))) => ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => (~(((in @ X3) @ X2))))) => (((binintersect @ X1) @ X2) = emptyset)))) => ((![X1:$i]:(![X2:$i]:((subset @ ((binintersect @ X1) @ X2)) @ X2))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ X1) => (((binintersect @ X1) @ X2) = X2)))) => ((![X1:$i]:(![X2:$i]:((((binintersect @ X1) @ X2) = X1) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((binintersect @ X1) @ ((binunion @ X2) @ X3)) = ((binunion @ ((binintersect @ X1) @ X2)) @ ((binintersect @ X1) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => ((in @ X3) @ ((setminus @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setminus @ X1) @ X2)) => ((in @ X3) @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setminus @ X1) @ X2)) => (~(((in @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((setminus @ X1) @ X2) = emptyset)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => (((in @ X3) @ X1) => ((in @ X3) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:((subset @ ((setminus @ X1) @ X2)) @ X1))) => ((![X1:$i]:(![X2:$i]:((((setminus @ X1) @ X2) = emptyset) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((symdiff @ X1) @ X2)) => (![X4:$o]:((((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => X4)) => (((~(((in @ X3) @ X1))) => (((in @ X3) @ X2) => X4)) => X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => ((in @ X3) @ ((symdiff @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => (((in @ X3) @ X2) => ((in @ X3) @ ((symdiff @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => (~(((in @ X3) @ ((symdiff @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ ((symdiff @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:((in @ X2) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:((in @ X1) @ (setunion @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)))))) => ((![X1:$i]:(![X2:$i]:((in @ X2) @ (setunion @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)))))) => ((![X1:$i]:(![X2:$i]:(iskpair @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(iskpair @ ((kpair @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((subset @ ((setadjoin @ X2) @ emptyset)) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((in @ ((setadjoin @ X2) @ emptyset)) @ (powerset @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((in @ ((setadjoin @ X3) @ emptyset)) @ (powerset @ ((binunion @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) => ((~((X3 = X1))) => (X3 = X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ ((binunion @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (~((X3 = ((kpair @ X4) @ X5)))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (iskpair @ X3))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) => (~((![X3:$i]:(((in @ X3) @ X1) => (~(((in @ X2) @ X3)))))))))) => ((![X1:$i]:((subset @ (setunion @ ((setadjoin @ X1) @ emptyset))) @ X1)) => ((![X1:$i]:((subset @ X1) @ (setunion @ ((setadjoin @ X1) @ emptyset)))) => ((![X1:$i]:((setunion @ ((setadjoin @ X1) @ emptyset)) = X1)) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => (singleton @ ((dsetconstr @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X4) => (X4 = X3)))) => ((ex1 @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => ((ex1 @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:((((setadjoin @ X1) @ emptyset) = ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:((in @ ((setadjoin @ X2) @ emptyset)) @ X1)))))) => ((![X1:$i]:((singleton @ X1) => ((in @ (setunion @ X1)) @ X1))) => ((![X1:$i]:(![X2:$i]:((kfst @ ((kpair @ X1) @ X2)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (kfst @ X3)) @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X1) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => ((X3 = X4) => (X2 = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X3) @ emptyset)) => (X1 = X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X2 = X4)))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:(X1 = ((kpair @ (kfst @ X1)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))) => ((![X1:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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 @ 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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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.25/276.03  thf(h33,assumption,(![X1:$o]:(![X2:$i]:(((in @ X2) @ (prop2set @ X1)) => X1))),introduced(assumption,[])).
% 276.25/276.03  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) @ 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X3)))) => (~(((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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.25/276.04  thf(h35,assumption,(![X1:$i]:(((in @ X1) @ emptyset) => (![X2:$o]:X2))),introduced(assumption,[])).
% 276.25/276.04  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:$i]:(((in @ X3) @ X1) => 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((![X1:$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:$i]:((X1 = X2) => (((setadjoin @ ((setadjoin @ X1) @ 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((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.25/276.04  thf(h37,assumption,(~(((![X1:$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:$i]:(((subset @ X1) @ X2) => ((subset @ (powerset 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((![X1:$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) @ 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((![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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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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.25/276.04  thf(h38,assumption,(~(((![X1:$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:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => 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((![X1:$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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => 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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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.25/276.05  thf(h39,assumption,(![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (~((![X2:$i]:(~((X1 @ X2)))))))),introduced(assumption,[])).
% 276.25/276.05  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 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((![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 @ 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((![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:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin 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=> (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))) => ((![X1:$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:$i]:(((in @ X4) @ X1) => 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(![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((((lam @ X1) @ X2) @ X3) = (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => ((in @ X4) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => ((in @ X3) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X3) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4)))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ X1))))))) => ((![X1:$i]:((singleton @ X1) => (![X2:$i]:(((in @ X2) @ X1) => ((setunion @ X1) = X2))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((((if @ X1) @ X2) @ X3) @ X4) = X3)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((((if @ X1) @ X2) @ X3) @ X4) = X4)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![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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(![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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.25/276.05  thf(h41,assumption,(![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1))) => (X1 = X2))))),introduced(assumption,[])).
% 276.25/276.05  thf(h42,assumption,(~(((![X1:$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:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))) => ((![X1:$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:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ 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((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ 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((![X1:$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]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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) 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(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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.25/276.05  thf(h43,assumption,(![X1:$i]:((![X2:$i]:(~(((in @ X2) @ X1)))) => (X1 = emptyset))),introduced(assumption,[])).
% 276.25/276.05  thf(h44,assumption,(~(((![X1:$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]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ 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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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.25/276.05  thf(h45,assumption,(~(((![X1:$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 @ 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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]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => 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X3))))))) => ((![X1:$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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(![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.25/276.06  thf(h46,assumption,(![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ ((dsetconstr @ X1) @ X2)) = (X2 @ X3)))))),introduced(assumption,[])).
% 276.25/276.06  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:$i]:((~(((in @ X3) @ 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@ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => 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((![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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.25/276.06  thf(h48,assumption,(![X1:$i]:((~((X1 = emptyset))) => (~((![X2:$i]:(~(((in @ X2) @ X1)))))))),introduced(assumption,[])).
% 276.25/276.06  thf(h49,assumption,(~(((![X1:$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 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(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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.25/276.06  thf(h50,assumption,(![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => (~((((dsetconstr @ X1) @ X2) = emptyset)))))))),introduced(assumption,[])).
% 276.25/276.06  thf(h51,assumption,(~(((![X1:$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:$i]:((subset @ ((binintersect @ X1) @ X2)) @ X2))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ X1) => (((binintersect @ X1) @ X2) = X2)))) => ((![X1:$i]:(![X2:$i]:((((binintersect @ X1) @ X2) = X1) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((binintersect @ X1) @ ((binunion @ X2) @ X3)) = ((binunion @ ((binintersect @ X1) @ X2)) @ ((binintersect @ X1) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => ((in @ X3) @ ((setminus @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setminus @ X1) @ X2)) => ((in @ X3) @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setminus @ X1) @ X2)) => (~(((in @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((setminus @ X1) @ X2) = emptyset)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => (((in @ X3) @ X1) => ((in @ X3) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:((subset @ ((setminus @ X1) @ X2)) @ X1))) => ((![X1:$i]:(![X2:$i]:((((setminus @ X1) @ X2) = emptyset) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((symdiff @ X1) @ X2)) => (![X4:$o]:((((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => X4)) => (((~(((in @ X3) @ X1))) => (((in @ X3) @ X2) => X4)) => X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => ((in @ X3) @ ((symdiff @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => (((in @ X3) @ X2) => ((in @ X3) @ ((symdiff @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => (~(((in @ X3) @ ((symdiff @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ ((symdiff @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:((in @ X2) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:((in @ X1) @ (setunion @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)))))) => ((![X1:$i]:(![X2:$i]:((in @ X2) @ (setunion @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)))))) => ((![X1:$i]:(![X2:$i]:(iskpair @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(iskpair @ ((kpair @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((subset @ ((setadjoin @ X2) @ emptyset)) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((in @ ((setadjoin @ X2) @ emptyset)) @ (powerset @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((in @ ((setadjoin @ X3) @ emptyset)) @ (powerset @ ((binunion @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) => ((~((X3 = X1))) => (X3 = X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ ((binunion @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (~((X3 = ((kpair @ X4) @ X5)))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (iskpair @ X3))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) => (~((![X3:$i]:(((in @ X3) @ X1) => (~(((in @ X2) @ X3)))))))))) => ((![X1:$i]:((subset @ (setunion @ ((setadjoin @ X1) @ emptyset))) @ X1)) => ((![X1:$i]:((subset @ X1) @ (setunion @ ((setadjoin @ X1) @ emptyset)))) => ((![X1:$i]:((setunion @ ((setadjoin @ X1) @ emptyset)) = X1)) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => (singleton @ ((dsetconstr @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X4) => (X4 = X3)))) => ((ex1 @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => ((ex1 @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:((((setadjoin @ X1) @ emptyset) = ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:((in @ ((setadjoin @ X2) @ emptyset)) @ X1)))))) => ((![X1:$i]:((singleton @ X1) => ((in @ (setunion @ X1)) @ X1))) => ((![X1:$i]:(![X2:$i]:((kfst @ ((kpair @ X1) @ X2)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (kfst @ X3)) @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X1) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => ((X3 = X4) => (X2 = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X3) @ emptyset)) => (X1 = X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X2 = X4)))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:(X1 = ((kpair @ (kfst @ X1)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))) => ((![X1:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$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)))))))))))))))) => 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X1) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))) => ((in @ X2) @ (powerset @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X2) @ (powerset @ X3)) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => ((in @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X2))) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => (((in @ X4) @ X3) => (~(((in @ X4) @ X2)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((subset @ X2) @ X3) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ X2)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ X3) => ((subset @ ((setminus @ X1) @ X3)) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ ((setminus @ X1) @ X3)) @ ((setminus @ X1) @ X2)) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => ((in @ X3) @ ((setminus @ X1) @ ((setminus @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ ((setminus @ X1) @ ((setminus @ X1) @ X2))) => ((in @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ X2) @ ((setminus @ X1) @ ((setminus @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ ((setminus @ X1) @ X2))) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (X2 = ((setminus @ X1) @ ((setminus @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X3) => ((in @ X4) @ ((setminus @ X1) @ X2))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ ((binunion @ X2) @ X3)))) => (~(((in @ X4) @ X2))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ ((binunion @ X2) @ X3)))) => (~(((in @ X4) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binintersect @ X2) @ X3)) => ((in @ X5) @ ((binunion @ X2) @ X4)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binintersect @ X2) @ X3)) => ((in @ X5) @ ((binunion @ X3) @ X4)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binintersect @ X2) @ X3)) => ((in @ X5) @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => (~(((in @ X4) @ X2))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$o]:(![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binunion @ X2) @ X3)) => ((((in @ X5) @ X2) => X4) => ((((in @ X5) @ X3) => X4) => X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X2))) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binunion @ X2) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ 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@ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => 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@ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.25/276.07  thf(h52,assumption,(![X1:$i]:((~((![X2:$i]:(~(((in @ X2) @ X1)))))) => (~((X1 = emptyset))))),introduced(assumption,[])).
% 276.25/276.07  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:$i]:(((subset @ X1) @ X2) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ X1)))))))) => ((![X1:$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:$i]:((~(((in @ X3) @ X1))) => (~(((in @ X3) @ ((setminus @ X1) @ 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((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.25/276.07  thf(h54,assumption,(![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ X2)))),introduced(assumption,[])).
% 276.25/276.07  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) @ 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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) @ 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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))))))))))) => 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@ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => 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X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.25/276.07  thf(h56,assumption,((in @ emptyset) @ ((setadjoin @ emptyset) @ emptyset)),introduced(assumption,[])).
% 276.25/276.07  thf(h57,assumption,(~(((![X1:$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:$i]:(((in @ X3) @ ((setadjoin @ X1) @ ((setadjoin @ X2) 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((![X1:$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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((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.25/276.08  thf(h58,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ ((setadjoin @ X1) @ X2)))))),introduced(assumption,[])).
% 276.25/276.08  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:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (~((X3 = ((kpair @ X4) @ X5)))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (iskpair @ X3))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) => (~((![X3:$i]:(((in @ X3) @ X1) => (~(((in @ X2) @ X3)))))))))) => ((![X1:$i]:((subset @ (setunion @ ((setadjoin @ X1) @ emptyset))) @ X1)) => ((![X1:$i]:((subset @ X1) @ (setunion @ ((setadjoin @ X1) @ emptyset)))) => ((![X1:$i]:((setunion @ ((setadjoin @ X1) @ emptyset)) = X1)) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => (singleton @ ((dsetconstr @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X4) => (X4 = X3)))) => ((ex1 @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => ((ex1 @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:((((setadjoin @ X1) @ emptyset) = ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:((in @ ((setadjoin @ X2) @ emptyset)) @ X1)))))) => ((![X1:$i]:((singleton @ X1) => ((in @ (setunion @ X1)) @ X1))) => ((![X1:$i]:(![X2:$i]:((kfst @ ((kpair @ X1) @ X2)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (kfst @ X3)) @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X1) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => ((X3 = X4) => (X2 = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X3) @ emptyset)) => (X1 = X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X2 = X4)))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:(X1 = ((kpair @ (kfst @ X1)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))) => ((![X1:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => 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@ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.25/276.08  thf(h60,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) => (![X4:$o]:(((X3 = X1) => X4) => ((((in @ X3) @ X2) => X4) => X4))))))),introduced(assumption,[])).
% 276.25/276.08  thf(h61,assumption,(~(((![X1:$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:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))))) => ((![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => ((![X2:$i]:(![X3:$i]:((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))) => (~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3)))))))))))) => ((![X1:$i>$o]:((~((![X2:$i]:(~((![X3:$i]:((X1 @ X3) = (X3 = X2)))))))) => (~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((in @ X3) @ X1) => ((in @ X4) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((in @ X3) @ X1) = ((in @ X4) @ X2)))))))) => ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (![X2:$i]:(![X3:$i]:((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))))) => ((![X1:$i>$o]:(![X2:$i>$o]:((![X3:$i]:(![X4:$i]:((X3 = X4) => ((X1 @ X3) = (X2 @ X4))))) => ((~((![X3:$i]:((X1 @ X3) => (~((![X4:$i]:((X1 @ X4) => (X3 = X4))))))))) = (~((![X3:$i]:((X2 @ X3) => (~((![X4:$i]:((X2 @ X4) => (X3 = X4))))))))))))) => ((emptyset = emptyset) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((setadjoin @ X1) @ X3) = ((setadjoin @ X2) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((powerset @ X1) = (powerset @ X2))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((setunion @ X1) = (setunion @ X2))))) => ((omega = omega) => ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (![X2:$i]:(![X3:$i]:((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))))) => ((![X1:$i>$o]:(![X2:$i>$o]:((![X3:$i]:(![X4:$i]:((X3 = X4) => ((X1 @ X3) = (X2 @ X4))))) => ((~((![X3:$i]:((X1 @ X3) => (~((![X4:$i]:((X1 @ X4) => (X3 = X4))))))))) => ((~((![X3:$i]:((X2 @ X3) => (~((![X4:$i]:((X2 @ X4) => (X3 = X4))))))))) => ((descr @ X1) = (descr @ X2))))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i>$o]:(![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => ((X5 = X6) => ((X3 @ X5) = (X4 @ X6))))))) => (((dsetconstr @ X1) @ X3) = ((dsetconstr @ X2) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((subset @ X2) @ X1)))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((subset @ X1) @ X2)))) => (((!!) @ (subset @ emptyset)) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => (((in @ X3) @ X1) => ((in @ X3) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => (~(((subset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:((~(((subset @ X1) @ X2))) => (~((X1 = X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => (~((X1 = X2)))))))) => ((![X1:$i]:((subset @ X1) @ X1)) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => (((subset @ X2) @ X3) => ((subset @ X1) @ X3)))))) => ((![X1:$i]:(![X2:$i]:((subset @ X2) @ ((setadjoin @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X3) => ((subset @ X1) @ ((setadjoin @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => ((in @ X1) @ (powerset @ X2))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((subset @ X2) @ X1) => (X1 = X2))))) => ((![X1:$i]:(((subset @ X1) @ emptyset) => (X1 = emptyset))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ X1) => ((in @ X2) @ (powerset @ X1))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ X2) @ X1)))) => ((![X1:$i]:((in @ X1) @ (powerset @ X1))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => ((subset @ (powerset @ X1)) @ (powerset @ X2))))) => ((![X1:$i]:(![X2:$i>$o]:((in @ ((dsetconstr @ X1) @ X2)) @ (powerset @ X1)))) => ((![X1:$i]:(![X2:$i>$o]:((subset @ ((dsetconstr @ X1) @ X2)) @ X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ ((binunion @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:((in @ X2) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ ((binunion @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$o]:(((in @ X3) @ ((binunion @ X1) @ X2)) => ((((in @ X3) @ X1) => X4) => ((((in @ X3) @ X2) => X4) => X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binunion @ X1) @ X2)) => ((~(((in @ X3) @ X1))) => ((in @ X3) @ X2)))))) => ((![X1:$i]:(![X2:$i]:((subset @ X1) @ ((binunion @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:((subset @ X2) @ ((binunion @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => ((in @ X3) @ ((binintersect @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X3) @ X1) => (((subset @ X3) @ X2) => ((subset @ X3) @ ((binintersect @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binintersect @ X1) @ X2)) => ((in @ X3) @ X1))))) => ((![X1:$i]:(![X2:$i]:((subset @ ((binintersect @ X1) @ X2)) @ X1))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((binintersect @ X1) @ X2) = X1)))) => ((![X1:$i]:(![X2:$i]:((((binintersect @ X1) @ X2) = X2) => ((subset @ X2) @ X1)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binintersect @ X1) @ X2)) => ((in @ X3) @ X2))))) => ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => (~(((in @ X3) @ X2))))) => (((binintersect @ X1) @ X2) = emptyset)))) => ((![X1:$i]:(![X2:$i]:((subset @ ((binintersect @ X1) @ X2)) @ X2))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ X1) => (((binintersect @ X1) @ X2) = X2)))) => ((![X1:$i]:(![X2:$i]:((((binintersect @ X1) @ X2) = X1) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((binintersect @ X1) @ ((binunion @ X2) @ X3)) = ((binunion @ ((binintersect @ X1) @ X2)) @ ((binintersect @ X1) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => ((in @ X3) @ ((setminus @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setminus @ X1) @ X2)) => ((in @ X3) @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setminus @ X1) @ X2)) => (~(((in @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((setminus @ X1) @ X2) = emptyset)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => (((in @ X3) @ X1) => ((in @ X3) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:((subset @ ((setminus @ X1) @ X2)) @ X1))) => ((![X1:$i]:(![X2:$i]:((((setminus @ X1) @ X2) = emptyset) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((symdiff @ X1) @ X2)) => (![X4:$o]:((((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => X4)) => (((~(((in @ X3) @ X1))) => (((in @ X3) @ X2) => X4)) => X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => ((in @ X3) @ ((symdiff @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => (((in @ X3) @ X2) => ((in @ X3) @ ((symdiff @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => (~(((in @ X3) @ ((symdiff @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ ((symdiff @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:((in @ X2) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:((in @ X1) @ (setunion @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)))))) => ((![X1:$i]:(![X2:$i]:((in @ X2) @ (setunion @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)))))) => ((![X1:$i]:(![X2:$i]:(iskpair @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(iskpair @ ((kpair @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((subset @ ((setadjoin @ X2) @ emptyset)) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((in @ ((setadjoin @ X2) @ emptyset)) @ (powerset @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((in @ ((setadjoin @ X3) @ emptyset)) @ (powerset @ ((binunion @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) => ((~((X3 = X1))) => (X3 = X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ ((binunion @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (~((X3 = ((kpair @ X4) @ X5)))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (iskpair @ X3))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) => (~((![X3:$i]:(((in @ X3) @ X1) => (~(((in @ X2) @ X3)))))))))) => ((![X1:$i]:((subset @ (setunion @ ((setadjoin @ X1) @ emptyset))) @ X1)) => ((![X1:$i]:((subset @ X1) @ (setunion @ ((setadjoin @ X1) @ emptyset)))) => ((![X1:$i]:((setunion @ ((setadjoin @ X1) @ emptyset)) = X1)) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => (singleton @ ((dsetconstr @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X4) => (X4 = X3)))) => ((ex1 @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => ((ex1 @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:((((setadjoin @ X1) @ emptyset) = ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:((in @ ((setadjoin @ X2) @ emptyset)) @ X1)))))) => ((![X1:$i]:((singleton @ X1) => ((in @ (setunion @ X1)) @ X1))) => ((![X1:$i]:(![X2:$i]:((kfst @ ((kpair @ X1) @ X2)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (kfst @ X3)) @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X1) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => ((X3 = X4) => (X2 = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X3) @ emptyset)) => (X1 = X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X2 = X4)))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:(X1 = ((kpair @ (kfst @ X1)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))) => ((![X1:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.25/276.08  thf(h62,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) => ((~((X3 = X1))) => ((in @ X3) @ X2)))))),introduced(assumption,[])).
% 276.25/276.08  thf(h63,assumption,(~(((![X1:$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:$i]:(((subset @ X1) @ X2) => (((binintersect @ X1) @ X2) = X1)))) => ((![X1:$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))))) => 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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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.25/276.09  thf(h64,assumption,(![X1:$i]:(((dsetconstr @ X1) @ (^[X2:$i]:(~($false)))) = X1)),introduced(assumption,[])).
% 276.25/276.09  thf(h65,assumption,(~(((![X1:$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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ 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((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.36/276.09  thf(h66,assumption,(![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1))) => ((in @ X2) @ (powerset @ X1))))),introduced(assumption,[])).
% 276.36/276.09  thf(h67,assumption,(~(((![X1:$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:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ 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((![X1:$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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ 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(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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.36/276.09  thf(h68,assumption,(![X1:$i]:((in @ emptyset) @ (powerset @ X1))),introduced(assumption,[])).
% 276.36/276.09  thf(h69,assumption,(~(((![X1:$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 @ 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((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => 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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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@ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => 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((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.36/276.09  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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) 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@ X2)) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))) => ((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.36/276.10  thf(h71,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X2) @ (powerset @ X1)) => (((in @ X3) @ X2) => ((in @ X3) @ X1)))))),introduced(assumption,[])).
% 276.36/276.10  thf(h72,assumption,(~(((![X1:$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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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) @ 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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:$i]:(((in @ 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=> (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.36/276.10  thf(h73,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X2) @ X3) => (((in @ X3) @ X1) => ((in @ X2) @ (setunion @ X1))))))),introduced(assumption,[])).
% 276.36/276.10  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:$i]:((X3 = X4) => (((in @ X3) @ X1) = ((in @ X4) @ X2)))))))) => ((![X1:$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 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((![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:$i]:((setunion @ ((setadjoin @ X1) @ emptyset)) = X1)) => 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((![X1:$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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ 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((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.36/276.10  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,[])).
% 276.36/276.10  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) @ 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) => 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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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.36/276.11  thf(h77,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((in @ X2) @ (powerset @ (setunion @ X1)))))),introduced(assumption,[])).
% 276.36/276.11  thf(h78,assumption,(~(((![X1:$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:$i]:((in @ X1) @ (setunion @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)))))) => ((![X1:$i]:(![X2:$i]:((in @ X2) @ (setunion @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)))))) => ((![X1:$i]:(![X2:$i]:(iskpair @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(iskpair @ ((kpair @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((subset @ ((setadjoin @ X2) @ emptyset)) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((in @ ((setadjoin @ X2) @ emptyset)) @ (powerset @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((in @ ((setadjoin @ X3) @ emptyset)) @ (powerset @ ((binunion @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) => ((~((X3 = X1))) => (X3 = X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ ((binunion @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (~((X3 = ((kpair @ X4) @ X5)))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (iskpair @ X3))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) => (~((![X3:$i]:(((in @ X3) @ X1) => (~(((in @ X2) @ X3)))))))))) => ((![X1:$i]:((subset @ (setunion @ ((setadjoin @ X1) @ emptyset))) @ X1)) => ((![X1:$i]:((subset @ X1) @ (setunion @ ((setadjoin @ X1) @ emptyset)))) => ((![X1:$i]:((setunion @ ((setadjoin @ X1) @ emptyset)) = X1)) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => (singleton @ ((dsetconstr @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X4) => (X4 = X3)))) => ((ex1 @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => ((ex1 @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:((((setadjoin @ X1) @ emptyset) = ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:((in @ ((setadjoin @ X2) @ emptyset)) @ X1)))))) => ((![X1:$i]:((singleton @ X1) => ((in @ (setunion @ X1)) @ X1))) => ((![X1:$i]:(![X2:$i]:((kfst @ ((kpair @ X1) @ X2)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (kfst @ X3)) @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X1) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => ((X3 = X4) => (X2 = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X3) @ emptyset)) => (X1 = X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X2 = X4)))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:(X1 = ((kpair @ (kfst @ X1)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))) => ((![X1:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ 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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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.36/276.11  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,[])).
% 276.36/276.11  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:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ 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(![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.36/276.11  thf(h81,assumption,(~(((![X1:$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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=> (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((((lam @ X1) @ X2) @ X3) = (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => ((in @ X4) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => ((in @ X3) @ ((dsetconstr @ X1) 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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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.36/276.12  thf(h82,assumption,(![X1:$i]:(![X2:$i]:(((in @ X1) @ ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))),introduced(assumption,[])).
% 276.36/276.12  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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ 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((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.36/276.12  thf(h84,assumption,(![X1:$i]:(![X2:$i]:((~((X1 = X2))) => (~(((in @ X2) @ ((setadjoin @ X1) @ emptyset))))))),introduced(assumption,[])).
% 276.36/276.12  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:$i]:((((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = 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((![X1:$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) @ 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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.36/276.12  thf(h86,assumption,(![X1:$i]:(![X2:$i]:((X1 = X2) => ((in @ X1) @ ((setadjoin @ X2) @ emptyset))))),introduced(assumption,[])).
% 276.36/276.12  thf(h87,assumption,(~(((![X1:$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:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ 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@ X3))))) @ X2))))))) => ((![X1:$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:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ 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((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.36/276.13  thf(h88,assumption,(![X1:$i]:(![X2:$i]:(((in @ X1) @ ((setadjoin @ X2) @ emptyset)) => ((in @ X2) @ ((setadjoin @ X1) @ emptyset))))),introduced(assumption,[])).
% 276.36/276.13  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))))) => 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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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.36/276.13  thf(h90,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) => ((~((X3 = X1))) => (X3 = X2)))))),introduced(assumption,[])).
% 276.36/276.13  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))))))) => 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((![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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.36/276.13  thf(h92,assumption,(![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))),introduced(assumption,[])).
% 276.36/276.13  thf(h93,assumption,(~(((![X1:$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:$i]:((((kpair @ 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(powerset @ X1)) => (![X3:$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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ 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(((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.36/276.14  thf(h94,assumption,(![X1:$i]:(![X2:$i]:((in @ X2) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))),introduced(assumption,[])).
% 276.36/276.14  thf(h95,assumption,(~(((![X1:$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 @ 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((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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.36/276.14  thf(h96,assumption,(![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => (~((((dsetconstr @ X1) @ X2) = emptyset)))))),introduced(assumption,[])).
% 276.36/276.14  thf(h97,assumption,(~(((![X1:$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) => 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((![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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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:$i]:(((in @ X4) @ X1) => (X2 => (((((if @ X1) @ X2) @ 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((in @ ((setminus @ X1) @ X2)) @ (powerset @ X1))))) => ((![X1:$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) @ 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(![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 @ 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((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binunion @ X2) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))) => ((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.36/276.14  thf(h98,assumption,(![X1:$i>$o]:(![X2:$i]:(((in @ X2) @ emptyset) => (X1 @ X2)))),introduced(assumption,[])).
% 276.36/276.14  thf(h99,assumption,(~(((![X1:$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:$i]:((in @ X2) @ (setunion @ ((setadjoin @ ((setadjoin 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((![X1:$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:$i]:(((in @ X3) @ X1) => (~((X2 @ 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((![X1:$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 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=> (((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) => 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(![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((((lam @ X1) @ X2) @ X3) = (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => ((in @ X4) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => ((in @ X3) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X3) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4)))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ X1))))))) => ((![X1:$i]:((singleton @ X1) => (![X2:$i]:(((in @ X2) @ X1) => ((setunion @ X1) = X2))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((((if @ X1) @ X2) @ X3) @ X4) = X3)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((((if @ X1) @ X2) @ X3) @ X4) = X4)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X2) @ (powerset @ X1)) => ((in @ ((setminus @ 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(![X3:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.36/276.15  thf(h100,assumption,(![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3))))) => (~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3)))))))),introduced(assumption,[])).
% 276.36/276.15  thf(h101,assumption,(~(((![X1:$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:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) 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@ X2)))) => ((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.36/276.15  thf(h102,assumption,(![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))) => (![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))),introduced(assumption,[])).
% 276.36/276.15  thf(h103,assumption,(~(((![X1:$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)) = 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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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X3) => ((in @ X4) @ ((setminus @ X1) @ X2))))))))))) => ((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.36/276.15  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) @ 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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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(![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:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ 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X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.36/276.16  thf(h105,assumption,(~(((![X1:$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)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X2 = X4)))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:(X1 = ((kpair @ (kfst @ X1)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))) => ((![X1:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ 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((![X1:$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:$i]:(((in @ X2) @ (powerset @ X1)) => 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@ (powerset @ X1)) => (![X3:$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:$i]:(((in @ X2) @ (powerset @ X1)) => 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X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.36/276.16  thf(h106,assumption,(![X1:$o]:(X1 => ((in @ emptyset) @ (prop2set @ X1)))),introduced(assumption,[])).
% 276.36/276.16  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:$i]:((subset @ ((binintersect @ X1) @ X2)) @ X2))) => 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=> ((![X1:$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)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((((lam @ X1) @ X2) @ X3) = (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => ((in @ X4) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => ((in @ X3) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X3) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4)))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ X1))))))) => ((![X1:$i]:((singleton @ X1) => (![X2:$i]:(((in @ X2) @ X1) => ((setunion @ X1) = X2))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((((if @ X1) @ X2) @ X3) @ X4) = X3)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((((if @ X1) @ X2) @ X3) @ X4) = X4)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.36/276.16  thf(h108,assumption,(![X1:$o]:(X1 => (set2prop @ (prop2set @ X1)))),introduced(assumption,[])).
% 276.36/276.16  thf(h109,assumption,(~(((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.36/276.16  thf(h110,assumption,(~(((![X1:$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) => 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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) @ 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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))))))))))) => 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@ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => 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X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.36/276.17  thf(h111,assumption,(~(((![X1:$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:$i]:((((setadjoin @ ((setadjoin @ X1) @ 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(![X3:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.36/276.17  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))) @ 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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((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)) @ 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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]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ 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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) 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(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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.36/276.17  thf(h113,assumption,(![X1:$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,[])).
% 276.36/276.17  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:$i]:(((subset @ X1) @ X3) => ((subset @ X1) @ ((setadjoin @ X2) @ X3)))))) => ((![X1:$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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) 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((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.36/276.17  thf(h115,assumption,(![X1:$i>$o]:((~((![X2:$i]:(~((![X3:$i]:((X1 @ X3) = (X3 = X2)))))))) => (~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))))),introduced(assumption,[])).
% 276.36/276.17  thf(h116,assumption,(~(((![X1:$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:$i]:(((in @ 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@ X2))))))))) => ((![X1:$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) @ 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X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((((lam @ X1) @ X2) @ X3) = (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => ((in @ X4) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => ((in @ X3) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X3) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4)))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ X1))))))) => ((![X1:$i]:((singleton @ X1) => (![X2:$i]:(((in @ X2) @ X1) => ((setunion @ X1) = X2))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((((if @ X1) @ X2) @ X3) @ X4) = X3)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((((if @ X1) @ X2) @ X3) @ X4) = X4)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.36/276.18  thf(h117,assumption,(![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((in @ X3) @ X1) => ((in @ X4) @ X2)))))))),introduced(assumption,[])).
% 276.36/276.18  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]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ 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((![X1:$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:$i]:(((in @ X2) @ (powerset @ X1)) => 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@ (powerset @ X1)) => (![X3:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.36/276.18  thf(h119,assumption,(![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((in @ X3) @ X1) = ((in @ X4) @ X2)))))))),introduced(assumption,[])).
% 276.36/276.18  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 @ 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((![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:$i]:((~(((in @ X3) @ X1))) => (~(((in @ X3) @ ((setminus @ X1) @ 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((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$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:$i]:(((in @ X2) @ (powerset @ X1)) => ((in @ 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((![X1:$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:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binintersect @ X2) @ 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@ X2) @ X3)) => ((((in @ X5) @ X2) => X4) => ((((in @ X5) @ X3) => X4) => X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X2))) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binunion @ X2) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))) => ((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.36/276.18  thf(h121,assumption,(![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (![X2:$i]:(![X3:$i]:((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))))),introduced(assumption,[])).
% 276.36/276.18  thf(h122,assumption,(~(((![X1:$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 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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:$i]:(((binintersect @ X1) @ 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((![X1:$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:$i]:((in @ X1) @ (setunion @ 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X1)) => (![X4:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.36/276.19  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,[])).
% 276.36/276.19  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 @ X4) @ X1) => ((X2 @ X4) => (X4 = X3)))) => ((ex1 @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => ((ex1 @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:((((setadjoin @ X1) @ emptyset) = ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:((in @ ((setadjoin @ X2) @ emptyset)) @ X1)))))) => ((![X1:$i]:((singleton @ X1) => ((in @ (setunion @ X1)) @ X1))) => ((![X1:$i]:(![X2:$i]:((kfst @ ((kpair @ X1) @ X2)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (kfst @ X3)) @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X1) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => ((X3 = X4) => (X2 = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X3) @ emptyset)) => (X1 = X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X2 = X4)))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:(X1 = ((kpair @ (kfst @ X1)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))) => ((![X1:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => 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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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.36/276.19  thf(h125,assumption,(emptyset = emptyset),introduced(assumption,[])).
% 276.36/276.19  thf(h126,assumption,(~(((![X1:$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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => 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((![X1:$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) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.47/276.19  thf(h127,assumption,(![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((setadjoin @ X1) @ X3) = ((setadjoin @ X2) @ X4)))))))),introduced(assumption,[])).
% 276.47/276.19  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]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ 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((![X1:$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) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.47/276.20  thf(h129,assumption,(![X1:$i]:(![X2:$i]:((X1 = X2) => ((powerset @ X1) = (powerset @ X2))))),introduced(assumption,[])).
% 276.47/276.20  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]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ 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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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.47/276.20  thf(h131,assumption,(![X1:$i]:(![X2:$i]:((X1 = X2) => ((setunion @ X1) = (setunion @ X2))))),introduced(assumption,[])).
% 276.47/276.20  thf(h132,assumption,(~(((omega = omega) => ((![X1:$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:$i]:(((in @ X3) @ ((binintersect @ X1) @ X2)) => ((in @ X3) @ X2))))) => ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => (~(((in @ X3) @ X2))))) => (((binintersect @ X1) @ X2) = emptyset)))) => ((![X1:$i]:(![X2:$i]:((subset @ ((binintersect @ X1) @ X2)) @ X2))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ X1) => (((binintersect @ X1) @ X2) = X2)))) => ((![X1:$i]:(![X2:$i]:((((binintersect @ X1) @ X2) = X1) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((binintersect @ X1) @ ((binunion @ X2) @ X3)) = ((binunion @ ((binintersect @ X1) @ X2)) @ ((binintersect @ X1) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => ((in @ X3) @ ((setminus @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setminus @ X1) @ X2)) => ((in @ X3) @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setminus @ X1) @ X2)) => (~(((in @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((setminus @ X1) @ X2) = emptyset)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => (((in @ X3) @ X1) => ((in @ X3) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:((subset @ ((setminus @ X1) @ X2)) @ X1))) => ((![X1:$i]:(![X2:$i]:((((setminus @ X1) @ X2) = emptyset) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((symdiff @ X1) @ X2)) => (![X4:$o]:((((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => X4)) => (((~(((in @ X3) @ X1))) => (((in @ X3) @ X2) => X4)) => X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => ((in @ X3) @ ((symdiff @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => (((in @ X3) @ X2) => ((in @ X3) @ ((symdiff @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => (~(((in @ X3) @ ((symdiff @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ ((symdiff @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:((in @ X2) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:((in @ X1) @ (setunion @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)))))) => ((![X1:$i]:(![X2:$i]:((in @ X2) @ (setunion @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)))))) => ((![X1:$i]:(![X2:$i]:(iskpair @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(iskpair @ ((kpair @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((subset @ ((setadjoin @ X2) @ emptyset)) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((in @ ((setadjoin @ X2) @ emptyset)) @ (powerset @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((in @ ((setadjoin @ X3) @ emptyset)) @ (powerset @ ((binunion @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) => ((~((X3 = X1))) => (X3 = X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ ((binunion @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (~((X3 = ((kpair @ X4) @ X5)))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (iskpair @ X3))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) => (~((![X3:$i]:(((in @ X3) @ X1) => (~(((in @ X2) @ X3)))))))))) => ((![X1:$i]:((subset @ (setunion @ ((setadjoin @ X1) @ emptyset))) @ X1)) => ((![X1:$i]:((subset @ X1) @ (setunion @ ((setadjoin @ X1) @ emptyset)))) => ((![X1:$i]:((setunion @ ((setadjoin @ X1) @ emptyset)) = X1)) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => (singleton @ ((dsetconstr @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X4) => (X4 = X3)))) => ((ex1 @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => ((ex1 @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:((((setadjoin @ X1) @ emptyset) = ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:((in @ ((setadjoin @ X2) @ emptyset)) @ X1)))))) => ((![X1:$i]:((singleton @ X1) => ((in @ (setunion @ X1)) @ X1))) => ((![X1:$i]:(![X2:$i]:((kfst @ ((kpair @ X1) @ X2)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (kfst @ X3)) @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X1) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => ((X3 = X4) => (X2 = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X3) @ emptyset)) => (X1 = X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X2 = X4)))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:(X1 = ((kpair @ (kfst @ X1)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))) => ((![X1:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ 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=> (![X3:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.47/276.20  thf(h133,assumption,(omega = omega),introduced(assumption,[])).
% 276.47/276.20  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:$i]:(((in @ X2) @ X1) => ((subset @ ((setadjoin @ X2) @ emptyset)) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((in @ ((setadjoin @ X2) @ emptyset)) @ (powerset @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((in @ ((setadjoin @ X3) @ emptyset)) @ (powerset @ ((binunion @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) => ((~((X3 = X1))) => (X3 = X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ ((binunion @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (~((X3 = ((kpair @ X4) @ X5)))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (iskpair @ X3))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) => (~((![X3:$i]:(((in @ X3) @ X1) => (~(((in @ X2) @ X3)))))))))) => ((![X1:$i]:((subset @ (setunion @ ((setadjoin @ X1) @ emptyset))) @ X1)) => ((![X1:$i]:((subset @ X1) @ (setunion @ ((setadjoin @ X1) @ emptyset)))) => ((![X1:$i]:((setunion @ ((setadjoin @ X1) @ emptyset)) = X1)) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => (singleton @ ((dsetconstr @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X4) => (X4 = X3)))) => ((ex1 @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => ((ex1 @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:((((setadjoin @ X1) @ emptyset) = ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:((in @ ((setadjoin @ X2) @ emptyset)) @ X1)))))) => ((![X1:$i]:((singleton @ X1) => ((in @ (setunion @ X1)) @ X1))) => ((![X1:$i]:(![X2:$i]:((kfst @ ((kpair @ X1) @ X2)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (kfst @ X3)) @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X1) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => ((X3 = X4) => (X2 = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X3) @ emptyset)) => (X1 = X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X2 = X4)))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:(X1 = ((kpair @ (kfst @ X1)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))) => ((![X1:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ 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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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.47/276.21  thf(h135,assumption,(~(((![X1:$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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => 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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 @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.47/276.21  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,[])).
% 276.47/276.21  thf(h137,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)))))))) => ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((subset @ X2) @ X1)))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((subset @ X1) @ X2)))) => (((!!) @ (subset @ emptyset)) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => (((in @ X3) @ X1) => ((in @ X3) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => (~(((subset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:((~(((subset @ X1) @ X2))) => (~((X1 = X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => (~((X1 = X2)))))))) => ((![X1:$i]:((subset @ X1) @ X1)) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => (((subset @ X2) @ X3) => ((subset @ X1) @ X3)))))) => ((![X1:$i]:(![X2:$i]:((subset @ X2) @ ((setadjoin @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X3) => ((subset @ X1) @ ((setadjoin @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => ((in @ X1) @ (powerset @ X2))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((subset @ X2) @ X1) => (X1 = X2))))) => ((![X1:$i]:(((subset @ X1) @ emptyset) => (X1 = emptyset))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ X1) => ((in @ X2) @ (powerset @ X1))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ X2) @ X1)))) => ((![X1:$i]:((in @ X1) @ (powerset @ X1))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => ((subset @ (powerset @ X1)) @ (powerset @ X2))))) => ((![X1:$i]:(![X2:$i>$o]:((in @ ((dsetconstr @ X1) @ X2)) @ (powerset @ X1)))) => ((![X1:$i]:(![X2:$i>$o]:((subset @ ((dsetconstr @ X1) @ X2)) @ X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ ((binunion @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:((in @ X2) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ ((binunion @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$o]:(((in @ X3) @ ((binunion @ X1) @ X2)) => ((((in @ X3) @ X1) => X4) => ((((in @ X3) @ X2) => X4) => X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binunion @ X1) @ X2)) => ((~(((in @ X3) @ X1))) => ((in @ X3) @ X2)))))) => ((![X1:$i]:(![X2:$i]:((subset @ X1) @ ((binunion @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:((subset @ X2) @ ((binunion @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => ((in @ X3) @ ((binintersect @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X3) @ X1) => (((subset @ X3) @ X2) => ((subset @ X3) @ ((binintersect @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binintersect @ X1) @ X2)) => ((in @ X3) @ X1))))) => ((![X1:$i]:(![X2:$i]:((subset @ ((binintersect @ X1) @ X2)) @ X1))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((binintersect @ X1) @ X2) = X1)))) => ((![X1:$i]:(![X2:$i]:((((binintersect @ X1) @ X2) = X2) => ((subset @ X2) @ X1)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binintersect @ X1) @ X2)) => ((in @ X3) @ X2))))) => ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => (~(((in @ X3) @ X2))))) => (((binintersect @ X1) @ X2) = emptyset)))) => ((![X1:$i]:(![X2:$i]:((subset @ ((binintersect @ X1) @ X2)) @ X2))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ X1) => (((binintersect @ X1) @ X2) = X2)))) => ((![X1:$i]:(![X2:$i]:((((binintersect @ X1) @ X2) = X1) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((binintersect @ X1) @ ((binunion @ X2) @ X3)) = ((binunion @ ((binintersect @ X1) @ X2)) @ ((binintersect @ X1) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => ((in @ X3) @ ((setminus @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setminus @ X1) @ X2)) => ((in @ X3) @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setminus @ X1) @ X2)) => (~(((in @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((setminus @ X1) @ X2) = emptyset)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => (((in @ X3) @ X1) => ((in @ X3) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:((subset @ ((setminus @ X1) @ X2)) @ X1))) => ((![X1:$i]:(![X2:$i]:((((setminus @ X1) @ X2) = emptyset) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((symdiff @ X1) @ X2)) => (![X4:$o]:((((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => X4)) => (((~(((in @ X3) @ X1))) => (((in @ X3) @ X2) => X4)) => X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => ((in @ X3) @ ((symdiff @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => (((in @ X3) @ X2) => ((in @ X3) @ ((symdiff @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => (~(((in @ X3) @ ((symdiff @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ ((symdiff @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:((in @ X2) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:((in @ X1) @ (setunion @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)))))) => ((![X1:$i]:(![X2:$i]:((in @ X2) @ (setunion @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)))))) => ((![X1:$i]:(![X2:$i]:(iskpair @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(iskpair @ ((kpair @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((subset @ ((setadjoin @ X2) @ emptyset)) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((in @ ((setadjoin @ X2) @ emptyset)) @ (powerset @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((in @ ((setadjoin @ X3) @ emptyset)) @ (powerset @ ((binunion @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) => ((~((X3 = X1))) => (X3 = X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ ((binunion @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (~((X3 = ((kpair @ X4) @ X5)))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (iskpair @ X3))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) => (~((![X3:$i]:(((in @ X3) @ X1) => (~(((in @ X2) @ X3)))))))))) => ((![X1:$i]:((subset @ (setunion @ ((setadjoin @ X1) @ emptyset))) @ X1)) => ((![X1:$i]:((subset @ X1) @ (setunion @ ((setadjoin @ X1) @ emptyset)))) => ((![X1:$i]:((setunion @ ((setadjoin @ X1) @ emptyset)) = X1)) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => (singleton @ ((dsetconstr @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X4) => (X4 = X3)))) => ((ex1 @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => ((ex1 @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:((((setadjoin @ X1) @ emptyset) = ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:((in @ ((setadjoin @ X2) @ emptyset)) @ X1)))))) => ((![X1:$i]:((singleton @ X1) => ((in @ (setunion @ X1)) @ X1))) => ((![X1:$i]:(![X2:$i]:((kfst @ ((kpair @ X1) @ X2)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (kfst @ X3)) @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X1) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => ((X3 = X4) => (X2 = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X3) @ emptyset)) => (X1 = X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X2 = X4)))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:(X1 = ((kpair @ (kfst @ X1)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))) => ((![X1:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => 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@ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.47/276.21  thf(h138,assumption,(![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i>$o]:(![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => ((X5 = X6) => ((X3 @ X5) = (X4 @ X6))))))) => (((dsetconstr @ X1) @ X3) = ((dsetconstr @ X2) @ X4)))))))),introduced(assumption,[])).
% 276.47/276.21  thf(h139,assumption,(~(((![X1:$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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => 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((![X1:$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) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.47/276.21  thf(h140,assumption,(![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((subset @ X1) @ X2)))),introduced(assumption,[])).
% 276.47/276.21  thf(h141,assumption,(~(((![X1:$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:$i]:(iskpair @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(iskpair @ ((kpair @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((subset @ ((setadjoin @ X2) @ emptyset)) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((in @ ((setadjoin @ X2) @ emptyset)) @ (powerset @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((in @ ((setadjoin @ X3) @ emptyset)) @ (powerset @ ((binunion @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) => ((~((X3 = X1))) => (X3 = X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ ((binunion @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (~((X3 = ((kpair @ X4) @ X5)))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (iskpair @ X3))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) => (~((![X3:$i]:(((in @ X3) @ X1) => (~(((in @ X2) @ X3)))))))))) => ((![X1:$i]:((subset @ (setunion @ ((setadjoin @ X1) @ emptyset))) @ X1)) => ((![X1:$i]:((subset @ X1) @ (setunion @ ((setadjoin @ X1) @ emptyset)))) => ((![X1:$i]:((setunion @ ((setadjoin @ X1) @ emptyset)) = X1)) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => (singleton @ ((dsetconstr @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X4) => (X4 = X3)))) => ((ex1 @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => ((ex1 @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:((((setadjoin @ X1) @ emptyset) = ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:((in @ ((setadjoin @ X2) @ emptyset)) @ X1)))))) => ((![X1:$i]:((singleton @ X1) => ((in @ (setunion @ X1)) @ X1))) => ((![X1:$i]:(![X2:$i]:((kfst @ ((kpair @ X1) @ X2)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (kfst @ X3)) @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X1) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => ((X3 = X4) => (X2 = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X3) @ emptyset)) => (X1 = X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X2 = X4)))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:(X1 = ((kpair @ (kfst @ X1)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))) => ((![X1:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) 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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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.50/276.21  thf(h142,assumption,(![X1:$i]:(![X2:$i]:((X1 = X2) => ((subset @ X2) @ X1)))),introduced(assumption,[])).
% 276.50/276.21  thf(h143,assumption,(~(((![X1:$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:$i]:((((binintersect @ X1) 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X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.51/276.22  thf(h144,assumption,(![X1:$i]:(![X2:$i]:((X1 = X2) => ((subset @ X1) @ X2)))),introduced(assumption,[])).
% 276.51/276.22  thf(h145,assumption,(~(((![X1:$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)) = ((setadjoin @ X3) @ emptyset)) => (X1 = X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X2 = X4)))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:(X1 = ((kpair @ (kfst @ X1)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))) => ((![X1:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ 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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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.51/276.22  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) @ 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@ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => 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((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.51/276.22  thf(h147,assumption,((!!) @ (subset @ emptyset)),introduced(assumption,[])).
% 276.51/276.22  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 @ 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@ 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:$i]:(((in @ X3) @ X1) => (~(((in @ X2) @ 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X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((((lam @ X1) @ X2) @ X3) = (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => ((in @ X4) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => ((in @ X3) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X3) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4)))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ X1))))))) => ((![X1:$i]:((singleton @ X1) => (![X2:$i]:(((in @ X2) @ X1) => ((setunion @ X1) = X2))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((((if @ X1) @ X2) @ X3) @ X4) = X3)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((((if @ X1) @ X2) @ X3) @ X4) = X4)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.51/276.23  thf(h149,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => (((in @ X3) @ X1) => ((in @ X3) @ X2)))))),introduced(assumption,[])).
% 276.51/276.23  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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ 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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)) => 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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)) => 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X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.51/276.23  thf(h151,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ X1)))))))),introduced(assumption,[])).
% 276.51/276.23  thf(h152,assumption,(~(((![X1:$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))))))))) => 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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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((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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.51/276.23  thf(h153,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => (~(((subset @ X1) @ X2)))))))),introduced(assumption,[])).
% 276.51/276.23  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) 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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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ 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((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.51/276.23  thf(h155,assumption,(![X1:$i]:(![X2:$i]:((~(((subset @ X1) @ X2))) => (~((X1 = X2)))))),introduced(assumption,[])).
% 276.51/276.23  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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((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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.51/276.24  thf(h157,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => (~((X1 = X2)))))))),introduced(assumption,[])).
% 276.51/276.24  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) @ 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((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:$i]:(((in @ X2) @ 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(![X3:$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 @ 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((~(((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:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ 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@ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.51/276.24  thf(h159,assumption,(![X1:$i]:((subset @ X1) @ X1)),introduced(assumption,[])).
% 276.51/276.24  thf(h160,assumption,(~(((![X1:$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 @ 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(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:$i]:(((in @ X3) 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=> (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.51/276.24  thf(h161,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => (((subset @ X2) @ X3) => ((subset @ X1) @ X3)))))),introduced(assumption,[])).
% 276.51/276.24  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:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))) => ((![X1:$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:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ 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@ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ 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((![X1:$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]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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:$i]:(((in @ X4) 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(~(((in @ X4) @ X2)))))))))))) => ((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ 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X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.51/276.25  thf(h163,assumption,(![X1:$i]:(![X2:$i]:((subset @ X2) @ ((setadjoin @ X1) @ X2)))),introduced(assumption,[])).
% 276.51/276.25  thf(h164,assumption,(~(((![X1:$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:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => 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=> (![X4:$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:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ 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((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ 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@ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.51/276.25  thf(h165,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X3) => ((subset @ X1) @ ((setadjoin @ X2) @ X3)))))),introduced(assumption,[])).
% 276.51/276.25  thf(h166,assumption,(~(((![X1:$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:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => ((X3 = X4) => (X2 = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X3) @ emptyset)) => (X1 = X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X2 = X4)))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:(X1 = ((kpair @ (kfst @ X1)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))) => ((![X1:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => 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((setminus @ X1) @ X3)) => (![X4:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.51/276.25  thf(h167,assumption,(![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => ((in @ X1) @ (powerset @ X2))))),introduced(assumption,[])).
% 276.51/276.25  thf(h168,assumption,(~(((![X1:$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:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (~((X3 = ((kpair @ X4) @ X5)))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (iskpair @ X3))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) => (~((![X3:$i]:(((in @ X3) @ X1) => (~(((in @ X2) @ X3)))))))))) => ((![X1:$i]:((subset @ (setunion @ ((setadjoin @ X1) @ emptyset))) @ X1)) => ((![X1:$i]:((subset @ X1) @ (setunion @ ((setadjoin @ X1) @ emptyset)))) => ((![X1:$i]:((setunion @ ((setadjoin @ X1) @ emptyset)) = X1)) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => (singleton @ ((dsetconstr @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X4) => (X4 = X3)))) => ((ex1 @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => ((ex1 @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:((((setadjoin @ X1) @ emptyset) = ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:((in @ ((setadjoin @ X2) @ emptyset)) @ X1)))))) => ((![X1:$i]:((singleton @ X1) => ((in @ (setunion @ X1)) @ X1))) => ((![X1:$i]:(![X2:$i]:((kfst @ ((kpair @ X1) @ X2)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (kfst @ X3)) @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X1) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => ((X3 = X4) => (X2 = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X3) @ emptyset)) => (X1 = X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X2 = X4)))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:(X1 = ((kpair @ (kfst @ X1)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))) => ((![X1:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ 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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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.51/276.26  thf(h169,assumption,(![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((subset @ X2) @ X1) => (X1 = X2))))),introduced(assumption,[])).
% 276.51/276.26  thf(h170,assumption,(~(((![X1:$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]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ 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((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ 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(![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$o]:(![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binunion @ X2) @ X3)) => ((((in @ X5) @ X2) => X4) => ((((in @ X5) @ X3) => X4) => X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X2))) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binunion @ X2) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))) => ((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.51/276.26  thf(h171,assumption,(![X1:$i]:(((subset @ X1) @ emptyset) => (X1 = emptyset))),introduced(assumption,[])).
% 276.51/276.26  thf(h172,assumption,(~(((![X1:$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) @ 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(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:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ 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((![X1:$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]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => 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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)) => 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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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.51/276.26  thf(h173,assumption,(![X1:$i]:(![X2:$i]:(((subset @ X2) @ X1) => ((in @ X2) @ (powerset @ X1))))),introduced(assumption,[])).
% 276.51/276.26  thf(h174,assumption,(~(((![X1:$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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.51/276.26  thf(h175,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ X2) @ X1)))),introduced(assumption,[])).
% 276.51/276.26  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:$i]:((setunion @ ((setadjoin @ X1) @ emptyset)) = 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@ emptyset))) @ emptyset))) => (X1 = X3))))) => ((![X1:$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:$i]:((X1 = 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(powerset @ X2)) @ (powerset @ (powerset @ X1)))))) => ((![X1:$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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))) => ((in @ X2) @ (powerset @ 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X2) @ (powerset @ X1)) => (![X3:$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:$i]:(((in @ X4) @ 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((![X1:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.51/276.26  thf(h177,assumption,(![X1:$i]:((in @ X1) @ (powerset @ X1))),introduced(assumption,[])).
% 276.51/276.26  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:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))) => 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((![X1:$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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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:$i]:((X2 => (~((X5 = X3)))) => 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X2) @ (powerset @ X1)) => (![X3:$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))))))))))) => 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@ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.51/276.27  thf(h179,assumption,(![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => ((subset @ (powerset @ X1)) @ (powerset @ X2))))),introduced(assumption,[])).
% 276.51/276.27  thf(h180,assumption,(~(((![X1:$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:$i]:(((in @ X3) @ X1) => 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(powerset @ X1)) => (![X3:$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:$i]:(((in @ X4) @ 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((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$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:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => 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@ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => 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X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.51/276.27  thf(h181,assumption,(![X1:$i]:(![X2:$i>$o]:((in @ ((dsetconstr @ X1) @ X2)) @ (powerset @ X1)))),introduced(assumption,[])).
% 276.51/276.27  thf(h182,assumption,(~(((![X1:$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 @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in 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X2) @ X3)))))))) => ((![X1:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.51/276.27  thf(h183,assumption,(![X1:$i]:(![X2:$i>$o]:((subset @ ((dsetconstr @ X1) @ X2)) @ X1))),introduced(assumption,[])).
% 276.51/276.27  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:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))) => ((![X1:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ 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((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binunion @ X2) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))) => ((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.51/276.27  thf(h185,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ ((binunion @ X1) @ X2)))))),introduced(assumption,[])).
% 276.51/276.27  thf(h186,assumption,(~(((![X1:$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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ 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((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((((lam @ X1) @ X2) @ X3) = (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => ((in @ X4) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => 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=> (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((((if @ X1) @ X2) @ X3) @ X4) = X4)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binunion @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((in @ (powerset @ X2)) @ (powerset @ (powerset @ X1)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ X1))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))) => ((![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X3) => ((in @ X4) @ X2)))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))) => ((in @ X2) @ (powerset @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X2) @ (powerset @ X3)) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ 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=> ((subset @ ((setminus @ X1) @ ((setminus @ X1) @ X2))) @ X2)))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ 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((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))) => ((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.51/276.28  thf(h187,assumption,(~(((![X1:$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)) @ 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((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ 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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:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) 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@ X1) => ((in @ (X3 @ X4)) @ X2))) => ((((lam @ X1) @ X2) @ X3) = (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.51/276.28  thf(h188,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ ((binunion @ X1) @ X2)))))),introduced(assumption,[])).
% 276.51/276.28  thf(h189,assumption,(~(((![X1:$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:$i]:(iskpair @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))))) => ((![X1:$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:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ 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((![X1:$i]:(![X2:$i]:(![X3:$i]:((((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X3) @ emptyset)) => (X1 = X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X2 = X4)))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:(X1 = ((kpair @ (kfst @ X1)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))) => ((![X1:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$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))))))))))))))))) => 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X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.51/276.28  thf(h190,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$o]:(((in @ X3) @ ((binunion @ X1) @ X2)) => ((((in @ X3) @ X1) => X4) => ((((in @ X3) @ X2) => X4) => X4))))))),introduced(assumption,[])).
% 276.51/276.28  thf(h191,assumption,(~(((![X1:$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]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) 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((![X1:$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:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ 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((~(((in @ X4) @ X2))) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))) => ((![X1:$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)) => 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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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.51/276.29  thf(h192,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binunion @ X1) @ X2)) => ((~(((in @ X3) @ X1))) => ((in @ X3) @ X2)))))),introduced(assumption,[])).
% 276.51/276.29  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]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => 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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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.51/276.29  thf(h194,assumption,(![X1:$i]:(![X2:$i]:((subset @ X1) @ ((binunion @ X1) @ X2)))),introduced(assumption,[])).
% 276.51/276.29  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:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:((in @ ((setadjoin @ X2) @ emptyset)) @ X1)))))) => ((![X1:$i]:((singleton @ X1) => ((in @ (setunion @ X1)) @ X1))) => ((![X1:$i]:(![X2:$i]:((kfst @ ((kpair @ X1) @ X2)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (kfst @ X3)) @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X1) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => ((X3 = X4) => (X2 = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X3) @ emptyset)) => (X1 = X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X2 = X4)))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:(X1 = ((kpair @ (kfst @ X1)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))) => ((![X1:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.51/276.29  thf(h196,assumption,(![X1:$i]:(![X2:$i]:((subset @ X2) @ ((binunion @ X1) @ X2)))),introduced(assumption,[])).
% 276.51/276.29  thf(h197,assumption,(~(((![X1:$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)) = 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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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((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 @ 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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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.51/276.29  thf(h198,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => ((in @ X3) @ ((binintersect @ X1) @ X2))))))),introduced(assumption,[])).
% 276.51/276.29  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) @ 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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:$i]:(((in @ X2) @ 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(powerset @ X1)) => (![X3:$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) @ 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((((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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@ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.51/276.29  thf(h200,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X3) @ X1) => (((subset @ X3) @ X2) => ((subset @ X3) @ ((binintersect @ X1) @ X2))))))),introduced(assumption,[])).
% 276.51/276.29  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 @ (kfst @ X1)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))) => ((![X1:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => 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((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.51/276.30  thf(h202,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binintersect @ X1) @ X2)) => ((in @ X3) @ X1))))),introduced(assumption,[])).
% 276.51/276.30  thf(h203,assumption,(~(((![X1:$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]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) 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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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.51/276.30  thf(h204,assumption,(![X1:$i]:(![X2:$i]:((subset @ ((binintersect @ X1) @ X2)) @ X1))),introduced(assumption,[])).
% 276.51/276.30  thf(h205,assumption,(~(((![X1:$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) @ 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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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.60/276.31  thf(h206,assumption,(![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((binintersect @ X1) @ X2) = X1)))),introduced(assumption,[])).
% 276.60/276.31  thf(h207,assumption,(~(((![X1:$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:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ 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((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ 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X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.60/276.31  thf(h208,assumption,(![X1:$i]:(![X2:$i]:((((binintersect @ X1) @ X2) = X2) => ((subset @ X2) @ X1)))),introduced(assumption,[])).
% 276.60/276.31  thf(h209,assumption,(~(((![X1:$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:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => ((X3 = X4) => (X2 = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X3) @ emptyset)) => (X1 = X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X2 = X4)))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:(X1 = ((kpair @ (kfst @ X1)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))) => ((![X1:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) 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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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.60/276.31  thf(h210,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binintersect @ X1) @ X2)) => ((in @ X3) @ X2))))),introduced(assumption,[])).
% 276.60/276.31  thf(h211,assumption,(~(((![X1:$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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.60/276.31  thf(h212,assumption,(![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => (~(((in @ X3) @ X2))))) => (((binintersect @ X1) @ X2) = emptyset)))),introduced(assumption,[])).
% 276.60/276.31  thf(h213,assumption,(~(((![X1:$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 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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:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ 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(powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.60/276.31  thf(h214,assumption,(![X1:$i]:(![X2:$i]:((subset @ ((binintersect @ X1) @ X2)) @ X2))),introduced(assumption,[])).
% 276.60/276.31  thf(h215,assumption,(~(((![X1:$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]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$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:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X1) @ 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(powerset @ X1)) => (![X3:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.60/276.32  thf(h216,assumption,(![X1:$i]:(![X2:$i]:(((subset @ X2) @ X1) => (((binintersect @ X1) @ X2) = X2)))),introduced(assumption,[])).
% 276.60/276.32  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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ 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((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.60/276.32  thf(h218,assumption,(![X1:$i]:(![X2:$i]:((((binintersect @ X1) @ X2) = X1) => ((subset @ X1) @ X2)))),introduced(assumption,[])).
% 276.60/276.32  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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.60/276.32  thf(h220,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((binintersect @ X1) @ ((binunion @ X2) @ X3)) = ((binunion @ ((binintersect @ X1) @ X2)) @ ((binintersect @ X1) @ X3)))))),introduced(assumption,[])).
% 276.60/276.32  thf(h221,assumption,(~(((![X1:$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]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ 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X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ 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@ (powerset @ X3)) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))))))))) => ((![X1:$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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ 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X1)) => (![X4:$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:$i]:(((in @ X4) @ 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(((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.60/276.32  thf(h222,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => ((in @ X3) @ ((setminus @ X1) @ X2))))))),introduced(assumption,[])).
% 276.60/276.32  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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ 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(![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((((lam @ X1) @ X2) @ X3) = (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => ((in @ X4) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => ((in @ X3) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X3) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4)))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ X1))))))) => ((![X1:$i]:((singleton @ X1) => (![X2:$i]:(((in @ X2) @ X1) => ((setunion @ X1) = X2))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((((if @ X1) @ X2) @ X3) @ X4) = X3)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((((if @ X1) @ X2) @ X3) @ X4) = X4)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X2) @ (powerset @ X1)) => ((in @ ((setminus @ 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((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.60/276.33  thf(h224,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setminus @ X1) @ X2)) => ((in @ X3) @ X1))))),introduced(assumption,[])).
% 276.60/276.33  thf(h225,assumption,(~(((![X1:$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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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) 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((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => 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((![X1:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.60/276.33  thf(h226,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setminus @ X1) @ X2)) => (~(((in @ X3) @ X2))))))),introduced(assumption,[])).
% 276.60/276.33  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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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:$i]:((X2 => (~((X5 = 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((![X4:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.60/276.33  thf(h228,assumption,(![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((setminus @ X1) @ X2) = emptyset)))),introduced(assumption,[])).
% 276.60/276.33  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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ 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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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X3) => ((in @ X4) @ ((setminus @ X1) @ 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(![X4:$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:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.60/276.33  thf(h230,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => (((in @ X3) @ X1) => ((in @ X3) @ X2)))))),introduced(assumption,[])).
% 276.60/276.33  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]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$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)) @ 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((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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.60/276.34  thf(h232,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ X1)))))))),introduced(assumption,[])).
% 276.60/276.34  thf(h233,assumption,(~(((![X1:$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)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X2 = X4)))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:(X1 = ((kpair @ (kfst @ X1)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))) => ((![X1:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$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:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X1) @ 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(powerset @ X1)) => (![X3:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.60/276.34  thf(h234,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))),introduced(assumption,[])).
% 276.60/276.34  thf(h235,assumption,(~(((![X1:$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)) = X1)) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => (singleton @ ((dsetconstr @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X4) => (X4 = X3)))) => ((ex1 @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => ((ex1 @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:((((setadjoin @ X1) @ emptyset) = ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:((in @ ((setadjoin @ X2) @ emptyset)) @ X1)))))) => ((![X1:$i]:((singleton @ X1) => ((in @ (setunion @ X1)) @ X1))) => ((![X1:$i]:(![X2:$i]:((kfst @ ((kpair @ X1) @ X2)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (kfst @ X3)) @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X1) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => ((X3 = X4) => (X2 = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X3) @ emptyset)) => (X1 = X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X2 = X4)))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:(X1 = ((kpair @ (kfst @ X1)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))) => ((![X1:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ 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X3)))) => (~(((in @ X4) @ X2))))))))))) => ((![X1:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.60/276.34  thf(h236,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))),introduced(assumption,[])).
% 276.60/276.34  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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 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((![X1:$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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((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.60/276.35  thf(h238,assumption,(![X1:$i]:(![X2:$i]:((subset @ ((setminus @ X1) @ X2)) @ X1))),introduced(assumption,[])).
% 276.60/276.35  thf(h239,assumption,(~(((![X1:$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))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => (singleton @ ((dsetconstr @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X4) => (X4 = X3)))) => ((ex1 @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => ((ex1 @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:((((setadjoin @ X1) @ emptyset) = ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:((in @ ((setadjoin @ X2) @ emptyset)) @ X1)))))) => ((![X1:$i]:((singleton @ X1) => ((in @ (setunion @ X1)) @ X1))) => ((![X1:$i]:(![X2:$i]:((kfst @ ((kpair @ X1) @ X2)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (kfst @ X3)) @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X1) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => ((X3 = X4) => (X2 = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X3) @ emptyset)) => (X1 = X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X2 = X4)))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:(X1 = ((kpair @ (kfst @ X1)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))) => ((![X1:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ 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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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.60/276.35  thf(h240,assumption,(![X1:$i]:(![X2:$i]:((((setminus @ X1) @ X2) = emptyset) => ((subset @ X1) @ X2)))),introduced(assumption,[])).
% 276.60/276.35  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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ 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(powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X2))) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binunion @ X2) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))) => ((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.60/276.35  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,[])).
% 276.60/276.35  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 @ 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)) @ 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((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ 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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:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$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:$i]:(((in @ X4) @ X1) => (X2 => ((in @ X3) @ ((dsetconstr @ X1) 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(powerset @ X1)) => ((![X4:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.60/276.35  thf(h244,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => ((in @ X3) @ ((symdiff @ X1) @ X2))))))),introduced(assumption,[])).
% 276.60/276.35  thf(h245,assumption,(~(((![X1:$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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) 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X1) @ X2)))))) => ((![X1:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.60/276.36  thf(h246,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => (((in @ X3) @ X2) => ((in @ X3) @ ((symdiff @ X1) @ X2))))))),introduced(assumption,[])).
% 276.60/276.36  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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.60/276.36  thf(h248,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => (~(((in @ X3) @ ((symdiff @ X1) @ X2))))))))),introduced(assumption,[])).
% 276.60/276.36  thf(h249,assumption,(~(((![X1:$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:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = 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(![X4:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.60/276.36  thf(h250,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ ((symdiff @ X1) @ X2))))))))),introduced(assumption,[])).
% 276.60/276.36  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)) = 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@ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X2 = X4)))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:(X1 = ((kpair @ (kfst @ X1)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))) => ((![X1:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 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((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))) => ((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.60/276.36  thf(h252,assumption,(~(((![X1:$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]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$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)))))))) => 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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:$i]:(((in @ X2) @ 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(powerset @ X1)) => (![X3:$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) @ 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((((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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@ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.60/276.37  thf(h253,assumption,(![X1:$i]:(![X2:$i]:((in @ X1) @ (setunion @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)))))),introduced(assumption,[])).
% 276.60/276.37  thf(h254,assumption,(~(((![X1:$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]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ 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((~(((in @ X4) @ ((binunion @ X2) @ X3)))) => (~(((in @ X4) @ X3))))))))))) => ((![X1:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.60/276.37  thf(h255,assumption,(![X1:$i]:(![X2:$i]:((in @ X2) @ (setunion @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)))))),introduced(assumption,[])).
% 276.60/276.37  thf(h256,assumption,(~(((![X1:$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]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.60/276.37  thf(h257,assumption,(![X1:$i]:(![X2:$i]:(iskpair @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))))),introduced(assumption,[])).
% 276.60/276.37  thf(h258,assumption,(~(((![X1:$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 @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) 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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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.60/276.37  thf(h259,assumption,(![X1:$i]:(![X2:$i]:(iskpair @ ((kpair @ X1) @ X2)))),introduced(assumption,[])).
% 276.60/276.37  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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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) @ 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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:$i]:(((in 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X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.60/276.37  thf(h261,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((subset @ ((setadjoin @ X2) @ emptyset)) @ X1)))),introduced(assumption,[])).
% 276.60/276.37  thf(h262,assumption,(~(((![X1:$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]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) 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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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.60/276.38  thf(h263,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((in @ ((setadjoin @ X2) @ emptyset)) @ (powerset @ X1))))),introduced(assumption,[])).
% 276.60/276.38  thf(h264,assumption,(~(((![X1:$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]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ 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((![X1:$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]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => 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X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ 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((![X1:$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)) => (![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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.60/276.38  thf(h265,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((in @ ((setadjoin @ X3) @ emptyset)) @ (powerset @ ((binunion @ X1) @ X2))))))),introduced(assumption,[])).
% 276.60/276.38  thf(h266,assumption,(~(((![X1:$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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ 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(![X5:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.38  thf(h267,assumption,(~(((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ ((binunion @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (~((X3 = ((kpair @ X4) @ X5)))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (iskpair @ X3))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) => (~((![X3:$i]:(((in @ X3) @ X1) => (~(((in @ X2) @ X3)))))))))) => ((![X1:$i]:((subset @ (setunion @ ((setadjoin @ X1) @ emptyset))) @ X1)) => ((![X1:$i]:((subset @ X1) @ (setunion @ ((setadjoin @ X1) @ emptyset)))) => ((![X1:$i]:((setunion @ ((setadjoin @ X1) @ emptyset)) = X1)) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => (singleton @ ((dsetconstr @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X4) => (X4 = X3)))) => ((ex1 @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => ((ex1 @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:((((setadjoin @ X1) @ emptyset) = ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:((in @ ((setadjoin @ X2) @ emptyset)) @ X1)))))) => ((![X1:$i]:((singleton @ X1) => ((in @ (setunion @ X1)) @ X1))) => ((![X1:$i]:(![X2:$i]:((kfst @ ((kpair @ X1) @ X2)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (kfst @ X3)) @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X1) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => ((X3 = X4) => (X2 = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X3) @ emptyset)) => (X1 = X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X2 = X4)))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:(X1 = ((kpair @ (kfst @ X1)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))) => ((![X1:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.38  thf(h268,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ ((binunion @ X1) @ X2)))))))),introduced(assumption,[])).
% 276.69/276.38  thf(h269,assumption,(~(((![X1:$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]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in 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(powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.39  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,[])).
% 276.69/276.39  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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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 @ 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=> (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.39  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,[])).
% 276.69/276.39  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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ 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@ (powerset @ X1)) => (((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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.39  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,[])).
% 276.69/276.39  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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))) => ((in @ X2) @ (powerset @ 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X2) @ (powerset @ X1)) => (![X3:$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:$i]:(((in @ X4) @ 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(^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.39  thf(h276,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))),introduced(assumption,[])).
% 276.69/276.39  thf(h277,assumption,(~(((![X1:$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]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ 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(powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X2))) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binunion @ X2) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))) => ((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.40  thf(h278,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)))))))),introduced(assumption,[])).
% 276.69/276.40  thf(h279,assumption,(~(((![X1:$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]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$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:$i]:(((in @ X3) @ (powerset @ 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@ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.40  thf(h280,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (~((X3 = ((kpair @ X4) @ X5)))))))))))))),introduced(assumption,[])).
% 276.69/276.40  thf(h281,assumption,(~(((![X1:$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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ 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((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.40  thf(h282,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (iskpair @ X3))))),introduced(assumption,[])).
% 276.69/276.40  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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ 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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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.40  thf(h284,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) => (~((![X3:$i]:(((in @ X3) @ X1) => (~(((in @ X2) @ X3)))))))))),introduced(assumption,[])).
% 276.69/276.40  thf(h285,assumption,(~(((![X1:$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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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) @ 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X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.41  thf(h286,assumption,(![X1:$i]:((subset @ (setunion @ ((setadjoin @ X1) @ emptyset))) @ X1)),introduced(assumption,[])).
% 276.69/276.41  thf(h287,assumption,(~(((![X1:$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]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => 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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)) => 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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)) => 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X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.41  thf(h288,assumption,(![X1:$i]:((subset @ X1) @ (setunion @ ((setadjoin @ X1) @ emptyset)))),introduced(assumption,[])).
% 276.69/276.41  thf(h289,assumption,(~(((![X1:$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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => 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(![X4:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.41  thf(h290,assumption,(![X1:$i]:((setunion @ ((setadjoin @ X1) @ emptyset)) = X1)),introduced(assumption,[])).
% 276.69/276.41  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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X3))) => (~(((in @ 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((setminus @ X1) @ ((setminus @ X1) @ X2))))))))) => ((![X1:$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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((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.41  thf(h292,assumption,(![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => (singleton @ ((dsetconstr @ X1) @ X2)))))),introduced(assumption,[])).
% 276.69/276.41  thf(h293,assumption,(~(((![X1:$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]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam 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X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.41  thf(h294,assumption,(![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))))),introduced(assumption,[])).
% 276.69/276.41  thf(h295,assumption,(~(((![X1:$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:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => ((X3 = X4) => (X2 = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X3) @ emptyset)) => (X1 = X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X2 = X4)))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:(X1 = ((kpair @ (kfst @ X1)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))) => ((![X1:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in 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(powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.41  thf(h296,assumption,(![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X4) => (X4 = X3)))) => ((ex1 @ X1) @ X2))))))),introduced(assumption,[])).
% 276.69/276.41  thf(h297,assumption,(~(((![X1:$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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ 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X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.42  thf(h298,assumption,(![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => ((ex1 @ X1) @ X2))))),introduced(assumption,[])).
% 276.69/276.42  thf(h299,assumption,(~(((![X1:$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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ 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((setadjoin @ X3) @ emptyset))))))))) => ((![X1:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.42  thf(h300,assumption,(![X1:$i]:(![X2:$i]:((((setadjoin @ X1) @ emptyset) = ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))),introduced(assumption,[])).
% 276.69/276.42  thf(h301,assumption,(~(((![X1:$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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => 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@ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.42  thf(h302,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))),introduced(assumption,[])).
% 276.69/276.42  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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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))))))))))) => 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@ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.42  thf(h304,assumption,(![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:((in @ ((setadjoin @ X2) @ emptyset)) @ X1)))))),introduced(assumption,[])).
% 276.69/276.42  thf(h305,assumption,(~(((![X1:$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))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.43  thf(h306,assumption,(![X1:$i]:((singleton @ X1) => ((in @ (setunion @ X1)) @ X1))),introduced(assumption,[])).
% 276.69/276.43  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]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ 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(powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X2))) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binunion @ X2) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))) => ((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.43  thf(h308,assumption,(![X1:$i]:(![X2:$i]:((kfst @ ((kpair @ X1) @ X2)) = X1))),introduced(assumption,[])).
% 276.69/276.43  thf(h309,assumption,(~(((![X1:$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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ 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X1) @ X2)))))) => ((![X1:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.43  thf(h310,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (kfst @ X3)) @ X1))))),introduced(assumption,[])).
% 276.69/276.43  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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ 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(~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.43  thf(h312,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X1 = X3)))))),introduced(assumption,[])).
% 276.69/276.43  thf(h313,assumption,(~(((![X1:$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]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.43  thf(h314,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X1 = X3)))))),introduced(assumption,[])).
% 276.69/276.43  thf(h315,assumption,(~(((![X1:$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]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.44  thf(h316,assumption,(![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X1) @ emptyset))))),introduced(assumption,[])).
% 276.69/276.44  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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binunion @ X2) @ X3)) @ (powerset @ 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X4) @ ((binintersect @ X2) @ X3)))))))))))) => ((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.44  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,[])).
% 276.69/276.44  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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.44  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,[])).
% 276.69/276.44  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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.44  thf(h322,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:((((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X3) @ emptyset)) => (X1 = X2))))),introduced(assumption,[])).
% 276.69/276.44  thf(h323,assumption,(~(((![X1:$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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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 => 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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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(![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:$i]:(((in 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X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.45  thf(h324,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))),introduced(assumption,[])).
% 276.69/276.45  thf(h325,assumption,(~(((![X1:$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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => 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((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))) => ((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.45  thf(h326,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X2 = X4)))))),introduced(assumption,[])).
% 276.69/276.45  thf(h327,assumption,(~(((![X1:$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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => 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((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ ((binunion @ X2) @ X3)))) => (~(((in @ X4) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.45  thf(h328,assumption,(![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:(X1 = ((kpair @ (kfst @ X1)) @ X2))))))),introduced(assumption,[])).
% 276.69/276.45  thf(h329,assumption,(~(((![X1:$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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.45  thf(h330,assumption,(![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))),introduced(assumption,[])).
% 276.69/276.45  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]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.45  thf(h332,assumption,(![X1:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))),introduced(assumption,[])).
% 276.69/276.45  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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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 @ 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@ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.46  thf(h334,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))),introduced(assumption,[])).
% 276.69/276.46  thf(h335,assumption,(~(((![X1:$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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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 @ 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=> (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.46  thf(h336,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))),introduced(assumption,[])).
% 276.69/276.46  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]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.46  thf(h338,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))),introduced(assumption,[])).
% 276.69/276.46  thf(h339,assumption,(~(((![X1:$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>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.46  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,[])).
% 276.69/276.46  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]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ 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((![X1:$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:$i]:(((in @ X2) @ (powerset @ X1)) => 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@ (powerset @ X1)) => (![X3:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.46  thf(h342,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))),introduced(assumption,[])).
% 276.69/276.46  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]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => 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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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.47  thf(h344,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))),introduced(assumption,[])).
% 276.69/276.47  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]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ 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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:$i]:(((in @ X4) @ X1) => (((subset 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X1)) => (![X4:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.47  thf(h346,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))),introduced(assumption,[])).
% 276.69/276.47  thf(h347,assumption,(~(((![X1:$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]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.47  thf(h348,assumption,(![X1:$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,[])).
% 276.69/276.47  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]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.69/276.47  thf(h350,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))),introduced(assumption,[])).
% 276.69/276.47  thf(h351,assumption,(~(((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.79/276.48  thf(h352,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))),introduced(assumption,[])).
% 276.79/276.48  thf(h353,assumption,(~(((![X1:$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))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.79/276.48  thf(h354,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))),introduced(assumption,[])).
% 276.79/276.48  thf(h355,assumption,(~(((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.79/276.48  thf(h356,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))),introduced(assumption,[])).
% 276.79/276.48  thf(h357,assumption,(~(((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.79/276.48  thf(h358,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))),introduced(assumption,[])).
% 276.79/276.48  thf(h359,assumption,(~(((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.79/276.48  thf(h360,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))),introduced(assumption,[])).
% 276.79/276.48  thf(h361,assumption,(~(((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.79/276.48  thf(h362,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))),introduced(assumption,[])).
% 276.79/276.48  thf(h363,assumption,(~(((![X1:$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))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.79/276.49  thf(h364,assumption,(![X1:$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,[])).
% 276.79/276.49  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))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.79/276.49  thf(h366,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))),introduced(assumption,[])).
% 276.79/276.49  thf(h367,assumption,(~(((![X1:$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]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.79/276.49  thf(h368,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))),introduced(assumption,[])).
% 276.79/276.49  thf(h369,assumption,(~(((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => 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((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))) => ((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.79/276.49  thf(h370,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))),introduced(assumption,[])).
% 276.79/276.49  thf(h371,assumption,(~(((![X1:$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:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$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 @ 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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:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binunion @ X2) @ X3)) => ((((in @ X5) @ X2) => 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(powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))) => ((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.81/276.49  thf(h372,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))),introduced(assumption,[])).
% 276.81/276.49  thf(h373,assumption,(~(((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((dsetconstr @ X1) @ 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((![X1:$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:$i]:(((in @ X3) @ (powerset @ 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(powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.81/276.49  thf(h374,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,[])).
% 276.81/276.49  thf(h375,assumption,(~(((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.81/276.49  thf(h376,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))),introduced(assumption,[])).
% 276.81/276.49  thf(h377,assumption,(~(((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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) @ 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((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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ 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((![X1:$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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(((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.81/276.50  thf(h378,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))),introduced(assumption,[])).
% 276.81/276.50  thf(h379,assumption,(~(((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![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) @ 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X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.81/276.50  thf(h380,assumption,(![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))))))))),introduced(assumption,[])).
% 276.81/276.50  thf(h381,assumption,(~(((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.81/276.50  thf(h382,assumption,(~(((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((((lam @ X1) @ X2) @ X3) = (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => ((in @ X4) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => ((in @ X3) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X3) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4)))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ X1))))))) => ((![X1:$i]:((singleton @ X1) => (![X2:$i]:(((in @ X2) @ X1) => ((setunion @ X1) = X2))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((((if @ X1) @ X2) @ X3) @ X4) = X3)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((((if @ X1) @ X2) @ X3) @ X4) = X4)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.81/276.50  thf(h383,assumption,(![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))),introduced(assumption,[])).
% 276.81/276.50  thf(h384,assumption,(~(((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((((lam @ X1) @ X2) @ X3) = (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => ((in @ X4) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => ((in @ X3) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X3) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4)))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ X1))))))) => ((![X1:$i]:((singleton @ X1) => (![X2:$i]:(((in @ X2) @ X1) => ((setunion @ X1) = X2))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((((if @ X1) @ X2) @ X3) @ X4) = X3)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((((if @ X1) @ X2) @ X3) @ X4) = X4)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.81/276.50  thf(h385,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))),introduced(assumption,[])).
% 276.81/276.50  thf(h386,assumption,(~(((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((((lam @ X1) @ X2) @ X3) = (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => ((in @ X4) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => ((in @ X3) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X3) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4)))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ X1))))))) => ((![X1:$i]:((singleton @ X1) => (![X2:$i]:(((in @ X2) @ X1) => ((setunion @ X1) = X2))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((((if @ X1) @ X2) @ X3) @ X4) = X3)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((((if @ X1) @ X2) @ X3) @ X4) = X4)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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) @ 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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:$i]:(((in @ X2) @ (powerset @ X1)) => (X2 = ((setminus @ X1) @ ((setminus @ 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((setminus @ X1) @ X3)) => (![X4:$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 @ 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((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.81/276.51  thf(h387,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,[])).
% 276.81/276.51  thf(h388,assumption,(~(((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((((lam @ X1) @ X2) @ X3) = (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => ((in @ X4) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => ((in @ X3) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X3) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4)))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ X1))))))) => ((![X1:$i]:((singleton @ X1) => (![X2:$i]:(((in @ X2) @ X1) => ((setunion @ X1) = X2))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((((if @ X1) @ X2) @ X3) @ X4) = X3)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((((if @ X1) @ X2) @ X3) @ X4) = X4)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.81/276.51  thf(h389,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))),introduced(assumption,[])).
% 276.81/276.51  thf(h390,assumption,(~(((![X1:$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))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((((lam @ X1) @ X2) @ X3) = (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => ((in @ X4) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => ((in @ X3) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X3) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4)))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ X1))))))) => ((![X1:$i]:((singleton @ X1) => (![X2:$i]:(((in @ X2) @ X1) => ((setunion @ X1) = X2))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((((if @ X1) @ X2) @ X3) @ X4) = X3)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((((if @ X1) @ X2) @ X3) @ X4) = X4)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.81/276.51  thf(h391,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:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))),introduced(assumption,[])).
% 276.81/276.51  thf(h392,assumption,(~(((![X1:$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)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((((lam @ X1) @ X2) @ X3) = (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => ((in @ X4) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => ((in @ X3) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X3) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4)))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ X1))))))) => ((![X1:$i]:((singleton @ X1) => (![X2:$i]:(((in @ X2) @ X1) => ((setunion @ X1) = X2))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((((if @ X1) @ X2) @ X3) @ X4) = X3)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((((if @ X1) @ X2) @ X3) @ X4) = X4)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.81/276.51  thf(h393,assumption,(![X1:$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,[])).
% 276.81/276.51  thf(h394,assumption,(~(((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((((lam @ X1) @ X2) @ X3) = (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => ((in @ X4) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => ((in @ X3) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X3) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4)))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ X1))))))) => ((![X1:$i]:((singleton @ X1) => (![X2:$i]:(((in @ X2) @ X1) => ((setunion @ X1) = X2))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((((if @ X1) @ X2) @ X3) @ X4) = X3)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((((if @ X1) @ X2) @ X3) @ X4) = X4)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.81/276.51  thf(h395,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))),introduced(assumption,[])).
% 276.81/276.51  thf(h396,assumption,(~(((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((((lam @ X1) @ X2) @ X3) = (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => ((in @ X4) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => ((in @ X3) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X3) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4)))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ X1))))))) => ((![X1:$i]:((singleton @ X1) => (![X2:$i]:(((in @ X2) @ X1) => ((setunion @ X1) = X2))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((((if @ X1) @ X2) @ X3) @ X4) = X3)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((((if @ X1) @ X2) @ X3) @ X4) = X4)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.52  thf(h397,assumption,(![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))))))))),introduced(assumption,[])).
% 276.83/276.52  thf(h398,assumption,(~(((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.52  thf(h399,assumption,(![X1:$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,[])).
% 276.83/276.52  thf(h400,assumption,(~(((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.52  thf(h401,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))),introduced(assumption,[])).
% 276.83/276.52  thf(h402,assumption,(~(((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.52  thf(h403,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,[])).
% 276.83/276.52  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)))))))) => ((![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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.52  thf(h405,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))),introduced(assumption,[])).
% 276.83/276.52  thf(h406,assumption,(~(((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$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 @ 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(![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ 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((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ 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((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.52  thf(h407,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,[])).
% 276.83/276.52  thf(h408,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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.52  thf(h409,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))),introduced(assumption,[])).
% 276.83/276.52  thf(h410,assumption,(~(((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((((lam @ X1) @ X2) @ X3) = (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$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 @ 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@ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.52  thf(h411,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((((lam @ X1) @ X2) @ X3) = (((lam @ X1) @ X2) @ X3)))))),introduced(assumption,[])).
% 276.83/276.52  thf(h412,assumption,(~(((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.52  thf(h413,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:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ 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X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.53  thf(h414,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))),introduced(assumption,[])).
% 276.83/276.53  thf(h415,assumption,(~(((![X1:$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))))))))))))))))) => ((![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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.53  thf(h416,assumption,(![X1:$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,[])).
% 276.83/276.53  thf(h417,assumption,(~(((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.53  thf(h418,assumption,(![X1:$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,[])).
% 276.83/276.53  thf(h419,assumption,(~(((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => ((in @ X3) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.53  thf(h420,assumption,(![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => ((in @ X3) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))),introduced(assumption,[])).
% 276.83/276.53  thf(h421,assumption,(~(((![X1:$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))))))))) => ((![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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.53  thf(h422,assumption,(![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X3) @ emptyset))))))))),introduced(assumption,[])).
% 276.83/276.53  thf(h423,assumption,(~(((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4)))))))))))))))) => ((![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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.53  thf(h424,assumption,(![X1:$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,[])).
% 276.83/276.53  thf(h425,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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.53  thf(h426,assumption,(![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ X1))))))),introduced(assumption,[])).
% 276.83/276.53  thf(h427,assumption,(~(((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.54  thf(h428,assumption,(![X1:$i]:((singleton @ X1) => (![X2:$i]:(((in @ X2) @ X1) => ((setunion @ X1) = X2))))),introduced(assumption,[])).
% 276.83/276.54  thf(h429,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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.54  thf(h430,assumption,(![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((((if @ X1) @ X2) @ X3) @ X4) = X3)))))))),introduced(assumption,[])).
% 276.83/276.54  thf(h431,assumption,(~(((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.54  thf(h432,assumption,(![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((((if @ X1) @ X2) @ X3) @ X4) = X4)))))))),introduced(assumption,[])).
% 276.83/276.54  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))))))))) => ((![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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.54  thf(h434,assumption,(![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))))))))),introduced(assumption,[])).
% 276.83/276.54  thf(h435,assumption,(~(((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.54  thf(h436,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))),introduced(assumption,[])).
% 276.83/276.54  thf(h437,assumption,(~(((![X1:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.54  thf(h438,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binunion @ X2) @ X3)) @ (powerset @ X1))))))),introduced(assumption,[])).
% 276.83/276.54  thf(h439,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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.55  thf(h440,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((in @ (powerset @ X2)) @ (powerset @ (powerset @ X1)))))),introduced(assumption,[])).
% 276.83/276.55  thf(h441,assumption,(~(((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.55  thf(h442,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X2) @ X3)) @ (powerset @ X1))))))),introduced(assumption,[])).
% 276.83/276.55  thf(h443,assumption,(~(((![X1:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.55  thf(h444,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ X1))))),introduced(assumption,[])).
% 276.83/276.55  thf(h445,assumption,(~(((![X1:$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)))))))) => ((![X1:$i]:(![X2:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.55  thf(h446,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))) => ((![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X3) => ((in @ X4) @ X2)))) => (X2 = X3)))))))),introduced(assumption,[])).
% 276.83/276.55  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))))))) => ((![X1:$i]:(![X2:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.55  thf(h448,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))) => ((subset @ X2) @ X3))))))),introduced(assumption,[])).
% 276.83/276.55  thf(h449,assumption,(~(((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))) => ((in @ X2) @ (powerset @ X3)))))))) => ((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.55  thf(h450,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,[])).
% 276.83/276.55  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)))))))))) => ((![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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.55  thf(h452,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X2) @ (powerset @ X3)) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))))))))),introduced(assumption,[])).
% 276.83/276.55  thf(h453,assumption,(~(((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.55  thf(h454,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))))),introduced(assumption,[])).
% 276.83/276.55  thf(h455,assumption,(~(((![X1:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.56  thf(h456,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => ((in @ X3) @ X2))))))),introduced(assumption,[])).
% 276.83/276.56  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)))))))))))) => ((![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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.56  thf(h458,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X2))) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))),introduced(assumption,[])).
% 276.83/276.56  thf(h459,assumption,(~(((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))) => ((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.56  thf(h460,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,[])).
% 276.83/276.56  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)))))))))))) => ((![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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.56  thf(h462,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => (((in @ X4) @ X3) => (~(((in @ X4) @ X2)))))))))))),introduced(assumption,[])).
% 276.83/276.56  thf(h463,assumption,(~(((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((subset @ X2) @ X3) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ X2)))))))))))) => ((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.56  thf(h464,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,[])).
% 276.83/276.56  thf(h465,assumption,(~(((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ X3) => ((subset @ ((setminus @ X1) @ X3)) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.56  thf(h466,assumption,(![X1:$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,[])).
% 276.83/276.56  thf(h467,assumption,(~(((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ ((setminus @ X1) @ X3)) @ ((setminus @ X1) @ X2)) => ((subset @ X2) @ X3))))))) => ((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.56  thf(h468,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ ((setminus @ X1) @ X3)) @ ((setminus @ X1) @ X2)) => ((subset @ X2) @ X3))))))),introduced(assumption,[])).
% 276.83/276.56  thf(h469,assumption,(~(((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => ((in @ X3) @ ((setminus @ X1) @ ((setminus @ X1) @ X2))))))))) => ((![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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.57  thf(h470,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => ((in @ X3) @ ((setminus @ X1) @ ((setminus @ X1) @ X2))))))))),introduced(assumption,[])).
% 276.83/276.57  thf(h471,assumption,(~(((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ ((setminus @ X1) @ ((setminus @ X1) @ X2))) => ((in @ X3) @ X2))))))) => ((![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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.57  thf(h472,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ ((setminus @ X1) @ ((setminus @ X1) @ X2))) => ((in @ X3) @ X2))))))),introduced(assumption,[])).
% 276.83/276.57  thf(h473,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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.57  thf(h474,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ X2) @ ((setminus @ X1) @ ((setminus @ X1) @ X2)))))),introduced(assumption,[])).
% 276.83/276.57  thf(h475,assumption,(~(((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.57  thf(h476,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ ((setminus @ X1) @ X2))) @ X2)))),introduced(assumption,[])).
% 276.83/276.57  thf(h477,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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.57  thf(h478,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (X2 = ((setminus @ X1) @ ((setminus @ X1) @ X2)))))),introduced(assumption,[])).
% 276.83/276.57  thf(h479,assumption,(~(((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.57  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) @ ((binintersect @ X2) @ X3)))))))))))),introduced(assumption,[])).
% 276.83/276.57  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))))))))))) => ((![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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.57  thf(h482,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))),introduced(assumption,[])).
% 276.83/276.57  thf(h483,assumption,(~(((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.57  thf(h484,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))),introduced(assumption,[])).
% 276.83/276.57  thf(h485,assumption,(~(((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.57  thf(h486,assumption,(![X1:$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,[])).
% 276.83/276.57  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))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.57  thf(h488,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X3) => ((in @ X4) @ ((setminus @ X1) @ X2))))))))))),introduced(assumption,[])).
% 276.83/276.57  thf(h489,assumption,(~(((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.57  thf(h490,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))),introduced(assumption,[])).
% 276.83/276.57  thf(h491,assumption,(~(((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ ((binunion @ X2) @ X3)))) => (~(((in @ X4) @ X2))))))))))) => ((![X1:$i]:(![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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.58  thf(h492,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ ((binunion @ X2) @ X3)))) => (~(((in @ X4) @ X2))))))))))),introduced(assumption,[])).
% 276.83/276.58  thf(h493,assumption,(~(((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ ((binunion @ X2) @ X3)))) => (~(((in @ X4) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.58  thf(h494,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ ((binunion @ X2) @ X3)))) => (~(((in @ X4) @ X3))))))))))),introduced(assumption,[])).
% 276.83/276.58  thf(h495,assumption,(~(((![X1:$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)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.58  thf(h496,assumption,(![X1:$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 @ X2) @ X4)))))))))))),introduced(assumption,[])).
% 276.83/276.58  thf(h497,assumption,(~(((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binintersect @ X2) @ X3)) => ((in @ X5) @ ((binunion @ X3) @ X4)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.58  thf(h498,assumption,(![X1:$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) @ ((binunion @ X3) @ X4)))))))))))),introduced(assumption,[])).
% 276.83/276.58  thf(h499,assumption,(~(((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binintersect @ X2) @ X3)) => ((in @ X5) @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => (~(((in @ X4) @ X2))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$o]:(![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binunion @ X2) @ X3)) => ((((in @ X5) @ X2) => X4) => ((((in @ X5) @ X3) => X4) => X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X2))) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binunion @ X2) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))) => ((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.58  thf(h500,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binintersect @ X2) @ X3)) => ((in @ X5) @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))))),introduced(assumption,[])).
% 276.83/276.58  thf(h501,assumption,(~(((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => (~(((in @ X4) @ X2))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$o]:(![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binunion @ X2) @ X3)) => ((((in @ X5) @ X2) => X4) => ((((in @ X5) @ X3) => X4) => X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X2))) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binunion @ X2) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))) => ((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.58  thf(h502,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,[])).
% 276.83/276.58  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))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$o]:(![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binunion @ X2) @ X3)) => ((((in @ X5) @ X2) => X4) => ((((in @ X5) @ X3) => X4) => X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X2))) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binunion @ X2) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))) => ((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.58  thf(h504,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => (~(((in @ X4) @ X2))))))))))),introduced(assumption,[])).
% 276.83/276.58  thf(h505,assumption,(~(((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$o]:(![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binunion @ X2) @ X3)) => ((((in @ X5) @ X2) => X4) => ((((in @ X5) @ X3) => X4) => X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X2))) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binunion @ X2) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))) => ((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.58  thf(h506,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,[])).
% 276.83/276.58  thf(h507,assumption,(~(((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$o]:(![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binunion @ X2) @ X3)) => ((((in @ X5) @ X2) => X4) => ((((in @ X5) @ X3) => X4) => X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X2))) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binunion @ X2) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))) => ((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.58  thf(h508,assumption,(![X1:$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,[])).
% 276.83/276.58  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))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))) => ((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.58  thf(h510,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,[])).
% 276.83/276.58  thf(h511,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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.58  thf(h512,assumption,(~(((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))) => ((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.58  thf(h513,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))),introduced(assumption,[])).
% 276.83/276.58  thf(h514,assumption,(~(((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))) => ((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.58  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) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))),introduced(assumption,[])).
% 276.83/276.58  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))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.59  thf(h517,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))) => ((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))),introduced(assumption,[])).
% 276.83/276.59  thf(h518,assumption,(~(((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.59  thf(h519,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,[])).
% 276.83/276.59  thf(h520,assumption,(~(((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.59  thf(h521,assumption,(![X1:$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,[])).
% 276.83/276.59  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))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.59  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) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))),introduced(assumption,[])).
% 276.83/276.59  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)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.59  thf(h525,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,[])).
% 276.83/276.59  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))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.59  thf(h527,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,[])).
% 276.83/276.59  thf(h528,assumption,(~(((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.59  thf(h529,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))),introduced(assumption,[])).
% 276.83/276.59  thf(h530,assumption,(~(((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.59  thf(h531,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,[])).
% 276.83/276.59  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))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.59  thf(h533,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))),introduced(assumption,[])).
% 276.83/276.59  thf(h534,assumption,(~(((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.59  thf(h535,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,[])).
% 276.83/276.59  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))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.59  thf(h537,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))),introduced(assumption,[])).
% 276.83/276.59  thf(h538,assumption,(~(((![X1:$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))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.59  thf(h539,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))),introduced(assumption,[])).
% 276.83/276.59  thf(h540,assumption,(~(((![X1:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.59  thf(h541,assumption,(~(((![X1:$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))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.59  thf(h542,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))),introduced(assumption,[])).
% 276.83/276.59  thf(h543,assumption,(~(((![X1:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.59  thf(h544,assumption,(~(((![X1:$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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.60  thf(h545,assumption,(~(((![X1:$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]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.60  thf(h546,assumption,(~(((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.60  thf(h547,assumption,(![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:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))),introduced(assumption,[])).
% 276.83/276.60  thf(h548,assumption,(~(((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.60  thf(h549,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))),introduced(assumption,[])).
% 276.83/276.60  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:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.60  thf(h551,assumption,(![X1:$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,[])).
% 276.83/276.60  thf(h552,assumption,(~(((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.60  thf(h553,assumption,(![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))),introduced(assumption,[])).
% 276.83/276.60  thf(h554,assumption,(~(((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.60  thf(h555,assumption,(~(((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.60  thf(h556,assumption,(![X1:$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))))))),introduced(assumption,[])).
% 276.83/276.60  thf(h557,assumption,(~(((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.60  thf(h558,assumption,(![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:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))),introduced(assumption,[])).
% 276.83/276.60  thf(h559,assumption,(~(((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.60  thf(h560,assumption,(![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))),introduced(assumption,[])).
% 276.83/276.60  thf(h561,assumption,(~(((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.83/276.60  thf(h562,assumption,(![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))),introduced(assumption,[])).
% 276.83/276.60  thf(h563,assumption,(~(((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.93/276.64  thf(h564,assumption,(![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))))))))),introduced(assumption,[])).
% 276.93/276.64  thf(h565,assumption,(~(((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.93/276.64  thf(h566,assumption,(![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))),introduced(assumption,[])).
% 276.93/276.64  thf(h567,assumption,(~(((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.93/276.64  thf(h568,assumption,(![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))))))))))))))),introduced(assumption,[])).
% 276.93/276.64  thf(h569,assumption,(~(((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.93/276.64  thf(h570,assumption,(![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))))))))))))))))),introduced(assumption,[])).
% 276.93/276.64  thf(h571,assumption,(~(((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.93/276.64  thf(h572,assumption,(![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:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))),introduced(assumption,[])).
% 276.93/276.64  thf(h573,assumption,(~(((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.93/276.64  thf(h574,assumption,(![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))),introduced(assumption,[])).
% 276.93/276.64  thf(h575,assumption,(~(((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.93/276.64  thf(h576,assumption,(![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))),introduced(assumption,[])).
% 276.93/276.64  thf(h577,assumption,(~(((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.93/276.64  thf(h578,assumption,(![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))),introduced(assumption,[])).
% 276.93/276.64  thf(h579,assumption,(~(((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))))),introduced(assumption,[])).
% 276.93/276.64  thf(h580,assumption,(![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))),introduced(assumption,[])).
% 276.93/276.64  thf(h581,assumption,(~(((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))),introduced(assumption,[])).
% 276.93/276.64  thf(h582,assumption,(![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))),introduced(assumption,[])).
% 276.93/276.64  thf(h583,assumption,(~(((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))))),introduced(assumption,[])).
% 276.93/276.64  thf(h584,assumption,(![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))),introduced(assumption,[])).
% 276.93/276.64  thf(h585,assumption,(~(((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))),introduced(assumption,[])).
% 276.93/276.64  thf(h586,assumption,(![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))),introduced(assumption,[])).
% 276.93/276.64  thf(h587,assumption,(~(((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))))),introduced(assumption,[])).
% 276.93/276.64  thf(h588,assumption,(![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))),introduced(assumption,[])).
% 276.93/276.64  thf(h589,assumption,(~(((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))),introduced(assumption,[])).
% 276.93/276.64  thf(h590,assumption,(![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))),introduced(assumption,[])).
% 276.93/276.64  thf(h591,assumption,(~(((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))))),introduced(assumption,[])).
% 276.93/276.64  thf(h592,assumption,(![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))),introduced(assumption,[])).
% 276.93/276.64  thf(h593,assumption,(~(((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))),introduced(assumption,[])).
% 276.93/276.64  thf(h594,assumption,(![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))),introduced(assumption,[])).
% 276.93/276.64  thf(h595,assumption,(~((![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))),introduced(assumption,[])).
% 276.93/276.64  thf(h596,assumption,(~((![X1:$i>$i]:(~((![X2:$i]:(~((![X3:$i]:(((in @ X3) @ X2) = (~((![X4:$i]:(((in @ X4) @ eigen__0) => (~((X3 = (X1 @ X4)))))))))))))))))),introduced(assumption,[])).
% 276.93/276.64  thf(h597,assumption,(![X1:$i]:(~((![X2:$i]:(((in @ X2) @ X1) = (~((![X3:$i]:(((in @ X3) @ eigen__0) => (~((X2 = (eigen__1 @ X3))))))))))))),introduced(assumption,[])).
% 276.93/276.64  thf(ax7224, axiom, (~(p280)|p1820), file('<stdin>', ax7224)).
% 276.93/276.64  thf(ax7226, axiom, (~(p1819)|~(p1818)|~(p1)), file('<stdin>', ax7226)).
% 276.93/276.64  thf(ax7225, axiom, (~(p1820)|p1819), file('<stdin>', ax7225)).
% 276.93/276.64  thf(ax8771, axiom, p280, file('<stdin>', ax8771)).
% 276.93/276.64  thf(ax9050, axiom, p1, file('<stdin>', ax9050)).
% 276.93/276.64  thf(nax1818, axiom, (p1818<=![X1:$i]:(fin @ X1 @ f__0=>~(![X2:$i]:((X2)=(f__1 @ X1)=>~(![X3:$i]:((X3)=(f__1 @ X1)=>(X2)=(X3))))))), file('<stdin>', nax1818)).
% 276.93/276.64  thf(c_0_6, plain, (~p280|p1820), inference(fof_simplification,[status(thm)],[ax7224])).
% 276.93/276.64  thf(c_0_7, plain, (~p1819|~p1818|~p1), inference(fof_simplification,[status(thm)],[ax7226])).
% 276.93/276.64  thf(c_0_8, plain, (~p1820|p1819), inference(fof_simplification,[status(thm)],[ax7225])).
% 276.93/276.64  thf(c_0_9, plain, (p1820|~p280), inference(split_conjunct,[status(thm)],[c_0_6])).
% 276.93/276.64  thf(c_0_10, plain, p280, inference(split_conjunct,[status(thm)],[ax8771])).
% 276.93/276.64  thf(c_0_11, plain, (~p1819|~p1818|~p1), inference(split_conjunct,[status(thm)],[c_0_7])).
% 276.93/276.64  thf(c_0_12, plain, p1, inference(split_conjunct,[status(thm)],[ax9050])).
% 276.93/276.64  thf(c_0_13, plain, (p1819|~p1820), inference(split_conjunct,[status(thm)],[c_0_8])).
% 276.93/276.64  thf(c_0_14, plain, p1820, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_9, c_0_10])])).
% 276.93/276.64  thf(c_0_15, plain, ![X445:$i]:((fin @ esk210_0 @ f__0|p1818)&(((esk211_1 @ X445)=(f__1 @ esk210_0)|(X445)!=(f__1 @ esk210_0)|p1818)&((X445)!=(esk211_1 @ X445)|(X445)!=(f__1 @ esk210_0)|p1818))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1818])])])])])])).
% 276.93/276.64  thf(c_0_16, plain, (~p1818|~p1819), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_11, c_0_12])])).
% 276.93/276.64  thf(c_0_17, plain, p1819, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13, c_0_14])])).
% 276.93/276.64  thf(c_0_18, plain, ![X1:$i]:(p1818|(X1)!=(esk211_1 @ X1)|(X1)!=(f__1 @ esk210_0)), inference(split_conjunct,[status(thm)],[c_0_15])).
% 276.93/276.64  thf(c_0_19, plain, ~p1818, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16, c_0_17])])).
% 276.93/276.64  thf(c_0_20, plain, ![X1:$i]:((esk211_1 @ X1)=(f__1 @ esk210_0)|p1818|(X1)!=(f__1 @ esk210_0)), inference(split_conjunct,[status(thm)],[c_0_15])).
% 276.93/276.64  thf(c_0_21, plain, (esk211_1 @ (f__1 @ esk210_0))!=(f__1 @ esk210_0), inference(er,[status(thm)],[inference(sr,[status(thm)],[c_0_18, c_0_19])])).
% 276.93/276.64  thf(c_0_22, plain, ($false), inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(sr,[status(thm)],[c_0_20, c_0_19])]), c_0_21]), ['proof']).
% 276.93/276.64  thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h597,h596,h594,h595,h592,h593,h590,h591,h588,h589,h586,h587,h584,h585,h582,h583,h580,h581,h578,h579,h576,h577,h574,h575,h572,h573,h570,h571,h568,h569,h566,h567,h564,h565,h562,h563,h560,h561,h558,h559,h556,h557,h547,h555,h553,h554,h551,h552,h549,h550,h547,h548,h513,h546,h490,h545,h502,h544,h542,h543,h486,h541,h539,h540,h537,h538,h535,h536,h533,h534,h531,h532,h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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])],[])).
% 276.93/276.64  thf(2,plain,$false,inference(tab_negall,[status(thm),assumptions([h596,h594,h595,h592,h593,h590,h591,h588,h589,h586,h587,h584,h585,h582,h583,h580,h581,h578,h579,h576,h577,h574,h575,h572,h573,h570,h571,h568,h569,h566,h567,h564,h565,h562,h563,h560,h561,h558,h559,h556,h557,h547,h555,h553,h554,h551,h552,h549,h550,h547,h548,h513,h546,h490,h545,h502,h544,h542,h543,h486,h541,h539,h540,h537,h538,h535,h536,h533,h534,h531,h532,h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h597]),tab_negall(eigenvar,eigen__1)],[h596,1,h597])).
% 276.93/276.64  thf(3,plain,$false,inference(tab_negall,[status(thm),assumptions([h594,h595,h592,h593,h590,h591,h588,h589,h586,h587,h584,h585,h582,h583,h580,h581,h578,h579,h576,h577,h574,h575,h572,h573,h570,h571,h568,h569,h566,h567,h564,h565,h562,h563,h560,h561,h558,h559,h556,h557,h547,h555,h553,h554,h551,h552,h549,h550,h547,h548,h513,h546,h490,h545,h502,h544,h542,h543,h486,h541,h539,h540,h537,h538,h535,h536,h533,h534,h531,h532,h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h596]),tab_negall(eigenvar,eigen__0)],[h595,2,h596])).
% 276.93/276.64  thf(4,plain,$false,inference(tab_negimp,[status(thm),assumptions([h592,h593,h590,h591,h588,h589,h586,h587,h584,h585,h582,h583,h580,h581,h578,h579,h576,h577,h574,h575,h572,h573,h570,h571,h568,h569,h566,h567,h564,h565,h562,h563,h560,h561,h558,h559,h556,h557,h547,h555,h553,h554,h551,h552,h549,h550,h547,h548,h513,h546,h490,h545,h502,h544,h542,h543,h486,h541,h539,h540,h537,h538,h535,h536,h533,h534,h531,h532,h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h594,h595])],[h593,3,h594,h595])).
% 276.93/276.64  thf(5,plain,$false,inference(tab_negimp,[status(thm),assumptions([h590,h591,h588,h589,h586,h587,h584,h585,h582,h583,h580,h581,h578,h579,h576,h577,h574,h575,h572,h573,h570,h571,h568,h569,h566,h567,h564,h565,h562,h563,h560,h561,h558,h559,h556,h557,h547,h555,h553,h554,h551,h552,h549,h550,h547,h548,h513,h546,h490,h545,h502,h544,h542,h543,h486,h541,h539,h540,h537,h538,h535,h536,h533,h534,h531,h532,h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h592,h593])],[h591,4,h592,h593])).
% 276.93/276.64  thf(6,plain,$false,inference(tab_negimp,[status(thm),assumptions([h588,h589,h586,h587,h584,h585,h582,h583,h580,h581,h578,h579,h576,h577,h574,h575,h572,h573,h570,h571,h568,h569,h566,h567,h564,h565,h562,h563,h560,h561,h558,h559,h556,h557,h547,h555,h553,h554,h551,h552,h549,h550,h547,h548,h513,h546,h490,h545,h502,h544,h542,h543,h486,h541,h539,h540,h537,h538,h535,h536,h533,h534,h531,h532,h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h590,h591])],[h589,5,h590,h591])).
% 276.93/276.64  thf(7,plain,$false,inference(tab_negimp,[status(thm),assumptions([h586,h587,h584,h585,h582,h583,h580,h581,h578,h579,h576,h577,h574,h575,h572,h573,h570,h571,h568,h569,h566,h567,h564,h565,h562,h563,h560,h561,h558,h559,h556,h557,h547,h555,h553,h554,h551,h552,h549,h550,h547,h548,h513,h546,h490,h545,h502,h544,h542,h543,h486,h541,h539,h540,h537,h538,h535,h536,h533,h534,h531,h532,h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h588,h589])],[h587,6,h588,h589])).
% 276.93/276.67  thf(8,plain,$false,inference(tab_negimp,[status(thm),assumptions([h584,h585,h582,h583,h580,h581,h578,h579,h576,h577,h574,h575,h572,h573,h570,h571,h568,h569,h566,h567,h564,h565,h562,h563,h560,h561,h558,h559,h556,h557,h547,h555,h553,h554,h551,h552,h549,h550,h547,h548,h513,h546,h490,h545,h502,h544,h542,h543,h486,h541,h539,h540,h537,h538,h535,h536,h533,h534,h531,h532,h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h586,h587])],[h585,7,h586,h587])).
% 276.93/276.68  thf(9,plain,$false,inference(tab_negimp,[status(thm),assumptions([h582,h583,h580,h581,h578,h579,h576,h577,h574,h575,h572,h573,h570,h571,h568,h569,h566,h567,h564,h565,h562,h563,h560,h561,h558,h559,h556,h557,h547,h555,h553,h554,h551,h552,h549,h550,h547,h548,h513,h546,h490,h545,h502,h544,h542,h543,h486,h541,h539,h540,h537,h538,h535,h536,h533,h534,h531,h532,h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h584,h585])],[h583,8,h584,h585])).
% 276.93/276.68  thf(10,plain,$false,inference(tab_negimp,[status(thm),assumptions([h580,h581,h578,h579,h576,h577,h574,h575,h572,h573,h570,h571,h568,h569,h566,h567,h564,h565,h562,h563,h560,h561,h558,h559,h556,h557,h547,h555,h553,h554,h551,h552,h549,h550,h547,h548,h513,h546,h490,h545,h502,h544,h542,h543,h486,h541,h539,h540,h537,h538,h535,h536,h533,h534,h531,h532,h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h582,h583])],[h581,9,h582,h583])).
% 276.93/276.68  thf(11,plain,$false,inference(tab_negimp,[status(thm),assumptions([h578,h579,h576,h577,h574,h575,h572,h573,h570,h571,h568,h569,h566,h567,h564,h565,h562,h563,h560,h561,h558,h559,h556,h557,h547,h555,h553,h554,h551,h552,h549,h550,h547,h548,h513,h546,h490,h545,h502,h544,h542,h543,h486,h541,h539,h540,h537,h538,h535,h536,h533,h534,h531,h532,h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h580,h581])],[h579,10,h580,h581])).
% 276.93/276.68  thf(12,plain,$false,inference(tab_negimp,[status(thm),assumptions([h576,h577,h574,h575,h572,h573,h570,h571,h568,h569,h566,h567,h564,h565,h562,h563,h560,h561,h558,h559,h556,h557,h547,h555,h553,h554,h551,h552,h549,h550,h547,h548,h513,h546,h490,h545,h502,h544,h542,h543,h486,h541,h539,h540,h537,h538,h535,h536,h533,h534,h531,h532,h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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])],[h577,11,h578,h579])).
% 276.93/276.68  thf(13,plain,$false,inference(tab_negimp,[status(thm),assumptions([h574,h575,h572,h573,h570,h571,h568,h569,h566,h567,h564,h565,h562,h563,h560,h561,h558,h559,h556,h557,h547,h555,h553,h554,h551,h552,h549,h550,h547,h548,h513,h546,h490,h545,h502,h544,h542,h543,h486,h541,h539,h540,h537,h538,h535,h536,h533,h534,h531,h532,h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h576,h577])],[h575,12,h576,h577])).
% 276.93/276.68  thf(14,plain,$false,inference(tab_negimp,[status(thm),assumptions([h572,h573,h570,h571,h568,h569,h566,h567,h564,h565,h562,h563,h560,h561,h558,h559,h556,h557,h547,h555,h553,h554,h551,h552,h549,h550,h547,h548,h513,h546,h490,h545,h502,h544,h542,h543,h486,h541,h539,h540,h537,h538,h535,h536,h533,h534,h531,h532,h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h574,h575])],[h573,13,h574,h575])).
% 276.93/276.68  thf(15,plain,$false,inference(tab_negimp,[status(thm),assumptions([h570,h571,h568,h569,h566,h567,h564,h565,h562,h563,h560,h561,h558,h559,h556,h557,h547,h555,h553,h554,h551,h552,h549,h550,h547,h548,h513,h546,h490,h545,h502,h544,h542,h543,h486,h541,h539,h540,h537,h538,h535,h536,h533,h534,h531,h532,h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h572,h573])],[h571,14,h572,h573])).
% 276.93/276.68  thf(16,plain,$false,inference(tab_negimp,[status(thm),assumptions([h568,h569,h566,h567,h564,h565,h562,h563,h560,h561,h558,h559,h556,h557,h547,h555,h553,h554,h551,h552,h549,h550,h547,h548,h513,h546,h490,h545,h502,h544,h542,h543,h486,h541,h539,h540,h537,h538,h535,h536,h533,h534,h531,h532,h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h570,h571])],[h569,15,h570,h571])).
% 276.93/276.68  thf(17,plain,$false,inference(tab_negimp,[status(thm),assumptions([h566,h567,h564,h565,h562,h563,h560,h561,h558,h559,h556,h557,h547,h555,h553,h554,h551,h552,h549,h550,h547,h548,h513,h546,h490,h545,h502,h544,h542,h543,h486,h541,h539,h540,h537,h538,h535,h536,h533,h534,h531,h532,h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h568,h569])],[h567,16,h568,h569])).
% 276.93/276.68  thf(18,plain,$false,inference(tab_negimp,[status(thm),assumptions([h564,h565,h562,h563,h560,h561,h558,h559,h556,h557,h547,h555,h553,h554,h551,h552,h549,h550,h547,h548,h513,h546,h490,h545,h502,h544,h542,h543,h486,h541,h539,h540,h537,h538,h535,h536,h533,h534,h531,h532,h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h566,h567])],[h565,17,h566,h567])).
% 276.93/276.68  thf(19,plain,$false,inference(tab_negimp,[status(thm),assumptions([h562,h563,h560,h561,h558,h559,h556,h557,h547,h555,h553,h554,h551,h552,h549,h550,h547,h548,h513,h546,h490,h545,h502,h544,h542,h543,h486,h541,h539,h540,h537,h538,h535,h536,h533,h534,h531,h532,h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h564,h565])],[h563,18,h564,h565])).
% 276.93/276.68  thf(20,plain,$false,inference(tab_negimp,[status(thm),assumptions([h560,h561,h558,h559,h556,h557,h547,h555,h553,h554,h551,h552,h549,h550,h547,h548,h513,h546,h490,h545,h502,h544,h542,h543,h486,h541,h539,h540,h537,h538,h535,h536,h533,h534,h531,h532,h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h562,h563])],[h561,19,h562,h563])).
% 276.93/276.68  thf(21,plain,$false,inference(tab_negimp,[status(thm),assumptions([h558,h559,h556,h557,h547,h555,h553,h554,h551,h552,h549,h550,h547,h548,h513,h546,h490,h545,h502,h544,h542,h543,h486,h541,h539,h540,h537,h538,h535,h536,h533,h534,h531,h532,h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h560,h561])],[h559,20,h560,h561])).
% 276.93/276.68  thf(22,plain,$false,inference(tab_negimp,[status(thm),assumptions([h556,h557,h547,h555,h553,h554,h551,h552,h549,h550,h547,h548,h513,h546,h490,h545,h502,h544,h542,h543,h486,h541,h539,h540,h537,h538,h535,h536,h533,h534,h531,h532,h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h558,h559])],[h557,21,h558,h559])).
% 276.93/276.68  thf(23,plain,$false,inference(tab_negimp,[status(thm),assumptions([h547,h555,h553,h554,h551,h552,h549,h550,h547,h548,h513,h546,h490,h545,h502,h544,h542,h543,h486,h541,h539,h540,h537,h538,h535,h536,h533,h534,h531,h532,h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h556,h557])],[h555,22,h556,h557])).
% 276.93/276.68  thf(24,plain,$false,inference(tab_negimp,[status(thm),assumptions([h553,h554,h551,h552,h549,h550,h547,h548,h513,h546,h490,h545,h502,h544,h542,h543,h486,h541,h539,h540,h537,h538,h535,h536,h533,h534,h531,h532,h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h547,h555])],[h554,23,h547,h555])).
% 276.93/276.68  thf(25,plain,$false,inference(tab_negimp,[status(thm),assumptions([h551,h552,h549,h550,h547,h548,h513,h546,h490,h545,h502,h544,h542,h543,h486,h541,h539,h540,h537,h538,h535,h536,h533,h534,h531,h532,h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h553,h554])],[h552,24,h553,h554])).
% 276.93/276.68  thf(26,plain,$false,inference(tab_negimp,[status(thm),assumptions([h549,h550,h547,h548,h513,h546,h490,h545,h502,h544,h542,h543,h486,h541,h539,h540,h537,h538,h535,h536,h533,h534,h531,h532,h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h551,h552])],[h550,25,h551,h552])).
% 276.93/276.68  thf(27,plain,$false,inference(tab_negimp,[status(thm),assumptions([h547,h548,h513,h546,h490,h545,h502,h544,h542,h543,h486,h541,h539,h540,h537,h538,h535,h536,h533,h534,h531,h532,h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h549,h550])],[h548,26,h549,h550])).
% 276.93/276.68  thf(28,plain,$false,inference(tab_negimp,[status(thm),assumptions([h513,h546,h490,h545,h502,h544,h542,h543,h486,h541,h539,h540,h537,h538,h535,h536,h533,h534,h531,h532,h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h547,h548])],[h546,27,h547,h548])).
% 276.93/276.68  thf(29,plain,$false,inference(tab_negimp,[status(thm),assumptions([h490,h545,h502,h544,h542,h543,h486,h541,h539,h540,h537,h538,h535,h536,h533,h534,h531,h532,h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h513,h546])],[h545,28,h513,h546])).
% 276.93/276.68  thf(30,plain,$false,inference(tab_negimp,[status(thm),assumptions([h502,h544,h542,h543,h486,h541,h539,h540,h537,h538,h535,h536,h533,h534,h531,h532,h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h490,h545])],[h544,29,h490,h545])).
% 277.02/276.70  thf(31,plain,$false,inference(tab_negimp,[status(thm),assumptions([h542,h543,h486,h541,h539,h540,h537,h538,h535,h536,h533,h534,h531,h532,h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h502,h544])],[h543,30,h502,h544])).
% 277.02/276.70  thf(32,plain,$false,inference(tab_negimp,[status(thm),assumptions([h486,h541,h539,h540,h537,h538,h535,h536,h533,h534,h531,h532,h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h542,h543])],[h541,31,h542,h543])).
% 277.02/276.70  thf(33,plain,$false,inference(tab_negimp,[status(thm),assumptions([h539,h540,h537,h538,h535,h536,h533,h534,h531,h532,h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h486,h541])],[h540,32,h486,h541])).
% 277.02/276.70  thf(34,plain,$false,inference(tab_negimp,[status(thm),assumptions([h537,h538,h535,h536,h533,h534,h531,h532,h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h539,h540])],[h538,33,h539,h540])).
% 277.02/276.70  thf(35,plain,$false,inference(tab_negimp,[status(thm),assumptions([h535,h536,h533,h534,h531,h532,h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h537,h538])],[h536,34,h537,h538])).
% 277.02/276.70  thf(36,plain,$false,inference(tab_negimp,[status(thm),assumptions([h533,h534,h531,h532,h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h535,h536])],[h534,35,h535,h536])).
% 277.02/276.70  thf(37,plain,$false,inference(tab_negimp,[status(thm),assumptions([h531,h532,h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h533,h534])],[h532,36,h533,h534])).
% 277.02/276.70  thf(38,plain,$false,inference(tab_negimp,[status(thm),assumptions([h529,h530,h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h531,h532])],[h530,37,h531,h532])).
% 277.02/276.70  thf(39,plain,$false,inference(tab_negimp,[status(thm),assumptions([h527,h528,h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h529,h530])],[h528,38,h529,h530])).
% 277.02/276.70  thf(40,plain,$false,inference(tab_negimp,[status(thm),assumptions([h525,h526,h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h527,h528])],[h526,39,h527,h528])).
% 277.02/276.70  thf(41,plain,$false,inference(tab_negimp,[status(thm),assumptions([h523,h524,h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h525,h526])],[h524,40,h525,h526])).
% 277.02/276.70  thf(42,plain,$false,inference(tab_negimp,[status(thm),assumptions([h521,h522,h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h523,h524])],[h522,41,h523,h524])).
% 277.02/276.70  thf(43,plain,$false,inference(tab_negimp,[status(thm),assumptions([h519,h520,h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h521,h522])],[h520,42,h521,h522])).
% 277.02/276.70  thf(44,plain,$false,inference(tab_negimp,[status(thm),assumptions([h517,h518,h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h519,h520])],[h518,43,h519,h520])).
% 277.02/276.70  thf(45,plain,$false,inference(tab_negimp,[status(thm),assumptions([h515,h516,h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h517,h518])],[h516,44,h517,h518])).
% 277.02/276.70  thf(46,plain,$false,inference(tab_negimp,[status(thm),assumptions([h513,h514,h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h515,h516])],[h514,45,h515,h516])).
% 277.02/276.70  thf(47,plain,$false,inference(tab_negimp,[status(thm),assumptions([h506,h512,h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h513,h514])],[h512,46,h513,h514])).
% 277.02/276.70  thf(48,plain,$false,inference(tab_negimp,[status(thm),assumptions([h510,h511,h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h506,h512])],[h511,47,h506,h512])).
% 277.02/276.70  thf(49,plain,$false,inference(tab_negimp,[status(thm),assumptions([h508,h509,h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h510,h511])],[h509,48,h510,h511])).
% 277.02/276.70  thf(50,plain,$false,inference(tab_negimp,[status(thm),assumptions([h506,h507,h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h508,h509])],[h507,49,h508,h509])).
% 277.02/276.70  thf(51,plain,$false,inference(tab_negimp,[status(thm),assumptions([h504,h505,h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h506,h507])],[h505,50,h506,h507])).
% 277.02/276.70  thf(52,plain,$false,inference(tab_negimp,[status(thm),assumptions([h502,h503,h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h504,h505])],[h503,51,h504,h505])).
% 277.02/276.70  thf(53,plain,$false,inference(tab_negimp,[status(thm),assumptions([h500,h501,h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h502,h503])],[h501,52,h502,h503])).
% 277.02/276.70  thf(54,plain,$false,inference(tab_negimp,[status(thm),assumptions([h498,h499,h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h500,h501])],[h499,53,h500,h501])).
% 277.02/276.72  thf(55,plain,$false,inference(tab_negimp,[status(thm),assumptions([h496,h497,h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h498,h499])],[h497,54,h498,h499])).
% 277.02/276.72  thf(56,plain,$false,inference(tab_negimp,[status(thm),assumptions([h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h496,h497])],[h495,55,h496,h497])).
% 277.02/276.72  thf(57,plain,$false,inference(tab_negimp,[status(thm),assumptions([h492,h493,h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h494,h495])],[h493,56,h494,h495])).
% 277.02/276.72  thf(58,plain,$false,inference(tab_negimp,[status(thm),assumptions([h490,h491,h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h492,h493])],[h491,57,h492,h493])).
% 277.02/276.72  thf(59,plain,$false,inference(tab_negimp,[status(thm),assumptions([h488,h489,h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h490,h491])],[h489,58,h490,h491])).
% 277.02/276.72  thf(60,plain,$false,inference(tab_negimp,[status(thm),assumptions([h486,h487,h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h488,h489])],[h487,59,h488,h489])).
% 277.02/276.72  thf(61,plain,$false,inference(tab_negimp,[status(thm),assumptions([h484,h485,h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h486,h487])],[h485,60,h486,h487])).
% 277.02/276.72  thf(62,plain,$false,inference(tab_negimp,[status(thm),assumptions([h482,h483,h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h484,h485])],[h483,61,h484,h485])).
% 277.02/276.72  thf(63,plain,$false,inference(tab_negimp,[status(thm),assumptions([h480,h481,h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h482,h483])],[h481,62,h482,h483])).
% 277.02/276.72  thf(64,plain,$false,inference(tab_negimp,[status(thm),assumptions([h478,h479,h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h480,h481])],[h479,63,h480,h481])).
% 277.02/276.72  thf(65,plain,$false,inference(tab_negimp,[status(thm),assumptions([h476,h477,h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h478,h479])],[h477,64,h478,h479])).
% 277.02/276.72  thf(66,plain,$false,inference(tab_negimp,[status(thm),assumptions([h474,h475,h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h476,h477])],[h475,65,h476,h477])).
% 277.02/276.72  thf(67,plain,$false,inference(tab_negimp,[status(thm),assumptions([h472,h473,h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h474,h475])],[h473,66,h474,h475])).
% 277.02/276.72  thf(68,plain,$false,inference(tab_negimp,[status(thm),assumptions([h470,h471,h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h472,h473])],[h471,67,h472,h473])).
% 277.02/276.72  thf(69,plain,$false,inference(tab_negimp,[status(thm),assumptions([h468,h469,h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h470,h471])],[h469,68,h470,h471])).
% 277.02/276.72  thf(70,plain,$false,inference(tab_negimp,[status(thm),assumptions([h466,h467,h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h468,h469])],[h467,69,h468,h469])).
% 277.02/276.72  thf(71,plain,$false,inference(tab_negimp,[status(thm),assumptions([h464,h465,h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h466,h467])],[h465,70,h466,h467])).
% 277.02/276.72  thf(72,plain,$false,inference(tab_negimp,[status(thm),assumptions([h462,h463,h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h464,h465])],[h463,71,h464,h465])).
% 277.02/276.72  thf(73,plain,$false,inference(tab_negimp,[status(thm),assumptions([h460,h461,h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h462,h463])],[h461,72,h462,h463])).
% 277.02/276.72  thf(74,plain,$false,inference(tab_negimp,[status(thm),assumptions([h458,h459,h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h460,h461])],[h459,73,h460,h461])).
% 277.02/276.72  thf(75,plain,$false,inference(tab_negimp,[status(thm),assumptions([h456,h457,h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h458,h459])],[h457,74,h458,h459])).
% 277.02/276.72  thf(76,plain,$false,inference(tab_negimp,[status(thm),assumptions([h454,h455,h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h456,h457])],[h455,75,h456,h457])).
% 277.02/276.72  thf(77,plain,$false,inference(tab_negimp,[status(thm),assumptions([h452,h453,h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h454,h455])],[h453,76,h454,h455])).
% 277.02/276.72  thf(78,plain,$false,inference(tab_negimp,[status(thm),assumptions([h450,h451,h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h452,h453])],[h451,77,h452,h453])).
% 277.02/276.72  thf(79,plain,$false,inference(tab_negimp,[status(thm),assumptions([h448,h449,h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h450,h451])],[h449,78,h450,h451])).
% 277.02/276.72  thf(80,plain,$false,inference(tab_negimp,[status(thm),assumptions([h446,h447,h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h448,h449])],[h447,79,h448,h449])).
% 277.02/276.72  thf(81,plain,$false,inference(tab_negimp,[status(thm),assumptions([h444,h445,h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h446,h447])],[h445,80,h446,h447])).
% 277.02/276.72  thf(82,plain,$false,inference(tab_negimp,[status(thm),assumptions([h442,h443,h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h444,h445])],[h443,81,h444,h445])).
% 277.02/276.72  thf(83,plain,$false,inference(tab_negimp,[status(thm),assumptions([h440,h441,h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h442,h443])],[h441,82,h442,h443])).
% 277.02/276.72  thf(84,plain,$false,inference(tab_negimp,[status(thm),assumptions([h438,h439,h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h440,h441])],[h439,83,h440,h441])).
% 277.02/276.72  thf(85,plain,$false,inference(tab_negimp,[status(thm),assumptions([h436,h437,h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h438,h439])],[h437,84,h438,h439])).
% 277.02/276.72  thf(86,plain,$false,inference(tab_negimp,[status(thm),assumptions([h434,h435,h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h436,h437])],[h435,85,h436,h437])).
% 277.02/276.72  thf(87,plain,$false,inference(tab_negimp,[status(thm),assumptions([h432,h433,h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h434,h435])],[h433,86,h434,h435])).
% 277.02/276.72  thf(88,plain,$false,inference(tab_negimp,[status(thm),assumptions([h430,h431,h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h432,h433])],[h431,87,h432,h433])).
% 277.02/276.72  thf(89,plain,$false,inference(tab_negimp,[status(thm),assumptions([h428,h429,h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h430,h431])],[h429,88,h430,h431])).
% 277.02/276.72  thf(90,plain,$false,inference(tab_negimp,[status(thm),assumptions([h426,h427,h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h428,h429])],[h427,89,h428,h429])).
% 277.02/276.72  thf(91,plain,$false,inference(tab_negimp,[status(thm),assumptions([h424,h425,h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h426,h427])],[h425,90,h426,h427])).
% 277.02/276.72  thf(92,plain,$false,inference(tab_negimp,[status(thm),assumptions([h422,h423,h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h424,h425])],[h423,91,h424,h425])).
% 277.02/276.72  thf(93,plain,$false,inference(tab_negimp,[status(thm),assumptions([h420,h421,h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h422,h423])],[h421,92,h422,h423])).
% 277.02/276.72  thf(94,plain,$false,inference(tab_negimp,[status(thm),assumptions([h418,h419,h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h420,h421])],[h419,93,h420,h421])).
% 277.02/276.72  thf(95,plain,$false,inference(tab_negimp,[status(thm),assumptions([h416,h417,h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h418,h419])],[h417,94,h418,h419])).
% 277.02/276.72  thf(96,plain,$false,inference(tab_negimp,[status(thm),assumptions([h414,h415,h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h416,h417])],[h415,95,h416,h417])).
% 277.02/276.72  thf(97,plain,$false,inference(tab_negimp,[status(thm),assumptions([h407,h413,h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h414,h415])],[h413,96,h414,h415])).
% 277.02/276.72  thf(98,plain,$false,inference(tab_negimp,[status(thm),assumptions([h411,h412,h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h407,h413])],[h412,97,h407,h413])).
% 277.02/276.72  thf(99,plain,$false,inference(tab_negimp,[status(thm),assumptions([h409,h410,h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h411,h412])],[h410,98,h411,h412])).
% 277.02/276.72  thf(100,plain,$false,inference(tab_negimp,[status(thm),assumptions([h407,h408,h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h409,h410])],[h408,99,h409,h410])).
% 277.02/276.72  thf(101,plain,$false,inference(tab_negimp,[status(thm),assumptions([h405,h406,h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h407,h408])],[h406,100,h407,h408])).
% 277.02/276.72  thf(102,plain,$false,inference(tab_negimp,[status(thm),assumptions([h403,h404,h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h405,h406])],[h404,101,h405,h406])).
% 277.02/276.72  thf(103,plain,$false,inference(tab_negimp,[status(thm),assumptions([h401,h402,h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h403,h404])],[h402,102,h403,h404])).
% 277.02/276.72  thf(104,plain,$false,inference(tab_negimp,[status(thm),assumptions([h399,h400,h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h401,h402])],[h400,103,h401,h402])).
% 277.02/276.72  thf(105,plain,$false,inference(tab_negimp,[status(thm),assumptions([h397,h398,h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h399,h400])],[h398,104,h399,h400])).
% 277.02/276.72  thf(106,plain,$false,inference(tab_negimp,[status(thm),assumptions([h395,h396,h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h397,h398])],[h396,105,h397,h398])).
% 277.02/276.72  thf(107,plain,$false,inference(tab_negimp,[status(thm),assumptions([h393,h394,h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h395,h396])],[h394,106,h395,h396])).
% 277.02/276.72  thf(108,plain,$false,inference(tab_negimp,[status(thm),assumptions([h391,h392,h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h393,h394])],[h392,107,h393,h394])).
% 277.02/276.72  thf(109,plain,$false,inference(tab_negimp,[status(thm),assumptions([h389,h390,h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h391,h392])],[h390,108,h391,h392])).
% 277.02/276.72  thf(110,plain,$false,inference(tab_negimp,[status(thm),assumptions([h387,h388,h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h389,h390])],[h388,109,h389,h390])).
% 277.02/276.72  thf(111,plain,$false,inference(tab_negimp,[status(thm),assumptions([h385,h386,h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h387,h388])],[h386,110,h387,h388])).
% 277.02/276.73  thf(112,plain,$false,inference(tab_negimp,[status(thm),assumptions([h383,h384,h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h385,h386])],[h384,111,h385,h386])).
% 277.02/276.73  thf(113,plain,$false,inference(tab_negimp,[status(thm),assumptions([h380,h382,h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h383,h384])],[h382,112,h383,h384])).
% 277.02/276.73  thf(114,plain,$false,inference(tab_negimp,[status(thm),assumptions([h380,h381,h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h380,h382])],[h381,113,h380,h382])).
% 277.02/276.73  thf(115,plain,$false,inference(tab_negimp,[status(thm),assumptions([h378,h379,h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h380,h381])],[h379,114,h380,h381])).
% 277.02/276.73  thf(116,plain,$false,inference(tab_negimp,[status(thm),assumptions([h376,h377,h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h378,h379])],[h377,115,h378,h379])).
% 277.02/276.73  thf(117,plain,$false,inference(tab_negimp,[status(thm),assumptions([h374,h375,h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h376,h377])],[h375,116,h376,h377])).
% 277.02/276.73  thf(118,plain,$false,inference(tab_negimp,[status(thm),assumptions([h372,h373,h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h374,h375])],[h373,117,h374,h375])).
% 277.02/276.73  thf(119,plain,$false,inference(tab_negimp,[status(thm),assumptions([h370,h371,h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h372,h373])],[h371,118,h372,h373])).
% 277.02/276.73  thf(120,plain,$false,inference(tab_negimp,[status(thm),assumptions([h368,h369,h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h370,h371])],[h369,119,h370,h371])).
% 277.02/276.73  thf(121,plain,$false,inference(tab_negimp,[status(thm),assumptions([h366,h367,h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h368,h369])],[h367,120,h368,h369])).
% 277.02/276.73  thf(122,plain,$false,inference(tab_negimp,[status(thm),assumptions([h364,h365,h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h366,h367])],[h365,121,h366,h367])).
% 277.02/276.73  thf(123,plain,$false,inference(tab_negimp,[status(thm),assumptions([h362,h363,h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h364,h365])],[h363,122,h364,h365])).
% 277.02/276.73  thf(124,plain,$false,inference(tab_negimp,[status(thm),assumptions([h360,h361,h358,h359,h356,h357,h354,h355,h352,h353,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,[h362,h363])],[h361,123,h362,h363])).
% 277.02/276.73  thf(125,plain,$false,inference(tab_negimp,[status(thm),assumptions([h358,h359,h356,h357,h354,h355,h352,h353,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h360,h361])],[h359,124,h360,h361])).
% 277.02/276.73  thf(126,plain,$false,inference(tab_negimp,[status(thm),assumptions([h356,h357,h354,h355,h352,h353,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,[h358,h359])],[h357,125,h358,h359])).
% 277.02/276.73  thf(127,plain,$false,inference(tab_negimp,[status(thm),assumptions([h354,h355,h352,h353,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h356,h357])],[h355,126,h356,h357])).
% 277.02/276.73  thf(128,plain,$false,inference(tab_negimp,[status(thm),assumptions([h352,h353,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,[h354,h355])],[h353,127,h354,h355])).
% 277.02/276.73  thf(129,plain,$false,inference(tab_negimp,[status(thm),assumptions([h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h352,h353])],[h351,128,h352,h353])).
% 277.02/276.73  thf(130,plain,$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])],[h349,129,h350,h351])).
% 277.02/276.73  thf(131,plain,$false,inference(tab_negimp,[status(thm),assumptions([h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h348,h349])],[h347,130,h348,h349])).
% 277.02/276.73  thf(132,plain,$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])],[h345,131,h346,h347])).
% 277.02/276.73  thf(133,plain,$false,inference(tab_negimp,[status(thm),assumptions([h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h344,h345])],[h343,132,h344,h345])).
% 277.02/276.73  thf(134,plain,$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])],[h341,133,h342,h343])).
% 277.02/276.73  thf(135,plain,$false,inference(tab_negimp,[status(thm),assumptions([h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h340,h341])],[h339,134,h340,h341])).
% 277.02/276.73  thf(136,plain,$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])],[h337,135,h338,h339])).
% 277.02/276.73  thf(137,plain,$false,inference(tab_negimp,[status(thm),assumptions([h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h336,h337])],[h335,136,h336,h337])).
% 277.02/276.73  thf(138,plain,$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])],[h333,137,h334,h335])).
% 277.02/276.73  thf(139,plain,$false,inference(tab_negimp,[status(thm),assumptions([h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h332,h333])],[h331,138,h332,h333])).
% 277.02/276.73  thf(140,plain,$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])],[h329,139,h330,h331])).
% 277.02/276.73  thf(141,plain,$false,inference(tab_negimp,[status(thm),assumptions([h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h328,h329])],[h327,140,h328,h329])).
% 277.02/276.73  thf(142,plain,$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])],[h325,141,h326,h327])).
% 277.02/276.73  thf(143,plain,$false,inference(tab_negimp,[status(thm),assumptions([h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h324,h325])],[h323,142,h324,h325])).
% 277.02/276.73  thf(144,plain,$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])],[h321,143,h322,h323])).
% 277.02/276.73  thf(145,plain,$false,inference(tab_negimp,[status(thm),assumptions([h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h320,h321])],[h319,144,h320,h321])).
% 277.02/276.73  thf(146,plain,$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])],[h317,145,h318,h319])).
% 277.02/276.73  thf(147,plain,$false,inference(tab_negimp,[status(thm),assumptions([h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h316,h317])],[h315,146,h316,h317])).
% 277.02/276.73  thf(148,plain,$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])],[h313,147,h314,h315])).
% 277.02/276.73  thf(149,plain,$false,inference(tab_negimp,[status(thm),assumptions([h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h312,h313])],[h311,148,h312,h313])).
% 277.02/276.73  thf(150,plain,$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])],[h309,149,h310,h311])).
% 277.02/276.73  thf(151,plain,$false,inference(tab_negimp,[status(thm),assumptions([h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h308,h309])],[h307,150,h308,h309])).
% 277.02/276.73  thf(152,plain,$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])],[h305,151,h306,h307])).
% 277.02/276.73  thf(153,plain,$false,inference(tab_negimp,[status(thm),assumptions([h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h304,h305])],[h303,152,h304,h305])).
% 277.02/276.73  thf(154,plain,$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])],[h301,153,h302,h303])).
% 277.02/276.73  thf(155,plain,$false,inference(tab_negimp,[status(thm),assumptions([h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h300,h301])],[h299,154,h300,h301])).
% 277.02/276.73  thf(156,plain,$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])],[h297,155,h298,h299])).
% 277.02/276.73  thf(157,plain,$false,inference(tab_negimp,[status(thm),assumptions([h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h296,h297])],[h295,156,h296,h297])).
% 277.02/276.73  thf(158,plain,$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])],[h293,157,h294,h295])).
% 277.02/276.73  thf(159,plain,$false,inference(tab_negimp,[status(thm),assumptions([h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h292,h293])],[h291,158,h292,h293])).
% 277.02/276.73  thf(160,plain,$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])],[h289,159,h290,h291])).
% 277.02/276.73  thf(161,plain,$false,inference(tab_negimp,[status(thm),assumptions([h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h288,h289])],[h287,160,h288,h289])).
% 277.02/276.73  thf(162,plain,$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])],[h285,161,h286,h287])).
% 277.02/276.73  thf(163,plain,$false,inference(tab_negimp,[status(thm),assumptions([h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h284,h285])],[h283,162,h284,h285])).
% 277.02/276.73  thf(164,plain,$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])],[h281,163,h282,h283])).
% 277.02/276.73  thf(165,plain,$false,inference(tab_negimp,[status(thm),assumptions([h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h280,h281])],[h279,164,h280,h281])).
% 277.02/276.73  thf(166,plain,$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])],[h277,165,h278,h279])).
% 277.02/276.73  thf(167,plain,$false,inference(tab_negimp,[status(thm),assumptions([h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h276,h277])],[h275,166,h276,h277])).
% 277.02/276.73  thf(168,plain,$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])],[h273,167,h274,h275])).
% 277.02/276.73  thf(169,plain,$false,inference(tab_negimp,[status(thm),assumptions([h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h272,h273])],[h271,168,h272,h273])).
% 277.02/276.73  thf(170,plain,$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])],[h269,169,h270,h271])).
% 277.02/276.73  thf(171,plain,$false,inference(tab_negimp,[status(thm),assumptions([h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h268,h269])],[h267,170,h268,h269])).
% 277.02/276.73  thf(172,plain,$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])],[h266,171,h90,h267])).
% 277.02/276.73  thf(173,plain,$false,inference(tab_negimp,[status(thm),assumptions([h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h265,h266])],[h264,172,h265,h266])).
% 277.02/276.73  thf(174,plain,$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])],[h262,173,h263,h264])).
% 277.02/276.73  thf(175,plain,$false,inference(tab_negimp,[status(thm),assumptions([h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h261,h262])],[h260,174,h261,h262])).
% 277.02/276.73  thf(176,plain,$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])],[h258,175,h259,h260])).
% 277.02/276.73  thf(177,plain,$false,inference(tab_negimp,[status(thm),assumptions([h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h257,h258])],[h256,176,h257,h258])).
% 277.02/276.73  thf(178,plain,$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])],[h254,177,h255,h256])).
% 277.02/276.73  thf(179,plain,$false,inference(tab_negimp,[status(thm),assumptions([h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h253,h254])],[h252,178,h253,h254])).
% 277.02/276.73  thf(180,plain,$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])],[h251,179,h94,h252])).
% 277.02/276.73  thf(181,plain,$false,inference(tab_negimp,[status(thm),assumptions([h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h250,h251])],[h249,180,h250,h251])).
% 277.02/276.73  thf(182,plain,$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])],[h247,181,h248,h249])).
% 277.02/276.73  thf(183,plain,$false,inference(tab_negimp,[status(thm),assumptions([h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h246,h247])],[h245,182,h246,h247])).
% 277.02/276.73  thf(184,plain,$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])],[h243,183,h244,h245])).
% 277.02/276.73  thf(185,plain,$false,inference(tab_negimp,[status(thm),assumptions([h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h242,h243])],[h241,184,h242,h243])).
% 277.02/276.73  thf(186,plain,$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])],[h239,185,h240,h241])).
% 277.02/276.73  thf(187,plain,$false,inference(tab_negimp,[status(thm),assumptions([h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h238,h239])],[h237,186,h238,h239])).
% 277.02/276.73  thf(188,plain,$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])],[h235,187,h236,h237])).
% 277.02/276.73  thf(189,plain,$false,inference(tab_negimp,[status(thm),assumptions([h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h234,h235])],[h233,188,h234,h235])).
% 277.02/276.73  thf(190,plain,$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])],[h231,189,h232,h233])).
% 277.02/276.73  thf(191,plain,$false,inference(tab_negimp,[status(thm),assumptions([h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h230,h231])],[h229,190,h230,h231])).
% 277.02/276.73  thf(192,plain,$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])],[h227,191,h228,h229])).
% 277.02/276.73  thf(193,plain,$false,inference(tab_negimp,[status(thm),assumptions([h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h226,h227])],[h225,192,h226,h227])).
% 277.02/276.73  thf(194,plain,$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])],[h223,193,h224,h225])).
% 277.02/276.73  thf(195,plain,$false,inference(tab_negimp,[status(thm),assumptions([h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h222,h223])],[h221,194,h222,h223])).
% 277.02/276.73  thf(196,plain,$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])],[h219,195,h220,h221])).
% 277.02/276.73  thf(197,plain,$false,inference(tab_negimp,[status(thm),assumptions([h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h218,h219])],[h217,196,h218,h219])).
% 277.02/276.73  thf(198,plain,$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])],[h215,197,h216,h217])).
% 277.02/276.73  thf(199,plain,$false,inference(tab_negimp,[status(thm),assumptions([h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h214,h215])],[h213,198,h214,h215])).
% 277.02/276.73  thf(200,plain,$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])],[h211,199,h212,h213])).
% 277.02/276.73  thf(201,plain,$false,inference(tab_negimp,[status(thm),assumptions([h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h210,h211])],[h209,200,h210,h211])).
% 277.02/276.73  thf(202,plain,$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])],[h207,201,h208,h209])).
% 277.02/276.73  thf(203,plain,$false,inference(tab_negimp,[status(thm),assumptions([h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h206,h207])],[h205,202,h206,h207])).
% 277.02/276.73  thf(204,plain,$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])],[h203,203,h204,h205])).
% 277.02/276.73  thf(205,plain,$false,inference(tab_negimp,[status(thm),assumptions([h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h202,h203])],[h201,204,h202,h203])).
% 277.02/276.73  thf(206,plain,$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])],[h199,205,h200,h201])).
% 277.02/276.73  thf(207,plain,$false,inference(tab_negimp,[status(thm),assumptions([h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h198,h199])],[h197,206,h198,h199])).
% 277.02/276.73  thf(208,plain,$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])],[h195,207,h196,h197])).
% 277.02/276.73  thf(209,plain,$false,inference(tab_negimp,[status(thm),assumptions([h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h194,h195])],[h193,208,h194,h195])).
% 277.02/276.73  thf(210,plain,$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])],[h191,209,h192,h193])).
% 277.02/276.73  thf(211,plain,$false,inference(tab_negimp,[status(thm),assumptions([h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h190,h191])],[h189,210,h190,h191])).
% 277.02/276.73  thf(212,plain,$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])],[h187,211,h188,h189])).
% 277.02/276.73  thf(213,plain,$false,inference(tab_negimp,[status(thm),assumptions([h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h94,h187])],[h186,212,h94,h187])).
% 277.02/276.73  thf(214,plain,$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])],[h184,213,h185,h186])).
% 277.02/276.73  thf(215,plain,$false,inference(tab_negimp,[status(thm),assumptions([h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h183,h184])],[h182,214,h183,h184])).
% 277.02/276.73  thf(216,plain,$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])],[h180,215,h181,h182])).
% 277.02/276.73  thf(217,plain,$false,inference(tab_negimp,[status(thm),assumptions([h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h179,h180])],[h178,216,h179,h180])).
% 277.02/276.73  thf(218,plain,$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])],[h176,217,h177,h178])).
% 277.02/276.73  thf(219,plain,$false,inference(tab_negimp,[status(thm),assumptions([h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h175,h176])],[h174,218,h175,h176])).
% 277.02/276.73  thf(220,plain,$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])],[h172,219,h173,h174])).
% 277.02/276.73  thf(221,plain,$false,inference(tab_negimp,[status(thm),assumptions([h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h171,h172])],[h170,220,h171,h172])).
% 277.02/276.73  thf(222,plain,$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])],[h168,221,h169,h170])).
% 277.02/276.73  thf(223,plain,$false,inference(tab_negimp,[status(thm),assumptions([h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h167,h168])],[h166,222,h167,h168])).
% 277.02/276.73  thf(224,plain,$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])],[h164,223,h165,h166])).
% 277.02/276.73  thf(225,plain,$false,inference(tab_negimp,[status(thm),assumptions([h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h163,h164])],[h162,224,h163,h164])).
% 277.02/276.73  thf(226,plain,$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])],[h160,225,h161,h162])).
% 277.02/276.73  thf(227,plain,$false,inference(tab_negimp,[status(thm),assumptions([h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h159,h160])],[h158,226,h159,h160])).
% 277.02/276.73  thf(228,plain,$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])],[h156,227,h157,h158])).
% 277.02/276.73  thf(229,plain,$false,inference(tab_negimp,[status(thm),assumptions([h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h155,h156])],[h154,228,h155,h156])).
% 277.02/276.73  thf(230,plain,$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])],[h152,229,h153,h154])).
% 277.02/276.73  thf(231,plain,$false,inference(tab_negimp,[status(thm),assumptions([h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h151,h152])],[h150,230,h151,h152])).
% 277.02/276.73  thf(232,plain,$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])],[h148,231,h149,h150])).
% 277.02/276.73  thf(233,plain,$false,inference(tab_negimp,[status(thm),assumptions([h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h147,h148])],[h146,232,h147,h148])).
% 277.02/276.73  thf(234,plain,$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])],[h145,233,h140,h146])).
% 277.02/276.73  thf(235,plain,$false,inference(tab_negimp,[status(thm),assumptions([h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h144,h145])],[h143,234,h144,h145])).
% 277.02/276.73  thf(236,plain,$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])],[h141,235,h142,h143])).
% 277.02/276.73  thf(237,plain,$false,inference(tab_negimp,[status(thm),assumptions([h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h140,h141])],[h139,236,h140,h141])).
% 277.02/276.73  thf(238,plain,$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])],[h137,237,h138,h139])).
% 277.02/276.73  thf(239,plain,$false,inference(tab_negimp,[status(thm),assumptions([h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h136,h137])],[h135,238,h136,h137])).
% 277.02/276.73  thf(240,plain,$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])],[h134,239,h121,h135])).
% 277.02/276.73  thf(241,plain,$false,inference(tab_negimp,[status(thm),assumptions([h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h133,h134])],[h132,240,h133,h134])).
% 277.02/276.73  thf(242,plain,$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])],[h130,241,h131,h132])).
% 277.02/276.73  thf(243,plain,$false,inference(tab_negimp,[status(thm),assumptions([h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h129,h130])],[h128,242,h129,h130])).
% 277.02/276.73  thf(244,plain,$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])],[h126,243,h127,h128])).
% 277.02/276.73  thf(245,plain,$false,inference(tab_negimp,[status(thm),assumptions([h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h125,h126])],[h124,244,h125,h126])).
% 277.02/276.73  thf(246,plain,$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])],[h122,245,h123,h124])).
% 277.02/276.73  thf(247,plain,$false,inference(tab_negimp,[status(thm),assumptions([h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h121,h122])],[h120,246,h121,h122])).
% 277.02/276.73  thf(248,plain,$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])],[h118,247,h119,h120])).
% 277.02/276.73  thf(249,plain,$false,inference(tab_negimp,[status(thm),assumptions([h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h117,h118])],[h116,248,h117,h118])).
% 277.02/276.73  thf(250,plain,$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])],[h114,249,h115,h116])).
% 277.02/276.73  thf(251,plain,$false,inference(tab_negimp,[status(thm),assumptions([h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h113,h114])],[h112,250,h113,h114])).
% 277.02/276.73  thf(252,plain,$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])],[h111,251,h31,h112])).
% 277.02/276.73  thf(253,plain,$false,inference(tab_negimp,[status(thm),assumptions([h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h100,h111])],[h110,252,h100,h111])).
% 277.02/276.73  thf(254,plain,$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])],[h109,253,h102,h110])).
% 277.02/276.73  thf(255,plain,$false,inference(tab_negimp,[status(thm),assumptions([h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h108,h109])],[h107,254,h108,h109])).
% 277.02/276.73  thf(256,plain,$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])],[h105,255,h106,h107])).
% 277.02/276.73  thf(257,plain,$false,inference(tab_negimp,[status(thm),assumptions([h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h100,h105])],[h104,256,h100,h105])).
% 277.02/276.73  thf(258,plain,$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])],[h103,257,h102,h104])).
% 277.02/276.73  thf(259,plain,$false,inference(tab_negimp,[status(thm),assumptions([h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h102,h103])],[h101,258,h102,h103])).
% 277.02/276.73  thf(260,plain,$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])],[h99,259,h100,h101])).
% 277.02/276.73  thf(261,plain,$false,inference(tab_negimp,[status(thm),assumptions([h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h98,h99])],[h97,260,h98,h99])).
% 277.02/276.73  thf(262,plain,$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])],[h95,261,h96,h97])).
% 277.02/276.73  thf(263,plain,$false,inference(tab_negimp,[status(thm),assumptions([h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h94,h95])],[h93,262,h94,h95])).
% 277.02/276.73  thf(264,plain,$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])],[h91,263,h92,h93])).
% 277.02/276.73  thf(265,plain,$false,inference(tab_negimp,[status(thm),assumptions([h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h90,h91])],[h89,264,h90,h91])).
% 277.02/276.73  thf(266,plain,$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])],[h87,265,h88,h89])).
% 277.02/276.73  thf(267,plain,$false,inference(tab_negimp,[status(thm),assumptions([h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h86,h87])],[h85,266,h86,h87])).
% 277.02/276.73  thf(268,plain,$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])],[h83,267,h84,h85])).
% 277.02/276.73  thf(269,plain,$false,inference(tab_negimp,[status(thm),assumptions([h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h82,h83])],[h81,268,h82,h83])).
% 277.02/276.73  thf(270,plain,$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])],[h80,269,h48,h81])).
% 277.02/276.73  thf(271,plain,$false,inference(tab_negimp,[status(thm),assumptions([h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h79,h80])],[h78,270,h79,h80])).
% 277.02/276.74  thf(272,plain,$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])],[h76,271,h77,h78])).
% 277.02/276.74  thf(273,plain,$false,inference(tab_negimp,[status(thm),assumptions([h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h75,h76])],[h74,272,h75,h76])).
% 277.02/276.74  thf(274,plain,$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])],[h72,273,h73,h74])).
% 277.02/276.74  thf(275,plain,$false,inference(tab_negimp,[status(thm),assumptions([h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h71,h72])],[h70,274,h71,h72])).
% 277.02/276.74  thf(276,plain,$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])],[h69,275,h68,h70])).
% 277.02/276.74  thf(277,plain,$false,inference(tab_negimp,[status(thm),assumptions([h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h68,h69])],[h67,276,h68,h69])).
% 277.02/276.74  thf(278,plain,$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])],[h65,277,h66,h67])).
% 277.02/276.74  thf(279,plain,$false,inference(tab_negimp,[status(thm),assumptions([h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h64,h65])],[h63,278,h64,h65])).
% 277.02/276.74  thf(280,plain,$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])],[h61,279,h62,h63])).
% 277.02/276.74  thf(281,plain,$false,inference(tab_negimp,[status(thm),assumptions([h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h60,h61])],[h59,280,h60,h61])).
% 277.02/276.74  thf(282,plain,$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])],[h57,281,h58,h59])).
% 277.02/276.74  thf(283,plain,$false,inference(tab_negimp,[status(thm),assumptions([h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h56,h57])],[h55,282,h56,h57])).
% 277.02/276.74  thf(284,plain,$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])],[h53,283,h54,h55])).
% 277.02/276.74  thf(285,plain,$false,inference(tab_negimp,[status(thm),assumptions([h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h52,h53])],[h51,284,h52,h53])).
% 277.02/276.74  thf(286,plain,$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])],[h49,285,h50,h51])).
% 277.02/276.74  thf(287,plain,$false,inference(tab_negimp,[status(thm),assumptions([h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h48,h49])],[h47,286,h48,h49])).
% 277.02/276.74  thf(288,plain,$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])],[h45,287,h46,h47])).
% 277.02/276.74  thf(289,plain,$false,inference(tab_negimp,[status(thm),assumptions([h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h43,h45])],[h44,288,h43,h45])).
% 277.02/276.74  thf(290,plain,$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])],[h42,289,h43,h44])).
% 277.02/276.74  thf(291,plain,$false,inference(tab_negimp,[status(thm),assumptions([h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h41,h42])],[h40,290,h41,h42])).
% 277.02/276.74  thf(292,plain,$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])],[h38,291,h39,h40])).
% 277.02/276.74  thf(293,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h3,h38])],[h37,292,h3,h38])).
% 277.02/276.74  thf(294,plain,$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])],[h36,293,h3,h37])).
% 277.02/276.74  thf(295,plain,$false,inference(tab_negimp,[status(thm),assumptions([h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h35,h36])],[h34,294,h35,h36])).
% 277.02/276.74  thf(296,plain,$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])],[h32,295,h33,h34])).
% 277.02/276.74  thf(297,plain,$false,inference(tab_negimp,[status(thm),assumptions([h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h31,h32])],[h30,296,h31,h32])).
% 277.02/276.74  thf(298,plain,$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])],[h28,297,h29,h30])).
% 277.02/276.74  thf(299,plain,$false,inference(tab_negimp,[status(thm),assumptions([h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h27,h28])],[h26,298,h27,h28])).
% 277.02/276.74  thf(300,plain,$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])],[h24,299,h25,h26])).
% 277.02/276.74  thf(301,plain,$false,inference(tab_negimp,[status(thm),assumptions([h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h23,h24])],[h22,300,h23,h24])).
% 277.02/276.74  thf(302,plain,$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])],[h20,301,h21,h22])).
% 277.02/276.74  thf(303,plain,$false,inference(tab_negimp,[status(thm),assumptions([h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h19,h20])],[h18,302,h19,h20])).
% 277.02/276.74  thf(304,plain,$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])],[h16,303,h17,h18])).
% 277.02/276.74  thf(305,plain,$false,inference(tab_negimp,[status(thm),assumptions([h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h15,h16])],[h14,304,h15,h16])).
% 277.02/276.74  thf(306,plain,$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])],[h12,305,h13,h14])).
% 277.02/276.74  thf(307,plain,$false,inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[h10,306,h11,h12])).
% 277.02/276.74  thf(308,plain,$false,inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h8,307,h9,h10])).
% 277.02/276.74  thf(309,plain,$false,inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h6,308,h7,h8])).
% 277.02/276.74  thf(310,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,309,h5,h6])).
% 277.02/276.74  thf(311,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,310,h3,h4])).
% 277.02/276.74  thf(312,plain,$false,inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,311,h1,h2])).
% 277.02/276.74  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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(![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:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[312,h0])).
% 277.02/276.74  % SZS output end Proof
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