Leo-III---1.8.0.THM-Ref.s

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SEU666^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39

% Computer : n004.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Sep 30 08:28:57 AM UTC 2026

% Result   : Theorem 30.26s 10.38s
% Output   : Refutation 32.55s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SEU666^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.08  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.09/0.20  % Computer : n004.cluster.edu
% 0.09/0.20  % Model    : x86_64 x86_64
% 0.09/0.20  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20  % Memory   : 8046.5625MB
% 0.09/0.20  % OS       : Linux 6.8.0-71-generic
% 0.09/0.20  % CPULimit : 300
% 0.09/0.20  % WCLimit  : 300
% 0.09/0.20  % DateTime : Tue Sep 29 14:06:37 UTC 2026
% 0.09/0.20  % CPUTime  : 
% 0.09/0.20  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.04/0.80  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 2.08/1.18  % [INFO] 	 Parsing done (383ms). 
% 2.38/1.20  % [INFO] 	 Running in sequential loop mode. 
% 3.01/1.58  % [INFO] 	 eprover registered as external prover. 
% 3.01/1.59  % [INFO] 	 Scanning for conjecture ... 
% 4.31/2.10  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 4.86/2.23  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 4.86/2.23  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 4.86/2.23  % [INFO] 	 Type checking passed. 
% 4.86/2.24  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 30.26/10.37  % [INFO] 	 Killing All external provers ... 
% 30.26/10.38  % Time passed: 10042ms (effective reasoning time: 9172ms)
% 30.26/10.38  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 30.26/10.38  % Axioms used in derivation (0): 
% 30.26/10.38  % No. of inferences in proof: 10
% 30.26/10.38  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 10042 ms resp. 9172 ms w/o parsing
% 32.55/10.82  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 32.55/10.82  thf(in_decl, type, in: ($i > ($i > $o))).
% 32.55/10.82  thf(exu_decl, type, exu: (($i > $o) > $o)).
% 32.55/10.82  thf(setextAx_decl, type, setextAx: $o).
% 32.55/10.82  thf(emptyset_decl, type, emptyset: $i).
% 32.55/10.82  thf(emptysetAx_decl, type, emptysetAx: $o).
% 32.55/10.82  thf(setadjoin_decl, type, setadjoin: ($i > ($i > $i))).
% 32.55/10.82  thf(setadjoinAx_decl, type, setadjoinAx: $o).
% 32.55/10.82  thf(powerset_decl, type, powerset: ($i > $i)).
% 32.55/10.82  thf(powersetAx_decl, type, powersetAx: $o).
% 32.55/10.82  thf(setunion_decl, type, setunion: ($i > $i)).
% 32.55/10.82  thf(setunionAx_decl, type, setunionAx: $o).
% 32.55/10.82  thf(omega_decl, type, omega: $i).
% 32.55/10.82  thf(omega0Ax_decl, type, omega0Ax: $o).
% 32.55/10.82  thf(omegaSAx_decl, type, omegaSAx: $o).
% 32.55/10.82  thf(omegaIndAx_decl, type, omegaIndAx: $o).
% 32.55/10.82  thf(replAx_decl, type, replAx: $o).
% 32.55/10.82  thf(foundationAx_decl, type, foundationAx: $o).
% 32.55/10.82  thf(wellorderingAx_decl, type, wellorderingAx: $o).
% 32.55/10.82  thf(descr_decl, type, descr: (($i > $o) > $i)).
% 32.55/10.82  thf(descrp_decl, type, descrp: $o).
% 32.55/10.82  thf(dsetconstr_decl, type, dsetconstr: ($i > (($i > $o) > $i))).
% 32.55/10.82  thf(dsetconstrI_decl, type, dsetconstrI: $o).
% 32.55/10.82  thf(dsetconstrEL_decl, type, dsetconstrEL: $o).
% 32.55/10.82  thf(dsetconstrER_decl, type, dsetconstrER: $o).
% 32.55/10.82  thf(exuE1_decl, type, exuE1: $o).
% 32.55/10.82  thf(prop2set_decl, type, prop2set: ($o > $i)).
% 32.55/10.82  thf(prop2setE_decl, type, prop2setE: $o).
% 32.55/10.82  thf(emptysetE_decl, type, emptysetE: $o).
% 32.55/10.82  thf(emptysetimpfalse_decl, type, emptysetimpfalse: $o).
% 32.55/10.82  thf(notinemptyset_decl, type, notinemptyset: $o).
% 32.55/10.82  thf(exuE3e_decl, type, exuE3e: $o).
% 32.55/10.82  thf(setext_decl, type, setext: $o).
% 32.55/10.82  thf(emptyI_decl, type, emptyI: $o).
% 32.55/10.82  thf(noeltsimpempty_decl, type, noeltsimpempty: $o).
% 32.55/10.82  thf(setbeta_decl, type, setbeta: $o).
% 32.55/10.82  thf(nonempty_decl, type, nonempty: ($i > $o)).
% 32.55/10.82  thf(nonemptyE1_decl, type, nonemptyE1: $o).
% 32.55/10.82  thf(nonemptyI_decl, type, nonemptyI: $o).
% 32.55/10.82  thf(nonemptyI1_decl, type, nonemptyI1: $o).
% 32.55/10.82  thf(setadjoinIL_decl, type, setadjoinIL: $o).
% 32.55/10.82  thf(emptyinunitempty_decl, type, emptyinunitempty: $o).
% 32.55/10.82  thf(setadjoinIR_decl, type, setadjoinIR: $o).
% 32.55/10.82  thf(setadjoinE_decl, type, setadjoinE: $o).
% 32.55/10.82  thf(setadjoinOr_decl, type, setadjoinOr: $o).
% 32.55/10.82  thf(setoftrueEq_decl, type, setoftrueEq: $o).
% 32.55/10.82  thf(powersetI_decl, type, powersetI: $o).
% 32.55/10.82  thf(emptyinPowerset_decl, type, emptyinPowerset: $o).
% 32.55/10.82  thf(emptyInPowerset_decl, type, emptyInPowerset: $o).
% 32.55/10.82  thf(powersetE_decl, type, powersetE: $o).
% 32.55/10.82  thf(setunionI_decl, type, setunionI: $o).
% 32.55/10.82  thf(setunionE_decl, type, setunionE: $o).
% 32.55/10.82  thf(subPowSU_decl, type, subPowSU: $o).
% 32.55/10.82  thf(exuE2_decl, type, exuE2: $o).
% 32.55/10.82  thf(nonemptyImpWitness_decl, type, nonemptyImpWitness: $o).
% 32.55/10.82  thf(uniqinunit_decl, type, uniqinunit: $o).
% 32.55/10.82  thf(notinsingleton_decl, type, notinsingleton: $o).
% 32.55/10.82  thf(eqinunit_decl, type, eqinunit: $o).
% 32.55/10.82  thf(singletonsswitch_decl, type, singletonsswitch: $o).
% 32.55/10.82  thf(upairsetE_decl, type, upairsetE: $o).
% 32.55/10.82  thf(upairsetIL_decl, type, upairsetIL: $o).
% 32.55/10.82  thf(upairsetIR_decl, type, upairsetIR: $o).
% 32.55/10.82  thf(emptyE1_decl, type, emptyE1: $o).
% 32.55/10.82  thf(vacuousDall_decl, type, vacuousDall: $o).
% 32.55/10.82  thf(quantDeMorgan1_decl, type, quantDeMorgan1: $o).
% 32.55/10.82  thf(quantDeMorgan2_decl, type, quantDeMorgan2: $o).
% 32.55/10.82  thf(quantDeMorgan3_decl, type, quantDeMorgan3: $o).
% 32.55/10.82  thf(quantDeMorgan4_decl, type, quantDeMorgan4: $o).
% 32.55/10.82  thf(prop2setI_decl, type, prop2setI: $o).
% 32.55/10.82  thf(set2prop_decl, type, set2prop: ($i > $o)).
% 32.55/10.82  thf(prop2set2propI_decl, type, prop2set2propI: $o).
% 32.55/10.82  thf(notdexE_decl, type, notdexE: $o).
% 32.55/10.82  thf(notdallE_decl, type, notdallE: $o).
% 32.55/10.82  thf(exuI1_decl, type, exuI1: $o).
% 32.55/10.82  thf(exuI3_decl, type, exuI3: $o).
% 32.55/10.82  thf(exuI2_decl, type, exuI2: $o).
% 32.55/10.82  thf(inCongP_decl, type, inCongP: $o).
% 32.55/10.82  thf(in__Cong_decl, type, in__Cong: $o).
% 32.55/10.82  thf(exuE3u_decl, type, exuE3u: $o).
% 32.55/10.82  thf(exu__Cong_decl, type, exu__Cong: $o).
% 32.55/10.82  thf(emptyset__Cong_decl, type, emptyset__Cong: $o).
% 32.55/10.82  thf(setadjoin__Cong_decl, type, setadjoin__Cong: $o).
% 32.55/10.82  thf(powerset__Cong_decl, type, powerset__Cong: $o).
% 32.55/10.82  thf(setunion__Cong_decl, type, setunion__Cong: $o).
% 32.55/10.82  thf(omega__Cong_decl, type, omega__Cong: $o).
% 32.55/10.82  thf(exuEu_decl, type, exuEu: $o).
% 32.55/10.82  thf(descr__Cong_decl, type, descr__Cong: $o).
% 32.55/10.82  thf(dsetconstr__Cong_decl, type, dsetconstr__Cong: $o).
% 32.55/10.82  thf(subset_decl, type, subset: ($i > ($i > $o))).
% 32.55/10.82  thf(subsetI1_decl, type, subsetI1: $o).
% 32.55/10.82  thf(eqimpsubset2_decl, type, eqimpsubset2: $o).
% 32.55/10.82  thf(eqimpsubset1_decl, type, eqimpsubset1: $o).
% 32.55/10.82  thf(subsetI2_decl, type, subsetI2: $o).
% 32.55/10.82  thf(emptysetsubset_decl, type, emptysetsubset: $o).
% 32.55/10.82  thf(subsetE_decl, type, subsetE: $o).
% 32.55/10.82  thf(subsetE2_decl, type, subsetE2: $o).
% 32.55/10.82  thf(notsubsetI_decl, type, notsubsetI: $o).
% 32.55/10.82  thf(notequalI1_decl, type, notequalI1: $o).
% 32.55/10.82  thf(notequalI2_decl, type, notequalI2: $o).
% 32.55/10.82  thf(subsetRefl_decl, type, subsetRefl: $o).
% 32.55/10.82  thf(subsetTrans_decl, type, subsetTrans: $o).
% 32.55/10.82  thf(setadjoinSub_decl, type, setadjoinSub: $o).
% 32.55/10.82  thf(setadjoinSub2_decl, type, setadjoinSub2: $o).
% 32.55/10.82  thf(subset2powerset_decl, type, subset2powerset: $o).
% 32.55/10.82  thf(setextsub_decl, type, setextsub: $o).
% 32.55/10.82  thf(subsetemptysetimpeq_decl, type, subsetemptysetimpeq: $o).
% 32.55/10.82  thf(powersetI1_decl, type, powersetI1: $o).
% 32.55/10.82  thf(powersetE1_decl, type, powersetE1: $o).
% 32.55/10.82  thf(inPowerset_decl, type, inPowerset: $o).
% 32.55/10.82  thf(powersetsubset_decl, type, powersetsubset: $o).
% 32.55/10.82  thf(sepInPowerset_decl, type, sepInPowerset: $o).
% 32.55/10.82  thf(sepSubset_decl, type, sepSubset: $o).
% 32.55/10.82  thf(binunion_decl, type, binunion: ($i > ($i > $i))).
% 32.55/10.82  thf(binunionIL_decl, type, binunionIL: $o).
% 32.55/10.82  thf(upairset2IR_decl, type, upairset2IR: $o).
% 32.55/10.82  thf(binunionIR_decl, type, binunionIR: $o).
% 32.55/10.82  thf(binunionEcases_decl, type, binunionEcases: $o).
% 32.55/10.82  thf(binunionE_decl, type, binunionE: $o).
% 32.55/10.82  thf(binunionLsub_decl, type, binunionLsub: $o).
% 32.55/10.82  thf(binunionRsub_decl, type, binunionRsub: $o).
% 32.55/10.82  thf(binintersect_decl, type, binintersect: ($i > ($i > $i))).
% 32.55/10.82  thf(binintersectI_decl, type, binintersectI: $o).
% 32.55/10.82  thf(binintersectSubset5_decl, type, binintersectSubset5: $o).
% 32.55/10.82  thf(binintersectEL_decl, type, binintersectEL: $o).
% 32.55/10.82  thf(binintersectLsub_decl, type, binintersectLsub: $o).
% 32.55/10.82  thf(binintersectSubset2_decl, type, binintersectSubset2: $o).
% 32.55/10.82  thf(binintersectSubset3_decl, type, binintersectSubset3: $o).
% 32.55/10.82  thf(binintersectER_decl, type, binintersectER: $o).
% 32.55/10.82  thf(disjointsetsI1_decl, type, disjointsetsI1: $o).
% 32.55/10.82  thf(binintersectRsub_decl, type, binintersectRsub: $o).
% 32.55/10.82  thf(binintersectSubset4_decl, type, binintersectSubset4: $o).
% 32.55/10.82  thf(binintersectSubset1_decl, type, binintersectSubset1: $o).
% 32.55/10.82  thf(bs114d_decl, type, bs114d: $o).
% 32.55/10.82  thf(setminus_decl, type, setminus: ($i > ($i > $i))).
% 32.55/10.82  thf(setminusI_decl, type, setminusI: $o).
% 32.55/10.82  thf(setminusEL_decl, type, setminusEL: $o).
% 32.55/10.82  thf(setminusER_decl, type, setminusER: $o).
% 32.55/10.82  thf(setminusSubset2_decl, type, setminusSubset2: $o).
% 32.55/10.82  thf(setminusERneg_decl, type, setminusERneg: $o).
% 32.55/10.82  thf(setminusELneg_decl, type, setminusELneg: $o).
% 32.55/10.82  thf(setminusILneg_decl, type, setminusILneg: $o).
% 32.55/10.82  thf(setminusIRneg_decl, type, setminusIRneg: $o).
% 32.55/10.82  thf(setminusLsub_decl, type, setminusLsub: $o).
% 32.55/10.82  thf(setminusSubset1_decl, type, setminusSubset1: $o).
% 32.55/10.82  thf(symdiff_decl, type, symdiff: ($i > ($i > $i))).
% 32.55/10.82  thf(symdiffE_decl, type, symdiffE: $o).
% 32.55/10.82  thf(symdiffI1_decl, type, symdiffI1: $o).
% 32.55/10.82  thf(symdiffI2_decl, type, symdiffI2: $o).
% 32.55/10.82  thf(symdiffIneg1_decl, type, symdiffIneg1: $o).
% 32.55/10.82  thf(symdiffIneg2_decl, type, symdiffIneg2: $o).
% 32.55/10.82  thf(iskpair_decl, type, iskpair: ($i > $o)).
% 32.55/10.82  thf(secondinupair_decl, type, secondinupair: $o).
% 32.55/10.82  thf(setukpairIL_decl, type, setukpairIL: $o).
% 32.55/10.82  thf(setukpairIR_decl, type, setukpairIR: $o).
% 32.55/10.82  thf(kpairiskpair_decl, type, kpairiskpair: $o).
% 32.55/10.82  thf(kpair_decl, type, kpair: ($i > ($i > $i))).
% 32.55/10.82  thf(kpairp_decl, type, kpairp: $o).
% 32.55/10.82  thf(cartprod_decl, type, cartprod: ($i > ($i > $i))).
% 32.55/10.82  thf(singletonsubset_decl, type, singletonsubset: $o).
% 32.55/10.82  thf(singletoninpowerset_decl, type, singletoninpowerset: $o).
% 32.55/10.82  thf(singletoninpowunion_decl, type, singletoninpowunion: $o).
% 32.55/10.82  thf(upairset2E_decl, type, upairset2E: $o).
% 32.55/10.82  thf(upairsubunion_decl, type, upairsubunion: $o).
% 32.55/10.82  thf(upairinpowunion_decl, type, upairinpowunion: $o).
% 32.55/10.82  thf(ubforcartprodlem1_decl, type, ubforcartprodlem1: $o).
% 32.55/10.82  thf(ubforcartprodlem2_decl, type, ubforcartprodlem2: $o).
% 32.55/10.82  thf(ubforcartprodlem3_decl, type, ubforcartprodlem3: $o).
% 32.55/10.82  thf(cartprodpairin_decl, type, cartprodpairin: $o).
% 32.55/10.82  thf(cartprodmempair1_decl, type, cartprodmempair1: $o).
% 32.55/10.82  thf(cartprodmempair_decl, type, cartprodmempair: $o).
% 32.55/10.82  thf(setunionE2_decl, type, setunionE2: $o).
% 32.55/10.82  thf(setunionsingleton1_decl, type, setunionsingleton1: $o).
% 32.55/10.82  thf(setunionsingleton2_decl, type, setunionsingleton2: $o).
% 32.55/10.82  thf(setunionsingleton_decl, type, setunionsingleton: $o).
% 32.55/10.82  thf(singleton_decl, type, singleton: ($i > $o)).
% 32.55/10.82  thf(singletonprop_decl, type, singletonprop: $o).
% 32.55/10.82  thf(ex1_decl, type, ex1: ($i > (($i > $o) > $o))).
% 32.55/10.82  thf(ex1E1_decl, type, ex1E1: $o).
% 32.55/10.82  thf(ex1I_decl, type, ex1I: $o).
% 32.55/10.82  thf(ex1I2_decl, type, ex1I2: $o).
% 32.55/10.82  thf(singletonsuniq_decl, type, singletonsuniq: $o).
% 32.55/10.82  thf(setukpairinjL1_decl, type, setukpairinjL1: $o).
% 32.55/10.82  thf(kfstsingleton_decl, type, kfstsingleton: $o).
% 32.55/10.82  thf(theprop_decl, type, theprop: $o).
% 32.55/10.82  thf(kfst_decl, type, kfst: ($i > $i)).
% 32.55/10.82  thf(kfstpairEq_decl, type, kfstpairEq: $o).
% 32.55/10.82  thf(cartprodfstin_decl, type, cartprodfstin: $o).
% 32.55/10.82  thf(setukpairinjL2_decl, type, setukpairinjL2: $o).
% 32.55/10.82  thf(setukpairinjL_decl, type, setukpairinjL: $o).
% 32.55/10.82  thf(setukpairinjR11_decl, type, setukpairinjR11: $o).
% 32.55/10.82  thf(setukpairinjR12_decl, type, setukpairinjR12: $o).
% 32.55/10.82  thf(setukpairinjR1_decl, type, setukpairinjR1: $o).
% 32.55/10.82  thf(upairequniteq_decl, type, upairequniteq: $o).
% 32.55/10.82  thf(setukpairinjR2_decl, type, setukpairinjR2: $o).
% 32.55/10.82  thf(setukpairinjR_decl, type, setukpairinjR: $o).
% 32.55/10.82  thf(ksndsingleton_decl, type, ksndsingleton: $o).
% 32.55/10.82  thf(ksnd_decl, type, ksnd: ($i > $i)).
% 32.55/10.82  thf(ksndpairEq_decl, type, ksndpairEq: $o).
% 32.55/10.82  thf(kpairsurjEq_decl, type, kpairsurjEq: $o).
% 32.55/10.82  thf(cartprodsndin_decl, type, cartprodsndin: $o).
% 32.55/10.82  thf(cartprodpairmemEL_decl, type, cartprodpairmemEL: $o).
% 32.55/10.82  thf(cartprodpairmemER_decl, type, cartprodpairmemER: $o).
% 32.55/10.82  thf(cartprodmempaircEq_decl, type, cartprodmempaircEq: $o).
% 32.55/10.82  thf(cartprodfstpairEq_decl, type, cartprodfstpairEq: $o).
% 32.55/10.82  thf(cartprodsndpairEq_decl, type, cartprodsndpairEq: $o).
% 32.55/10.82  thf(cartprodpairsurjEq_decl, type, cartprodpairsurjEq: $o).
% 32.55/10.82  thf(dpsetconstr_decl, type, dpsetconstr: ($i > ($i > (($i > ($i > $o)) > $i)))).
% 32.55/10.82  thf(dpsetconstrI_decl, type, dpsetconstrI: $o).
% 32.55/10.82  thf(sk1_decl, type, sk1: ($i > ($i > $i))).
% 32.55/10.82  thf(sk2_decl, type, sk2: ($i > $i)).
% 32.55/10.82  thf(sk3_decl, type, sk3: ($i > (($i > ($i > $o)) > $i))).
% 32.55/10.82  thf(sk4_decl, type, sk4: ($i > ($i > (($i > ($i > $o)) > $i)))).
% 32.55/10.82  thf(sk5_decl, type, sk5: ($i > (($i > ($i > $o)) > $i))).
% 32.55/10.82  thf(sk6_decl, type, sk6: ($i > $i)).
% 32.55/10.82  thf(sk7_decl, type, sk7: ($i > $i)).
% 32.55/10.82  thf(sk8_decl, type, sk8: ($i > ($i > ($i > $i)))).
% 32.55/10.82  thf(sk9_decl, type, sk9: ($i > ($i > $o))).
% 32.55/10.82  thf(sk10_decl, type, sk10: ($i > ($i > $i))).
% 32.55/10.82  thf(sk11_decl, type, sk11: ($i > ($i > $i))).
% 32.55/10.82  thf(sk12_decl, type, sk12: ($i > ($i > $i))).
% 32.55/10.82  thf(sk13_decl, type, sk13: ($i > (($i > $o) > $i))).
% 32.55/10.82  thf(sk14_decl, type, sk14: ($i > (($i > $o) > $i))).
% 32.55/10.82  thf(sk15_decl, type, sk15: (($i > $o) > $i)).
% 32.55/10.82  thf(sk16_decl, type, sk16: ($i > ($i > $i))).
% 32.55/10.82  thf(sk17_decl, type, sk17: ($i > ($i > $i))).
% 32.55/10.82  thf(sk18_decl, type, sk18: ($i > $i)).
% 32.55/10.82  thf(sk19_decl, type, sk19: ($i > $i)).
% 32.55/10.82  thf(sk20_decl, type, sk20: ($i > $i)).
% 32.55/10.82  thf(sk21_decl, type, sk21: ($i > ($i > $i))).
% 32.55/10.82  thf(sk22_decl, type, sk22: ($o > ($i > ($i > $i)))).
% 32.55/10.82  thf(sk23_decl, type, sk23: ($i > (($i > $o) > $i))).
% 32.55/10.82  thf(sk24_decl, type, sk24: (($i > $o) > $i)).
% 32.55/10.82  thf(sk25_decl, type, sk25: ($i > $i)).
% 32.55/10.82  thf(sk26_decl, type, sk26: (($i > $o) > ($i > $i))).
% 32.55/10.82  thf(sk27_decl, type, sk27: (($i > $o) > ($i > $i))).
% 32.55/10.82  thf(sk28_decl, type, sk28: (($i > $o) > ($i > $i))).
% 32.55/10.82  thf(sk29_decl, type, sk29: (($i > $o) > ($i > $i))).
% 32.55/10.82  thf(sk30_decl, type, sk30: (($i > $o) > ($i > $i))).
% 32.55/10.82  thf(sk31_decl, type, sk31: (($i > $o) > ($i > $i))).
% 32.55/10.82  thf(sk32_decl, type, sk32: (($i > $o) > $i)).
% 32.55/10.82  thf(sk33_decl, type, sk33: (($i > $o) > $i)).
% 32.55/10.82  thf(sk34_decl, type, sk34: (($i > $o) > $i)).
% 32.55/10.82  thf(sk35_decl, type, sk35: ($i > (($i > $o) > $i))).
% 32.55/10.82  thf(sk36_decl, type, sk36: (($i > $o) > $i)).
% 32.55/10.82  thf(sk37_decl, type, sk37: ($i > (($i > $o) > $i))).
% 32.55/10.82  thf(sk38_decl, type, sk38: (($i > $o) > (($i > $o) > $i))).
% 32.55/10.82  thf(sk39_decl, type, sk39: (($i > $o) > (($i > $o) > $i))).
% 32.55/10.82  thf(sk40_decl, type, sk40: ($i > (($i > $o) > $i))).
% 32.55/10.82  thf(sk41_decl, type, sk41: (($i > $o) > (($i > $o) > $o))).
% 32.55/10.82  thf(sk42_decl, type, sk42: (($i > $o) > (($i > $o) > $i))).
% 32.55/10.82  thf(sk43_decl, type, sk43: (($i > $o) > (($i > $o) > $i))).
% 32.55/10.82  thf(sk44_decl, type, sk44: ($i > (($i > $o) > (($i > $o) > $i)))).
% 32.55/10.82  thf(sk45_decl, type, sk45: ($i > (($i > $o) > (($i > $o) > $i)))).
% 32.55/10.82  thf(sk46_decl, type, sk46: (($i > $o) > (($i > $o) > ($i > ($i > $i))))).
% 32.55/10.82  thf(sk47_decl, type, sk47: (($i > $o) > (($i > $o) > ($i > ($i > $i))))).
% 32.55/10.82  thf(sk48_decl, type, sk48: ($i > ($i > $i))).
% 32.55/10.82  thf(sk49_decl, type, sk49: ($i > ($i > $i))).
% 32.55/10.82  thf(sk50_decl, type, sk50: ($i > ($i > $i))).
% 32.55/10.82  thf(sk51_decl, type, sk51: ($i > ($i > ($i > $i)))).
% 32.55/10.82  thf(sk52_decl, type, sk52: ($i > ($i > ($i > $i)))).
% 32.55/10.82  thf(sk53_decl, type, sk53: ($i > ($i > $i))).
% 32.55/10.82  thf(sk54_decl, type, sk54: (($i > $o) > ($i > $i))).
% 32.55/10.82  thf(sk55_decl, type, sk55: (($i > $o) > ($i > $i))).
% 32.55/10.82  thf(sk56_decl, type, sk56: (($i > $o) > ($i > $i))).
% 32.55/10.82  thf(sk57_decl, type, sk57: (($i > $o) > ($i > $i))).
% 32.55/10.82  thf(sk58_decl, type, sk58: ($i > (($i > $o) > ($i > $i)))).
% 32.55/10.82  thf(sk59_decl, type, sk59: ($i > (($i > $o) > ($i > $i)))).
% 32.55/10.82  thf(sk60_decl, type, sk60: (($i > $o) > ($i > $i))).
% 32.55/10.82  thf(sk61_decl, type, sk61: (($i > $o) > ($i > $i))).
% 32.55/10.82  thf(sk62_decl, type, sk62: (($i > $o) > ($i > $i))).
% 32.55/10.82  thf(sk63_decl, type, sk63: ($i > $i)).
% 32.55/10.82  thf(sk64_decl, type, sk64: ($i > $i)).
% 32.55/10.82  thf(sk65_decl, type, sk65: $i).
% 32.55/10.82  thf(sk66_decl, type, sk66: $i).
% 32.55/10.82  thf(sk67_decl, type, sk67: ($i > ($i > $o))).
% 32.55/10.82  thf(exu_def, definition, exu = (^ [A:($i > $o)]: ? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))) ).
% 32.55/10.82  thf(setextAx_def, definition, setextAx = (! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) = (in @ C @ B))) => (A = B))) ).
% 32.55/10.82  thf(emptysetAx_def, definition, emptysetAx = (! [A:$i]: ~ (in @ A @ emptyset)) ).
% 32.55/10.82  thf(setadjoinAx_def, definition, setadjoinAx = (! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ B)) = ((C = A) | (in @ C @ B)))) ).
% 32.55/10.82  thf(powersetAx_def, definition, powersetAx = (! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) = (! [C:$i]: ((in @ C @ B) => (in @ C @ A))))) ).
% 32.55/10.82  thf(setunionAx_def, definition, setunionAx = (! [A:$i,B:$i]: ((in @ B @ (setunion @ A)) = (? [C:$i]: ((in @ B @ C) & (in @ C @ A))))) ).
% 32.55/10.82  thf(omega0Ax_def, definition, omega0Ax = (in @ emptyset @ omega) ).
% 32.55/10.82  thf(omegaSAx_def, definition, omegaSAx = (! [A:$i]: ((in @ A @ omega) => (in @ (setadjoin @ A @ A) @ omega))) ).
% 32.55/10.82  thf(omegaIndAx_def, definition, omegaIndAx = (! [A:$i]: (((in @ emptyset @ A) & ! [B:$i]: (((in @ B @ omega) & (in @ B @ A)) => (in @ (setadjoin @ B @ B) @ A))) => (! [B:$i]: ((in @ B @ omega) => (in @ B @ A))))) ).
% 32.55/10.82  thf(replAx_def, definition, replAx = (! [A:($i > ($i > $o)),B:$i]: ((! [C:$i]: ((in @ C @ B) => (exu @ (A @ C)))) => (? [C:$i]: ! [D:$i]: ((in @ D @ C) = (? [E:$i]: ((in @ E @ B) & (A @ E @ D))))))) ).
% 32.55/10.82  thf(foundationAx_def, definition, foundationAx = (! [A:$i]: ((? [B:$i]: (in @ B @ A)) => (? [B:$i]: ((in @ B @ A) & ~ (? [C:$i]: ((in @ C @ B) & (in @ C @ A))))))) ).
% 32.55/10.82  thf(wellorderingAx_def, definition, wellorderingAx = (! [A:$i]: ? [B:$i]: (! [C:$i]: ((in @ C @ B) => (! [D:$i]: ((in @ D @ C) => (in @ D @ A)))) & ! [C:$i,D:$i]: (((in @ C @ A) & (in @ D @ A)) => ((! [E:$i]: ((in @ E @ B) => ((in @ C @ E) = (in @ D @ E)))) => (C = D))) & ! [C:$i,D:$i]: (((in @ C @ B) & (in @ D @ B)) => (! [E:$i]: ((in @ E @ C) => (in @ E @ D)) | ! [E:$i]: ((in @ E @ D) => (in @ E @ C)))) & ! [C:$i]: ((! [D:$i]: ((in @ D @ C) => (in @ D @ A)) & ? [D:$i]: (in @ D @ C)) => (? [D:$i,E:$i]: ((in @ D @ B) & (in @ E @ C) & ~ (? [F:$i]: ((in @ F @ D) & (in @ F @ C))) & ! [F:$i]: ((in @ F @ B) => (! [G:$i]: ((in @ G @ F) => (in @ G @ D)) | (in @ E @ F)))))))) ).
% 32.55/10.82  thf(descrp_def, definition, descrp = (! [A:($i > $o)]: ((exu @ (A)) => (A @ (descr @ (A))))) ).
% 32.55/10.82  thf(dsetconstrI_def, definition, dsetconstrI = (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((B @ C) => (in @ C @ (dsetconstr @ A @ (B)))))) ).
% 32.55/10.82  thf(dsetconstrEL_def, definition, dsetconstrEL = (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ (dsetconstr @ A @ (B))) => (in @ C @ A))) ).
% 32.55/10.82  thf(dsetconstrER_def, definition, dsetconstrER = (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ (dsetconstr @ A @ (B))) => (B @ C))) ).
% 32.55/10.82  thf(exuE1_def, definition, exuE1 = (! [A:($i > $o)]: ((exu @ (A)) => (? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))))) ).
% 32.55/10.82  thf(prop2setE_def, definition, prop2setE = (! [A:$o,B:$i]: ((in @ B @ (prop2set @ A)) => (A))) ).
% 32.55/10.82  thf(emptysetE_def, definition, emptysetE = (! [A:$i]: ((in @ A @ emptyset) => (! [B:$o]: (B)))) ).
% 32.55/10.82  thf(emptysetimpfalse_def, definition, emptysetimpfalse = (! [A:$i]: ((in @ A @ emptyset) => (($false)))) ).
% 32.55/10.82  thf(notinemptyset_def, definition, notinemptyset = (! [A:$i]: ~ (in @ A @ emptyset)) ).
% 32.55/10.82  thf(exuE3e_def, definition, exuE3e = (! [A:($i > $o)]: ((exu @ (A)) => (? [B:$i]: (A @ B)))) ).
% 32.55/10.82  thf(setext_def, definition, setext = (! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) => (in @ C @ B))) => ((! [C:$i]: ((in @ C @ B) => (in @ C @ A))) => (A = B)))) ).
% 32.55/10.82  thf(emptyI_def, definition, emptyI = (! [A:$i]: ((! [B:$i]: ~ (in @ B @ A)) => (A = emptyset))) ).
% 32.55/10.82  thf(noeltsimpempty_def, definition, noeltsimpempty = (! [A:$i]: ((! [B:$i]: ~ (in @ B @ A)) => (A = emptyset))) ).
% 32.55/10.82  thf(setbeta_def, definition, setbeta = (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((in @ C @ (dsetconstr @ A @ (B))) = (B @ C)))) ).
% 32.55/10.82  thf(nonempty_def, definition, nonempty = (^ [A:$i]: (A != emptyset)) ).
% 32.55/10.82  thf(nonemptyE1_def, definition, nonemptyE1 = (! [A:$i]: ((nonempty @ A) => (? [B:$i]: (in @ B @ A)))) ).
% 32.55/10.82  thf(nonemptyI_def, definition, nonemptyI = (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((B @ C) => (nonempty @ (dsetconstr @ A @ (B)))))) ).
% 32.55/10.82  thf(nonemptyI1_def, definition, nonemptyI1 = (! [A:$i]: ((? [B:$i]: (in @ B @ A)) => (nonempty @ A))) ).
% 32.55/10.82  thf(setadjoinIL_def, definition, setadjoinIL = (! [A:$i,B:$i]: (in @ A @ (setadjoin @ A @ B))) ).
% 32.55/10.82  thf(emptyinunitempty_def, definition, emptyinunitempty = (in @ emptyset @ (setadjoin @ emptyset @ emptyset)) ).
% 32.55/10.82  thf(setadjoinIR_def, definition, setadjoinIR = (! [A:$i,B:$i,C:$i]: ((in @ C @ B) => (in @ C @ (setadjoin @ A @ B)))) ).
% 32.55/10.82  thf(setadjoinE_def, definition, setadjoinE = (! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ B)) => (! [D:$o]: (((C = A) => (D)) => (((in @ C @ B) => (D)) => (D)))))) ).
% 32.55/10.82  thf(setadjoinOr_def, definition, setadjoinOr = (! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ B)) => ((C = A) | (in @ C @ B)))) ).
% 32.55/10.82  thf(setoftrueEq_def, definition, setoftrueEq = (! [A:$i]: ((dsetconstr @ A @ (^ [B:$i]: (($true)))) = A)) ).
% 32.55/10.82  thf(powersetI_def, definition, powersetI = (! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ B) => (in @ C @ A))) => (in @ B @ (powerset @ A)))) ).
% 32.55/10.82  thf(emptyinPowerset_def, definition, emptyinPowerset = (! [A:$i]: (in @ emptyset @ (powerset @ A))) ).
% 32.55/10.82  thf(emptyInPowerset_def, definition, emptyInPowerset = (! [A:$i]: (in @ emptyset @ (powerset @ A))) ).
% 32.55/10.82  thf(powersetE_def, definition, powersetE = (! [A:$i,B:$i,C:$i]: ((in @ B @ (powerset @ A)) => ((in @ C @ B) => (in @ C @ A)))) ).
% 32.55/10.82  thf(setunionI_def, definition, setunionI = (! [A:$i,B:$i,C:$i]: ((in @ B @ C) => ((in @ C @ A) => (in @ B @ (setunion @ A))))) ).
% 32.55/10.82  thf(setunionE_def, definition, setunionE = (! [A:$i,B:$i]: ((in @ B @ (setunion @ A)) => (! [C:$o]: ((! [D:$i]: ((in @ B @ D) => ((in @ D @ A) => (C)))) => (C))))) ).
% 32.55/10.82  thf(subPowSU_def, definition, subPowSU = (! [A:$i,B:$i]: ((in @ B @ A) => (in @ B @ (powerset @ (setunion @ A))))) ).
% 32.55/10.82  thf(exuE2_def, definition, exuE2 = (! [A:($i > $o)]: ((exu @ (A)) => (? [B:$i]: ! [C:$i]: ((A @ C) = (C = B))))) ).
% 32.55/10.82  thf(nonemptyImpWitness_def, definition, nonemptyImpWitness = (! [A:$i]: ((nonempty @ A) => (? [B:$i]: ((in @ B @ A) & (($true)))))) ).
% 32.55/10.82  thf(uniqinunit_def, definition, uniqinunit = (! [A:$i,B:$i]: ((in @ A @ (setadjoin @ B @ emptyset)) => (A = B))) ).
% 32.55/10.82  thf(notinsingleton_def, definition, notinsingleton = (! [A:$i,B:$i]: ((A != B) => (~ (in @ B @ (setadjoin @ A @ emptyset))))) ).
% 32.55/10.82  thf(eqinunit_def, definition, eqinunit = (! [A:$i,B:$i]: ((A = B) => (in @ A @ (setadjoin @ B @ emptyset)))) ).
% 32.55/10.82  thf(singletonsswitch_def, definition, singletonsswitch = (! [A:$i,B:$i]: ((in @ A @ (setadjoin @ B @ emptyset)) => (in @ B @ (setadjoin @ A @ emptyset)))) ).
% 32.55/10.82  thf(upairsetE_def, definition, upairsetE = (! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ (setadjoin @ B @ emptyset))) => ((C = A) | (C = B)))) ).
% 32.55/10.82  thf(upairsetIL_def, definition, upairsetIL = (! [A:$i,B:$i]: (in @ A @ (setadjoin @ A @ (setadjoin @ B @ emptyset)))) ).
% 32.55/10.82  thf(upairsetIR_def, definition, upairsetIR = (! [A:$i,B:$i]: (in @ B @ (setadjoin @ A @ (setadjoin @ B @ emptyset)))) ).
% 32.55/10.82  thf(emptyE1_def, definition, emptyE1 = (! [A:$i,B:($i > $o)]: ((? [C:$i]: ((in @ C @ A) & (B @ C))) => (((dsetconstr @ A @ (B)) = emptyset) => (($false))))) ).
% 32.55/10.82  thf(vacuousDall_def, definition, vacuousDall = (! [A:($i > $o),B:$i]: ((in @ B @ emptyset) => (A @ B))) ).
% 32.55/10.82  thf(quantDeMorgan1_def, definition, quantDeMorgan1 = (! [A:$i,B:($i > $o)]: ((~ (! [C:$i]: ((in @ C @ A) => (B @ C)))) => (? [C:$i]: ((in @ C @ A) & ~ (B @ C))))) ).
% 32.55/10.82  thf(quantDeMorgan2_def, definition, quantDeMorgan2 = (! [A:$i,B:($i > $o)]: ((! [C:$i]: ((in @ C @ A) => (~ (B @ C)))) => (~ (? [C:$i]: ((in @ C @ A) & (B @ C)))))) ).
% 32.55/10.82  thf(quantDeMorgan3_def, definition, quantDeMorgan3 = (! [A:$i,B:($i > $o)]: ((~ (? [C:$i]: ((in @ C @ A) & (B @ C)))) => (! [C:$i]: ((in @ C @ A) => (~ (B @ C)))))) ).
% 32.55/10.82  thf(quantDeMorgan4_def, definition, quantDeMorgan4 = (! [A:$i,B:($i > $o)]: ((? [C:$i]: ((in @ C @ A) & ~ (B @ C))) => (~ (! [C:$i]: ((in @ C @ A) => (B @ C)))))) ).
% 32.55/10.82  thf(prop2setI_def, definition, prop2setI = (! [A:$o]: ((A) => (in @ emptyset @ (prop2set @ A)))) ).
% 32.55/10.82  thf(prop2set2propI_def, definition, prop2set2propI = (! [A:$o]: ((A) => (set2prop @ (prop2set @ A)))) ).
% 32.55/10.82  thf(notdexE_def, definition, notdexE = (! [A:$i,B:($i > $o)]: ((~ (? [C:$i]: ((in @ C @ A) & (B @ C)))) => (! [C:$i]: ((in @ C @ A) => (~ (B @ C)))))) ).
% 32.55/10.82  thf(notdallE_def, definition, notdallE = (! [A:$i,B:($i > $o)]: ((~ (! [C:$i]: ((in @ C @ A) => (B @ C)))) => (? [C:$i]: ((in @ C @ A) & ~ (B @ C))))) ).
% 32.55/10.82  thf(exuI1_def, definition, exuI1 = (! [A:($i > $o)]: ((? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))) => (exu @ (A)))) ).
% 32.55/10.82  thf(exuI3_def, definition, exuI3 = (! [A:($i > $o)]: ((? [B:$i]: (A @ B)) => ((! [B:$i,C:$i]: ((A @ B) => ((A @ C) => (B = C)))) => (exu @ (A))))) ).
% 32.55/10.82  thf(exuI2_def, definition, exuI2 = (! [A:($i > $o)]: ((? [B:$i]: ! [C:$i]: ((A @ C) = (C = B))) => (exu @ (A)))) ).
% 32.55/10.82  thf(inCongP_def, definition, inCongP = (! [A:$i,B:$i]: ((A = B) => (! [C:$i,D:$i]: ((C = D) => ((in @ C @ A) => (in @ D @ B)))))) ).
% 32.55/10.82  thf(in__Cong_def, definition, in__Cong = (! [A:$i,B:$i]: ((A = B) => (! [C:$i,D:$i]: ((C = D) => ((in @ C @ A) = (in @ D @ B)))))) ).
% 32.55/10.82  thf(exuE3u_def, definition, exuE3u = (! [A:($i > $o)]: ((exu @ (A)) => (! [B:$i,C:$i]: ((A @ B) => ((A @ C) => (B = C)))))) ).
% 32.55/10.82  thf(exu__Cong_def, definition, exu__Cong = (! [A:($i > $o),B:($i > $o)]: ((! [C:$i,D:$i]: ((C = D) => ((A @ C) = (B @ D)))) => ((exu @ (A)) = (exu @ (B))))) ).
% 32.55/10.82  thf(emptyset__Cong_def, definition, emptyset__Cong = (emptyset = emptyset) ).
% 32.55/10.82  thf(setadjoin__Cong_def, definition, setadjoin__Cong = (! [A:$i,B:$i]: ((A = B) => (! [C:$i,D:$i]: ((C = D) => ((setadjoin @ A @ C) = (setadjoin @ B @ D)))))) ).
% 32.55/10.82  thf(powerset__Cong_def, definition, powerset__Cong = (! [A:$i,B:$i]: ((A = B) => ((powerset @ A) = (powerset @ B)))) ).
% 32.55/10.82  thf(setunion__Cong_def, definition, setunion__Cong = (! [A:$i,B:$i]: ((A = B) => ((setunion @ A) = (setunion @ B)))) ).
% 32.55/10.82  thf(omega__Cong_def, definition, omega__Cong = (omega = omega) ).
% 32.55/10.82  thf(exuEu_def, definition, exuEu = (! [A:($i > $o)]: ((exu @ (A)) => (! [B:$i,C:$i]: ((A @ B) => ((A @ C) => (B = C)))))) ).
% 32.55/10.82  thf(descr__Cong_def, definition, descr__Cong = (! [A:($i > $o),B:($i > $o)]: ((! [C:$i,D:$i]: ((C = D) => ((A @ C) = (B @ D)))) => ((exu @ (A)) => ((exu @ (B)) => ((descr @ (A)) = (descr @ (B))))))) ).
% 32.55/10.82  thf(dsetconstr__Cong_def, definition, dsetconstr__Cong = (! [A:$i,B:$i]: ((A = B) => (! [C:($i > $o),D:($i > $o)]: ((! [E:$i]: ((in @ E @ A) => (! [F:$i]: ((in @ F @ B) => ((E = F) => ((C @ E) = (D @ F))))))) => ((dsetconstr @ A @ (C)) = (dsetconstr @ B @ (D))))))) ).
% 32.55/10.82  thf(subsetI1_def, definition, subsetI1 = (! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) => (in @ C @ B))) => (subset @ A @ B))) ).
% 32.55/10.82  thf(eqimpsubset2_def, definition, eqimpsubset2 = (! [A:$i,B:$i]: ((A = B) => (subset @ B @ A))) ).
% 32.55/10.82  thf(eqimpsubset1_def, definition, eqimpsubset1 = (! [A:$i,B:$i]: ((A = B) => (subset @ A @ B))) ).
% 32.55/10.82  thf(subsetI2_def, definition, subsetI2 = (! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) => (in @ C @ B))) => (subset @ A @ B))) ).
% 32.55/10.82  thf(emptysetsubset_def, definition, emptysetsubset = (! [A:$i]: (subset @ emptyset @ A)) ).
% 32.55/10.82  thf(subsetE_def, definition, subsetE = (! [A:$i,B:$i,C:$i]: ((subset @ A @ B) => ((in @ C @ A) => (in @ C @ B)))) ).
% 32.55/10.82  thf(subsetE2_def, definition, subsetE2 = (! [A:$i,B:$i,C:$i]: ((subset @ A @ B) => ((~ (in @ C @ B)) => (~ (in @ C @ A))))) ).
% 32.55/10.82  thf(notsubsetI_def, definition, notsubsetI = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (~ (subset @ A @ B))))) ).
% 32.55/10.82  thf(notequalI1_def, definition, notequalI1 = (! [A:$i,B:$i]: ((~ (subset @ A @ B)) => (A != B))) ).
% 32.55/10.82  thf(notequalI2_def, definition, notequalI2 = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (A != B)))) ).
% 32.55/10.82  thf(subsetRefl_def, definition, subsetRefl = (! [A:$i]: (subset @ A @ A)) ).
% 32.55/10.82  thf(subsetTrans_def, definition, subsetTrans = (! [A:$i,B:$i,C:$i]: ((subset @ A @ B) => ((subset @ B @ C) => (subset @ A @ C)))) ).
% 32.55/10.82  thf(setadjoinSub_def, definition, setadjoinSub = (! [A:$i,B:$i]: (subset @ B @ (setadjoin @ A @ B))) ).
% 32.55/10.82  thf(setadjoinSub2_def, definition, setadjoinSub2 = (! [A:$i,B:$i,C:$i]: ((subset @ A @ C) => (subset @ A @ (setadjoin @ B @ C)))) ).
% 32.55/10.82  thf(subset2powerset_def, definition, subset2powerset = (! [A:$i,B:$i]: ((subset @ A @ B) => (in @ A @ (powerset @ B)))) ).
% 32.55/10.82  thf(setextsub_def, definition, setextsub = (! [A:$i,B:$i]: ((subset @ A @ B) => ((subset @ B @ A) => (A = B)))) ).
% 32.55/10.82  thf(subsetemptysetimpeq_def, definition, subsetemptysetimpeq = (! [A:$i]: ((subset @ A @ emptyset) => (A = emptyset))) ).
% 32.55/10.82  thf(powersetI1_def, definition, powersetI1 = (! [A:$i,B:$i]: ((subset @ B @ A) => (in @ B @ (powerset @ A)))) ).
% 32.55/10.82  thf(powersetE1_def, definition, powersetE1 = (! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (subset @ B @ A))) ).
% 32.55/10.82  thf(inPowerset_def, definition, inPowerset = (! [A:$i]: (in @ A @ (powerset @ A))) ).
% 32.55/10.82  thf(powersetsubset_def, definition, powersetsubset = (! [A:$i,B:$i]: ((subset @ A @ B) => (subset @ (powerset @ A) @ (powerset @ B)))) ).
% 32.55/10.82  thf(sepInPowerset_def, definition, sepInPowerset = (! [A:$i,B:($i > $o)]: (in @ (dsetconstr @ A @ (B)) @ (powerset @ A))) ).
% 32.55/10.82  thf(sepSubset_def, definition, sepSubset = (! [A:$i,B:($i > $o)]: (subset @ (dsetconstr @ A @ (B)) @ A)) ).
% 32.55/10.82  thf(binunionIL_def, definition, binunionIL = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (in @ C @ (binunion @ A @ B)))) ).
% 32.55/10.82  thf(upairset2IR_def, definition, upairset2IR = (! [A:$i,B:$i]: (in @ B @ (setadjoin @ A @ (setadjoin @ B @ emptyset)))) ).
% 32.55/10.82  thf(binunionIR_def, definition, binunionIR = (! [A:$i,B:$i,C:$i]: ((in @ C @ B) => (in @ C @ (binunion @ A @ B)))) ).
% 32.55/10.82  thf(binunionEcases_def, definition, binunionEcases = (! [A:$i,B:$i,C:$i,D:$o]: ((in @ C @ (binunion @ A @ B)) => (((in @ C @ A) => (D)) => (((in @ C @ B) => (D)) => (D))))) ).
% 32.55/10.82  thf(binunionE_def, definition, binunionE = (! [A:$i,B:$i,C:$i]: ((in @ C @ (binunion @ A @ B)) => ((in @ C @ A) | (in @ C @ B)))) ).
% 32.55/10.82  thf(binunionLsub_def, definition, binunionLsub = (! [A:$i,B:$i]: (subset @ A @ (binunion @ A @ B))) ).
% 32.55/10.82  thf(binunionRsub_def, definition, binunionRsub = (! [A:$i,B:$i]: (subset @ B @ (binunion @ A @ B))) ).
% 32.55/10.82  thf(binintersectI_def, definition, binintersectI = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((in @ C @ B) => (in @ C @ (binintersect @ A @ B))))) ).
% 32.55/10.82  thf(binintersectSubset5_def, definition, binintersectSubset5 = (! [A:$i,B:$i,C:$i]: ((subset @ C @ A) => ((subset @ C @ B) => (subset @ C @ (binintersect @ A @ B))))) ).
% 32.55/10.82  thf(binintersectEL_def, definition, binintersectEL = (! [A:$i,B:$i,C:$i]: ((in @ C @ (binintersect @ A @ B)) => (in @ C @ A))) ).
% 32.55/10.82  thf(binintersectLsub_def, definition, binintersectLsub = (! [A:$i,B:$i]: (subset @ (binintersect @ A @ B) @ A)) ).
% 32.55/10.82  thf(binintersectSubset2_def, definition, binintersectSubset2 = (! [A:$i,B:$i]: ((subset @ A @ B) => ((binintersect @ A @ B) = A))) ).
% 32.55/10.82  thf(binintersectSubset3_def, definition, binintersectSubset3 = (! [A:$i,B:$i]: (((binintersect @ A @ B) = B) => (subset @ B @ A))) ).
% 32.55/10.82  thf(binintersectER_def, definition, binintersectER = (! [A:$i,B:$i,C:$i]: ((in @ C @ (binintersect @ A @ B)) => (in @ C @ B))) ).
% 32.55/10.82  thf(disjointsetsI1_def, definition, disjointsetsI1 = (! [A:$i,B:$i]: ((~ (? [C:$i]: ((in @ C @ A) & (in @ C @ B)))) => ((binintersect @ A @ B) = emptyset))) ).
% 32.55/10.82  thf(binintersectRsub_def, definition, binintersectRsub = (! [A:$i,B:$i]: (subset @ (binintersect @ A @ B) @ B)) ).
% 32.55/10.82  thf(binintersectSubset4_def, definition, binintersectSubset4 = (! [A:$i,B:$i]: ((subset @ B @ A) => ((binintersect @ A @ B) = B))) ).
% 32.55/10.82  thf(binintersectSubset1_def, definition, binintersectSubset1 = (! [A:$i,B:$i]: (((binintersect @ A @ B) = A) => (subset @ A @ B))) ).
% 32.55/10.82  thf(bs114d_def, definition, bs114d = (! [A:$i,B:$i,C:$i]: ((binintersect @ A @ (binunion @ B @ C)) = (binunion @ (binintersect @ A @ B) @ (binintersect @ A @ C)))) ).
% 32.55/10.82  thf(setminusI_def, definition, setminusI = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (in @ C @ (setminus @ A @ B))))) ).
% 32.55/10.82  thf(setminusEL_def, definition, setminusEL = (! [A:$i,B:$i,C:$i]: ((in @ C @ (setminus @ A @ B)) => (in @ C @ A))) ).
% 32.55/10.82  thf(setminusER_def, definition, setminusER = (! [A:$i,B:$i,C:$i]: ((in @ C @ (setminus @ A @ B)) => (~ (in @ C @ B)))) ).
% 32.55/10.82  thf(setminusSubset2_def, definition, setminusSubset2 = (! [A:$i,B:$i]: ((subset @ A @ B) => ((setminus @ A @ B) = emptyset))) ).
% 32.55/10.82  thf(setminusERneg_def, definition, setminusERneg = (! [A:$i,B:$i,C:$i]: ((~ (in @ C @ (setminus @ A @ B))) => ((in @ C @ A) => (in @ C @ B)))) ).
% 32.55/10.82  thf(setminusELneg_def, definition, setminusELneg = (! [A:$i,B:$i,C:$i]: ((~ (in @ C @ (setminus @ A @ B))) => ((~ (in @ C @ B)) => (~ (in @ C @ A))))) ).
% 32.55/10.82  thf(setminusILneg_def, definition, setminusILneg = (! [A:$i,B:$i,C:$i]: ((~ (in @ C @ A)) => (~ (in @ C @ (setminus @ A @ B))))) ).
% 32.55/10.82  thf(setminusIRneg_def, definition, setminusIRneg = (! [A:$i,B:$i,C:$i]: ((in @ C @ B) => (~ (in @ C @ (setminus @ A @ B))))) ).
% 32.55/10.82  thf(setminusLsub_def, definition, setminusLsub = (! [A:$i,B:$i]: (subset @ (setminus @ A @ B) @ A)) ).
% 32.55/10.82  thf(setminusSubset1_def, definition, setminusSubset1 = (! [A:$i,B:$i]: (((setminus @ A @ B) = emptyset) => (subset @ A @ B))) ).
% 32.55/10.82  thf(symdiffE_def, definition, symdiffE = (! [A:$i,B:$i,C:$i]: ((in @ C @ (symdiff @ A @ B)) => (! [D:$o]: (((in @ C @ A) => ((~ (in @ C @ B)) => (D))) => (((~ (in @ C @ A)) => ((in @ C @ B) => (D))) => (D)))))) ).
% 32.55/10.82  thf(symdiffI1_def, definition, symdiffI1 = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (in @ C @ (symdiff @ A @ B))))) ).
% 32.55/10.82  thf(symdiffI2_def, definition, symdiffI2 = (! [A:$i,B:$i,C:$i]: ((~ (in @ C @ A)) => ((in @ C @ B) => (in @ C @ (symdiff @ A @ B))))) ).
% 32.55/10.82  thf(symdiffIneg1_def, definition, symdiffIneg1 = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((in @ C @ B) => (~ (in @ C @ (symdiff @ A @ B)))))) ).
% 32.55/10.82  thf(symdiffIneg2_def, definition, symdiffIneg2 = (! [A:$i,B:$i,C:$i]: ((~ (in @ C @ A)) => ((~ (in @ C @ B)) => (~ (in @ C @ (symdiff @ A @ B)))))) ).
% 32.55/10.82  thf(secondinupair_def, definition, secondinupair = (! [A:$i,B:$i]: (in @ B @ (setadjoin @ A @ (setadjoin @ B @ emptyset)))) ).
% 32.55/10.82  thf(setukpairIL_def, definition, setukpairIL = (! [A:$i,B:$i]: (in @ A @ (setunion @ (setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset))))) ).
% 32.55/10.82  thf(setukpairIR_def, definition, setukpairIR = (! [A:$i,B:$i]: (in @ B @ (setunion @ (setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset))))) ).
% 32.55/10.82  thf(kpairiskpair_def, definition, kpairiskpair = (! [A:$i,B:$i]: (iskpair @ (setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset)))) ).
% 32.55/10.82  thf(kpairp_def, definition, kpairp = (! [A:$i,B:$i]: (iskpair @ (kpair @ A @ B))) ).
% 32.55/10.82  thf(singletonsubset_def, definition, singletonsubset = (! [A:$i,B:$i]: ((in @ B @ A) => (subset @ (setadjoin @ B @ emptyset) @ A))) ).
% 32.55/10.82  thf(singletoninpowerset_def, definition, singletoninpowerset = (! [A:$i,B:$i]: ((in @ B @ A) => (in @ (setadjoin @ B @ emptyset) @ (powerset @ A)))) ).
% 32.55/10.82  thf(singletoninpowunion_def, definition, singletoninpowunion = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (in @ (setadjoin @ C @ emptyset) @ (powerset @ (binunion @ A @ B))))) ).
% 32.55/10.82  thf(upairset2E_def, definition, upairset2E = (! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ (setadjoin @ B @ emptyset))) => ((C = A) | (C = B)))) ).
% 32.55/10.82  thf(upairsubunion_def, definition, upairsubunion = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => (subset @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ (binunion @ A @ B)))))) ).
% 32.55/10.82  thf(upairinpowunion_def, definition, upairinpowunion = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => (in @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ (powerset @ (binunion @ A @ B))))))) ).
% 32.55/10.82  thf(ubforcartprodlem1_def, definition, ubforcartprodlem1 = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => (subset @ (setadjoin @ (setadjoin @ C @ emptyset) @ (setadjoin @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ A @ B))))))) ).
% 32.55/10.82  thf(ubforcartprodlem2_def, definition, ubforcartprodlem2 = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => (in @ (setadjoin @ (setadjoin @ C @ emptyset) @ (setadjoin @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ A @ B)))))))) ).
% 32.55/10.82  thf(ubforcartprodlem3_def, definition, ubforcartprodlem3 = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => (in @ (kpair @ C @ D) @ (powerset @ (powerset @ (binunion @ A @ B)))))))) ).
% 32.55/10.82  thf(cartprodpairin_def, definition, cartprodpairin = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => (in @ (kpair @ C @ D) @ (cartprod @ A @ B)))))) ).
% 32.55/10.82  thf(cartprodmempair1_def, definition, cartprodmempair1 = (! [A:$i,B:$i,C:$i]: ((in @ C @ (cartprod @ A @ B)) => (? [D:$i]: ((in @ D @ A) & ? [E:$i]: ((in @ E @ B) & (C = (kpair @ D @ E))))))) ).
% 32.55/10.82  thf(cartprodmempair_def, definition, cartprodmempair = (! [A:$i,B:$i,C:$i]: ((in @ C @ (cartprod @ A @ B)) => (iskpair @ C))) ).
% 32.55/10.82  thf(setunionE2_def, definition, setunionE2 = (! [A:$i,B:$i]: ((in @ B @ (setunion @ A)) => (? [C:$i]: ((in @ C @ A) & (in @ B @ C))))) ).
% 32.55/10.82  thf(setunionsingleton1_def, definition, setunionsingleton1 = (! [A:$i]: (subset @ (setunion @ (setadjoin @ A @ emptyset)) @ A)) ).
% 32.55/10.82  thf(setunionsingleton2_def, definition, setunionsingleton2 = (! [A:$i]: (subset @ A @ (setunion @ (setadjoin @ A @ emptyset)))) ).
% 32.55/10.82  thf(setunionsingleton_def, definition, setunionsingleton = (! [A:$i]: ((setunion @ (setadjoin @ A @ emptyset)) = A)) ).
% 32.55/10.82  thf(singleton_def, definition, singleton = (^ [A:$i]: ? [B:$i]: ((in @ B @ A) & (A = (setadjoin @ B @ emptyset)))) ).
% 32.55/10.82  thf(singletonprop_def, definition, singletonprop = (! [A:$i,B:($i > $o)]: ((! [C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ A) => ((B @ C) => ((B @ D) => (C = D))))))) => ((? [C:$i]: ((in @ C @ A) & (B @ C))) => (singleton @ (dsetconstr @ A @ (B)))))) ).
% 32.55/10.82  thf(ex1_def, definition, ex1 = (^ [A:$i,B:($i > $o)]: (singleton @ (dsetconstr @ A @ B))) ).
% 32.55/10.82  thf(ex1E1_def, definition, ex1E1 = (! [A:$i,B:($i > $o)]: ((ex1 @ A @ (B)) => (? [C:$i]: ((in @ C @ A) & (B @ C))))) ).
% 32.55/10.82  thf(ex1I_def, definition, ex1I = (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((B @ C) => ((! [D:$i]: ((in @ D @ A) => ((B @ D) => (D = C)))) => (ex1 @ A @ (B)))))) ).
% 32.55/10.82  thf(ex1I2_def, definition, ex1I2 = (! [A:$i,B:($i > $o)]: ((! [C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ A) => ((B @ C) => ((B @ D) => (C = D))))))) => ((? [C:$i]: ((in @ C @ A) & (B @ C))) => (ex1 @ A @ (B))))) ).
% 32.55/10.82  thf(singletonsuniq_def, definition, singletonsuniq = (! [A:$i,B:$i]: (((setadjoin @ A @ emptyset) = (setadjoin @ B @ emptyset)) => (A = B))) ).
% 32.55/10.82  thf(setukpairinjL1_def, definition, setukpairinjL1 = (! [A:$i,B:$i,C:$i]: ((in @ (setadjoin @ C @ emptyset) @ (setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset))) => (A = C))) ).
% 32.55/10.82  thf(kfstsingleton_def, definition, kfstsingleton = (! [A:$i]: ((iskpair @ A) => (singleton @ (dsetconstr @ (setunion @ A) @ (^ [B:$i]: (in @ (setadjoin @ B @ emptyset) @ A)))))) ).
% 32.55/10.82  thf(theprop_def, definition, theprop = (! [A:$i]: ((singleton @ A) => (in @ (setunion @ A) @ A))) ).
% 32.55/10.82  thf(kfstpairEq_def, definition, kfstpairEq = (! [A:$i,B:$i]: ((kfst @ (kpair @ A @ B)) = A)) ).
% 32.55/10.82  thf(cartprodfstin_def, definition, cartprodfstin = (! [A:$i,B:$i,C:$i]: ((in @ C @ (cartprod @ A @ B)) => (in @ (kfst @ C) @ A))) ).
% 32.55/10.82  thf(setukpairinjL2_def, definition, setukpairinjL2 = (! [A:$i,B:$i,C:$i,D:$i]: (((setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ C @ emptyset) @ (setadjoin @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ emptyset))) => (A = C))) ).
% 32.55/10.82  thf(setukpairinjL_def, definition, setukpairinjL = (! [A:$i,B:$i,C:$i,D:$i]: (((kpair @ A @ B) = (kpair @ C @ D)) => (A = C))) ).
% 32.55/10.82  thf(setukpairinjR11_def, definition, setukpairinjR11 = (! [A:$i,B:$i]: ((A = B) => ((setadjoin @ A @ (setadjoin @ B @ emptyset)) = (setadjoin @ A @ emptyset)))) ).
% 32.55/10.82  thf(setukpairinjR12_def, definition, setukpairinjR12 = (! [A:$i,B:$i]: ((A = B) => ((setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ A @ emptyset) @ emptyset)))) ).
% 32.55/10.82  thf(setukpairinjR1_def, definition, setukpairinjR1 = (! [A:$i,B:$i,C:$i,D:$i]: (((setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ C @ emptyset) @ (setadjoin @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ emptyset))) => ((C = D) => (B = D)))) ).
% 32.55/10.82  thf(upairequniteq_def, definition, upairequniteq = (! [A:$i,B:$i,C:$i]: (((setadjoin @ A @ (setadjoin @ B @ emptyset)) = (setadjoin @ C @ emptyset)) => (A = B))) ).
% 32.55/10.82  thf(setukpairinjR2_def, definition, setukpairinjR2 = (! [A:$i,B:$i,C:$i,D:$i]: (((setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ C @ emptyset) @ (setadjoin @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ emptyset))) => (B = D))) ).
% 32.55/10.82  thf(setukpairinjR_def, definition, setukpairinjR = (! [A:$i,B:$i,C:$i,D:$i]: (((kpair @ A @ B) = (kpair @ C @ D)) => (B = D))) ).
% 32.55/10.82  thf(ksndsingleton_def, definition, ksndsingleton = (! [A:$i]: ((iskpair @ A) => (singleton @ (dsetconstr @ (setunion @ A) @ (^ [B:$i]: (A = (kpair @ (kfst @ A) @ B))))))) ).
% 32.55/10.82  thf(ksndpairEq_def, definition, ksndpairEq = (! [A:$i,B:$i]: ((ksnd @ (kpair @ A @ B)) = B)) ).
% 32.55/10.82  thf(kpairsurjEq_def, definition, kpairsurjEq = (! [A:$i]: ((iskpair @ A) => ((kpair @ (kfst @ A) @ (ksnd @ A)) = A))) ).
% 32.55/10.82  thf(cartprodsndin_def, definition, cartprodsndin = (! [A:$i,B:$i,C:$i]: ((in @ C @ (cartprod @ A @ B)) => (in @ (ksnd @ C) @ B))) ).
% 32.55/10.82  thf(cartprodpairmemEL_def, definition, cartprodpairmemEL = (! [A:$i,B:$i,C:$i,D:$i]: ((in @ (kpair @ C @ D) @ (cartprod @ A @ B)) => (in @ C @ A))) ).
% 32.55/10.82  thf(cartprodpairmemER_def, definition, cartprodpairmemER = (! [A:$i,B:$i,C:$i,D:$i]: ((in @ (kpair @ C @ D) @ (cartprod @ A @ B)) => (in @ D @ B))) ).
% 32.55/10.82  thf(cartprodmempaircEq_def, definition, cartprodmempaircEq = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => ((kpair @ C @ D) = (kpair @ C @ D)))))) ).
% 32.55/10.82  thf(cartprodfstpairEq_def, definition, cartprodfstpairEq = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => ((kfst @ (kpair @ C @ D)) = C))))) ).
% 32.55/10.82  thf(cartprodsndpairEq_def, definition, cartprodsndpairEq = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => ((ksnd @ (kpair @ C @ D)) = D))))) ).
% 32.55/10.82  thf(cartprodpairsurjEq_def, definition, cartprodpairsurjEq = (! [A:$i,B:$i,C:$i]: ((in @ C @ (cartprod @ A @ B)) => ((kpair @ (kfst @ C) @ (ksnd @ C)) = C))) ).
% 32.55/10.82  thf(dpsetconstr_def, definition, dpsetconstr = (^ [A:$i,B:$i,C:($i > ($i > $o))]: (dsetconstr @ (cartprod @ A @ B) @ (^ [D:$i]: ? [E:$i]: ((in @ E @ A) & ? [F:$i]: ((in @ F @ B) & (C @ E @ F) & (D = (kpair @ E @ F))))))) ).
% 32.55/10.82  thf(dpsetconstrI_def, definition, dpsetconstrI = (! [A:$i,B:$i,C:($i > ($i > $o)),D:$i]: ((in @ D @ A) => (! [E:$i]: ((in @ E @ B) => ((C @ D @ E) => (in @ (kpair @ D @ E) @ (dpsetconstr @ A @ B @ (C)))))))) ).
% 32.55/10.82  thf(sk1_def, definition, sk1 = (^ [A:$i,B:$i]: (@+ [C:$i]: ~ ((in @ C @ B) = (in @ C @ A)))) ).
% 32.55/10.82  thf(sk2_def, definition, sk2 = (^ [A:$i]: (@+ [B:$i]: ~ (((in @ B @ omega) & (in @ B @ A)) => (in @ (setadjoin @ B @ B) @ A)))) ).
% 32.55/10.82  thf(sk3_def, definition, sk3 = (^ [A:$i,B:($i > ($i > $o))]: (@+ [C:$i]: ~ ((in @ C @ A) => (? [D:$i]: ((B @ C @ D) & ! [E:$i]: ((B @ C @ E) => (D = E))))))) ).
% 32.55/10.82  thf(sk4_def, definition, sk4 = (^ [A:$i,B:$i,C:($i > ($i > $o))]: (@+ [D:$i]: ~ ((C @ (sk3 @ B @ C) @ D) => (A = D)))) ).
% 32.55/10.82  thf(sk5_def, definition, sk5 = (^ [A:$i,B:($i > ($i > $o))]: (@+ [C:$i]: ! [D:$i]: ((in @ D @ C) = (? [E:$i]: ((in @ E @ A) & (B @ E @ D)))))) ).
% 32.55/10.82  thf(sk6_def, definition, sk6 = (^ [A:$i]: (@+ [B:$i]: ((in @ B @ A) & ~ (? [C:$i]: ((in @ C @ B) & (in @ C @ A)))))) ).
% 32.55/10.82  thf(sk7_def, definition, sk7 = (^ [A:$i]: (@+ [B:$i]: (! [C:$i]: ((in @ C @ B) => (! [D:$i]: ((in @ D @ C) => (in @ D @ A)))) & ! [C:$i,D:$i]: (((in @ C @ A) & (in @ D @ A)) => ((! [E:$i]: ((in @ E @ B) => ((in @ C @ E) = (in @ D @ E)))) => (C = D))) & ! [C:$i,D:$i]: (((in @ C @ B) & (in @ D @ B)) => (! [E:$i]: ((in @ E @ C) => (in @ E @ D)) | ! [E:$i]: ((in @ E @ D) => (in @ E @ C)))) & ! [C:$i]: ((! [D:$i]: ((in @ D @ C) => (in @ D @ A)) & ? [D:$i]: (in @ D @ C)) => (? [D:$i]: ((in @ D @ B) & ? [E:$i]: ((in @ E @ C) & ~ (? [F:$i]: ((in @ F @ D) & (in @ F @ C))) & ! [F:$i]: ((in @ F @ B) => (! [G:$i]: ((in @ G @ F) => (in @ G @ D)) | (in @ E @ F)))))))))) ).
% 32.55/10.82  thf(sk8_def, definition, sk8 = (^ [A:$i,B:$i,C:$i]: (@+ [D:$i]: ~ ((in @ D @ (sk7 @ C)) => ((in @ B @ D) = (in @ A @ D))))) ).
% 32.55/10.82  thf(sk10_def, definition, sk10 = (^ [A:$i,B:$i]: (@+ [C:$i]: ~ ((in @ C @ A) => (in @ C @ B)))) ).
% 32.55/10.82  thf(sk11_def, definition, sk11 = (^ [A:$i,B:$i]: (@+ [C:$i]: ((in @ C @ (sk7 @ B)) & ? [D:$i]: ((in @ D @ A) & ~ (? [E:$i]: ((in @ E @ C) & (in @ E @ A))) & ! [E:$i]: ((in @ E @ (sk7 @ B)) => (! [F:$i]: ((in @ F @ E) => (in @ F @ C)) | (in @ D @ E))))))) ).
% 32.55/10.82  thf(sk12_def, definition, sk12 = (^ [A:$i,B:$i]: (@+ [C:$i]: ((in @ C @ A) & ~ (? [D:$i]: ((in @ D @ (sk11 @ A @ B)) & (in @ D @ A))) & ! [D:$i]: ((in @ D @ (sk7 @ B)) => (! [E:$i]: ((in @ E @ D) => (in @ E @ (sk11 @ A @ B))) | (in @ C @ D)))))) ).
% 32.55/10.82  thf(sk13_def, definition, sk13 = (^ [A:$i,B:($i > $o)]: (@+ [C:$i]: ~ ((B @ C) => (A = C)))) ).
% 32.55/10.82  thf(sk14_def, definition, sk14 = (^ [A:$i,B:($i > $o)]: (@+ [C:$i]: ~ ((B @ C) => (A = C)))) ).
% 32.55/10.82  thf(sk15_def, definition, sk15 = ((@+) @ $i) ).
% 32.55/10.82  thf(sk16_def, definition, sk16 = (^ [A:$i,B:$i]: (@+ [C:$i]: ~ ((in @ C @ B) => (in @ C @ A)))) ).
% 32.55/10.82  thf(sk17_def, definition, sk17 = (^ [A:$i,B:$i]: (@+ [C:$i]: ~ ((in @ C @ A) => (in @ C @ B)))) ).
% 32.55/10.82  thf(sk18_def, definition, sk18 = (^ [A:$i]: (@+ [B:$i]: (in @ B @ A))) ).
% 32.55/10.82  thf(sk19_def, definition, sk19 = (^ [A:$i]: (@+ [B:$i]: (in @ B @ A))) ).
% 32.55/10.82  thf(sk20_def, definition, sk20 = (^ [A:$i]: (@+ [B:$i]: (in @ B @ A))) ).
% 32.55/10.82  thf(sk21_def, definition, sk21 = (^ [A:$i,B:$i]: (@+ [C:$i]: ~ ((in @ C @ A) => (in @ C @ B)))) ).
% 32.55/10.82  thf(sk22_def, definition, sk22 = (^ [A:$o,B:$i,C:$i]: (@+ [D:$i]: ~ ((in @ B @ D) => ((in @ D @ C) => (A))))) ).
% 32.55/10.82  thf(sk23_def, definition, sk23 = (^ [A:$i,B:($i > $o)]: (@+ [C:$i]: ~ ((B @ C) => (A = C)))) ).
% 32.55/10.82  thf(sk24_def, definition, sk24 = (^ [A:($i > $o)]: (@+ [B:$i]: ! [C:$i]: ((A @ C) = (C = B)))) ).
% 32.55/10.82  thf(sk25_def, definition, sk25 = (^ [A:$i]: (@+ [B:$i]: (in @ B @ A))) ).
% 32.55/10.82  thf(sk26_def, definition, sk26 = (^ [A:($i > $o),B:$i]: (@+ [C:$i]: ((in @ C @ B) & ~ (A @ C)))) ).
% 32.55/10.82  thf(sk27_def, definition, sk27 = (^ [A:($i > $o),B:$i]: (@+ [C:$i]: ~ ((in @ C @ B) => (~ (A @ C))))) ).
% 32.55/10.82  thf(sk28_def, definition, sk28 = (^ [A:($i > $o),B:$i]: (@+ [C:$i]: ((in @ C @ B) & (A @ C)))) ).
% 32.55/10.82  thf(sk29_def, definition, sk29 = (^ [A:($i > $o),B:$i]: (@+ [C:$i]: ~ ((in @ C @ B) => (A @ C)))) ).
% 32.55/10.82  thf(sk30_def, definition, sk30 = (^ [A:($i > $o),B:$i]: (@+ [C:$i]: ((in @ C @ B) & (A @ C)))) ).
% 32.55/10.82  thf(sk31_def, definition, sk31 = (^ [A:($i > $o),B:$i]: (@+ [C:$i]: ((in @ C @ B) & ~ (A @ C)))) ).
% 32.55/10.82  thf(sk32_def, definition, sk32 = (^ [A:($i > $o)]: (@+ [B:$i]: ~ ((A @ B) => (! [C:$i]: ((A @ C) => (B = C)))))) ).
% 32.55/10.82  thf(sk33_def, definition, sk33 = (^ [A:($i > $o)]: (@+ [B:$i]: ~ ((A @ B) => ((sk32 @ A) = B)))) ).
% 32.55/10.82  thf(sk34_def, definition, sk34 = (^ [A:($i > $o)]: (@+ [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C))))) ).
% 32.55/10.82  thf(sk35_def, definition, sk35 = (^ [A:$i,B:($i > $o)]: (@+ [C:$i]: ~ ((B @ C) = (C = A)))) ).
% 32.55/10.82  thf(sk36_def, definition, sk36 = (^ [A:($i > $o)]: (@+ [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C))))) ).
% 32.55/10.82  thf(sk37_def, definition, sk37 = (^ [A:$i,B:($i > $o)]: (@+ [C:$i]: ~ ((B @ C) => (A = C)))) ).
% 32.55/10.82  thf(sk38_def, definition, sk38 = (^ [A:($i > $o),B:($i > $o)]: (@+ [C:$i]: ~ (! [D:$i]: ((C = D) => ((B @ C) = (A @ D)))))) ).
% 32.55/10.82  thf(sk39_def, definition, sk39 = (^ [A:($i > $o),B:($i > $o)]: (@+ [C:$i]: ~ (((sk38 @ A @ B) = C) => ((B @ (sk38 @ A @ B)) = (A @ C))))) ).
% 32.55/10.82  thf(sk40_def, definition, sk40 = (^ [A:$i,B:($i > $o)]: (@+ [C:$i]: ~ ((B @ C) => (A = C)))) ).
% 32.55/10.82  thf(sk42_def, definition, sk42 = (^ [A:($i > $o),B:($i > $o)]: (@+ [C:$i]: ~ (! [D:$i]: ((C = D) => ((B @ C) = (A @ D)))))) ).
% 32.55/10.82  thf(sk43_def, definition, sk43 = (^ [A:($i > $o),B:($i > $o)]: (@+ [C:$i]: ~ (((sk42 @ A @ B) = C) => ((B @ (sk42 @ A @ B)) = (A @ C))))) ).
% 32.55/10.82  thf(sk44_def, definition, sk44 = (^ [A:$i,B:($i > $o),C:($i > $o)]: (@+ [D:$i]: ~ ((C @ D) => (A = D)))) ).
% 32.55/10.82  thf(sk45_def, definition, sk45 = (^ [A:$i,B:($i > $o),C:($i > $o)]: (@+ [D:$i]: ~ ((B @ D) => (A = D)))) ).
% 32.55/10.82  thf(sk46_def, definition, sk46 = (^ [A:($i > $o),B:($i > $o),C:$i,D:$i]: (@+ [E:$i]: ~ ((in @ E @ D) => (! [F:$i]: ((in @ F @ C) => ((E = F) => ((B @ E) = (A @ F)))))))) ).
% 32.55/10.82  thf(sk47_def, definition, sk47 = (^ [A:($i > $o),B:($i > $o),C:$i,D:$i]: (@+ [E:$i]: ~ ((in @ E @ C) => (((sk46 @ A @ B @ C @ D) = E) => ((B @ (sk46 @ A @ B @ C @ D)) = (A @ E)))))) ).
% 32.55/10.82  thf(sk48_def, definition, sk48 = (^ [A:$i,B:$i]: (@+ [C:$i]: ~ ((in @ C @ B) => (in @ C @ A)))) ).
% 32.55/10.82  thf(sk49_def, definition, sk49 = (^ [A:$i,B:$i]: (@+ [C:$i]: ~ ((in @ C @ B) => (in @ C @ A)))) ).
% 32.55/10.82  thf(sk50_def, definition, sk50 = (^ [A:$i,B:$i]: (@+ [C:$i]: ((in @ C @ B) & (in @ C @ A)))) ).
% 32.55/10.82  thf(sk51_def, definition, sk51 = (^ [A:$i,B:$i,C:$i]: (@+ [D:$i]: ((in @ D @ C) & ? [E:$i]: ((in @ E @ B) & (A = (kpair @ D @ E)))))) ).
% 32.55/10.82  thf(sk52_def, definition, sk52 = (^ [A:$i,B:$i,C:$i]: (@+ [D:$i]: ((in @ D @ B) & (A = (kpair @ (sk51 @ A @ B @ C) @ D))))) ).
% 32.55/10.82  thf(sk53_def, definition, sk53 = (^ [A:$i,B:$i]: (@+ [C:$i]: ((in @ C @ B) & (in @ A @ C)))) ).
% 32.55/10.82  thf(sk54_def, definition, sk54 = (^ [A:($i > $o),B:$i]: (@+ [C:$i]: ~ ((in @ C @ B) => (! [D:$i]: ((in @ D @ B) => ((A @ C) => ((A @ D) => (C = D)))))))) ).
% 32.55/10.82  thf(sk55_def, definition, sk55 = (^ [A:($i > $o),B:$i]: (@+ [C:$i]: ~ ((in @ C @ B) => ((A @ (sk54 @ A @ B)) => ((A @ C) => ((sk54 @ A @ B) = C)))))) ).
% 32.55/10.82  thf(sk56_def, definition, sk56 = (^ [A:($i > $o),B:$i]: (@+ [C:$i]: ((in @ C @ (dsetconstr @ B @ A)) & ((dsetconstr @ B @ A) = (setadjoin @ C @ emptyset))))) ).
% 32.55/10.82  thf(sk57_def, definition, sk57 = (^ [A:($i > $o),B:$i]: (@+ [C:$i]: ((in @ C @ B) & (A @ C)))) ).
% 32.55/10.82  thf(sk58_def, definition, sk58 = (^ [A:$i,B:($i > $o),C:$i]: (@+ [D:$i]: ~ ((in @ D @ C) => ((B @ D) => (D = A))))) ).
% 32.55/10.82  thf(sk59_def, definition, sk59 = (^ [A:$i,B:($i > $o),C:$i]: (@+ [D:$i]: ((in @ D @ (dsetconstr @ C @ B)) & ((dsetconstr @ C @ B) = (setadjoin @ D @ emptyset))))) ).
% 32.55/10.82  thf(sk60_def, definition, sk60 = (^ [A:($i > $o),B:$i]: (@+ [C:$i]: ~ ((in @ C @ B) => (! [D:$i]: ((in @ D @ B) => ((A @ C) => ((A @ D) => (C = D)))))))) ).
% 32.55/10.82  thf(sk61_def, definition, sk61 = (^ [A:($i > $o),B:$i]: (@+ [C:$i]: ~ ((in @ C @ B) => ((A @ (sk60 @ A @ B)) => ((A @ C) => ((sk60 @ A @ B) = C)))))) ).
% 32.55/10.82  thf(sk62_def, definition, sk62 = (^ [A:($i > $o),B:$i]: (@+ [C:$i]: ((in @ C @ (dsetconstr @ B @ A)) & ((dsetconstr @ B @ A) = (setadjoin @ C @ emptyset))))) ).
% 32.55/10.82  thf(sk63_def, definition, sk63 = (^ [A:$i]: (@+ [B:$i]: ((in @ B @ (dsetconstr @ (setunion @ A) @ (^ [C:$i]: (in @ (setadjoin @ C @ emptyset) @ A)))) & ((dsetconstr @ (setunion @ A) @ (^ [C:$i]: (in @ (setadjoin @ C @ emptyset) @ A))) = (setadjoin @ B @ emptyset))))) ).
% 32.55/10.82  thf(sk64_def, definition, sk64 = (^ [A:$i]: (@+ [B:$i]: ((in @ B @ (dsetconstr @ (setunion @ A) @ (^ [C:$i]: (A = (kpair @ (kfst @ A) @ C))))) & ((dsetconstr @ (setunion @ A) @ (^ [C:$i]: (A = (kpair @ (kfst @ A) @ C)))) = (setadjoin @ B @ emptyset))))) ).
% 32.55/10.82  thf(sk65_def, definition, sk65 = (@+ [A:$i]: ~ (! [B:$i,C:($i > ($i > $o))]: (subset @ (dsetconstr @ (cartprod @ A @ B) @ (^ [D:$i]: ? [E:$i]: ((in @ E @ A) & ? [F:$i]: ((in @ F @ B) & (C @ E @ F) & (D = (kpair @ E @ F)))))) @ (cartprod @ A @ B)))) ).
% 32.55/10.82  thf(sk66_def, definition, sk66 = (@+ [A:$i]: ~ (! [B:($i > ($i > $o))]: (subset @ (dsetconstr @ (cartprod @ sk65 @ A) @ (^ [C:$i]: ? [D:$i]: ((in @ D @ sk65) & ? [E:$i]: ((in @ E @ A) & (B @ D @ E) & (C = (kpair @ D @ E)))))) @ (cartprod @ sk65 @ A)))) ).
% 32.55/10.82  thf(sk67_def, definition, sk67 = (@+ [A:($i > ($i > $o))]: ~ (subset @ (dsetconstr @ (cartprod @ sk65 @ sk66) @ (^ [B:$i]: ? [C:$i]: ((in @ C @ sk65) & ? [D:$i]: ((in @ D @ sk66) & (A @ C @ D) & (B = (kpair @ C @ D)))))) @ (cartprod @ sk65 @ sk66))) ).
% 32.55/10.82  thf(1,conjecture,(((setextAx) => ((emptysetAx) => ((setadjoinAx) => ((powersetAx) => ((setunionAx) => ((omega0Ax) => ((omegaSAx) => ((omegaIndAx) => ((replAx) => ((foundationAx) => ((wellorderingAx) => ((descrp) => ((dsetconstrI) => ((dsetconstrEL) => ((dsetconstrER) => ((exuE1) => ((prop2setE) => ((emptysetE) => ((emptysetimpfalse) => ((notinemptyset) => ((exuE3e) => ((setext) => ((emptyI) => ((noeltsimpempty) => ((setbeta) => ((nonemptyE1) => ((nonemptyI) => ((nonemptyI1) => ((setadjoinIL) => ((emptyinunitempty) => ((setadjoinIR) => ((setadjoinE) => ((setadjoinOr) => ((setoftrueEq) => ((powersetI) => ((emptyinPowerset) => ((emptyInPowerset) => ((powersetE) => ((setunionI) => ((setunionE) => ((subPowSU) => ((exuE2) => ((nonemptyImpWitness) => ((uniqinunit) => ((notinsingleton) => ((eqinunit) => ((singletonsswitch) => ((upairsetE) => ((upairsetIL) => ((upairsetIR) => ((emptyE1) => ((vacuousDall) => ((quantDeMorgan1) => ((quantDeMorgan2) => ((quantDeMorgan3) => ((quantDeMorgan4) => ((prop2setI) => ((prop2set2propI) => ((notdexE) => ((notdallE) => ((exuI1) => ((exuI3) => ((exuI2) => ((inCongP) => ((in__Cong) => ((exuE3u) => ((exu__Cong) => ((emptyset__Cong) => ((setadjoin__Cong) => ((powerset__Cong) => ((setunion__Cong) => ((omega__Cong) => ((exuEu) => ((descr__Cong) => ((dsetconstr__Cong) => ((subsetI1) => ((eqimpsubset2) => ((eqimpsubset1) => ((subsetI2) => ((emptysetsubset) => ((subsetE) => ((subsetE2) => ((notsubsetI) => ((notequalI1) => ((notequalI2) => ((subsetRefl) => ((subsetTrans) => ((setadjoinSub) => ((setadjoinSub2) => ((subset2powerset) => ((setextsub) => ((subsetemptysetimpeq) => ((powersetI1) => ((powersetE1) => ((inPowerset) => ((powersetsubset) => ((sepInPowerset) => ((sepSubset) => ((binunionIL) => ((upairset2IR) => ((binunionIR) => ((binunionEcases) => ((binunionE) => ((binunionLsub) => ((binunionRsub) => ((binintersectI) => ((binintersectSubset5) => ((binintersectEL) => ((binintersectLsub) => ((binintersectSubset2) => ((binintersectSubset3) => ((binintersectER) => ((disjointsetsI1) => ((binintersectRsub) => ((binintersectSubset4) => ((binintersectSubset1) => ((bs114d) => ((setminusI) => ((setminusEL) => ((setminusER) => ((setminusSubset2) => ((setminusERneg) => ((setminusELneg) => ((setminusILneg) => ((setminusIRneg) => ((setminusLsub) => ((setminusSubset1) => ((symdiffE) => ((symdiffI1) => ((symdiffI2) => ((symdiffIneg1) => ((symdiffIneg2) => ((secondinupair) => ((setukpairIL) => ((setukpairIR) => ((kpairiskpair) => ((kpairp) => ((singletonsubset) => ((singletoninpowerset) => ((singletoninpowunion) => ((upairset2E) => ((upairsubunion) => ((upairinpowunion) => ((ubforcartprodlem1) => ((ubforcartprodlem2) => ((ubforcartprodlem3) => ((cartprodpairin) => ((cartprodmempair1) => ((cartprodmempair) => ((setunionE2) => ((setunionsingleton1) => ((setunionsingleton2) => ((setunionsingleton) => ((singletonprop) => ((ex1E1) => ((ex1I) => ((ex1I2) => ((singletonsuniq) => ((setukpairinjL1) => ((kfstsingleton) => ((theprop) => ((kfstpairEq) => ((cartprodfstin) => ((setukpairinjL2) => ((setukpairinjL) => ((setukpairinjR11) => ((setukpairinjR12) => ((setukpairinjR1) => ((upairequniteq) => ((setukpairinjR2) => ((setukpairinjR) => ((ksndsingleton) => ((ksndpairEq) => ((kpairsurjEq) => ((cartprodsndin) => ((cartprodpairmemEL) => ((cartprodpairmemER) => ((cartprodmempaircEq) => ((cartprodfstpairEq) => ((cartprodsndpairEq) => ((cartprodpairsurjEq) => ((dpsetconstrI) => (! [A:$i,B:$i,C:($i > ($i > $o))]: (subset @ (dpsetconstr @ A @ B @ (C)) @ (cartprod @ A @ B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrSub)).
% 32.55/10.82  thf(2,negated_conjecture,((~ ((setextAx) => ((emptysetAx) => ((setadjoinAx) => ((powersetAx) => ((setunionAx) => ((omega0Ax) => ((omegaSAx) => ((omegaIndAx) => ((replAx) => ((foundationAx) => ((wellorderingAx) => ((descrp) => ((dsetconstrI) => ((dsetconstrEL) => ((dsetconstrER) => ((exuE1) => ((prop2setE) => ((emptysetE) => ((emptysetimpfalse) => ((notinemptyset) => ((exuE3e) => ((setext) => ((emptyI) => ((noeltsimpempty) => ((setbeta) => ((nonemptyE1) => ((nonemptyI) => ((nonemptyI1) => ((setadjoinIL) => ((emptyinunitempty) => ((setadjoinIR) => ((setadjoinE) => ((setadjoinOr) => ((setoftrueEq) => ((powersetI) => ((emptyinPowerset) => ((emptyInPowerset) => ((powersetE) => ((setunionI) => ((setunionE) => ((subPowSU) => ((exuE2) => ((nonemptyImpWitness) => ((uniqinunit) => ((notinsingleton) => ((eqinunit) => ((singletonsswitch) => ((upairsetE) => ((upairsetIL) => ((upairsetIR) => ((emptyE1) => ((vacuousDall) => ((quantDeMorgan1) => ((quantDeMorgan2) => ((quantDeMorgan3) => ((quantDeMorgan4) => ((prop2setI) => ((prop2set2propI) => ((notdexE) => ((notdallE) => ((exuI1) => ((exuI3) => ((exuI2) => ((inCongP) => ((in__Cong) => ((exuE3u) => ((exu__Cong) => ((emptyset__Cong) => ((setadjoin__Cong) => ((powerset__Cong) => ((setunion__Cong) => ((omega__Cong) => ((exuEu) => ((descr__Cong) => ((dsetconstr__Cong) => ((subsetI1) => ((eqimpsubset2) => ((eqimpsubset1) => ((subsetI2) => ((emptysetsubset) => ((subsetE) => ((subsetE2) => ((notsubsetI) => ((notequalI1) => ((notequalI2) => ((subsetRefl) => ((subsetTrans) => ((setadjoinSub) => ((setadjoinSub2) => ((subset2powerset) => ((setextsub) => ((subsetemptysetimpeq) => ((powersetI1) => ((powersetE1) => ((inPowerset) => ((powersetsubset) => ((sepInPowerset) => ((sepSubset) => ((binunionIL) => ((upairset2IR) => ((binunionIR) => ((binunionEcases) => ((binunionE) => ((binunionLsub) => ((binunionRsub) => ((binintersectI) => ((binintersectSubset5) => ((binintersectEL) => ((binintersectLsub) => ((binintersectSubset2) => ((binintersectSubset3) => ((binintersectER) => ((disjointsetsI1) => ((binintersectRsub) => ((binintersectSubset4) => ((binintersectSubset1) => ((bs114d) => ((setminusI) => ((setminusEL) => ((setminusER) => ((setminusSubset2) => ((setminusERneg) => ((setminusELneg) => ((setminusILneg) => ((setminusIRneg) => ((setminusLsub) => ((setminusSubset1) => ((symdiffE) => ((symdiffI1) => ((symdiffI2) => ((symdiffIneg1) => ((symdiffIneg2) => ((secondinupair) => ((setukpairIL) => ((setukpairIR) => ((kpairiskpair) => ((kpairp) => ((singletonsubset) => ((singletoninpowerset) => ((singletoninpowunion) => ((upairset2E) => ((upairsubunion) => ((upairinpowunion) => ((ubforcartprodlem1) => ((ubforcartprodlem2) => ((ubforcartprodlem3) => ((cartprodpairin) => ((cartprodmempair1) => ((cartprodmempair) => ((setunionE2) => ((setunionsingleton1) => ((setunionsingleton2) => ((setunionsingleton) => ((singletonprop) => ((ex1E1) => ((ex1I) => ((ex1I2) => ((singletonsuniq) => ((setukpairinjL1) => ((kfstsingleton) => ((theprop) => ((kfstpairEq) => ((cartprodfstin) => ((setukpairinjL2) => ((setukpairinjL) => ((setukpairinjR11) => ((setukpairinjR12) => ((setukpairinjR1) => ((upairequniteq) => ((setukpairinjR2) => ((setukpairinjR) => ((ksndsingleton) => ((ksndpairEq) => ((kpairsurjEq) => ((cartprodsndin) => ((cartprodpairmemEL) => ((cartprodpairmemER) => ((cartprodmempaircEq) => ((cartprodfstpairEq) => ((cartprodsndpairEq) => ((cartprodpairsurjEq) => ((dpsetconstrI) => (! [A:$i,B:$i,C:($i > ($i > $o))]: (subset @ (dpsetconstr @ A @ B @ (C)) @ (cartprod @ A @ B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),inference(neg_conjecture,[status(cth)],[1])).
% 32.55/10.82  thf(3,plain,((~ ((! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) = (in @ C @ B))) => (A = B))) => ((! [A:$i]: ~ (in @ A @ emptyset)) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ B)) = ((C = A) | (in @ C @ B)))) => ((! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) = (! [C:$i]: ((in @ C @ B) => (in @ C @ A))))) => ((! [A:$i,B:$i]: ((in @ B @ (setunion @ A)) = (? [C:$i]: ((in @ B @ C) & (in @ C @ A))))) => ((in @ emptyset @ omega) => ((! [A:$i]: ((in @ A @ omega) => (in @ (setadjoin @ A @ A) @ omega))) => ((! [A:$i]: (((in @ emptyset @ A) & ! [B:$i]: (((in @ B @ omega) & (in @ B @ A)) => (in @ (setadjoin @ B @ B) @ A))) => (! [B:$i]: ((in @ B @ omega) => (in @ B @ A))))) => ((! [A:($i > ($i > $o)),B:$i]: ((! [C:$i]: ((in @ C @ B) => (? [D:$i]: ((A @ C @ D) & ! [E:$i]: ((A @ C @ E) => (D = E)))))) => (? [C:$i]: ! [D:$i]: ((in @ D @ C) = (? [E:$i]: ((in @ E @ B) & (A @ E @ D))))))) => ((! [A:$i]: ((? [B:$i]: (in @ B @ A)) => (? [B:$i]: ((in @ B @ A) & ~ (? [C:$i]: ((in @ C @ B) & (in @ C @ A))))))) => ((! [A:$i]: ? [B:$i]: (! [C:$i]: ((in @ C @ B) => (! [D:$i]: ((in @ D @ C) => (in @ D @ A)))) & ! [C:$i,D:$i]: (((in @ C @ A) & (in @ D @ A)) => ((! [E:$i]: ((in @ E @ B) => ((in @ C @ E) = (in @ D @ E)))) => (C = D))) & ! [C:$i,D:$i]: (((in @ C @ B) & (in @ D @ B)) => (! [E:$i]: ((in @ E @ C) => (in @ E @ D)) | ! [E:$i]: ((in @ E @ D) => (in @ E @ C)))) & ! [C:$i]: ((! [D:$i]: ((in @ D @ C) => (in @ D @ A)) & ? [D:$i]: (in @ D @ C)) => (? [D:$i,E:$i]: ((in @ D @ B) & (in @ E @ C) & ~ (? [F:$i]: ((in @ F @ D) & (in @ F @ C))) & ! [F:$i]: ((in @ F @ B) => (! [G:$i]: ((in @ G @ F) => (in @ G @ D)) | (in @ E @ F)))))))) => ((! [A:($i > $o)]: ((? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))) => (A @ (descr @ (A))))) => ((! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((B @ C) => (in @ C @ (dsetconstr @ A @ (B)))))) => ((! [A:$i,B:($i > $o),C:$i]: ((in @ C @ (dsetconstr @ A @ (B))) => (in @ C @ A))) => ((! [A:$i,B:($i > $o),C:$i]: ((in @ C @ (dsetconstr @ A @ (B))) => (B @ C))) => ((! [A:$o,B:$i]: ((in @ B @ (prop2set @ A)) => (A))) => ((! [A:$i]: ((in @ A @ emptyset) => (! [B:$o]: (B)))) => ((! [A:$i]: ~ (in @ A @ emptyset)) => ((! [A:$i]: ~ (in @ A @ emptyset)) => ((! [A:($i > $o)]: ((? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))) => (? [B:$i]: (A @ B)))) => ((! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) => (in @ C @ B))) => ((! [C:$i]: ((in @ C @ B) => (in @ C @ A))) => (A = B)))) => ((! [A:$i]: ((! [B:$i]: ~ (in @ B @ A)) => (A = emptyset))) => ((! [A:$i]: ((! [B:$i]: ~ (in @ B @ A)) => (A = emptyset))) => ((! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((in @ C @ (dsetconstr @ A @ (B))) = (B @ C)))) => ((! [A:$i]: ((~ (A = emptyset)) => (? [B:$i]: (in @ B @ A)))) => ((! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((B @ C) => (~ ((dsetconstr @ A @ (B)) = emptyset))))) => ((! [A:$i]: ((? [B:$i]: (in @ B @ A)) => (~ (A = emptyset)))) => ((! [A:$i,B:$i]: (in @ A @ (setadjoin @ A @ B))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ B) => (in @ C @ (setadjoin @ A @ B)))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ B)) => (! [D:$o]: (((C = A) => (D)) => (((in @ C @ B) => (D)) => (D)))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ B)) => ((C = A) | (in @ C @ B)))) => ((! [A:$i]: ((dsetconstr @ A @ (^ [B:$i]: (($true)))) = A)) => ((! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ B) => (in @ C @ A))) => (in @ B @ (powerset @ A)))) => ((! [A:$i]: (in @ emptyset @ (powerset @ A))) => ((! [A:$i]: (in @ emptyset @ (powerset @ A))) => ((! [A:$i,B:$i,C:$i]: ((in @ B @ (powerset @ A)) => ((in @ C @ B) => (in @ C @ A)))) => ((! [A:$i,B:$i,C:$i]: ((in @ B @ C) => ((in @ C @ A) => (in @ B @ (setunion @ A))))) => ((! [A:$i,B:$i]: ((in @ B @ (setunion @ A)) => (! [C:$o]: ((! [D:$i]: ((in @ B @ D) => ((in @ D @ A) => (C)))) => (C))))) => ((! [A:$i,B:$i]: ((in @ B @ A) => (in @ B @ (powerset @ (setunion @ A))))) => ((! [A:($i > $o)]: ((? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))) => (? [B:$i]: ! [C:$i]: ((A @ C) = (C = B))))) => ((! [A:$i]: ((~ (A = emptyset)) => (? [B:$i]: (in @ B @ A)))) => ((! [A:$i,B:$i]: ((in @ A @ (setadjoin @ B @ emptyset)) => (A = B))) => ((! [A:$i,B:$i]: ((~ (A = B)) => (~ (in @ B @ (setadjoin @ A @ emptyset))))) => ((! [A:$i,B:$i]: ((A = B) => (in @ A @ (setadjoin @ B @ emptyset)))) => ((! [A:$i,B:$i]: ((in @ A @ (setadjoin @ B @ emptyset)) => (in @ B @ (setadjoin @ A @ emptyset)))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ (setadjoin @ B @ emptyset))) => ((C = A) | (C = B)))) => ((! [A:$i,B:$i]: (in @ A @ (setadjoin @ A @ (setadjoin @ B @ emptyset)))) => ((! [A:$i,B:$i]: (in @ B @ (setadjoin @ A @ (setadjoin @ B @ emptyset)))) => ((! [A:$i,B:($i > $o)]: ((? [C:$i]: ((in @ C @ A) & (B @ C))) => (~ ((dsetconstr @ A @ (B)) = emptyset)))) => ((! [A:($i > $o),B:$i]: ((in @ B @ emptyset) => (A @ B))) => ((! [A:$i,B:($i > $o)]: ((~ (! [C:$i]: ((in @ C @ A) => (B @ C)))) => (? [C:$i]: ((in @ C @ A) & ~ (B @ C))))) => ((! [A:$i,B:($i > $o)]: ((! [C:$i]: ((in @ C @ A) => (~ (B @ C)))) => (~ (? [C:$i]: ((in @ C @ A) & (B @ C)))))) => ((! [A:$i,B:($i > $o)]: ((~ (? [C:$i]: ((in @ C @ A) & (B @ C)))) => (! [C:$i]: ((in @ C @ A) => (~ (B @ C)))))) => ((! [A:$i,B:($i > $o)]: ((? [C:$i]: ((in @ C @ A) & ~ (B @ C))) => (~ (! [C:$i]: ((in @ C @ A) => (B @ C)))))) => ((! [A:$o]: ((A) => (in @ emptyset @ (prop2set @ A)))) => ((! [A:$o]: ((A) => (set2prop @ (prop2set @ A)))) => ((! [A:$i,B:($i > $o)]: ((~ (? [C:$i]: ((in @ C @ A) & (B @ C)))) => (! [C:$i]: ((in @ C @ A) => (~ (B @ C)))))) => ((! [A:$i,B:($i > $o)]: ((~ (! [C:$i]: ((in @ C @ A) => (B @ C)))) => (? [C:$i]: ((in @ C @ A) & ~ (B @ C))))) => ((! [A:($i > $o)]: ((? [B:$i]: (A @ B)) => ((! [B:$i,C:$i]: ((A @ B) => ((A @ C) => (B = C)))) => (? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C))))))) => ((! [A:($i > $o)]: ((? [B:$i]: ! [C:$i]: ((A @ C) = (C = B))) => (? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))))) => ((! [A:$i,B:$i]: ((A = B) => (! [C:$i,D:$i]: ((C = D) => ((in @ C @ A) => (in @ D @ B)))))) => ((! [A:$i,B:$i]: ((A = B) => (! [C:$i,D:$i]: ((C = D) => ((in @ C @ A) = (in @ D @ B)))))) => ((! [A:($i > $o)]: ((? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))) => (! [B:$i,C:$i]: ((A @ B) => ((A @ C) => (B = C)))))) => ((! [A:($i > $o),B:($i > $o)]: ((! [C:$i,D:$i]: ((C = D) => ((A @ C) = (B @ D)))) => ((? [C:$i]: ((A @ C) & ! [D:$i]: ((A @ D) => (C = D)))) = (? [C:$i]: ((B @ C) & ! [D:$i]: ((B @ D) => (C = D))))))) => ((! [A:$i,B:$i]: ((A = B) => (! [C:$i,D:$i]: ((C = D) => ((setadjoin @ A @ C) = (setadjoin @ B @ D)))))) => ((! [A:$i,B:$i]: ((A = B) => ((powerset @ A) = (powerset @ B)))) => ((! [A:$i,B:$i]: ((A = B) => ((setunion @ A) = (setunion @ B)))) => ((! [A:($i > $o)]: ((? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))) => (! [B:$i,C:$i]: ((A @ B) => ((A @ C) => (B = C)))))) => ((! [A:($i > $o),B:($i > $o)]: ((! [C:$i,D:$i]: ((C = D) => ((A @ C) = (B @ D)))) => ((? [C:$i]: ((A @ C) & ! [D:$i]: ((A @ D) => (C = D)))) => ((? [C:$i]: ((B @ C) & ! [D:$i]: ((B @ D) => (C = D)))) => ((descr @ (A)) = (descr @ (B))))))) => ((! [A:$i,B:$i]: ((A = B) => (! [C:($i > $o),D:($i > $o)]: ((! [E:$i]: ((in @ E @ A) => (! [F:$i]: ((in @ F @ B) => ((E = F) => ((C @ E) = (D @ F))))))) => ((dsetconstr @ A @ (C)) = (dsetconstr @ B @ (D))))))) => ((! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) => (in @ C @ B))) => (subset @ A @ B))) => ((! [A:$i,B:$i]: ((A = B) => (subset @ B @ A))) => ((! [A:$i,B:$i]: ((A = B) => (subset @ A @ B))) => ((! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) => (in @ C @ B))) => (subset @ A @ B))) => ((! [A:$i]: (subset @ emptyset @ A)) => ((! [A:$i,B:$i,C:$i]: ((subset @ A @ B) => ((in @ C @ A) => (in @ C @ B)))) => ((! [A:$i,B:$i,C:$i]: ((subset @ A @ B) => ((~ (in @ C @ B)) => (~ (in @ C @ A))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (~ (subset @ A @ B))))) => ((! [A:$i,B:$i]: ((~ (subset @ A @ B)) => (~ (A = B)))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (~ (A = B))))) => ((! [A:$i]: (subset @ A @ A)) => ((! [A:$i,B:$i,C:$i]: ((subset @ A @ B) => ((subset @ B @ C) => (subset @ A @ C)))) => ((! [A:$i,B:$i]: (subset @ B @ (setadjoin @ A @ B))) => ((! [A:$i,B:$i,C:$i]: ((subset @ A @ C) => (subset @ A @ (setadjoin @ B @ C)))) => ((! [A:$i,B:$i]: ((subset @ A @ B) => (in @ A @ (powerset @ B)))) => ((! [A:$i,B:$i]: ((subset @ A @ B) => ((subset @ B @ A) => (A = B)))) => ((! [A:$i]: ((subset @ A @ emptyset) => (A = emptyset))) => ((! [A:$i,B:$i]: ((subset @ B @ A) => (in @ B @ (powerset @ A)))) => ((! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (subset @ B @ A))) => ((! [A:$i]: (in @ A @ (powerset @ A))) => ((! [A:$i,B:$i]: ((subset @ A @ B) => (subset @ (powerset @ A) @ (powerset @ B)))) => ((! [A:$i,B:($i > $o)]: (in @ (dsetconstr @ A @ (B)) @ (powerset @ A))) => ((! [A:$i,B:($i > $o)]: (subset @ (dsetconstr @ A @ (B)) @ A)) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (in @ C @ (binunion @ A @ B)))) => ((! [A:$i,B:$i]: (in @ B @ (setadjoin @ A @ (setadjoin @ B @ emptyset)))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ B) => (in @ C @ (binunion @ A @ B)))) => ((! [A:$i,B:$i,C:$i,D:$o]: ((in @ C @ (binunion @ A @ B)) => (((in @ C @ A) => (D)) => (((in @ C @ B) => (D)) => (D))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (binunion @ A @ B)) => ((in @ C @ A) | (in @ C @ B)))) => ((! [A:$i,B:$i]: (subset @ A @ (binunion @ A @ B))) => ((! [A:$i,B:$i]: (subset @ B @ (binunion @ A @ B))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((in @ C @ B) => (in @ C @ (binintersect @ A @ B))))) => ((! [A:$i,B:$i,C:$i]: ((subset @ C @ A) => ((subset @ C @ B) => (subset @ C @ (binintersect @ A @ B))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (binintersect @ A @ B)) => (in @ C @ A))) => ((! [A:$i,B:$i]: (subset @ (binintersect @ A @ B) @ A)) => ((! [A:$i,B:$i]: ((subset @ A @ B) => ((binintersect @ A @ B) = A))) => ((! [A:$i,B:$i]: (((binintersect @ A @ B) = B) => (subset @ B @ A))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (binintersect @ A @ B)) => (in @ C @ B))) => ((! [A:$i,B:$i]: ((~ (? [C:$i]: ((in @ C @ A) & (in @ C @ B)))) => ((binintersect @ A @ B) = emptyset))) => ((! [A:$i,B:$i]: (subset @ (binintersect @ A @ B) @ B)) => ((! [A:$i,B:$i]: ((subset @ B @ A) => ((binintersect @ A @ B) = B))) => ((! [A:$i,B:$i]: (((binintersect @ A @ B) = A) => (subset @ A @ B))) => ((! [A:$i,B:$i,C:$i]: ((binintersect @ A @ (binunion @ B @ C)) = (binunion @ (binintersect @ A @ B) @ (binintersect @ A @ C)))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (in @ C @ (setminus @ A @ B))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (setminus @ A @ B)) => (in @ C @ A))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (setminus @ A @ B)) => (~ (in @ C @ B)))) => ((! [A:$i,B:$i]: ((subset @ A @ B) => ((setminus @ A @ B) = emptyset))) => ((! [A:$i,B:$i,C:$i]: ((~ (in @ C @ (setminus @ A @ B))) => ((in @ C @ A) => (in @ C @ B)))) => ((! [A:$i,B:$i,C:$i]: ((~ (in @ C @ (setminus @ A @ B))) => ((~ (in @ C @ B)) => (~ (in @ C @ A))))) => ((! [A:$i,B:$i,C:$i]: ((~ (in @ C @ A)) => (~ (in @ C @ (setminus @ A @ B))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ B) => (~ (in @ C @ (setminus @ A @ B))))) => ((! [A:$i,B:$i]: (subset @ (setminus @ A @ B) @ A)) => ((! [A:$i,B:$i]: (((setminus @ A @ B) = emptyset) => (subset @ A @ B))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (symdiff @ A @ B)) => (! [D:$o]: (((in @ C @ A) => ((~ (in @ C @ B)) => (D))) => (((~ (in @ C @ A)) => ((in @ C @ B) => (D))) => (D)))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (in @ C @ (symdiff @ A @ B))))) => ((! [A:$i,B:$i,C:$i]: ((~ (in @ C @ A)) => ((in @ C @ B) => (in @ C @ (symdiff @ A @ B))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((in @ C @ B) => (~ (in @ C @ (symdiff @ A @ B)))))) => ((! [A:$i,B:$i,C:$i]: ((~ (in @ C @ A)) => ((~ (in @ C @ B)) => (~ (in @ C @ (symdiff @ A @ B)))))) => ((! [A:$i,B:$i]: (in @ B @ (setadjoin @ A @ (setadjoin @ B @ emptyset)))) => ((! [A:$i,B:$i]: (in @ A @ (setunion @ (setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset))))) => ((! [A:$i,B:$i]: (in @ B @ (setunion @ (setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset))))) => ((! [A:$i,B:$i]: (iskpair @ (setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset)))) => ((! [A:$i,B:$i]: (iskpair @ (kpair @ A @ B))) => ((! [A:$i,B:$i]: ((in @ B @ A) => (subset @ (setadjoin @ B @ emptyset) @ A))) => ((! [A:$i,B:$i]: ((in @ B @ A) => (in @ (setadjoin @ B @ emptyset) @ (powerset @ A)))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (in @ (setadjoin @ C @ emptyset) @ (powerset @ (binunion @ A @ B))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ (setadjoin @ B @ emptyset))) => ((C = A) | (C = B)))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => (subset @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ (binunion @ A @ B)))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => (in @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ (powerset @ (binunion @ A @ B))))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => (subset @ (setadjoin @ (setadjoin @ C @ emptyset) @ (setadjoin @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ A @ B))))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => (in @ (setadjoin @ (setadjoin @ C @ emptyset) @ (setadjoin @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ A @ B)))))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => (in @ (kpair @ C @ D) @ (powerset @ (powerset @ (binunion @ A @ B)))))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => (in @ (kpair @ C @ D) @ (cartprod @ A @ B)))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (cartprod @ A @ B)) => (? [D:$i]: ((in @ D @ A) & ? [E:$i]: ((in @ E @ B) & (C = (kpair @ D @ E))))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (cartprod @ A @ B)) => (iskpair @ C))) => ((! [A:$i,B:$i]: ((in @ B @ (setunion @ A)) => (? [C:$i]: ((in @ C @ A) & (in @ B @ C))))) => ((! [A:$i]: (subset @ (setunion @ (setadjoin @ A @ emptyset)) @ A)) => ((! [A:$i]: (subset @ A @ (setunion @ (setadjoin @ A @ emptyset)))) => ((! [A:$i]: ((setunion @ (setadjoin @ A @ emptyset)) = A)) => ((! [A:$i,B:($i > $o)]: ((! [C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ A) => ((B @ C) => ((B @ D) => (C = D))))))) => ((? [C:$i]: ((in @ C @ A) & (B @ C))) => (? [C:$i]: ((in @ C @ (dsetconstr @ A @ (B))) & ((dsetconstr @ A @ (B)) = (setadjoin @ C @ emptyset))))))) => ((! [A:$i,B:($i > $o)]: ((? [C:$i]: ((in @ C @ (dsetconstr @ A @ (B))) & ((dsetconstr @ A @ (B)) = (setadjoin @ C @ emptyset)))) => (? [C:$i]: ((in @ C @ A) & (B @ C))))) => ((! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((B @ C) => ((! [D:$i]: ((in @ D @ A) => ((B @ D) => (D = C)))) => (? [D:$i]: ((in @ D @ (dsetconstr @ A @ (B))) & ((dsetconstr @ A @ (B)) = (setadjoin @ D @ emptyset)))))))) => ((! [A:$i,B:($i > $o)]: ((! [C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ A) => ((B @ C) => ((B @ D) => (C = D))))))) => ((? [C:$i]: ((in @ C @ A) & (B @ C))) => (? [C:$i]: ((in @ C @ (dsetconstr @ A @ (B))) & ((dsetconstr @ A @ (B)) = (setadjoin @ C @ emptyset))))))) => ((! [A:$i,B:$i]: (((setadjoin @ A @ emptyset) = (setadjoin @ B @ emptyset)) => (A = B))) => ((! [A:$i,B:$i,C:$i]: ((in @ (setadjoin @ C @ emptyset) @ (setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset))) => (A = C))) => ((! [A:$i]: ((iskpair @ A) => (? [B:$i]: ((in @ B @ (dsetconstr @ (setunion @ A) @ (^ [C:$i]: (in @ (setadjoin @ C @ emptyset) @ A)))) & ((dsetconstr @ (setunion @ A) @ (^ [C:$i]: (in @ (setadjoin @ C @ emptyset) @ A))) = (setadjoin @ B @ emptyset)))))) => ((! [A:$i]: ((? [B:$i]: ((in @ B @ A) & (A = (setadjoin @ B @ emptyset)))) => (in @ (setunion @ A) @ A))) => ((! [A:$i,B:$i]: ((kfst @ (kpair @ A @ B)) = A)) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (cartprod @ A @ B)) => (in @ (kfst @ C) @ A))) => ((! [A:$i,B:$i,C:$i,D:$i]: (((setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ C @ emptyset) @ (setadjoin @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ emptyset))) => (A = C))) => ((! [A:$i,B:$i,C:$i,D:$i]: (((kpair @ A @ B) = (kpair @ C @ D)) => (A = C))) => ((! [A:$i,B:$i]: ((A = B) => ((setadjoin @ A @ (setadjoin @ B @ emptyset)) = (setadjoin @ A @ emptyset)))) => ((! [A:$i,B:$i]: ((A = B) => ((setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ A @ emptyset) @ emptyset)))) => ((! [A:$i,B:$i,C:$i,D:$i]: (((setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ C @ emptyset) @ (setadjoin @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ emptyset))) => ((C = D) => (B = D)))) => ((! [A:$i,B:$i,C:$i]: (((setadjoin @ A @ (setadjoin @ B @ emptyset)) = (setadjoin @ C @ emptyset)) => (A = B))) => ((! [A:$i,B:$i,C:$i,D:$i]: (((setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ C @ emptyset) @ (setadjoin @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ emptyset))) => (B = D))) => ((! [A:$i,B:$i,C:$i,D:$i]: (((kpair @ A @ B) = (kpair @ C @ D)) => (B = D))) => ((! [A:$i]: ((iskpair @ A) => (? [B:$i]: ((in @ B @ (dsetconstr @ (setunion @ A) @ (^ [C:$i]: (A = (kpair @ (kfst @ A) @ C))))) & ((dsetconstr @ (setunion @ A) @ (^ [C:$i]: (A = (kpair @ (kfst @ A) @ C)))) = (setadjoin @ B @ emptyset)))))) => ((! [A:$i,B:$i]: ((ksnd @ (kpair @ A @ B)) = B)) => ((! [A:$i]: ((iskpair @ A) => ((kpair @ (kfst @ A) @ (ksnd @ A)) = A))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (cartprod @ A @ B)) => (in @ (ksnd @ C) @ B))) => ((! [A:$i,B:$i,C:$i,D:$i]: ((in @ (kpair @ C @ D) @ (cartprod @ A @ B)) => (in @ C @ A))) => ((! [A:$i,B:$i,C:$i,D:$i]: ((in @ (kpair @ C @ D) @ (cartprod @ A @ B)) => (in @ D @ B))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => ((kfst @ (kpair @ C @ D)) = C))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => ((ksnd @ (kpair @ C @ D)) = D))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (cartprod @ A @ B)) => ((kpair @ (kfst @ C) @ (ksnd @ C)) = C))) => ((! [A:$i,B:$i,C:($i > ($i > $o)),D:$i]: ((in @ D @ A) => (! [E:$i]: ((in @ E @ B) => ((C @ D @ E) => (in @ (kpair @ D @ E) @ (dsetconstr @ (cartprod @ A @ B) @ (^ [F:$i]: ? [G:$i]: ((in @ G @ A) & ? [H:$i]: ((in @ H @ B) & (C @ G @ H) & (F = (kpair @ G @ H)))))))))))) => (! [A:$i,B:$i,C:($i > ($i > $o))]: (subset @ (dsetconstr @ (cartprod @ A @ B) @ (^ [D:$i]: ? [E:$i]: ((in @ E @ A) & ? [F:$i]: ((in @ F @ B) & (C @ E @ F) & (D = (kpair @ E @ F)))))) @ (cartprod @ A @ B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 32.55/10.82  thf(4,plain,((~ ((! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) = (in @ C @ B))) => (A = B))) => ((~ (? [A:$i]: (in @ A @ emptyset))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ B)) = ((C = A) | (in @ C @ B)))) => ((! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) = (! [C:$i]: ((in @ C @ B) => (in @ C @ A))))) => ((! [A:$i,B:$i]: ((in @ B @ (setunion @ A)) = (? [C:$i]: ((in @ B @ C) & (in @ C @ A))))) => ((in @ emptyset @ omega) => ((! [A:$i]: ((in @ A @ omega) => (in @ (setadjoin @ A @ A) @ omega))) => ((! [A:$i]: (((in @ emptyset @ A) & ! [B:$i]: (((in @ B @ omega) & (in @ B @ A)) => (in @ (setadjoin @ B @ B) @ A))) => (! [B:$i]: ((in @ B @ omega) => (in @ B @ A))))) => ((! [A:($i > ($i > $o)),B:$i]: ((! [C:$i]: ((in @ C @ B) => (? [D:$i]: ((A @ C @ D) & ! [E:$i]: ((A @ C @ E) => (D = E)))))) => (? [C:$i]: ! [D:$i]: ((in @ D @ C) = (? [E:$i]: ((in @ E @ B) & (A @ E @ D))))))) => ((! [A:$i]: ((? [B:$i]: (in @ B @ A)) => (? [B:$i]: ((in @ B @ A) & ~ (? [C:$i]: ((in @ C @ B) & (in @ C @ A))))))) => ((! [A:$i]: ? [B:$i]: (! [C:$i]: ((in @ C @ B) => (! [D:$i]: ((in @ D @ C) => (in @ D @ A)))) & ! [C:$i,D:$i]: (((in @ C @ A) & (in @ D @ A)) => ((! [E:$i]: ((in @ E @ B) => ((in @ C @ E) = (in @ D @ E)))) => (C = D))) & ! [C:$i,D:$i]: (((in @ C @ B) & (in @ D @ B)) => (! [E:$i]: ((in @ E @ C) => (in @ E @ D)) | ! [E:$i]: ((in @ E @ D) => (in @ E @ C)))) & ! [C:$i]: ((! [D:$i]: ((in @ D @ C) => (in @ D @ A)) & ? [D:$i]: (in @ D @ C)) => (? [D:$i]: ((in @ D @ B) & ? [E:$i]: ((in @ E @ C) & ~ (? [F:$i]: ((in @ F @ D) & (in @ F @ C))) & ! [F:$i]: ((in @ F @ B) => (! [G:$i]: ((in @ G @ F) => (in @ G @ D)) | (in @ E @ F))))))))) => ((! [A:($i > $o)]: ((? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))) => (A @ (descr @ (A))))) => ((! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((B @ C) => (in @ C @ (dsetconstr @ A @ (B)))))) => ((! [A:$i,B:($i > $o),C:$i]: ((in @ C @ (dsetconstr @ A @ (B))) => (in @ C @ A))) => ((! [A:$i,B:($i > $o),C:$i]: ((in @ C @ (dsetconstr @ A @ (B))) => (B @ C))) => ((! [A:$o]: ((? [B:$i]: (in @ B @ (prop2set @ A))) => (A))) => (((? [A:$i]: (in @ A @ emptyset)) => (! [A:$o]: (A))) => ((~ (? [A:$i]: (in @ A @ emptyset))) => ((~ (? [A:$i]: (in @ A @ emptyset))) => ((! [A:($i > $o)]: ((? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))) => (? [B:$i]: (A @ B)))) => ((! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) => (in @ C @ B))) => ((! [C:$i]: ((in @ C @ B) => (in @ C @ A))) => (A = B)))) => ((! [A:$i]: ((~ (? [B:$i]: (in @ B @ A))) => (A = emptyset))) => ((! [A:$i]: ((~ (? [B:$i]: (in @ B @ A))) => (A = emptyset))) => ((! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((in @ C @ (dsetconstr @ A @ (B))) = (B @ C)))) => ((! [A:$i]: ((~ (A = emptyset)) => (? [B:$i]: (in @ B @ A)))) => ((! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((B @ C) => (~ ((dsetconstr @ A @ (B)) = emptyset))))) => ((! [A:$i]: ((? [B:$i]: (in @ B @ A)) => (~ (A = emptyset)))) => ((! [A:$i,B:$i]: (in @ A @ (setadjoin @ A @ B))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ B) => (in @ C @ (setadjoin @ A @ B)))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ B)) => (! [D:$o]: (((C = A) => (D)) => (((in @ C @ B) => (D)) => (D)))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ B)) => ((C = A) | (in @ C @ B)))) => ((! [A:$i]: ((dsetconstr @ A @ (^ [B:$i]: (($true)))) = A)) => ((! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ B) => (in @ C @ A))) => (in @ B @ (powerset @ A)))) => ((! [A:$i]: (in @ emptyset @ (powerset @ A))) => ((! [A:$i]: (in @ emptyset @ (powerset @ A))) => ((! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (! [C:$i]: ((in @ C @ B) => (in @ C @ A))))) => ((! [A:$i,B:$i,C:$i]: ((in @ B @ C) => ((in @ C @ A) => (in @ B @ (setunion @ A))))) => ((! [A:$i,B:$i]: ((in @ B @ (setunion @ A)) => (! [C:$o]: ((! [D:$i]: ((in @ B @ D) => ((in @ D @ A) => (C)))) => (C))))) => ((! [A:$i,B:$i]: ((in @ B @ A) => (in @ B @ (powerset @ (setunion @ A))))) => ((! [A:($i > $o)]: ((? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))) => (? [B:$i]: ! [C:$i]: ((A @ C) = (C = B))))) => ((! [A:$i]: ((~ (A = emptyset)) => (? [B:$i]: (in @ B @ A)))) => ((! [A:$i,B:$i]: ((in @ A @ (setadjoin @ B @ emptyset)) => (A = B))) => ((! [A:$i,B:$i]: ((~ (A = B)) => (~ (in @ B @ (setadjoin @ A @ emptyset))))) => ((! [A:$i,B:$i]: ((A = B) => (in @ A @ (setadjoin @ B @ emptyset)))) => ((! [A:$i,B:$i]: ((in @ A @ (setadjoin @ B @ emptyset)) => (in @ B @ (setadjoin @ A @ emptyset)))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ (setadjoin @ B @ emptyset))) => ((C = A) | (C = B)))) => ((! [A:$i,B:$i]: (in @ A @ (setadjoin @ A @ (setadjoin @ B @ emptyset)))) => ((! [A:$i,B:$i]: (in @ B @ (setadjoin @ A @ (setadjoin @ B @ emptyset)))) => ((! [A:$i,B:($i > $o)]: ((? [C:$i]: ((in @ C @ A) & (B @ C))) => (~ ((dsetconstr @ A @ (B)) = emptyset)))) => ((! [A:($i > $o),B:$i]: ((in @ B @ emptyset) => (A @ B))) => ((! [A:$i,B:($i > $o)]: ((~ (! [C:$i]: ((in @ C @ A) => (B @ C)))) => (? [C:$i]: ((in @ C @ A) & ~ (B @ C))))) => ((! [A:$i,B:($i > $o)]: ((! [C:$i]: ((in @ C @ A) => (~ (B @ C)))) => (~ (? [C:$i]: ((in @ C @ A) & (B @ C)))))) => ((! [A:$i,B:($i > $o)]: ((~ (? [C:$i]: ((in @ C @ A) & (B @ C)))) => (! [C:$i]: ((in @ C @ A) => (~ (B @ C)))))) => ((! [A:$i,B:($i > $o)]: ((? [C:$i]: ((in @ C @ A) & ~ (B @ C))) => (~ (! [C:$i]: ((in @ C @ A) => (B @ C)))))) => ((! [A:$o]: ((A) => (in @ emptyset @ (prop2set @ A)))) => ((! [A:$o]: ((A) => (set2prop @ (prop2set @ A)))) => ((! [A:$i,B:($i > $o)]: ((~ (? [C:$i]: ((in @ C @ A) & (B @ C)))) => (! [C:$i]: ((in @ C @ A) => (~ (B @ C)))))) => ((! [A:$i,B:($i > $o)]: ((~ (! [C:$i]: ((in @ C @ A) => (B @ C)))) => (? [C:$i]: ((in @ C @ A) & ~ (B @ C))))) => ((! [A:($i > $o)]: ((? [B:$i]: (A @ B)) => ((! [B:$i]: ((A @ B) => (! [C:$i]: ((A @ C) => (B = C))))) => (? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C))))))) => ((! [A:($i > $o)]: ((? [B:$i]: ! [C:$i]: ((A @ C) = (C = B))) => (? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))))) => ((! [A:$i,B:$i]: ((A = B) => (! [C:$i,D:$i]: ((C = D) => ((in @ C @ A) => (in @ D @ B)))))) => ((! [A:$i,B:$i]: ((A = B) => (! [C:$i,D:$i]: ((C = D) => ((in @ C @ A) = (in @ D @ B)))))) => ((! [A:($i > $o)]: ((? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))) => (! [B:$i]: ((A @ B) => (! [C:$i]: ((A @ C) => (B = C))))))) => ((! [A:($i > $o),B:($i > $o)]: ((! [C:$i,D:$i]: ((C = D) => ((A @ C) = (B @ D)))) => ((? [C:$i]: ((A @ C) & ! [D:$i]: ((A @ D) => (C = D)))) = (? [C:$i]: ((B @ C) & ! [D:$i]: ((B @ D) => (C = D))))))) => ((! [A:$i,B:$i]: ((A = B) => (! [C:$i,D:$i]: ((C = D) => ((setadjoin @ A @ C) = (setadjoin @ B @ D)))))) => ((! [A:$i,B:$i]: ((A = B) => ((powerset @ A) = (powerset @ B)))) => ((! [A:$i,B:$i]: ((A = B) => ((setunion @ A) = (setunion @ B)))) => ((! [A:($i > $o)]: ((? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))) => (! [B:$i]: ((A @ B) => (! [C:$i]: ((A @ C) => (B = C))))))) => ((! [A:($i > $o),B:($i > $o)]: ((! [C:$i,D:$i]: ((C = D) => ((A @ C) = (B @ D)))) => ((? [C:$i]: ((A @ C) & ! [D:$i]: ((A @ D) => (C = D)))) => ((? [C:$i]: ((B @ C) & ! [D:$i]: ((B @ D) => (C = D)))) => ((descr @ (A)) = (descr @ (B))))))) => ((! [A:$i,B:$i]: ((A = B) => (! [C:($i > $o),D:($i > $o)]: ((! [E:$i]: ((in @ E @ A) => (! [F:$i]: ((in @ F @ B) => ((E = F) => ((C @ E) = (D @ F))))))) => ((dsetconstr @ A @ (C)) = (dsetconstr @ B @ (D))))))) => ((! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) => (in @ C @ B))) => (subset @ A @ B))) => ((! [A:$i,B:$i]: ((A = B) => (subset @ B @ A))) => ((! [A:$i,B:$i]: ((A = B) => (subset @ A @ B))) => ((! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) => (in @ C @ B))) => (subset @ A @ B))) => ((! [A:$i]: (subset @ emptyset @ A)) => ((! [A:$i,B:$i]: ((subset @ A @ B) => (! [C:$i]: ((in @ C @ A) => (in @ C @ B))))) => ((! [A:$i,B:$i]: ((subset @ A @ B) => (! [C:$i]: ((~ (in @ C @ B)) => (~ (in @ C @ A)))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (~ (subset @ A @ B))))) => ((! [A:$i,B:$i]: ((~ (subset @ A @ B)) => (~ (A = B)))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (~ (A = B))))) => ((! [A:$i]: (subset @ A @ A)) => ((! [A:$i,B:$i]: ((subset @ A @ B) => (! [C:$i]: ((subset @ B @ C) => (subset @ A @ C))))) => ((! [A:$i,B:$i]: (subset @ B @ (setadjoin @ A @ B))) => ((! [A:$i,B:$i,C:$i]: ((subset @ A @ C) => (subset @ A @ (setadjoin @ B @ C)))) => ((! [A:$i,B:$i]: ((subset @ A @ B) => (in @ A @ (powerset @ B)))) => ((! [A:$i,B:$i]: ((subset @ A @ B) => ((subset @ B @ A) => (A = B)))) => ((! [A:$i]: ((subset @ A @ emptyset) => (A = emptyset))) => ((! [A:$i,B:$i]: ((subset @ B @ A) => (in @ B @ (powerset @ A)))) => ((! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (subset @ B @ A))) => ((! [A:$i]: (in @ A @ (powerset @ A))) => ((! [A:$i,B:$i]: ((subset @ A @ B) => (subset @ (powerset @ A) @ (powerset @ B)))) => ((! [A:$i,B:($i > $o)]: (in @ (dsetconstr @ A @ (B)) @ (powerset @ A))) => ((! [A:$i,B:($i > $o)]: (subset @ (dsetconstr @ A @ (B)) @ A)) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (in @ C @ (binunion @ A @ B)))) => ((! [A:$i,B:$i]: (in @ B @ (setadjoin @ A @ (setadjoin @ B @ emptyset)))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ B) => (in @ C @ (binunion @ A @ B)))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (binunion @ A @ B)) => (! [D:$o]: (((in @ C @ A) => (D)) => (((in @ C @ B) => (D)) => (D)))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (binunion @ A @ B)) => ((in @ C @ A) | (in @ C @ B)))) => ((! [A:$i,B:$i]: (subset @ A @ (binunion @ A @ B))) => ((! [A:$i,B:$i]: (subset @ B @ (binunion @ A @ B))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((in @ C @ B) => (in @ C @ (binintersect @ A @ B))))) => ((! [A:$i,B:$i,C:$i]: ((subset @ C @ A) => ((subset @ C @ B) => (subset @ C @ (binintersect @ A @ B))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (binintersect @ A @ B)) => (in @ C @ A))) => ((! [A:$i,B:$i]: (subset @ (binintersect @ A @ B) @ A)) => ((! [A:$i,B:$i]: ((subset @ A @ B) => ((binintersect @ A @ B) = A))) => ((! [A:$i,B:$i]: (((binintersect @ A @ B) = B) => (subset @ B @ A))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (binintersect @ A @ B)) => (in @ C @ B))) => ((! [A:$i,B:$i]: ((~ (? [C:$i]: ((in @ C @ A) & (in @ C @ B)))) => ((binintersect @ A @ B) = emptyset))) => ((! [A:$i,B:$i]: (subset @ (binintersect @ A @ B) @ B)) => ((! [A:$i,B:$i]: ((subset @ B @ A) => ((binintersect @ A @ B) = B))) => ((! [A:$i,B:$i]: (((binintersect @ A @ B) = A) => (subset @ A @ B))) => ((! [A:$i,B:$i,C:$i]: ((binintersect @ A @ (binunion @ B @ C)) = (binunion @ (binintersect @ A @ B) @ (binintersect @ A @ C)))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (in @ C @ (setminus @ A @ B))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (setminus @ A @ B)) => (in @ C @ A))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (setminus @ A @ B)) => (~ (in @ C @ B)))) => ((! [A:$i,B:$i]: ((subset @ A @ B) => ((setminus @ A @ B) = emptyset))) => ((! [A:$i,B:$i,C:$i]: ((~ (in @ C @ (setminus @ A @ B))) => ((in @ C @ A) => (in @ C @ B)))) => ((! [A:$i,B:$i,C:$i]: ((~ (in @ C @ (setminus @ A @ B))) => ((~ (in @ C @ B)) => (~ (in @ C @ A))))) => ((! [A:$i,B:$i,C:$i]: ((~ (in @ C @ A)) => (~ (in @ C @ (setminus @ A @ B))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ B) => (~ (in @ C @ (setminus @ A @ B))))) => ((! [A:$i,B:$i]: (subset @ (setminus @ A @ B) @ A)) => ((! [A:$i,B:$i]: (((setminus @ A @ B) = emptyset) => (subset @ A @ B))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (symdiff @ A @ B)) => (! [D:$o]: (((in @ C @ A) => ((~ (in @ C @ B)) => (D))) => (((~ (in @ C @ A)) => ((in @ C @ B) => (D))) => (D)))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (in @ C @ (symdiff @ A @ B))))) => ((! [A:$i,B:$i,C:$i]: ((~ (in @ C @ A)) => ((in @ C @ B) => (in @ C @ (symdiff @ A @ B))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((in @ C @ B) => (~ (in @ C @ (symdiff @ A @ B)))))) => ((! [A:$i,B:$i,C:$i]: ((~ (in @ C @ A)) => ((~ (in @ C @ B)) => (~ (in @ C @ (symdiff @ A @ B)))))) => ((! [A:$i,B:$i]: (in @ B @ (setadjoin @ A @ (setadjoin @ B @ emptyset)))) => ((! [A:$i,B:$i]: (in @ A @ (setunion @ (setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset))))) => ((! [A:$i,B:$i]: (in @ B @ (setunion @ (setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset))))) => ((! [A:$i,B:$i]: (iskpair @ (setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset)))) => ((! [A:$i,B:$i]: (iskpair @ (kpair @ A @ B))) => ((! [A:$i,B:$i]: ((in @ B @ A) => (subset @ (setadjoin @ B @ emptyset) @ A))) => ((! [A:$i,B:$i]: ((in @ B @ A) => (in @ (setadjoin @ B @ emptyset) @ (powerset @ A)))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (in @ (setadjoin @ C @ emptyset) @ (powerset @ (binunion @ A @ B))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ (setadjoin @ B @ emptyset))) => ((C = A) | (C = B)))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => (subset @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ (binunion @ A @ B)))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => (in @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ (powerset @ (binunion @ A @ B))))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => (subset @ (setadjoin @ (setadjoin @ C @ emptyset) @ (setadjoin @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ A @ B))))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => (in @ (setadjoin @ (setadjoin @ C @ emptyset) @ (setadjoin @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ A @ B)))))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => (in @ (kpair @ C @ D) @ (powerset @ (powerset @ (binunion @ A @ B)))))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => (in @ (kpair @ C @ D) @ (cartprod @ A @ B)))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (cartprod @ A @ B)) => (? [D:$i]: ((in @ D @ A) & ? [E:$i]: ((in @ E @ B) & (C = (kpair @ D @ E))))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (cartprod @ A @ B)) => (iskpair @ C))) => ((! [A:$i,B:$i]: ((in @ B @ (setunion @ A)) => (? [C:$i]: ((in @ C @ A) & (in @ B @ C))))) => ((! [A:$i]: (subset @ (setunion @ (setadjoin @ A @ emptyset)) @ A)) => ((! [A:$i]: (subset @ A @ (setunion @ (setadjoin @ A @ emptyset)))) => ((! [A:$i]: ((setunion @ (setadjoin @ A @ emptyset)) = A)) => ((! [A:$i,B:($i > $o)]: ((! [C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ A) => ((B @ C) => ((B @ D) => (C = D))))))) => ((? [C:$i]: ((in @ C @ A) & (B @ C))) => (? [C:$i]: ((in @ C @ (dsetconstr @ A @ (B))) & ((dsetconstr @ A @ (B)) = (setadjoin @ C @ emptyset))))))) => ((! [A:$i,B:($i > $o)]: ((? [C:$i]: ((in @ C @ (dsetconstr @ A @ (B))) & ((dsetconstr @ A @ (B)) = (setadjoin @ C @ emptyset)))) => (? [C:$i]: ((in @ C @ A) & (B @ C))))) => ((! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((B @ C) => ((! [D:$i]: ((in @ D @ A) => ((B @ D) => (D = C)))) => (? [D:$i]: ((in @ D @ (dsetconstr @ A @ (B))) & ((dsetconstr @ A @ (B)) = (setadjoin @ D @ emptyset)))))))) => ((! [A:$i,B:($i > $o)]: ((! [C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ A) => ((B @ C) => ((B @ D) => (C = D))))))) => ((? [C:$i]: ((in @ C @ A) & (B @ C))) => (? [C:$i]: ((in @ C @ (dsetconstr @ A @ (B))) & ((dsetconstr @ A @ (B)) = (setadjoin @ C @ emptyset))))))) => ((! [A:$i,B:$i]: (((setadjoin @ A @ emptyset) = (setadjoin @ B @ emptyset)) => (A = B))) => ((! [A:$i,B:$i,C:$i]: ((in @ (setadjoin @ C @ emptyset) @ (setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset))) => (A = C))) => ((! [A:$i]: ((iskpair @ A) => (? [B:$i]: ((in @ B @ (dsetconstr @ (setunion @ A) @ (^ [C:$i]: (in @ (setadjoin @ C @ emptyset) @ A)))) & ((dsetconstr @ (setunion @ A) @ (^ [C:$i]: (in @ (setadjoin @ C @ emptyset) @ A))) = (setadjoin @ B @ emptyset)))))) => ((! [A:$i]: ((? [B:$i]: ((in @ B @ A) & (A = (setadjoin @ B @ emptyset)))) => (in @ (setunion @ A) @ A))) => ((! [A:$i,B:$i]: ((kfst @ (kpair @ A @ B)) = A)) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (cartprod @ A @ B)) => (in @ (kfst @ C) @ A))) => ((! [A:$i,B:$i,C:$i]: ((? [D:$i]: ((setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ C @ emptyset) @ (setadjoin @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ emptyset)))) => (A = C))) => ((! [A:$i,B:$i,C:$i]: ((? [D:$i]: ((kpair @ A @ B) = (kpair @ C @ D))) => (A = C))) => ((! [A:$i,B:$i]: ((A = B) => ((setadjoin @ A @ (setadjoin @ B @ emptyset)) = (setadjoin @ A @ emptyset)))) => ((! [A:$i,B:$i]: ((A = B) => ((setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ A @ emptyset) @ emptyset)))) => ((! [A:$i,B:$i,C:$i,D:$i]: (((setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ C @ emptyset) @ (setadjoin @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ emptyset))) => ((C = D) => (B = D)))) => ((! [A:$i,B:$i]: ((? [C:$i]: ((setadjoin @ A @ (setadjoin @ B @ emptyset)) = (setadjoin @ C @ emptyset))) => (A = B))) => ((! [A:$i,B:$i,C:$i,D:$i]: (((setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ C @ emptyset) @ (setadjoin @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ emptyset))) => (B = D))) => ((! [A:$i,B:$i,C:$i,D:$i]: (((kpair @ A @ B) = (kpair @ C @ D)) => (B = D))) => ((! [A:$i]: ((iskpair @ A) => (? [B:$i]: ((in @ B @ (dsetconstr @ (setunion @ A) @ (^ [C:$i]: (A = (kpair @ (kfst @ A) @ C))))) & ((dsetconstr @ (setunion @ A) @ (^ [C:$i]: (A = (kpair @ (kfst @ A) @ C)))) = (setadjoin @ B @ emptyset)))))) => ((! [A:$i,B:$i]: ((ksnd @ (kpair @ A @ B)) = B)) => ((! [A:$i]: ((iskpair @ A) => ((kpair @ (kfst @ A) @ (ksnd @ A)) = A))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (cartprod @ A @ B)) => (in @ (ksnd @ C) @ B))) => ((! [A:$i,B:$i,C:$i]: ((? [D:$i]: (in @ (kpair @ C @ D) @ (cartprod @ A @ B))) => (in @ C @ A))) => ((! [A:$i,B:$i,C:$i,D:$i]: ((in @ (kpair @ C @ D) @ (cartprod @ A @ B)) => (in @ D @ B))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => ((kfst @ (kpair @ C @ D)) = C))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => ((ksnd @ (kpair @ C @ D)) = D))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (cartprod @ A @ B)) => ((kpair @ (kfst @ C) @ (ksnd @ C)) = C))) => ((! [A:$i,B:$i,C:($i > ($i > $o)),D:$i]: ((in @ D @ A) => (! [E:$i]: ((in @ E @ B) => ((C @ D @ E) => (in @ (kpair @ D @ E) @ (dsetconstr @ (cartprod @ A @ B) @ (^ [F:$i]: ? [G:$i]: ((in @ G @ A) & ? [H:$i]: ((in @ H @ B) & (C @ G @ H) & (F = (kpair @ G @ H)))))))))))) => (! [A:$i,B:$i,C:($i > ($i > $o))]: (subset @ (dsetconstr @ (cartprod @ A @ B) @ (^ [D:$i]: ? [E:$i]: ((in @ E @ A) & ? [F:$i]: ((in @ F @ B) & (C @ E @ F) & (D = (kpair @ E @ F)))))) @ (cartprod @ A @ B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),inference(miniscope,[status(thm)],[3])).
% 32.55/10.82  thf(5,plain,(! [ZZZZZZZZZZZZZZZZZM:$i,ZZZZZZZZZZZZZZZZZL:$i,ZZZZZZZZZZZZZZZZZK:($i > ($i > $o)),ZZZZZZZZZZZZZZZZZJ:$i,ZZZZZZZZZZZZZZZZZI:$i,ZZZZZZZZZZZZZZZZZH:$i,ZZZZZZZZZZZZZZZZZG:$i,ZZZZZZZZZZZZZZZZZF:$i,ZZZZZZZZZZZZZZZZZE:$i,ZZZZZZZZZZZZZZZZZD:$i,ZZZZZZZZZZZZZZZZZC:$i,ZZZZZZZZZZZZZZZZZB:$i,ZZZZZZZZZZZZZZZZZA:$i,ZZZZZZZZZZZZZZZZZ:$i,ZZZZZZZZZZZZZZZZY:$i,ZZZZZZZZZZZZZZZZX:$i,ZZZZZZZZZZZZZZZZW:$i,ZZZZZZZZZZZZZZZZV:$i,ZZZZZZZZZZZZZZZZU:$i,ZZZZZZZZZZZZZZZZT:$i,ZZZZZZZZZZZZZZZZS:$i,ZZZZZZZZZZZZZZZZR:$i,ZZZZZZZZZZZZZZZZQ:$i,ZZZZZZZZZZZZZZZZP:$i,ZZZZZZZZZZZZZZZZO:$i,ZZZZZZZZZZZZZZZZN:$i,ZZZZZZZZZZZZZZZZM:$i,ZZZZZZZZZZZZZZZZL:$i,ZZZZZZZZZZZZZZZZK:$i,ZZZZZZZZZZZZZZZZJ:$i,ZZZZZZZZZZZZZZZZI:$i,ZZZZZZZZZZZZZZZZH:$i,ZZZZZZZZZZZZZZZZG:$i,ZZZZZZZZZZZZZZZZF:$i,ZZZZZZZZZZZZZZZZE:$i,ZZZZZZZZZZZZZZZZD:$i,ZZZZZZZZZZZZZZZZC:$i,ZZZZZZZZZZZZZZZZB:$i,ZZZZZZZZZZZZZZZZA:$i,ZZZZZZZZZZZZZZZZ:$i,ZZZZZZZZZZZZZZZY:$i,ZZZZZZZZZZZZZZZX:$i,ZZZZZZZZZZZZZZZW:$i,ZZZZZZZZZZZZZZZV:$i,ZZZZZZZZZZZZZZZU:$i,ZZZZZZZZZZZZZZZT:$i,ZZZZZZZZZZZZZZZS:$i,ZZZZZZZZZZZZZZZR:$i,ZZZZZZZZZZZZZZZQ:$i,ZZZZZZZZZZZZZZZP:$i,ZZZZZZZZZZZZZZZO:$i,ZZZZZZZZZZZZZZZN:$i,ZZZZZZZZZZZZZZZM:$i,ZZZZZZZZZZZZZZZL:$i,ZZZZZZZZZZZZZZZK:$i,ZZZZZZZZZZZZZZZJ:$i,ZZZZZZZZZZZZZZZI:$i,ZZZZZZZZZZZZZZZH:$i,ZZZZZZZZZZZZZZZG:$i,ZZZZZZZZZZZZZZZF:$i,ZZZZZZZZZZZZZZZE:$i,ZZZZZZZZZZZZZZZD:$i,ZZZZZZZZZZZZZZZC:$i,ZZZZZZZZZZZZZZZB:$i,ZZZZZZZZZZZZZZZA:$i,ZZZZZZZZZZZZZZZ:$i,ZZZZZZZZZZZZZZY:$i,ZZZZZZZZZZZZZZX:$i,ZZZZZZZZZZZZZZW:$i,ZZZZZZZZZZZZZZV:$i,ZZZZZZZZZZZZZZU:$i,ZZZZZZZZZZZZZZT:$i,ZZZZZZZZZZZZZZS:($i > $o),ZZZZZZZZZZZZZZR:$i,ZZZZZZZZZZZZZZQ:$i,ZZZZZZZZZZZZZZP:($i > $o),ZZZZZZZZZZZZZZO:$i,ZZZZZZZZZZZZZZN:$i,ZZZZZZZZZZZZZZM:($i > $o),ZZZZZZZZZZZZZZL:$i,ZZZZZZZZZZZZZZK:$i,ZZZZZZZZZZZZZZJ:($i > $o),ZZZZZZZZZZZZZZI:$i,ZZZZZZZZZZZZZZH:$i,ZZZZZZZZZZZZZZG:$i,ZZZZZZZZZZZZZZF:$i,ZZZZZZZZZZZZZZE:$i,ZZZZZZZZZZZZZZD:$i,ZZZZZZZZZZZZZZC:$i,ZZZZZZZZZZZZZZB:$i,ZZZZZZZZZZZZZZA:$i,ZZZZZZZZZZZZZZ:$i,ZZZZZZZZZZZZZY:$i,ZZZZZZZZZZZZZX:$i,ZZZZZZZZZZZZZW:$i,ZZZZZZZZZZZZZV:$i,ZZZZZZZZZZZZZU:$i,ZZZZZZZZZZZZZT:$i,ZZZZZZZZZZZZZS:$i,ZZZZZZZZZZZZZR:$i,ZZZZZZZZZZZZZQ:$i,ZZZZZZZZZZZZZP:$i,ZZZZZZZZZZZZZO:$i,ZZZZZZZZZZZZZN:$i,ZZZZZZZZZZZZZM:$i,ZZZZZZZZZZZZZL:$i,ZZZZZZZZZZZZZK:$i,ZZZZZZZZZZZZZJ:$i,ZZZZZZZZZZZZZI:$i,ZZZZZZZZZZZZZH:$i,ZZZZZZZZZZZZZG:$i,ZZZZZZZZZZZZZF:$i,ZZZZZZZZZZZZZE:$i,ZZZZZZZZZZZZZD:$i,ZZZZZZZZZZZZZC:$i,ZZZZZZZZZZZZZB:$i,ZZZZZZZZZZZZZA:$i,ZZZZZZZZZZZZZ:$i,ZZZZZZZZZZZZY:$i,ZZZZZZZZZZZZX:$i,ZZZZZZZZZZZZW:$i,ZZZZZZZZZZZZV:$i,ZZZZZZZZZZZZU:$i,ZZZZZZZZZZZZT:$i,ZZZZZZZZZZZZS:$i,ZZZZZZZZZZZZR:$i,ZZZZZZZZZZZZQ:$i,ZZZZZZZZZZZZP:$i,ZZZZZZZZZZZZO:$i,ZZZZZZZZZZZZN:$i,ZZZZZZZZZZZZM:$i,ZZZZZZZZZZZZL:$i,ZZZZZZZZZZZZK:$i,ZZZZZZZZZZZZJ:$i,ZZZZZZZZZZZZI:$i,ZZZZZZZZZZZZH:$i,ZZZZZZZZZZZZG:$i,ZZZZZZZZZZZZF:$i,ZZZZZZZZZZZZE:$i,ZZZZZZZZZZZZD:$i,ZZZZZZZZZZZZC:$i,ZZZZZZZZZZZZB:$i,ZZZZZZZZZZZZA:$i,ZZZZZZZZZZZZ:$i,ZZZZZZZZZZZY:$i,ZZZZZZZZZZZX:$i,ZZZZZZZZZZZW:$i,ZZZZZZZZZZZV:$i,ZZZZZZZZZZZU:$i,ZZZZZZZZZZZT:$i,ZZZZZZZZZZZS:$o,ZZZZZZZZZZZR:$i,ZZZZZZZZZZZQ:$i,ZZZZZZZZZZZP:$i,ZZZZZZZZZZZO:$i,ZZZZZZZZZZZN:$i,ZZZZZZZZZZZM:$i,ZZZZZZZZZZZL:$i,ZZZZZZZZZZZK:$i,ZZZZZZZZZZZJ:$i,ZZZZZZZZZZZI:$i,ZZZZZZZZZZZH:$i,ZZZZZZZZZZZG:$i,ZZZZZZZZZZZF:$i,ZZZZZZZZZZZE:$i,ZZZZZZZZZZZD:$i,ZZZZZZZZZZZC:$i,ZZZZZZZZZZZB:$i,ZZZZZZZZZZZA:$i,ZZZZZZZZZZZ:$i,ZZZZZZZZZZY:$i,ZZZZZZZZZZX:$i,ZZZZZZZZZZW:$i,ZZZZZZZZZZV:$i,ZZZZZZZZZZU:$i,ZZZZZZZZZZT:$i,ZZZZZZZZZZS:$i,ZZZZZZZZZZR:$i,ZZZZZZZZZZQ:$i,ZZZZZZZZZZP:$i,ZZZZZZZZZZO:$i,ZZZZZZZZZZN:$i,ZZZZZZZZZZM:$i,ZZZZZZZZZZL:$i,ZZZZZZZZZZK:$i,ZZZZZZZZZZJ:$i,ZZZZZZZZZZI:$i,ZZZZZZZZZZH:$i,ZZZZZZZZZZG:$i,ZZZZZZZZZZF:$i,ZZZZZZZZZZE:$i,ZZZZZZZZZZD:$i,ZZZZZZZZZZC:$i,ZZZZZZZZZZB:$i,ZZZZZZZZZZA:$i,ZZZZZZZZZZ:$i,ZZZZZZZZZY:$i,ZZZZZZZZZX:$i,ZZZZZZZZZW:$i,ZZZZZZZZZV:$i,ZZZZZZZZZU:$i,ZZZZZZZZZT:$i,ZZZZZZZZZS:$i,ZZZZZZZZZR:$i,ZZZZZZZZZQ:$i,ZZZZZZZZZP:$i,ZZZZZZZZZO:$i,ZZZZZZZZZN:$i,ZZZZZZZZZM:$i,ZZZZZZZZZL:$i,ZZZZZZZZZK:$i,ZZZZZZZZZJ:$i,ZZZZZZZZZI:$i,ZZZZZZZZZH:$i,ZZZZZZZZZG:$i,ZZZZZZZZZF:$i,ZZZZZZZZZE:$i,ZZZZZZZZZD:$o,ZZZZZZZZZC:$i,ZZZZZZZZZB:$i,ZZZZZZZZZA:$i,ZZZZZZZZZ:$i,ZZZZZZZZY:$i,ZZZZZZZZX:$i,ZZZZZZZZW:$i,ZZZZZZZZV:$i,ZZZZZZZZU:$i,ZZZZZZZZT:$i,ZZZZZZZZS:$i,ZZZZZZZZR:($i > $o),ZZZZZZZZQ:$i,ZZZZZZZZP:($i > $o),ZZZZZZZZO:$i,ZZZZZZZZN:$i,ZZZZZZZZM:$i,ZZZZZZZZL:$i,ZZZZZZZZK:$i,ZZZZZZZZJ:$i,ZZZZZZZZI:$i,ZZZZZZZZH:$i,ZZZZZZZZG:$i,ZZZZZZZZF:$i,ZZZZZZZZE:$i,ZZZZZZZZD:$i,ZZZZZZZZC:$i,ZZZZZZZZB:$i,ZZZZZZZZA:$i,ZZZZZZZZ:$i,ZZZZZZZY:$i,ZZZZZZZX:$i,ZZZZZZZW:$i,ZZZZZZZV:$i,ZZZZZZZU:$i,ZZZZZZZT:$i,ZZZZZZZS:$i,ZZZZZZZR:$i,ZZZZZZZQ:$i,ZZZZZZZP:$i,ZZZZZZZO:$i,ZZZZZZZN:$i,ZZZZZZZM:$i,ZZZZZZZL:$i,ZZZZZZZK:$i,ZZZZZZZJ:$i,ZZZZZZZI:$i,ZZZZZZZH:$i,ZZZZZZZG:$i,ZZZZZZZF:$i,ZZZZZZZE:$i,ZZZZZZZD:$i,ZZZZZZZC:$i,ZZZZZZZB:$i,ZZZZZZZA:$i,ZZZZZZZ:$i,ZZZZZZY:$i,ZZZZZZX:$i,ZZZZZZW:$i,ZZZZZZV:($i > $o),ZZZZZZU:($i > $o),ZZZZZZT:$i,ZZZZZZS:$i,ZZZZZZR:$i,ZZZZZZQ:$i,ZZZZZZP:($i > $o),ZZZZZZO:($i > $o),ZZZZZZN:$i,ZZZZZZM:$i,ZZZZZZL:$i,ZZZZZZK:($i > $o),ZZZZZZJ:$i,ZZZZZZI:$i,ZZZZZZH:$i,ZZZZZZG:$i,ZZZZZZF:$i,ZZZZZZE:$i,ZZZZZZD:$i,ZZZZZZC:$i,ZZZZZZB:($i > $o),ZZZZZZA:($i > $o),ZZZZZZ:$i,ZZZZZY:$i,ZZZZZX:$i,ZZZZZW:($i > $o),ZZZZZV:$i,ZZZZZU:$i,ZZZZZT:$i,ZZZZZS:$i,ZZZZZR:$i,ZZZZZQ:$i,ZZZZZP:$i,ZZZZZO:$i,ZZZZZN:$i,ZZZZZM:$i,ZZZZZL:($i > $o),ZZZZZK:$i,ZZZZZJ:$i,ZZZZZI:($i > $o),ZZZZZH:$i,ZZZZZG:($i > $o),ZZZZZF:$i,ZZZZZE:$i,ZZZZZD:($i > $o),ZZZZZC:$i,ZZZZZB:$o,ZZZZZA:$o,ZZZZZ:$i,ZZZZY:($i > $o),ZZZZX:$i,ZZZZW:$i,ZZZZV:($i > $o),ZZZZU:$i,ZZZZT:$i,ZZZZS:($i > $o),ZZZZR:$i,ZZZZQ:$i,ZZZZP:($i > $o),ZZZZO:$i,ZZZZN:$i,ZZZZM:($i > $o),ZZZZL:$i,ZZZZK:($i > $o),ZZZZJ:$i,ZZZZI:$i,ZZZZH:$i,ZZZZG:$i,ZZZZF:$i,ZZZZE:$i,ZZZZD:$i,ZZZZC:$i,ZZZZB:$i,ZZZZA:$i,ZZZZ:$i,ZZZY:$i,ZZZX:$i,ZZZW:$i,ZZZV:$i,ZZZU:$i,ZZZT:$i,ZZZS:$i,ZZZR:$i,ZZZQ:($i > $o),ZZZP:$i,ZZZO:$i,ZZZN:$o,ZZZM:$i,ZZZL:$i,ZZZK:$i,ZZZJ:$i,ZZZI:$i,ZZZH:$i,ZZZG:$i,ZZZF:$i,ZZZE:$i,ZZZD:$i,ZZZC:$i,ZZZB:$i,ZZZA:$i,ZZZ:$i,ZZY:$i,ZZX:$i,ZZW:$o,ZZV:$i,ZZU:$i,ZZT:$i,ZZS:$i,ZZR:$i,ZZQ:$i,ZZP:$i,ZZO:$i,ZZN:$i,ZZM:$i,ZZL:$i,ZZK:($i > $o),ZZJ:$i,ZZI:$i,ZZH:$i,ZZG:($i > $o),ZZF:$i,ZZE:$i,ZZD:$i,ZZC:$i,ZZB:$i,ZZA:$i,ZZ:($i > $o),ZY:$i,ZX:$i,ZW:$o,ZV:$i,ZU:$i,ZT:$o,ZS:$i,ZR:($i > $o),ZQ:$i,ZP:$i,ZO:($i > $o),ZN:$i,ZM:$i,ZL:($i > $o),ZK:$i,ZJ:$i,ZI:($i > $o),ZH:$i,ZG:$i,ZF:$i,ZE:$i,ZD:$i,ZC:$i,ZB:$i,ZA:$i,Z:$i,Y:$i,X:$i,W:$i,V:$i,U:$i,T:$i,S:$i,R:$i,Q:$i,P:$i,O:$i,N:($i > ($i > $o)),M:$i,L:$i,K:$i,J:$i,I:$i,H:$i,G:$i,F:$i,E:$i,D:$i,C:$i,B:$i,A:$i] : (((~ ((in @ (sk1 @ B @ A) @ A) = (in @ (sk1 @ B @ A) @ B)) | (A = B)) & ~ (in @ C @ emptyset) & ((in @ F @ (setadjoin @ D @ E)) = ((F = D) | (in @ F @ E))) & ((in @ H @ (powerset @ G)) = (! [ZZZZZZZZZZZZZZZZZN:$i]: ((in @ ZZZZZZZZZZZZZZZZZN @ H) => (in @ ZZZZZZZZZZZZZZZZZN @ G)))) & ((in @ J @ (setunion @ I)) = (? [ZZZZZZZZZZZZZZZZZN:$i]: ((in @ J @ ZZZZZZZZZZZZZZZZZN) & (in @ ZZZZZZZZZZZZZZZZZN @ I)))) & (in @ emptyset @ omega) & (~ (in @ K @ omega) | (in @ (setadjoin @ K @ K) @ omega)) & (~ (in @ emptyset @ L) | (in @ (sk2 @ L) @ omega) | ~ (in @ M @ omega) | (in @ M @ L)) & (~ (in @ emptyset @ L) | (in @ (sk2 @ L) @ L) | ~ (in @ M @ omega) | (in @ M @ L)) & (~ (in @ emptyset @ L) | ~ (in @ (setadjoin @ (sk2 @ L) @ (sk2 @ L)) @ L) | ~ (in @ M @ omega) | (in @ M @ L)) & ((in @ (sk3 @ O @ (N)) @ O) | ((in @ Q @ (sk5 @ O @ (N))) = (? [ZZZZZZZZZZZZZZZZZN:$i]: ((in @ ZZZZZZZZZZZZZZZZZN @ O) & (N @ ZZZZZZZZZZZZZZZZZN @ Q))))) & (~ (N @ (sk3 @ O @ (N)) @ P) | (N @ (sk3 @ O @ (N)) @ (sk4 @ P @ O @ (N))) | ((in @ Q @ (sk5 @ O @ (N))) = (? [ZZZZZZZZZZZZZZZZZN:$i]: ((in @ ZZZZZZZZZZZZZZZZZN @ O) & (N @ ZZZZZZZZZZZZZZZZZN @ Q))))) & (~ (N @ (sk3 @ O @ (N)) @ P) | ~ (P = (sk4 @ P @ O @ (N))) | ((in @ Q @ (sk5 @ O @ (N))) = (? [ZZZZZZZZZZZZZZZZZN:$i]: ((in @ ZZZZZZZZZZZZZZZZZN @ O) & (N @ ZZZZZZZZZZZZZZZZZN @ Q))))) & (~ (in @ S @ R) | (in @ (sk6 @ R) @ R)) & (~ (in @ S @ R) | ~ (in @ T @ (sk6 @ R)) | ~ (in @ T @ R)) & (~ (in @ V @ (sk7 @ U)) | ~ (in @ W @ V) | (in @ W @ U)) & (~ (in @ X @ U) | ~ (in @ Y @ U) | (in @ (sk8 @ Y @ X @ U) @ (sk7 @ U)) | (X = Y)) & (~ (in @ X @ U) | ~ (in @ Y @ U) | ~ ((in @ X @ (sk8 @ Y @ X @ U)) = (in @ Y @ (sk8 @ Y @ X @ U))) | (X = Y)) & (~ (in @ Z @ (sk7 @ U)) | ~ (in @ ZA @ (sk7 @ U)) | ~ (in @ ZB @ Z) | (in @ ZB @ ZA) | ~ (in @ ZC @ ZA) | (in @ ZC @ Z)) & ((in @ (sk10 @ ZD @ U) @ ZD) | ~ (in @ ZE @ ZD) | (sk9 @ U @ ZD)) & (~ (in @ (sk10 @ ZD @ U) @ U) | ~ (in @ ZE @ ZD) | (sk9 @ U @ ZD)) & (~ (sk9 @ U @ ZD) | (in @ (sk11 @ ZD @ U) @ (sk7 @ U))) & (~ (sk9 @ U @ ZD) | (in @ (sk12 @ ZD @ U) @ ZD)) & (~ (sk9 @ U @ ZD) | ~ (in @ ZF @ (sk11 @ ZD @ U)) | ~ (in @ ZF @ ZD)) & (~ (sk9 @ U @ ZD) | ~ (in @ ZG @ (sk7 @ U)) | ~ (in @ ZH @ ZG) | (in @ ZH @ (sk11 @ ZD @ U)) | (in @ (sk12 @ ZD @ U) @ ZG)) & (~ (ZI @ ZJ) | (ZI @ (sk13 @ ZJ @ (ZI))) | (ZI @ (descr @ (ZI)))) & (~ (ZI @ ZJ) | ~ (ZJ = (sk13 @ ZJ @ (ZI))) | (ZI @ (descr @ (ZI)))) & (~ (in @ ZM @ ZK) | ~ (ZL @ ZM) | (in @ ZM @ (dsetconstr @ ZK @ (ZL)))) & (~ (in @ ZP @ (dsetconstr @ ZN @ (ZO))) | (in @ ZP @ ZN)) & (~ (in @ ZS @ (dsetconstr @ ZQ @ (ZR))) | (ZR @ ZS)) & (~ (in @ ZU @ (prop2set @ ZT)) | (ZT)) & (~ (in @ ZV @ emptyset) | (ZW)) & ~ (in @ ZX @ emptyset) & ~ (in @ ZY @ emptyset) & (~ (ZZ @ ZZA) | (ZZ @ (sk14 @ ZZA @ (ZZ))) | (ZZ @ (sk15 @ (ZZ)))) & (~ (ZZ @ ZZA) | ~ (ZZA = (sk14 @ ZZA @ (ZZ))) | (ZZ @ (sk15 @ (ZZ)))) & ((in @ (sk16 @ ZZC @ ZZB) @ ZZB) | (in @ (sk17 @ ZZC @ ZZB) @ ZZC) | (ZZB = ZZC)) & ((in @ (sk16 @ ZZC @ ZZB) @ ZZB) | ~ (in @ (sk17 @ ZZC @ ZZB) @ ZZB) | (ZZB = ZZC)) & (~ (in @ (sk16 @ ZZC @ ZZB) @ ZZC) | (in @ (sk17 @ ZZC @ ZZB) @ ZZC) | (ZZB = ZZC)) & (~ (in @ (sk16 @ ZZC @ ZZB) @ ZZC) | ~ (in @ (sk17 @ ZZC @ ZZB) @ ZZB) | (ZZB = ZZC)) & ((in @ (sk18 @ ZZD) @ ZZD) | (ZZD = emptyset)) & ((in @ (sk19 @ ZZE) @ ZZE) | (ZZE = emptyset)) & (~ (in @ ZZH @ ZZF) | ((in @ ZZH @ (dsetconstr @ ZZF @ (ZZG))) = (ZZG @ ZZH))) & ((ZZI = emptyset) | (in @ (sk20 @ ZZI) @ ZZI)) & (~ (in @ ZZL @ ZZJ) | ~ (ZZK @ ZZL) | ~ ((dsetconstr @ ZZJ @ (ZZK)) = emptyset)) & (~ (in @ ZZN @ ZZM) | ~ (ZZM = emptyset)) & (in @ ZZO @ (setadjoin @ ZZO @ ZZP)) & (in @ emptyset @ (setadjoin @ emptyset @ emptyset)) & (~ (in @ ZZS @ ZZR) | (in @ ZZS @ (setadjoin @ ZZQ @ ZZR))) & (~ (in @ ZZV @ (setadjoin @ ZZT @ ZZU)) | (ZZV = ZZT) | (in @ ZZV @ ZZU) | (ZZW)) & (~ (in @ ZZV @ (setadjoin @ ZZT @ ZZU)) | (ZZV = ZZT) | ~ (ZZW) | (ZZW)) & (~ (in @ ZZV @ (setadjoin @ ZZT @ ZZU)) | ~ (ZZW) | (in @ ZZV @ ZZU) | (ZZW)) & (~ (in @ ZZV @ (setadjoin @ ZZT @ ZZU)) | ~ (ZZW) | ~ (ZZW) | (ZZW)) & (~ (in @ ZZZ @ (setadjoin @ ZZX @ ZZY)) | (ZZZ = ZZX) | (in @ ZZZ @ ZZY)) & ((dsetconstr @ ZZZA @ (^ [ZZZZZZZZZZZZZZZZZN:$i]: (($true)))) = ZZZA) & ((in @ (sk21 @ ZZZC @ ZZZB) @ ZZZC) | (in @ ZZZC @ (powerset @ ZZZB))) & (~ (in @ (sk21 @ ZZZC @ ZZZB) @ ZZZB) | (in @ ZZZC @ (powerset @ ZZZB))) & (in @ emptyset @ (powerset @ ZZZD)) & (in @ emptyset @ (powerset @ ZZZE)) & (~ (in @ ZZZG @ (powerset @ ZZZF)) | ~ (in @ ZZZH @ ZZZG) | (in @ ZZZH @ ZZZF)) & (~ (in @ ZZZJ @ ZZZK) | ~ (in @ ZZZK @ ZZZI) | (in @ ZZZJ @ (setunion @ ZZZI))) & (~ (in @ ZZZM @ (setunion @ ZZZL)) | (in @ ZZZM @ (sk22 @ ZZZN @ ZZZM @ ZZZL)) | (ZZZN)) & (~ (in @ ZZZM @ (setunion @ ZZZL)) | (in @ (sk22 @ ZZZN @ ZZZM @ ZZZL) @ ZZZL) | (ZZZN)) & (~ (in @ ZZZM @ (setunion @ ZZZL)) | ~ (ZZZN) | (ZZZN)) & (~ (in @ ZZZP @ ZZZO) | (in @ ZZZP @ (powerset @ (setunion @ ZZZO)))) & (~ (ZZZQ @ ZZZR) | (ZZZQ @ (sk23 @ ZZZR @ (ZZZQ))) | ((ZZZQ @ ZZZS) = (ZZZS = (sk24 @ (ZZZQ))))) & (~ (ZZZQ @ ZZZR) | ~ (ZZZR = (sk23 @ ZZZR @ (ZZZQ))) | ((ZZZQ @ ZZZS) = (ZZZS = (sk24 @ (ZZZQ))))) & ((ZZZT = emptyset) | (in @ (sk25 @ ZZZT) @ ZZZT)) & (~ (in @ ZZZU @ (setadjoin @ ZZZV @ emptyset)) | (ZZZU = ZZZV)) & ((ZZZW = ZZZX) | ~ (in @ ZZZX @ (setadjoin @ ZZZW @ emptyset))) & (~ (ZZZY = ZZZZ) | (in @ ZZZY @ (setadjoin @ ZZZZ @ emptyset))) & (~ (in @ ZZZZA @ (setadjoin @ ZZZZB @ emptyset)) | (in @ ZZZZB @ (setadjoin @ ZZZZA @ emptyset))) & (~ (in @ ZZZZE @ (setadjoin @ ZZZZC @ (setadjoin @ ZZZZD @ emptyset))) | (ZZZZE = ZZZZC) | (ZZZZE = ZZZZD)) & (in @ ZZZZF @ (setadjoin @ ZZZZF @ (setadjoin @ ZZZZG @ emptyset))) & (in @ ZZZZI @ (setadjoin @ ZZZZH @ (setadjoin @ ZZZZI @ emptyset))) & (~ (in @ ZZZZL @ ZZZZJ) | ~ (ZZZZK @ ZZZZL) | ~ ((dsetconstr @ ZZZZJ @ (ZZZZK)) = emptyset)) & (~ (in @ ZZZZN @ emptyset) | (ZZZZM @ ZZZZN)) & (~ (in @ ZZZZQ @ ZZZZO) | (ZZZZP @ ZZZZQ) | (in @ (sk26 @ (ZZZZP) @ ZZZZO) @ ZZZZO)) & (~ (in @ ZZZZQ @ ZZZZO) | (ZZZZP @ ZZZZQ) | ~ (ZZZZP @ (sk26 @ (ZZZZP) @ ZZZZO))) & ((in @ (sk27 @ (ZZZZS) @ ZZZZR) @ ZZZZR) | ~ (in @ ZZZZT @ ZZZZR) | ~ (ZZZZS @ ZZZZT)) & ((ZZZZS @ (sk27 @ (ZZZZS) @ ZZZZR)) | ~ (in @ ZZZZT @ ZZZZR) | ~ (ZZZZS @ ZZZZT)) & ((in @ (sk28 @ (ZZZZV) @ ZZZZU) @ ZZZZU) | ~ (in @ ZZZZW @ ZZZZU) | ~ (ZZZZV @ ZZZZW)) & ((ZZZZV @ (sk28 @ (ZZZZV) @ ZZZZU)) | ~ (in @ ZZZZW @ ZZZZU) | ~ (ZZZZV @ ZZZZW)) & (~ (in @ ZZZZZ @ ZZZZX) | (ZZZZY @ ZZZZZ) | (in @ (sk29 @ (ZZZZY) @ ZZZZX) @ ZZZZX)) & (~ (in @ ZZZZZ @ ZZZZX) | (ZZZZY @ ZZZZZ) | ~ (ZZZZY @ (sk29 @ (ZZZZY) @ ZZZZX))) & (~ (ZZZZZA) | (in @ emptyset @ (prop2set @ ZZZZZA))) & (~ (ZZZZZB) | (set2prop @ (prop2set @ ZZZZZB))) & ((in @ (sk30 @ (ZZZZZD) @ ZZZZZC) @ ZZZZZC) | ~ (in @ ZZZZZE @ ZZZZZC) | ~ (ZZZZZD @ ZZZZZE)) & ((ZZZZZD @ (sk30 @ (ZZZZZD) @ ZZZZZC)) | ~ (in @ ZZZZZE @ ZZZZZC) | ~ (ZZZZZD @ ZZZZZE)) & (~ (in @ ZZZZZH @ ZZZZZF) | (ZZZZZG @ ZZZZZH) | (in @ (sk31 @ (ZZZZZG) @ ZZZZZF) @ ZZZZZF)) & (~ (in @ ZZZZZH @ ZZZZZF) | (ZZZZZG @ ZZZZZH) | ~ (ZZZZZG @ (sk31 @ (ZZZZZG) @ ZZZZZF))) & (~ (ZZZZZI @ ZZZZZJ) | (ZZZZZI @ (sk32 @ (ZZZZZI))) | (ZZZZZI @ (sk34 @ (ZZZZZI)))) & (~ (ZZZZZI @ ZZZZZJ) | (ZZZZZI @ (sk32 @ (ZZZZZI))) | ~ (ZZZZZI @ ZZZZZK) | ((sk34 @ (ZZZZZI)) = ZZZZZK)) & (~ (ZZZZZI @ ZZZZZJ) | (ZZZZZI @ (sk33 @ (ZZZZZI))) | (ZZZZZI @ (sk34 @ (ZZZZZI)))) & (~ (ZZZZZI @ ZZZZZJ) | (ZZZZZI @ (sk33 @ (ZZZZZI))) | ~ (ZZZZZI @ ZZZZZK) | ((sk34 @ (ZZZZZI)) = ZZZZZK)) & (~ (ZZZZZI @ ZZZZZJ) | ~ ((sk32 @ (ZZZZZI)) = (sk33 @ (ZZZZZI))) | (ZZZZZI @ (sk34 @ (ZZZZZI)))) & (~ (ZZZZZI @ ZZZZZJ) | ~ ((sk32 @ (ZZZZZI)) = (sk33 @ (ZZZZZI))) | ~ (ZZZZZI @ ZZZZZK) | ((sk34 @ (ZZZZZI)) = ZZZZZK)) & (~ ((ZZZZZL @ (sk35 @ ZZZZZM @ (ZZZZZL))) = ((sk35 @ ZZZZZM @ (ZZZZZL)) = ZZZZZM)) | (ZZZZZL @ (sk36 @ (ZZZZZL)))) & (~ ((ZZZZZL @ (sk35 @ ZZZZZM @ (ZZZZZL))) = ((sk35 @ ZZZZZM @ (ZZZZZL)) = ZZZZZM)) | ~ (ZZZZZL @ ZZZZZN) | ((sk36 @ (ZZZZZL)) = ZZZZZN)) & (~ (ZZZZZO = ZZZZZP) | ~ (ZZZZZQ = ZZZZZR) | ~ (in @ ZZZZZQ @ ZZZZZO) | (in @ ZZZZZR @ ZZZZZP)) & (~ (ZZZZZS = ZZZZZT) | ~ (ZZZZZU = ZZZZZV) | ((in @ ZZZZZU @ ZZZZZS) = (in @ ZZZZZV @ ZZZZZT))) & (~ (ZZZZZW @ ZZZZZX) | (ZZZZZW @ (sk37 @ ZZZZZX @ (ZZZZZW))) | ~ (ZZZZZW @ ZZZZZY) | ~ (ZZZZZW @ ZZZZZZ) | (ZZZZZY = ZZZZZZ)) & (~ (ZZZZZW @ ZZZZZX) | ~ (ZZZZZX = (sk37 @ ZZZZZX @ (ZZZZZW))) | ~ (ZZZZZW @ ZZZZZY) | ~ (ZZZZZW @ ZZZZZZ) | (ZZZZZY = ZZZZZZ)) & (((sk38 @ (ZZZZZZB) @ (ZZZZZZA)) = (sk39 @ (ZZZZZZB) @ (ZZZZZZA))) | ((? [ZZZZZZZZZZZZZZZZZN:$i]: ((ZZZZZZA @ ZZZZZZZZZZZZZZZZZN) & ! [ZZZZZZZZZZZZZZZZZO:$i]: ((ZZZZZZA @ ZZZZZZZZZZZZZZZZZO) => (ZZZZZZZZZZZZZZZZZN = ZZZZZZZZZZZZZZZZZO)))) = (? [ZZZZZZZZZZZZZZZZZN:$i]: ((ZZZZZZB @ ZZZZZZZZZZZZZZZZZN) & ! [ZZZZZZZZZZZZZZZZZO:$i]: ((ZZZZZZB @ ZZZZZZZZZZZZZZZZZO) => (ZZZZZZZZZZZZZZZZZN = ZZZZZZZZZZZZZZZZZO)))))) & (~ ((ZZZZZZA @ (sk38 @ (ZZZZZZB) @ (ZZZZZZA))) = (ZZZZZZB @ (sk39 @ (ZZZZZZB) @ (ZZZZZZA)))) | ((? [ZZZZZZZZZZZZZZZZZN:$i]: ((ZZZZZZA @ ZZZZZZZZZZZZZZZZZN) & ! [ZZZZZZZZZZZZZZZZZO:$i]: ((ZZZZZZA @ ZZZZZZZZZZZZZZZZZO) => (ZZZZZZZZZZZZZZZZZN = ZZZZZZZZZZZZZZZZZO)))) = (? [ZZZZZZZZZZZZZZZZZN:$i]: ((ZZZZZZB @ ZZZZZZZZZZZZZZZZZN) & ! [ZZZZZZZZZZZZZZZZZO:$i]: ((ZZZZZZB @ ZZZZZZZZZZZZZZZZZO) => (ZZZZZZZZZZZZZZZZZN = ZZZZZZZZZZZZZZZZZO)))))) & (~ (ZZZZZZC = ZZZZZZD) | ~ (ZZZZZZE = ZZZZZZF) | ((setadjoin @ ZZZZZZC @ ZZZZZZE) = (setadjoin @ ZZZZZZD @ ZZZZZZF))) & (~ (ZZZZZZG = ZZZZZZH) | ((powerset @ ZZZZZZG) = (powerset @ ZZZZZZH))) & (~ (ZZZZZZI = ZZZZZZJ) | ((setunion @ ZZZZZZI) = (setunion @ ZZZZZZJ))) & (~ (ZZZZZZK @ ZZZZZZL) | (ZZZZZZK @ (sk40 @ ZZZZZZL @ (ZZZZZZK))) | ~ (ZZZZZZK @ ZZZZZZM) | ~ (ZZZZZZK @ ZZZZZZN) | (ZZZZZZM = ZZZZZZN)) & (~ (ZZZZZZK @ ZZZZZZL) | ~ (ZZZZZZL = (sk40 @ ZZZZZZL @ (ZZZZZZK))) | ~ (ZZZZZZK @ ZZZZZZM) | ~ (ZZZZZZK @ ZZZZZZN) | (ZZZZZZM = ZZZZZZN)) & (((sk42 @ (ZZZZZZP) @ (ZZZZZZO)) = (sk43 @ (ZZZZZZP) @ (ZZZZZZO))) | (sk41 @ ZZZZZZO @ ZZZZZZP)) & (~ ((ZZZZZZO @ (sk42 @ (ZZZZZZP) @ (ZZZZZZO))) = (ZZZZZZP @ (sk43 @ (ZZZZZZP) @ (ZZZZZZO)))) | (sk41 @ ZZZZZZO @ ZZZZZZP)) & (~ (sk41 @ ZZZZZZO @ ZZZZZZP) | ~ (ZZZZZZO @ ZZZZZZQ) | (ZZZZZZO @ (sk44 @ ZZZZZZQ @ (ZZZZZZP) @ (ZZZZZZO))) | ~ (ZZZZZZP @ ZZZZZZR) | (ZZZZZZP @ (sk45 @ ZZZZZZR @ (ZZZZZZP) @ (ZZZZZZO))) | ((descr @ (ZZZZZZO)) = (descr @ (ZZZZZZP)))) & (~ (sk41 @ ZZZZZZO @ ZZZZZZP) | ~ (ZZZZZZO @ ZZZZZZQ) | (ZZZZZZO @ (sk44 @ ZZZZZZQ @ (ZZZZZZP) @ (ZZZZZZO))) | ~ (ZZZZZZP @ ZZZZZZR) | ~ (ZZZZZZR = (sk45 @ ZZZZZZR @ (ZZZZZZP) @ (ZZZZZZO))) | ((descr @ (ZZZZZZO)) = (descr @ (ZZZZZZP)))) & (~ (sk41 @ ZZZZZZO @ ZZZZZZP) | ~ (ZZZZZZO @ ZZZZZZQ) | ~ (ZZZZZZQ = (sk44 @ ZZZZZZQ @ (ZZZZZZP) @ (ZZZZZZO))) | ~ (ZZZZZZP @ ZZZZZZR) | (ZZZZZZP @ (sk45 @ ZZZZZZR @ (ZZZZZZP) @ (ZZZZZZO))) | ((descr @ (ZZZZZZO)) = (descr @ (ZZZZZZP)))) & (~ (sk41 @ ZZZZZZO @ ZZZZZZP) | ~ (ZZZZZZO @ ZZZZZZQ) | ~ (ZZZZZZQ = (sk44 @ ZZZZZZQ @ (ZZZZZZP) @ (ZZZZZZO))) | ~ (ZZZZZZP @ ZZZZZZR) | ~ (ZZZZZZR = (sk45 @ ZZZZZZR @ (ZZZZZZP) @ (ZZZZZZO))) | ((descr @ (ZZZZZZO)) = (descr @ (ZZZZZZP)))) & (~ (ZZZZZZS = ZZZZZZT) | (in @ (sk46 @ (ZZZZZZV) @ (ZZZZZZU) @ ZZZZZZT @ ZZZZZZS) @ ZZZZZZS) | ((dsetconstr @ ZZZZZZS @ (ZZZZZZU)) = (dsetconstr @ ZZZZZZT @ (ZZZZZZV)))) & (~ (ZZZZZZS = ZZZZZZT) | (in @ (sk47 @ (ZZZZZZV) @ (ZZZZZZU) @ ZZZZZZT @ ZZZZZZS) @ ZZZZZZT) | ((dsetconstr @ ZZZZZZS @ (ZZZZZZU)) = (dsetconstr @ ZZZZZZT @ (ZZZZZZV)))) & (~ (ZZZZZZS = ZZZZZZT) | ((sk46 @ (ZZZZZZV) @ (ZZZZZZU) @ ZZZZZZT @ ZZZZZZS) = (sk47 @ (ZZZZZZV) @ (ZZZZZZU) @ ZZZZZZT @ ZZZZZZS)) | ((dsetconstr @ ZZZZZZS @ (ZZZZZZU)) = (dsetconstr @ ZZZZZZT @ (ZZZZZZV)))) & (~ (ZZZZZZS = ZZZZZZT) | ~ ((ZZZZZZU @ (sk46 @ (ZZZZZZV) @ (ZZZZZZU) @ ZZZZZZT @ ZZZZZZS)) = (ZZZZZZV @ (sk47 @ (ZZZZZZV) @ (ZZZZZZU) @ ZZZZZZT @ ZZZZZZS))) | ((dsetconstr @ ZZZZZZS @ (ZZZZZZU)) = (dsetconstr @ ZZZZZZT @ (ZZZZZZV)))) & ((in @ (sk48 @ ZZZZZZX @ ZZZZZZW) @ ZZZZZZW) | (subset @ ZZZZZZW @ ZZZZZZX)) & (~ (in @ (sk48 @ ZZZZZZX @ ZZZZZZW) @ ZZZZZZX) | (subset @ ZZZZZZW @ ZZZZZZX)) & (~ (ZZZZZZY = ZZZZZZZ) | (subset @ ZZZZZZZ @ ZZZZZZY)) & (~ (ZZZZZZZA = ZZZZZZZB) | (subset @ ZZZZZZZA @ ZZZZZZZB)) & ((in @ (sk49 @ ZZZZZZZD @ ZZZZZZZC) @ ZZZZZZZC) | (subset @ ZZZZZZZC @ ZZZZZZZD)) & (~ (in @ (sk49 @ ZZZZZZZD @ ZZZZZZZC) @ ZZZZZZZD) | (subset @ ZZZZZZZC @ ZZZZZZZD)) & (subset @ emptyset @ ZZZZZZZE) & (~ (subset @ ZZZZZZZF @ ZZZZZZZG) | ~ (in @ ZZZZZZZH @ ZZZZZZZF) | (in @ ZZZZZZZH @ ZZZZZZZG)) & (~ (subset @ ZZZZZZZI @ ZZZZZZZJ) | (in @ ZZZZZZZK @ ZZZZZZZJ) | ~ (in @ ZZZZZZZK @ ZZZZZZZI)) & (~ (in @ ZZZZZZZN @ ZZZZZZZL) | (in @ ZZZZZZZN @ ZZZZZZZM) | ~ (subset @ ZZZZZZZL @ ZZZZZZZM)) & ((subset @ ZZZZZZZO @ ZZZZZZZP) | ~ (ZZZZZZZO = ZZZZZZZP)) & (~ (in @ ZZZZZZZS @ ZZZZZZZQ) | (in @ ZZZZZZZS @ ZZZZZZZR) | ~ (ZZZZZZZQ = ZZZZZZZR)) & (subset @ ZZZZZZZT @ ZZZZZZZT) & (~ (subset @ ZZZZZZZU @ ZZZZZZZV) | ~ (subset @ ZZZZZZZV @ ZZZZZZZW) | (subset @ ZZZZZZZU @ ZZZZZZZW)) & (subset @ ZZZZZZZY @ (setadjoin @ ZZZZZZZX @ ZZZZZZZY)) & (~ (subset @ ZZZZZZZZ @ ZZZZZZZZB) | (subset @ ZZZZZZZZ @ (setadjoin @ ZZZZZZZZA @ ZZZZZZZZB))) & (~ (subset @ ZZZZZZZZC @ ZZZZZZZZD) | (in @ ZZZZZZZZC @ (powerset @ ZZZZZZZZD))) & (~ (subset @ ZZZZZZZZE @ ZZZZZZZZF) | ~ (subset @ ZZZZZZZZF @ ZZZZZZZZE) | (ZZZZZZZZE = ZZZZZZZZF)) & (~ (subset @ ZZZZZZZZG @ emptyset) | (ZZZZZZZZG = emptyset)) & (~ (subset @ ZZZZZZZZI @ ZZZZZZZZH) | (in @ ZZZZZZZZI @ (powerset @ ZZZZZZZZH))) & (~ (in @ ZZZZZZZZK @ (powerset @ ZZZZZZZZJ)) | (subset @ ZZZZZZZZK @ ZZZZZZZZJ)) & (in @ ZZZZZZZZL @ (powerset @ ZZZZZZZZL)) & (~ (subset @ ZZZZZZZZM @ ZZZZZZZZN) | (subset @ (powerset @ ZZZZZZZZM) @ (powerset @ ZZZZZZZZN))) & (in @ (dsetconstr @ ZZZZZZZZO @ (ZZZZZZZZP)) @ (powerset @ ZZZZZZZZO)) & (subset @ (dsetconstr @ ZZZZZZZZQ @ (ZZZZZZZZR)) @ ZZZZZZZZQ) & (~ (in @ ZZZZZZZZU @ ZZZZZZZZS) | (in @ ZZZZZZZZU @ (binunion @ ZZZZZZZZS @ ZZZZZZZZT))) & (in @ ZZZZZZZZW @ (setadjoin @ ZZZZZZZZV @ (setadjoin @ ZZZZZZZZW @ emptyset))) & (~ (in @ ZZZZZZZZZ @ ZZZZZZZZY) | (in @ ZZZZZZZZZ @ (binunion @ ZZZZZZZZX @ ZZZZZZZZY))) & (~ (in @ ZZZZZZZZZC @ (binunion @ ZZZZZZZZZA @ ZZZZZZZZZB)) | (in @ ZZZZZZZZZC @ ZZZZZZZZZA) | (in @ ZZZZZZZZZC @ ZZZZZZZZZB) | (ZZZZZZZZZD)) & (~ (in @ ZZZZZZZZZC @ (binunion @ ZZZZZZZZZA @ ZZZZZZZZZB)) | (in @ ZZZZZZZZZC @ ZZZZZZZZZA) | ~ (ZZZZZZZZZD) | (ZZZZZZZZZD)) & (~ (in @ ZZZZZZZZZC @ (binunion @ ZZZZZZZZZA @ ZZZZZZZZZB)) | ~ (ZZZZZZZZZD) | (in @ ZZZZZZZZZC @ ZZZZZZZZZB) | (ZZZZZZZZZD)) & (~ (in @ ZZZZZZZZZC @ (binunion @ ZZZZZZZZZA @ ZZZZZZZZZB)) | ~ (ZZZZZZZZZD) | ~ (ZZZZZZZZZD) | (ZZZZZZZZZD)) & (~ (in @ ZZZZZZZZZG @ (binunion @ ZZZZZZZZZE @ ZZZZZZZZZF)) | (in @ ZZZZZZZZZG @ ZZZZZZZZZE) | (in @ ZZZZZZZZZG @ ZZZZZZZZZF)) & (subset @ ZZZZZZZZZH @ (binunion @ ZZZZZZZZZH @ ZZZZZZZZZI)) & (subset @ ZZZZZZZZZK @ (binunion @ ZZZZZZZZZJ @ ZZZZZZZZZK)) & (~ (in @ ZZZZZZZZZN @ ZZZZZZZZZL) | ~ (in @ ZZZZZZZZZN @ ZZZZZZZZZM) | (in @ ZZZZZZZZZN @ (binintersect @ ZZZZZZZZZL @ ZZZZZZZZZM))) & (~ (subset @ ZZZZZZZZZQ @ ZZZZZZZZZO) | ~ (subset @ ZZZZZZZZZQ @ ZZZZZZZZZP) | (subset @ ZZZZZZZZZQ @ (binintersect @ ZZZZZZZZZO @ ZZZZZZZZZP))) & (~ (in @ ZZZZZZZZZT @ (binintersect @ ZZZZZZZZZR @ ZZZZZZZZZS)) | (in @ ZZZZZZZZZT @ ZZZZZZZZZR)) & (subset @ (binintersect @ ZZZZZZZZZU @ ZZZZZZZZZV) @ ZZZZZZZZZU) & (~ (subset @ ZZZZZZZZZW @ ZZZZZZZZZX) | ((binintersect @ ZZZZZZZZZW @ ZZZZZZZZZX) = ZZZZZZZZZW)) & (~ ((binintersect @ ZZZZZZZZZY @ ZZZZZZZZZZ) = ZZZZZZZZZZ) | (subset @ ZZZZZZZZZZ @ ZZZZZZZZZY)) & (~ (in @ ZZZZZZZZZZC @ (binintersect @ ZZZZZZZZZZA @ ZZZZZZZZZZB)) | (in @ ZZZZZZZZZZC @ ZZZZZZZZZZB)) & ((in @ (sk50 @ ZZZZZZZZZZE @ ZZZZZZZZZZD) @ ZZZZZZZZZZD) | ((binintersect @ ZZZZZZZZZZD @ ZZZZZZZZZZE) = emptyset)) & ((in @ (sk50 @ ZZZZZZZZZZE @ ZZZZZZZZZZD) @ ZZZZZZZZZZE) | ((binintersect @ ZZZZZZZZZZD @ ZZZZZZZZZZE) = emptyset)) & (subset @ (binintersect @ ZZZZZZZZZZF @ ZZZZZZZZZZG) @ ZZZZZZZZZZG) & (~ (subset @ ZZZZZZZZZZI @ ZZZZZZZZZZH) | ((binintersect @ ZZZZZZZZZZH @ ZZZZZZZZZZI) = ZZZZZZZZZZI)) & (~ ((binintersect @ ZZZZZZZZZZJ @ ZZZZZZZZZZK) = ZZZZZZZZZZJ) | (subset @ ZZZZZZZZZZJ @ ZZZZZZZZZZK)) & ((binintersect @ ZZZZZZZZZZL @ (binunion @ ZZZZZZZZZZM @ ZZZZZZZZZZN)) = (binunion @ (binintersect @ ZZZZZZZZZZL @ ZZZZZZZZZZM) @ (binintersect @ ZZZZZZZZZZL @ ZZZZZZZZZZN))) & (~ (in @ ZZZZZZZZZZQ @ ZZZZZZZZZZO) | (in @ ZZZZZZZZZZQ @ ZZZZZZZZZZP) | (in @ ZZZZZZZZZZQ @ (setminus @ ZZZZZZZZZZO @ ZZZZZZZZZZP))) & (~ (in @ ZZZZZZZZZZT @ (setminus @ ZZZZZZZZZZR @ ZZZZZZZZZZS)) | (in @ ZZZZZZZZZZT @ ZZZZZZZZZZR)) & (~ (in @ ZZZZZZZZZZW @ (setminus @ ZZZZZZZZZZU @ ZZZZZZZZZZV)) | ~ (in @ ZZZZZZZZZZW @ ZZZZZZZZZZV)) & (~ (subset @ ZZZZZZZZZZX @ ZZZZZZZZZZY) | ((setminus @ ZZZZZZZZZZX @ ZZZZZZZZZZY) = emptyset)) & ((in @ ZZZZZZZZZZZB @ (setminus @ ZZZZZZZZZZZ @ ZZZZZZZZZZZA)) | ~ (in @ ZZZZZZZZZZZB @ ZZZZZZZZZZZ) | (in @ ZZZZZZZZZZZB @ ZZZZZZZZZZZA)) & ((in @ ZZZZZZZZZZZE @ (setminus @ ZZZZZZZZZZZC @ ZZZZZZZZZZZD)) | (in @ ZZZZZZZZZZZE @ ZZZZZZZZZZZD) | ~ (in @ ZZZZZZZZZZZE @ ZZZZZZZZZZZC)) & ((in @ ZZZZZZZZZZZH @ ZZZZZZZZZZZF) | ~ (in @ ZZZZZZZZZZZH @ (setminus @ ZZZZZZZZZZZF @ ZZZZZZZZZZZG))) & (~ (in @ ZZZZZZZZZZZK @ ZZZZZZZZZZZJ) | ~ (in @ ZZZZZZZZZZZK @ (setminus @ ZZZZZZZZZZZI @ ZZZZZZZZZZZJ))) & (subset @ (setminus @ ZZZZZZZZZZZL @ ZZZZZZZZZZZM) @ ZZZZZZZZZZZL) & (~ ((setminus @ ZZZZZZZZZZZN @ ZZZZZZZZZZZO) = emptyset) | (subset @ ZZZZZZZZZZZN @ ZZZZZZZZZZZO)) & (~ (in @ ZZZZZZZZZZZR @ (symdiff @ ZZZZZZZZZZZP @ ZZZZZZZZZZZQ)) | (in @ ZZZZZZZZZZZR @ ZZZZZZZZZZZP) | ~ (in @ ZZZZZZZZZZZR @ ZZZZZZZZZZZP) | (ZZZZZZZZZZZS)) & (~ (in @ ZZZZZZZZZZZR @ (symdiff @ ZZZZZZZZZZZP @ ZZZZZZZZZZZQ)) | (in @ ZZZZZZZZZZZR @ ZZZZZZZZZZZP) | (in @ ZZZZZZZZZZZR @ ZZZZZZZZZZZQ) | (ZZZZZZZZZZZS)) & (~ (in @ ZZZZZZZZZZZR @ (symdiff @ ZZZZZZZZZZZP @ ZZZZZZZZZZZQ)) | (in @ ZZZZZZZZZZZR @ ZZZZZZZZZZZP) | ~ (ZZZZZZZZZZZS) | (ZZZZZZZZZZZS)) & (~ (in @ ZZZZZZZZZZZR @ (symdiff @ ZZZZZZZZZZZP @ ZZZZZZZZZZZQ)) | ~ (in @ ZZZZZZZZZZZR @ ZZZZZZZZZZZQ) | ~ (in @ ZZZZZZZZZZZR @ ZZZZZZZZZZZP) | (ZZZZZZZZZZZS)) & (~ (in @ ZZZZZZZZZZZR @ (symdiff @ ZZZZZZZZZZZP @ ZZZZZZZZZZZQ)) | ~ (in @ ZZZZZZZZZZZR @ ZZZZZZZZZZZQ) | (in @ ZZZZZZZZZZZR @ ZZZZZZZZZZZQ) | (ZZZZZZZZZZZS)) & (~ (in @ ZZZZZZZZZZZR @ (symdiff @ ZZZZZZZZZZZP @ ZZZZZZZZZZZQ)) | ~ (in @ ZZZZZZZZZZZR @ ZZZZZZZZZZZQ) | ~ (ZZZZZZZZZZZS) | (ZZZZZZZZZZZS)) & (~ (in @ ZZZZZZZZZZZR @ (symdiff @ ZZZZZZZZZZZP @ ZZZZZZZZZZZQ)) | ~ (ZZZZZZZZZZZS) | ~ (in @ ZZZZZZZZZZZR @ ZZZZZZZZZZZP) | (ZZZZZZZZZZZS)) & (~ (in @ ZZZZZZZZZZZR @ (symdiff @ ZZZZZZZZZZZP @ ZZZZZZZZZZZQ)) | ~ (ZZZZZZZZZZZS) | (in @ ZZZZZZZZZZZR @ ZZZZZZZZZZZQ) | (ZZZZZZZZZZZS)) & (~ (in @ ZZZZZZZZZZZR @ (symdiff @ ZZZZZZZZZZZP @ ZZZZZZZZZZZQ)) | ~ (ZZZZZZZZZZZS) | ~ (ZZZZZZZZZZZS) | (ZZZZZZZZZZZS)) & (~ (in @ ZZZZZZZZZZZV @ ZZZZZZZZZZZT) | (in @ ZZZZZZZZZZZV @ ZZZZZZZZZZZU) | (in @ ZZZZZZZZZZZV @ (symdiff @ ZZZZZZZZZZZT @ ZZZZZZZZZZZU))) & ((in @ ZZZZZZZZZZZY @ ZZZZZZZZZZZW) | ~ (in @ ZZZZZZZZZZZY @ ZZZZZZZZZZZX) | (in @ ZZZZZZZZZZZY @ (symdiff @ ZZZZZZZZZZZW @ ZZZZZZZZZZZX))) & (~ (in @ ZZZZZZZZZZZZB @ ZZZZZZZZZZZZ) | ~ (in @ ZZZZZZZZZZZZB @ ZZZZZZZZZZZZA) | ~ (in @ ZZZZZZZZZZZZB @ (symdiff @ ZZZZZZZZZZZZ @ ZZZZZZZZZZZZA))) & ((in @ ZZZZZZZZZZZZE @ ZZZZZZZZZZZZC) | (in @ ZZZZZZZZZZZZE @ ZZZZZZZZZZZZD) | ~ (in @ ZZZZZZZZZZZZE @ (symdiff @ ZZZZZZZZZZZZC @ ZZZZZZZZZZZZD))) & (in @ ZZZZZZZZZZZZG @ (setadjoin @ ZZZZZZZZZZZZF @ (setadjoin @ ZZZZZZZZZZZZG @ emptyset))) & (in @ ZZZZZZZZZZZZH @ (setunion @ (setadjoin @ (setadjoin @ ZZZZZZZZZZZZH @ emptyset) @ (setadjoin @ (setadjoin @ ZZZZZZZZZZZZH @ (setadjoin @ ZZZZZZZZZZZZI @ emptyset)) @ emptyset)))) & (in @ ZZZZZZZZZZZZK @ (setunion @ (setadjoin @ (setadjoin @ ZZZZZZZZZZZZJ @ emptyset) @ (setadjoin @ (setadjoin @ ZZZZZZZZZZZZJ @ (setadjoin @ ZZZZZZZZZZZZK @ emptyset)) @ emptyset)))) & (iskpair @ (setadjoin @ (setadjoin @ ZZZZZZZZZZZZL @ emptyset) @ (setadjoin @ (setadjoin @ ZZZZZZZZZZZZL @ (setadjoin @ ZZZZZZZZZZZZM @ emptyset)) @ emptyset))) & (iskpair @ (kpair @ ZZZZZZZZZZZZN @ ZZZZZZZZZZZZO)) & (~ (in @ ZZZZZZZZZZZZQ @ ZZZZZZZZZZZZP) | (subset @ (setadjoin @ ZZZZZZZZZZZZQ @ emptyset) @ ZZZZZZZZZZZZP)) & (~ (in @ ZZZZZZZZZZZZS @ ZZZZZZZZZZZZR) | (in @ (setadjoin @ ZZZZZZZZZZZZS @ emptyset) @ (powerset @ ZZZZZZZZZZZZR))) & (~ (in @ ZZZZZZZZZZZZV @ ZZZZZZZZZZZZT) | (in @ (setadjoin @ ZZZZZZZZZZZZV @ emptyset) @ (powerset @ (binunion @ ZZZZZZZZZZZZT @ ZZZZZZZZZZZZU)))) & (~ (in @ ZZZZZZZZZZZZY @ (setadjoin @ ZZZZZZZZZZZZW @ (setadjoin @ ZZZZZZZZZZZZX @ emptyset))) | (ZZZZZZZZZZZZY = ZZZZZZZZZZZZW) | (ZZZZZZZZZZZZY = ZZZZZZZZZZZZX)) & (~ (in @ ZZZZZZZZZZZZZB @ ZZZZZZZZZZZZZ) | ~ (in @ ZZZZZZZZZZZZZC @ ZZZZZZZZZZZZZA) | (subset @ (setadjoin @ ZZZZZZZZZZZZZB @ (setadjoin @ ZZZZZZZZZZZZZC @ emptyset)) @ (binunion @ ZZZZZZZZZZZZZ @ ZZZZZZZZZZZZZA))) & (~ (in @ ZZZZZZZZZZZZZF @ ZZZZZZZZZZZZZD) | ~ (in @ ZZZZZZZZZZZZZG @ ZZZZZZZZZZZZZE) | (in @ (setadjoin @ ZZZZZZZZZZZZZF @ (setadjoin @ ZZZZZZZZZZZZZG @ emptyset)) @ (powerset @ (binunion @ ZZZZZZZZZZZZZD @ ZZZZZZZZZZZZZE)))) & (~ (in @ ZZZZZZZZZZZZZJ @ ZZZZZZZZZZZZZH) | ~ (in @ ZZZZZZZZZZZZZK @ ZZZZZZZZZZZZZI) | (subset @ (setadjoin @ (setadjoin @ ZZZZZZZZZZZZZJ @ emptyset) @ (setadjoin @ (setadjoin @ ZZZZZZZZZZZZZJ @ (setadjoin @ ZZZZZZZZZZZZZK @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ ZZZZZZZZZZZZZH @ ZZZZZZZZZZZZZI)))) & (~ (in @ ZZZZZZZZZZZZZN @ ZZZZZZZZZZZZZL) | ~ (in @ ZZZZZZZZZZZZZO @ ZZZZZZZZZZZZZM) | (in @ (setadjoin @ (setadjoin @ ZZZZZZZZZZZZZN @ emptyset) @ (setadjoin @ (setadjoin @ ZZZZZZZZZZZZZN @ (setadjoin @ ZZZZZZZZZZZZZO @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ ZZZZZZZZZZZZZL @ ZZZZZZZZZZZZZM))))) & (~ (in @ ZZZZZZZZZZZZZR @ ZZZZZZZZZZZZZP) | ~ (in @ ZZZZZZZZZZZZZS @ ZZZZZZZZZZZZZQ) | (in @ (kpair @ ZZZZZZZZZZZZZR @ ZZZZZZZZZZZZZS) @ (powerset @ (powerset @ (binunion @ ZZZZZZZZZZZZZP @ ZZZZZZZZZZZZZQ))))) & (~ (in @ ZZZZZZZZZZZZZV @ ZZZZZZZZZZZZZT) | ~ (in @ ZZZZZZZZZZZZZW @ ZZZZZZZZZZZZZU) | (in @ (kpair @ ZZZZZZZZZZZZZV @ ZZZZZZZZZZZZZW) @ (cartprod @ ZZZZZZZZZZZZZT @ ZZZZZZZZZZZZZU))) & (~ (in @ ZZZZZZZZZZZZZZ @ (cartprod @ ZZZZZZZZZZZZZX @ ZZZZZZZZZZZZZY)) | (in @ (sk51 @ ZZZZZZZZZZZZZZ @ ZZZZZZZZZZZZZY @ ZZZZZZZZZZZZZX) @ ZZZZZZZZZZZZZX)) & (~ (in @ ZZZZZZZZZZZZZZ @ (cartprod @ ZZZZZZZZZZZZZX @ ZZZZZZZZZZZZZY)) | (in @ (sk52 @ ZZZZZZZZZZZZZZ @ ZZZZZZZZZZZZZY @ ZZZZZZZZZZZZZX) @ ZZZZZZZZZZZZZY)) & (~ (in @ ZZZZZZZZZZZZZZ @ (cartprod @ ZZZZZZZZZZZZZX @ ZZZZZZZZZZZZZY)) | (ZZZZZZZZZZZZZZ = (kpair @ (sk51 @ ZZZZZZZZZZZZZZ @ ZZZZZZZZZZZZZY @ ZZZZZZZZZZZZZX) @ (sk52 @ ZZZZZZZZZZZZZZ @ ZZZZZZZZZZZZZY @ ZZZZZZZZZZZZZX)))) & (~ (in @ ZZZZZZZZZZZZZZC @ (cartprod @ ZZZZZZZZZZZZZZA @ ZZZZZZZZZZZZZZB)) | (iskpair @ ZZZZZZZZZZZZZZC)) & (~ (in @ ZZZZZZZZZZZZZZE @ (setunion @ ZZZZZZZZZZZZZZD)) | (in @ (sk53 @ ZZZZZZZZZZZZZZE @ ZZZZZZZZZZZZZZD) @ ZZZZZZZZZZZZZZD)) & (~ (in @ ZZZZZZZZZZZZZZE @ (setunion @ ZZZZZZZZZZZZZZD)) | (in @ ZZZZZZZZZZZZZZE @ (sk53 @ ZZZZZZZZZZZZZZE @ ZZZZZZZZZZZZZZD))) & (subset @ (setunion @ (setadjoin @ ZZZZZZZZZZZZZZF @ emptyset)) @ ZZZZZZZZZZZZZZF) & (subset @ ZZZZZZZZZZZZZZG @ (setunion @ (setadjoin @ ZZZZZZZZZZZZZZG @ emptyset))) & ((setunion @ (setadjoin @ ZZZZZZZZZZZZZZH @ emptyset)) = ZZZZZZZZZZZZZZH) & ((in @ (sk54 @ (ZZZZZZZZZZZZZZJ) @ ZZZZZZZZZZZZZZI) @ ZZZZZZZZZZZZZZI) | ~ (in @ ZZZZZZZZZZZZZZK @ ZZZZZZZZZZZZZZI) | ~ (ZZZZZZZZZZZZZZJ @ ZZZZZZZZZZZZZZK) | (in @ (sk56 @ (ZZZZZZZZZZZZZZJ) @ ZZZZZZZZZZZZZZI) @ (dsetconstr @ ZZZZZZZZZZZZZZI @ (ZZZZZZZZZZZZZZJ)))) & ((in @ (sk54 @ (ZZZZZZZZZZZZZZJ) @ ZZZZZZZZZZZZZZI) @ ZZZZZZZZZZZZZZI) | ~ (in @ ZZZZZZZZZZZZZZK @ ZZZZZZZZZZZZZZI) | ~ (ZZZZZZZZZZZZZZJ @ ZZZZZZZZZZZZZZK) | ((dsetconstr @ ZZZZZZZZZZZZZZI @ (ZZZZZZZZZZZZZZJ)) = (setadjoin @ (sk56 @ (ZZZZZZZZZZZZZZJ) @ ZZZZZZZZZZZZZZI) @ emptyset))) & ((in @ (sk55 @ (ZZZZZZZZZZZZZZJ) @ ZZZZZZZZZZZZZZI) @ ZZZZZZZZZZZZZZI) | ~ (in @ ZZZZZZZZZZZZZZK @ ZZZZZZZZZZZZZZI) | ~ (ZZZZZZZZZZZZZZJ @ ZZZZZZZZZZZZZZK) | (in @ (sk56 @ (ZZZZZZZZZZZZZZJ) @ ZZZZZZZZZZZZZZI) @ (dsetconstr @ ZZZZZZZZZZZZZZI @ (ZZZZZZZZZZZZZZJ)))) & ((in @ (sk55 @ (ZZZZZZZZZZZZZZJ) @ ZZZZZZZZZZZZZZI) @ ZZZZZZZZZZZZZZI) | ~ (in @ ZZZZZZZZZZZZZZK @ ZZZZZZZZZZZZZZI) | ~ (ZZZZZZZZZZZZZZJ @ ZZZZZZZZZZZZZZK) | ((dsetconstr @ ZZZZZZZZZZZZZZI @ (ZZZZZZZZZZZZZZJ)) = (setadjoin @ (sk56 @ (ZZZZZZZZZZZZZZJ) @ ZZZZZZZZZZZZZZI) @ emptyset))) & ((ZZZZZZZZZZZZZZJ @ (sk54 @ (ZZZZZZZZZZZZZZJ) @ ZZZZZZZZZZZZZZI)) | ~ (in @ ZZZZZZZZZZZZZZK @ ZZZZZZZZZZZZZZI) | ~ (ZZZZZZZZZZZZZZJ @ ZZZZZZZZZZZZZZK) | (in @ (sk56 @ (ZZZZZZZZZZZZZZJ) @ ZZZZZZZZZZZZZZI) @ (dsetconstr @ ZZZZZZZZZZZZZZI @ (ZZZZZZZZZZZZZZJ)))) & ((ZZZZZZZZZZZZZZJ @ (sk54 @ (ZZZZZZZZZZZZZZJ) @ ZZZZZZZZZZZZZZI)) | ~ (in @ ZZZZZZZZZZZZZZK @ ZZZZZZZZZZZZZZI) | ~ (ZZZZZZZZZZZZZZJ @ ZZZZZZZZZZZZZZK) | ((dsetconstr @ ZZZZZZZZZZZZZZI @ (ZZZZZZZZZZZZZZJ)) = (setadjoin @ (sk56 @ (ZZZZZZZZZZZZZZJ) @ ZZZZZZZZZZZZZZI) @ emptyset))) & ((ZZZZZZZZZZZZZZJ @ (sk55 @ (ZZZZZZZZZZZZZZJ) @ ZZZZZZZZZZZZZZI)) | ~ (in @ ZZZZZZZZZZZZZZK @ ZZZZZZZZZZZZZZI) | ~ (ZZZZZZZZZZZZZZJ @ ZZZZZZZZZZZZZZK) | (in @ (sk56 @ (ZZZZZZZZZZZZZZJ) @ ZZZZZZZZZZZZZZI) @ (dsetconstr @ ZZZZZZZZZZZZZZI @ (ZZZZZZZZZZZZZZJ)))) & ((ZZZZZZZZZZZZZZJ @ (sk55 @ (ZZZZZZZZZZZZZZJ) @ ZZZZZZZZZZZZZZI)) | ~ (in @ ZZZZZZZZZZZZZZK @ ZZZZZZZZZZZZZZI) | ~ (ZZZZZZZZZZZZZZJ @ ZZZZZZZZZZZZZZK) | ((dsetconstr @ ZZZZZZZZZZZZZZI @ (ZZZZZZZZZZZZZZJ)) = (setadjoin @ (sk56 @ (ZZZZZZZZZZZZZZJ) @ ZZZZZZZZZZZZZZI) @ emptyset))) & (~ ((sk54 @ (ZZZZZZZZZZZZZZJ) @ ZZZZZZZZZZZZZZI) = (sk55 @ (ZZZZZZZZZZZZZZJ) @ ZZZZZZZZZZZZZZI)) | ~ (in @ ZZZZZZZZZZZZZZK @ ZZZZZZZZZZZZZZI) | ~ (ZZZZZZZZZZZZZZJ @ ZZZZZZZZZZZZZZK) | (in @ (sk56 @ (ZZZZZZZZZZZZZZJ) @ ZZZZZZZZZZZZZZI) @ (dsetconstr @ ZZZZZZZZZZZZZZI @ (ZZZZZZZZZZZZZZJ)))) & (~ ((sk54 @ (ZZZZZZZZZZZZZZJ) @ ZZZZZZZZZZZZZZI) = (sk55 @ (ZZZZZZZZZZZZZZJ) @ ZZZZZZZZZZZZZZI)) | ~ (in @ ZZZZZZZZZZZZZZK @ ZZZZZZZZZZZZZZI) | ~ (ZZZZZZZZZZZZZZJ @ ZZZZZZZZZZZZZZK) | ((dsetconstr @ ZZZZZZZZZZZZZZI @ (ZZZZZZZZZZZZZZJ)) = (setadjoin @ (sk56 @ (ZZZZZZZZZZZZZZJ) @ ZZZZZZZZZZZZZZI) @ emptyset))) & (~ (in @ ZZZZZZZZZZZZZZN @ (dsetconstr @ ZZZZZZZZZZZZZZL @ (ZZZZZZZZZZZZZZM))) | ~ ((dsetconstr @ ZZZZZZZZZZZZZZL @ (ZZZZZZZZZZZZZZM)) = (setadjoin @ ZZZZZZZZZZZZZZN @ emptyset)) | (in @ (sk57 @ (ZZZZZZZZZZZZZZM) @ ZZZZZZZZZZZZZZL) @ ZZZZZZZZZZZZZZL)) & (~ (in @ ZZZZZZZZZZZZZZN @ (dsetconstr @ ZZZZZZZZZZZZZZL @ (ZZZZZZZZZZZZZZM))) | ~ ((dsetconstr @ ZZZZZZZZZZZZZZL @ (ZZZZZZZZZZZZZZM)) = (setadjoin @ ZZZZZZZZZZZZZZN @ emptyset)) | (ZZZZZZZZZZZZZZM @ (sk57 @ (ZZZZZZZZZZZZZZM) @ ZZZZZZZZZZZZZZL))) & (~ (in @ ZZZZZZZZZZZZZZQ @ ZZZZZZZZZZZZZZO) | ~ (ZZZZZZZZZZZZZZP @ ZZZZZZZZZZZZZZQ) | (in @ (sk58 @ ZZZZZZZZZZZZZZQ @ (ZZZZZZZZZZZZZZP) @ ZZZZZZZZZZZZZZO) @ ZZZZZZZZZZZZZZO) | (in @ (sk59 @ ZZZZZZZZZZZZZZQ @ (ZZZZZZZZZZZZZZP) @ ZZZZZZZZZZZZZZO) @ (dsetconstr @ ZZZZZZZZZZZZZZO @ (ZZZZZZZZZZZZZZP)))) & (~ (in @ ZZZZZZZZZZZZZZQ @ ZZZZZZZZZZZZZZO) | ~ (ZZZZZZZZZZZZZZP @ ZZZZZZZZZZZZZZQ) | (in @ (sk58 @ ZZZZZZZZZZZZZZQ @ (ZZZZZZZZZZZZZZP) @ ZZZZZZZZZZZZZZO) @ ZZZZZZZZZZZZZZO) | ((dsetconstr @ ZZZZZZZZZZZZZZO @ (ZZZZZZZZZZZZZZP)) = (setadjoin @ (sk59 @ ZZZZZZZZZZZZZZQ @ (ZZZZZZZZZZZZZZP) @ ZZZZZZZZZZZZZZO) @ emptyset))) & (~ (in @ ZZZZZZZZZZZZZZQ @ ZZZZZZZZZZZZZZO) | ~ (ZZZZZZZZZZZZZZP @ ZZZZZZZZZZZZZZQ) | (ZZZZZZZZZZZZZZP @ (sk58 @ ZZZZZZZZZZZZZZQ @ (ZZZZZZZZZZZZZZP) @ ZZZZZZZZZZZZZZO)) | (in @ (sk59 @ ZZZZZZZZZZZZZZQ @ (ZZZZZZZZZZZZZZP) @ ZZZZZZZZZZZZZZO) @ (dsetconstr @ ZZZZZZZZZZZZZZO @ (ZZZZZZZZZZZZZZP)))) & (~ (in @ ZZZZZZZZZZZZZZQ @ ZZZZZZZZZZZZZZO) | ~ (ZZZZZZZZZZZZZZP @ ZZZZZZZZZZZZZZQ) | (ZZZZZZZZZZZZZZP @ (sk58 @ ZZZZZZZZZZZZZZQ @ (ZZZZZZZZZZZZZZP) @ ZZZZZZZZZZZZZZO)) | ((dsetconstr @ ZZZZZZZZZZZZZZO @ (ZZZZZZZZZZZZZZP)) = (setadjoin @ (sk59 @ ZZZZZZZZZZZZZZQ @ (ZZZZZZZZZZZZZZP) @ ZZZZZZZZZZZZZZO) @ emptyset))) & (~ (in @ ZZZZZZZZZZZZZZQ @ ZZZZZZZZZZZZZZO) | ~ (ZZZZZZZZZZZZZZP @ ZZZZZZZZZZZZZZQ) | ~ ((sk58 @ ZZZZZZZZZZZZZZQ @ (ZZZZZZZZZZZZZZP) @ ZZZZZZZZZZZZZZO) = ZZZZZZZZZZZZZZQ) | (in @ (sk59 @ ZZZZZZZZZZZZZZQ @ (ZZZZZZZZZZZZZZP) @ ZZZZZZZZZZZZZZO) @ (dsetconstr @ ZZZZZZZZZZZZZZO @ (ZZZZZZZZZZZZZZP)))) & (~ (in @ ZZZZZZZZZZZZZZQ @ ZZZZZZZZZZZZZZO) | ~ (ZZZZZZZZZZZZZZP @ ZZZZZZZZZZZZZZQ) | ~ ((sk58 @ ZZZZZZZZZZZZZZQ @ (ZZZZZZZZZZZZZZP) @ ZZZZZZZZZZZZZZO) = ZZZZZZZZZZZZZZQ) | ((dsetconstr @ ZZZZZZZZZZZZZZO @ (ZZZZZZZZZZZZZZP)) = (setadjoin @ (sk59 @ ZZZZZZZZZZZZZZQ @ (ZZZZZZZZZZZZZZP) @ ZZZZZZZZZZZZZZO) @ emptyset))) & ((in @ (sk60 @ (ZZZZZZZZZZZZZZS) @ ZZZZZZZZZZZZZZR) @ ZZZZZZZZZZZZZZR) | ~ (in @ ZZZZZZZZZZZZZZT @ ZZZZZZZZZZZZZZR) | ~ (ZZZZZZZZZZZZZZS @ ZZZZZZZZZZZZZZT) | (in @ (sk62 @ (ZZZZZZZZZZZZZZS) @ ZZZZZZZZZZZZZZR) @ (dsetconstr @ ZZZZZZZZZZZZZZR @ (ZZZZZZZZZZZZZZS)))) & ((in @ (sk60 @ (ZZZZZZZZZZZZZZS) @ ZZZZZZZZZZZZZZR) @ ZZZZZZZZZZZZZZR) | ~ (in @ ZZZZZZZZZZZZZZT @ ZZZZZZZZZZZZZZR) | ~ (ZZZZZZZZZZZZZZS @ ZZZZZZZZZZZZZZT) | ((dsetconstr @ ZZZZZZZZZZZZZZR @ (ZZZZZZZZZZZZZZS)) = (setadjoin @ (sk62 @ (ZZZZZZZZZZZZZZS) @ ZZZZZZZZZZZZZZR) @ emptyset))) & ((in @ (sk61 @ (ZZZZZZZZZZZZZZS) @ ZZZZZZZZZZZZZZR) @ ZZZZZZZZZZZZZZR) | ~ (in @ ZZZZZZZZZZZZZZT @ ZZZZZZZZZZZZZZR) | ~ (ZZZZZZZZZZZZZZS @ ZZZZZZZZZZZZZZT) | (in @ (sk62 @ (ZZZZZZZZZZZZZZS) @ ZZZZZZZZZZZZZZR) @ (dsetconstr @ ZZZZZZZZZZZZZZR @ (ZZZZZZZZZZZZZZS)))) & ((in @ (sk61 @ (ZZZZZZZZZZZZZZS) @ ZZZZZZZZZZZZZZR) @ ZZZZZZZZZZZZZZR) | ~ (in @ ZZZZZZZZZZZZZZT @ ZZZZZZZZZZZZZZR) | ~ (ZZZZZZZZZZZZZZS @ ZZZZZZZZZZZZZZT) | ((dsetconstr @ ZZZZZZZZZZZZZZR @ (ZZZZZZZZZZZZZZS)) = (setadjoin @ (sk62 @ (ZZZZZZZZZZZZZZS) @ ZZZZZZZZZZZZZZR) @ emptyset))) & ((ZZZZZZZZZZZZZZS @ (sk60 @ (ZZZZZZZZZZZZZZS) @ ZZZZZZZZZZZZZZR)) | ~ (in @ ZZZZZZZZZZZZZZT @ ZZZZZZZZZZZZZZR) | ~ (ZZZZZZZZZZZZZZS @ ZZZZZZZZZZZZZZT) | (in @ (sk62 @ (ZZZZZZZZZZZZZZS) @ ZZZZZZZZZZZZZZR) @ (dsetconstr @ ZZZZZZZZZZZZZZR @ (ZZZZZZZZZZZZZZS)))) & ((ZZZZZZZZZZZZZZS @ (sk60 @ (ZZZZZZZZZZZZZZS) @ ZZZZZZZZZZZZZZR)) | ~ (in @ ZZZZZZZZZZZZZZT @ ZZZZZZZZZZZZZZR) | ~ (ZZZZZZZZZZZZZZS @ ZZZZZZZZZZZZZZT) | ((dsetconstr @ ZZZZZZZZZZZZZZR @ (ZZZZZZZZZZZZZZS)) = (setadjoin @ (sk62 @ (ZZZZZZZZZZZZZZS) @ ZZZZZZZZZZZZZZR) @ emptyset))) & ((ZZZZZZZZZZZZZZS @ (sk61 @ (ZZZZZZZZZZZZZZS) @ ZZZZZZZZZZZZZZR)) | ~ (in @ ZZZZZZZZZZZZZZT @ ZZZZZZZZZZZZZZR) | ~ (ZZZZZZZZZZZZZZS @ ZZZZZZZZZZZZZZT) | (in @ (sk62 @ (ZZZZZZZZZZZZZZS) @ ZZZZZZZZZZZZZZR) @ (dsetconstr @ ZZZZZZZZZZZZZZR @ (ZZZZZZZZZZZZZZS)))) & ((ZZZZZZZZZZZZZZS @ (sk61 @ (ZZZZZZZZZZZZZZS) @ ZZZZZZZZZZZZZZR)) | ~ (in @ ZZZZZZZZZZZZZZT @ ZZZZZZZZZZZZZZR) | ~ (ZZZZZZZZZZZZZZS @ ZZZZZZZZZZZZZZT) | ((dsetconstr @ ZZZZZZZZZZZZZZR @ (ZZZZZZZZZZZZZZS)) = (setadjoin @ (sk62 @ (ZZZZZZZZZZZZZZS) @ ZZZZZZZZZZZZZZR) @ emptyset))) & (~ ((sk60 @ (ZZZZZZZZZZZZZZS) @ ZZZZZZZZZZZZZZR) = (sk61 @ (ZZZZZZZZZZZZZZS) @ ZZZZZZZZZZZZZZR)) | ~ (in @ ZZZZZZZZZZZZZZT @ ZZZZZZZZZZZZZZR) | ~ (ZZZZZZZZZZZZZZS @ ZZZZZZZZZZZZZZT) | (in @ (sk62 @ (ZZZZZZZZZZZZZZS) @ ZZZZZZZZZZZZZZR) @ (dsetconstr @ ZZZZZZZZZZZZZZR @ (ZZZZZZZZZZZZZZS)))) & (~ ((sk60 @ (ZZZZZZZZZZZZZZS) @ ZZZZZZZZZZZZZZR) = (sk61 @ (ZZZZZZZZZZZZZZS) @ ZZZZZZZZZZZZZZR)) | ~ (in @ ZZZZZZZZZZZZZZT @ ZZZZZZZZZZZZZZR) | ~ (ZZZZZZZZZZZZZZS @ ZZZZZZZZZZZZZZT) | ((dsetconstr @ ZZZZZZZZZZZZZZR @ (ZZZZZZZZZZZZZZS)) = (setadjoin @ (sk62 @ (ZZZZZZZZZZZZZZS) @ ZZZZZZZZZZZZZZR) @ emptyset))) & (~ ((setadjoin @ ZZZZZZZZZZZZZZU @ emptyset) = (setadjoin @ ZZZZZZZZZZZZZZV @ emptyset)) | (ZZZZZZZZZZZZZZU = ZZZZZZZZZZZZZZV)) & (~ (in @ (setadjoin @ ZZZZZZZZZZZZZZY @ emptyset) @ (setadjoin @ (setadjoin @ ZZZZZZZZZZZZZZW @ emptyset) @ (setadjoin @ (setadjoin @ ZZZZZZZZZZZZZZW @ (setadjoin @ ZZZZZZZZZZZZZZX @ emptyset)) @ emptyset))) | (ZZZZZZZZZZZZZZW = ZZZZZZZZZZZZZZY)) & (~ (iskpair @ ZZZZZZZZZZZZZZZ) | (in @ (sk63 @ ZZZZZZZZZZZZZZZ) @ (dsetconstr @ (setunion @ ZZZZZZZZZZZZZZZ) @ (^ [ZZZZZZZZZZZZZZZZZN:$i]: (in @ (setadjoin @ ZZZZZZZZZZZZZZZZZN @ emptyset) @ ZZZZZZZZZZZZZZZ))))) & (~ (iskpair @ ZZZZZZZZZZZZZZZ) | ((dsetconstr @ (setunion @ ZZZZZZZZZZZZZZZ) @ (^ [ZZZZZZZZZZZZZZZZZN:$i]: (in @ (setadjoin @ ZZZZZZZZZZZZZZZZZN @ emptyset) @ ZZZZZZZZZZZZZZZ))) = (setadjoin @ (sk63 @ ZZZZZZZZZZZZZZZ) @ emptyset))) & (~ (in @ ZZZZZZZZZZZZZZZB @ ZZZZZZZZZZZZZZZA) | ~ (ZZZZZZZZZZZZZZZA = (setadjoin @ ZZZZZZZZZZZZZZZB @ emptyset)) | (in @ (setunion @ ZZZZZZZZZZZZZZZA) @ ZZZZZZZZZZZZZZZA)) & ((kfst @ (kpair @ ZZZZZZZZZZZZZZZC @ ZZZZZZZZZZZZZZZD)) = ZZZZZZZZZZZZZZZC) & (~ (in @ ZZZZZZZZZZZZZZZG @ (cartprod @ ZZZZZZZZZZZZZZZE @ ZZZZZZZZZZZZZZZF)) | (in @ (kfst @ ZZZZZZZZZZZZZZZG) @ ZZZZZZZZZZZZZZZE)) & (~ ((setadjoin @ (setadjoin @ ZZZZZZZZZZZZZZZH @ emptyset) @ (setadjoin @ (setadjoin @ ZZZZZZZZZZZZZZZH @ (setadjoin @ ZZZZZZZZZZZZZZZI @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ ZZZZZZZZZZZZZZZJ @ emptyset) @ (setadjoin @ (setadjoin @ ZZZZZZZZZZZZZZZJ @ (setadjoin @ ZZZZZZZZZZZZZZZK @ emptyset)) @ emptyset))) | (ZZZZZZZZZZZZZZZH = ZZZZZZZZZZZZZZZJ)) & (~ ((kpair @ ZZZZZZZZZZZZZZZL @ ZZZZZZZZZZZZZZZM) = (kpair @ ZZZZZZZZZZZZZZZN @ ZZZZZZZZZZZZZZZO)) | (ZZZZZZZZZZZZZZZL = ZZZZZZZZZZZZZZZN)) & (~ (ZZZZZZZZZZZZZZZP = ZZZZZZZZZZZZZZZQ) | ((setadjoin @ ZZZZZZZZZZZZZZZP @ (setadjoin @ ZZZZZZZZZZZZZZZQ @ emptyset)) = (setadjoin @ ZZZZZZZZZZZZZZZP @ emptyset))) & (~ (ZZZZZZZZZZZZZZZR = ZZZZZZZZZZZZZZZS) | ((setadjoin @ (setadjoin @ ZZZZZZZZZZZZZZZR @ emptyset) @ (setadjoin @ (setadjoin @ ZZZZZZZZZZZZZZZR @ (setadjoin @ ZZZZZZZZZZZZZZZS @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ ZZZZZZZZZZZZZZZR @ emptyset) @ emptyset))) & (~ ((setadjoin @ (setadjoin @ ZZZZZZZZZZZZZZZT @ emptyset) @ (setadjoin @ (setadjoin @ ZZZZZZZZZZZZZZZT @ (setadjoin @ ZZZZZZZZZZZZZZZU @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ ZZZZZZZZZZZZZZZV @ emptyset) @ (setadjoin @ (setadjoin @ ZZZZZZZZZZZZZZZV @ (setadjoin @ ZZZZZZZZZZZZZZZW @ emptyset)) @ emptyset))) | ~ (ZZZZZZZZZZZZZZZV = ZZZZZZZZZZZZZZZW) | (ZZZZZZZZZZZZZZZU = ZZZZZZZZZZZZZZZW)) & (~ ((setadjoin @ ZZZZZZZZZZZZZZZX @ (setadjoin @ ZZZZZZZZZZZZZZZY @ emptyset)) = (setadjoin @ ZZZZZZZZZZZZZZZZ @ emptyset)) | (ZZZZZZZZZZZZZZZX = ZZZZZZZZZZZZZZZY)) & (~ ((setadjoin @ (setadjoin @ ZZZZZZZZZZZZZZZZA @ emptyset) @ (setadjoin @ (setadjoin @ ZZZZZZZZZZZZZZZZA @ (setadjoin @ ZZZZZZZZZZZZZZZZB @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ ZZZZZZZZZZZZZZZZC @ emptyset) @ (setadjoin @ (setadjoin @ ZZZZZZZZZZZZZZZZC @ (setadjoin @ ZZZZZZZZZZZZZZZZD @ emptyset)) @ emptyset))) | (ZZZZZZZZZZZZZZZZB = ZZZZZZZZZZZZZZZZD)) & (~ ((kpair @ ZZZZZZZZZZZZZZZZE @ ZZZZZZZZZZZZZZZZF) = (kpair @ ZZZZZZZZZZZZZZZZG @ ZZZZZZZZZZZZZZZZH)) | (ZZZZZZZZZZZZZZZZF = ZZZZZZZZZZZZZZZZH)) & (~ (iskpair @ ZZZZZZZZZZZZZZZZI) | (in @ (sk64 @ ZZZZZZZZZZZZZZZZI) @ (dsetconstr @ (setunion @ ZZZZZZZZZZZZZZZZI) @ (^ [ZZZZZZZZZZZZZZZZZN:$i]: (ZZZZZZZZZZZZZZZZI = (kpair @ (kfst @ ZZZZZZZZZZZZZZZZI) @ ZZZZZZZZZZZZZZZZZN)))))) & (~ (iskpair @ ZZZZZZZZZZZZZZZZI) | ((dsetconstr @ (setunion @ ZZZZZZZZZZZZZZZZI) @ (^ [ZZZZZZZZZZZZZZZZZN:$i]: (ZZZZZZZZZZZZZZZZI = (kpair @ (kfst @ ZZZZZZZZZZZZZZZZI) @ ZZZZZZZZZZZZZZZZZN)))) = (setadjoin @ (sk64 @ ZZZZZZZZZZZZZZZZI) @ emptyset))) & ((ksnd @ (kpair @ ZZZZZZZZZZZZZZZZJ @ ZZZZZZZZZZZZZZZZK)) = ZZZZZZZZZZZZZZZZK) & (~ (iskpair @ ZZZZZZZZZZZZZZZZL) | ((kpair @ (kfst @ ZZZZZZZZZZZZZZZZL) @ (ksnd @ ZZZZZZZZZZZZZZZZL)) = ZZZZZZZZZZZZZZZZL)) & (~ (in @ ZZZZZZZZZZZZZZZZO @ (cartprod @ ZZZZZZZZZZZZZZZZM @ ZZZZZZZZZZZZZZZZN)) | (in @ (ksnd @ ZZZZZZZZZZZZZZZZO) @ ZZZZZZZZZZZZZZZZN)) & (~ (in @ (kpair @ ZZZZZZZZZZZZZZZZR @ ZZZZZZZZZZZZZZZZS) @ (cartprod @ ZZZZZZZZZZZZZZZZP @ ZZZZZZZZZZZZZZZZQ)) | (in @ ZZZZZZZZZZZZZZZZR @ ZZZZZZZZZZZZZZZZP)) & (~ (in @ (kpair @ ZZZZZZZZZZZZZZZZV @ ZZZZZZZZZZZZZZZZW) @ (cartprod @ ZZZZZZZZZZZZZZZZT @ ZZZZZZZZZZZZZZZZU)) | (in @ ZZZZZZZZZZZZZZZZW @ ZZZZZZZZZZZZZZZZU)) & (~ (in @ ZZZZZZZZZZZZZZZZZ @ ZZZZZZZZZZZZZZZZX) | ~ (in @ ZZZZZZZZZZZZZZZZZA @ ZZZZZZZZZZZZZZZZY) | ((kfst @ (kpair @ ZZZZZZZZZZZZZZZZZ @ ZZZZZZZZZZZZZZZZZA)) = ZZZZZZZZZZZZZZZZZ)) & (~ (in @ ZZZZZZZZZZZZZZZZZD @ ZZZZZZZZZZZZZZZZZB) | ~ (in @ ZZZZZZZZZZZZZZZZZE @ ZZZZZZZZZZZZZZZZZC) | ((ksnd @ (kpair @ ZZZZZZZZZZZZZZZZZD @ ZZZZZZZZZZZZZZZZZE)) = ZZZZZZZZZZZZZZZZZE)) & (~ (in @ ZZZZZZZZZZZZZZZZZH @ (cartprod @ ZZZZZZZZZZZZZZZZZF @ ZZZZZZZZZZZZZZZZZG)) | ((kpair @ (kfst @ ZZZZZZZZZZZZZZZZZH) @ (ksnd @ ZZZZZZZZZZZZZZZZZH)) = ZZZZZZZZZZZZZZZZZH)) & (~ (in @ ZZZZZZZZZZZZZZZZZL @ ZZZZZZZZZZZZZZZZZI) | ~ (in @ ZZZZZZZZZZZZZZZZZM @ ZZZZZZZZZZZZZZZZZJ) | ~ (ZZZZZZZZZZZZZZZZZK @ ZZZZZZZZZZZZZZZZZL @ ZZZZZZZZZZZZZZZZZM) | (in @ (kpair @ ZZZZZZZZZZZZZZZZZL @ ZZZZZZZZZZZZZZZZZM) @ (dsetconstr @ (cartprod @ ZZZZZZZZZZZZZZZZZI @ ZZZZZZZZZZZZZZZZZJ) @ (^ [ZZZZZZZZZZZZZZZZZN:$i]: ? [ZZZZZZZZZZZZZZZZZO:$i]: ((in @ ZZZZZZZZZZZZZZZZZO @ ZZZZZZZZZZZZZZZZZI) & ? [ZZZZZZZZZZZZZZZZZP:$i]: ((in @ ZZZZZZZZZZZZZZZZZP @ ZZZZZZZZZZZZZZZZZJ) & (ZZZZZZZZZZZZZZZZZK @ ZZZZZZZZZZZZZZZZZO @ ZZZZZZZZZZZZZZZZZP) & (ZZZZZZZZZZZZZZZZZN = (kpair @ ZZZZZZZZZZZZZZZZZO @ ZZZZZZZZZZZZZZZZZP)))))))) & ~ (subset @ (dsetconstr @ (cartprod @ sk65 @ sk66) @ (^ [ZZZZZZZZZZZZZZZZZN:$i]: ? [ZZZZZZZZZZZZZZZZZO:$i]: ((in @ ZZZZZZZZZZZZZZZZZO @ sk65) & ? [ZZZZZZZZZZZZZZZZZP:$i]: ((in @ ZZZZZZZZZZZZZZZZZP @ sk66) & (sk67 @ ZZZZZZZZZZZZZZZZZO @ ZZZZZZZZZZZZZZZZZP) & (ZZZZZZZZZZZZZZZZZN = (kpair @ ZZZZZZZZZZZZZZZZZO @ ZZZZZZZZZZZZZZZZZP)))))) @ (cartprod @ sk65 @ sk66))))),inference(cnf,[status(esa)],[4])).
% 32.55/10.82  thf(92,plain,((~ (subset @ (dsetconstr @ (cartprod @ sk65 @ sk66) @ (^ [A:$i]: ? [B:$i]: ((in @ B @ sk65) & ? [C:$i]: ((in @ C @ sk66) & (sk67 @ B @ C) & (A = (kpair @ B @ C)))))) @ (cartprod @ sk65 @ sk66)))),inference(cnfConj,[status(thm)],[5])).
% 32.55/10.82  thf(260,plain,(! [B:($i > $o),A:$i] : ((subset @ (dsetconstr @ A @ (B)) @ A))),inference(cnfConj,[status(thm)],[5])).
% 32.55/10.82  thf(420,plain,(! [B:($i > $o),A:$i] : ((subset @ (dsetconstr @ A @ (B)) @ A))),inference(simp,[status(thm)],[260])).
% 32.55/10.82  thf(2389,plain,(~ (($true))),inference(rewrite,[status(thm)],[92,420])).
% 32.55/10.82  thf(2390,plain,(($false)),inference(simp,[status(thm)],[2389])).
% 32.55/10.82  % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 32.55/10.82  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------