0.03/0.10	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.10/0.13	% Command    : eprover-ho %s --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --free-numbers -auto-schedule -p --cpu-limit=%d --neg-ext=all --pos-ext=all --ext-sup-max-depth=2 --schedule-kind=CASC
0.13/0.34	% Computer   : n028.cluster.edu
0.13/0.34	% Model      : x86_64 x86_64
0.13/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.34	% Memory     : 8042.1875MB
0.13/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.34	% CPULimit   : 1200
0.13/0.34	% WCLimit    : 120
0.13/0.34	% DateTime   : Tue Jul 13 15:56:31 EDT 2021
0.13/0.34	% CPUTime    : 
0.13/0.34	% Number of cores: 8
0.18/0.34	% Python version: Python 3.6.8
0.18/0.34	# Version: 2.6rc1-ho
0.18/0.35	# No SInE strategy applied
0.18/0.35	# Trying AutoSched0 for 59 seconds
59.04/59.43	# AutoSched0-Mode selected heuristic G_E___303_C18_F1_URBAN_S0Y
59.04/59.43	# and selection function SelectMaxLComplexAvoidPosPred.
59.04/59.43	#
59.04/59.43	# Preprocessing time       : 0.123 s
59.15/59.44	# No success with AutoSched0
59.15/59.44	# Trying AutoSched1 for 26 seconds
85.10/85.45	# AutoSched1-Mode selected heuristic G_E___008_C45_F1_PI_SE_Q4_CS_SP_S4SI
85.10/85.45	# and selection function SelectNewComplexAHPNS.
85.10/85.45	#
85.10/85.45	# Preprocessing time       : 0.074 s
85.27/85.58	# No success with AutoSched1
85.27/85.58	# Trying AutoSched2 for 8 seconds
85.30/85.71	# AutoSched2-Mode selected heuristic U_____100_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_ND_S04AN
85.30/85.71	# and selection function SelectComplexExceptUniqMaxHorn.
85.30/85.71	#
85.30/85.71	# Preprocessing time       : 0.033 s
85.30/85.71	# Presaturation interreduction done
85.30/85.71	
85.30/85.71	# Proof found!
85.30/85.71	# SZS status Theorem
85.30/85.71	# SZS output start CNFRefutation
85.30/85.71	thf(replAx, axiom, (replAx<=>![X6:$i > $i > $o, X4:$i]:(![X2:$i]:(in @ X2 @ X4=>exu @ (^[X3:$i]:X6 @ X2 @ X3))=>?[X5:$i]:![X2:$i]:(in @ X2 @ X5<=>?[X3:$i]:(in @ X3 @ X4&X6 @ X3 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', replAx)).
85.30/85.71	thf(exu, axiom, (exu)=(^[X1:$i > $o]:?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exu)).
85.30/85.71	thf(descrp, axiom, (descrp<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>X1 @ (descr @ (^[X2:$i]:X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', descrp)).
85.30/85.71	thf(exuE1, axiom, (exuE1<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuE1)).
85.30/85.71	thf(exuE3e, axiom, (exuE3e<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>?[X2:$i]:X1 @ X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuE3e)).
85.30/85.71	thf(nonemptyE1, axiom, (nonemptyE1<=>![X4:$i]:(nonempty @ X4=>?[X2:$i]:in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyE1)).
85.30/85.71	thf(nonempty, axiom, (nonempty)=(^[X2:$i]:(X2)!=(emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonempty)).
85.30/85.71	thf(nonemptyI, axiom, (nonemptyI<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyI)).
85.30/85.71	thf(nonemptyI1, axiom, (nonemptyI1<=>![X4:$i]:(?[X2:$i]:in @ X2 @ X4=>nonempty @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyI1)).
85.30/85.71	thf(exuE2, axiom, (exuE2<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuE2)).
85.30/85.71	thf(nonemptyImpWitness, axiom, (nonemptyImpWitness<=>![X4:$i]:(nonempty @ X4=>?[X2:$i]:(in @ X2 @ X4&$true))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyImpWitness)).
85.30/85.71	thf(exuI1, axiom, (exuI1<=>![X1:$i > $o]:(?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3)))=>exu @ (^[X2:$i]:X1 @ X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuI1)).
85.30/85.71	thf(exuI3, axiom, (exuI3<=>![X1:$i > $o]:(?[X2:$i]:X1 @ X2=>(![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3)))=>exu @ (^[X2:$i]:X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuI3)).
85.30/85.71	thf(exuI2, axiom, (exuI2<=>![X1:$i > $o]:(?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2))=>exu @ (^[X2:$i]:X1 @ X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuI2)).
85.30/85.71	thf(exuE3u, axiom, (exuE3u<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuE3u)).
85.30/85.71	thf(exu__Cong, axiom, (exu__Cong<=>![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(exu @ (^[X2:$i]:X1 @ X2)<=>exu @ (^[X2:$i]:X17 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exu__Cong)).
85.30/85.71	thf(exuEu, axiom, (exuEu<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuEu)).
85.30/85.71	thf(descr__Cong, axiom, (descr__Cong<=>![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(exu @ (^[X2:$i]:X1 @ X2)=>(exu @ (^[X2:$i]:X17 @ X2)=>(descr @ (^[X2:$i]:X1 @ X2))=(descr @ (^[X2:$i]:X17 @ X2)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', descr__Cong)).
85.30/85.71	thf(ex1E1, axiom, (ex1E1<=>![X4:$i, X1:$i > $o]:(ex1 @ X4 @ (^[X2:$i]:X1 @ X2)=>?[X2:$i]:(in @ X2 @ X4&X1 @ X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ex1E1)).
85.30/85.71	thf(ex1, axiom, (ex1)=(^[X4:$i, X1:$i > $o]:singleton @ (dsetconstr @ X4 @ (^[X2:$i]:X1 @ X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ex1)).
85.30/85.71	thf(ex1I, axiom, (ex1I<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>(![X3:$i]:(in @ X3 @ X4=>(X1 @ X3=>(X3)=(X2)))=>ex1 @ X4 @ (^[X3:$i]:X1 @ X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ex1I)).
85.30/85.71	thf(ex1I2, axiom, (ex1I2<=>![X4:$i, X1:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(X1 @ X2=>(X1 @ X3=>(X2)=(X3)))))=>(?[X2:$i]:(in @ X2 @ X4&X1 @ X2)=>ex1 @ X4 @ (^[X2:$i]:X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ex1I2)).
85.30/85.71	thf(setOfPairsIsBReln, axiom, (setOfPairsIsBReln<=>![X4:$i, X5:$i, X24:$i > $i > $o]:breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:X24 @ X2 @ X3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setOfPairsIsBReln)).
85.30/85.71	thf(breln, axiom, (breln)=(^[X4:$i, X5:$i, X7:$i]:subset @ X7 @ (cartprod @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln)).
85.30/85.71	thf(brelnall1, axiom, (brelnall1<=>![X4:$i, X5:$i, X33:$i]:(breln @ X4 @ X5 @ X33=>![X1:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ X33=>X1 @ (kpair @ X2 @ X3))))=>![X2:$i]:(in @ X2 @ X33=>X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', brelnall1)).
85.30/85.71	thf(brelnall2, axiom, (brelnall2<=>![X4:$i, X5:$i, X33:$i]:(breln @ X4 @ X5 @ X33=>![X1:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ X33=>X1 @ (kpair @ X2 @ X3))))=>![X2:$i]:(in @ X2 @ X33=>X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', brelnall2)).
85.30/85.71	thf(ex1E2, axiom, (ex1E2<=>![X4:$i, X1:$i > $o]:(ex1 @ X4 @ (^[X2:$i]:X1 @ X2)=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ex1E2)).
85.30/85.71	thf(subbreln, axiom, (subbreln<=>![X4:$i, X5:$i, X33:$i]:(breln @ X4 @ X5 @ X33=>![X35:$i]:(breln @ X4 @ X5 @ X35=>(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ X33=>in @ (kpair @ X2 @ X3) @ X35)))=>subset @ X33 @ X35)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subbreln)).
85.30/85.71	thf(eqbreln, axiom, (eqbreln<=>![X4:$i, X5:$i, X33:$i]:(breln @ X4 @ X5 @ X33=>![X35:$i]:(breln @ X4 @ X5 @ X35=>(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ X33=>in @ (kpair @ X2 @ X3) @ X35)))=>(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ X35=>in @ (kpair @ X2 @ X3) @ X33)))=>(X33)=(X35)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqbreln)).
85.30/85.71	thf(setminusT_lem, conjecture, (setextAx=>(emptysetAx=>((powersetAx=>(setunionAx=>(omega0Ax=>(omegaSAx=>(omegaIndAx=>(replAx=>(foundationAx=>(wellorderingAx=>(descrp=>(dsetconstrI=>(dsetconstrEL=>(((prop2setE=>(((notinemptyset=>(exuE3e=>(setext=>(emptyI=>(((nonemptyE1=>(nonemptyI=>(nonemptyI1=>(((setadjoinIR=>((setadjoinOr=>((powersetI=>(emptyinPowerset=>(emptyInPowerset=>(powersetE=>((setunionE=>(subPowSU=>(exuE2=>((uniqinunit=>(notinsingleton=>(eqinunit=>(singletonsswitch=>(upairsetE=>(upairsetIL=>(upairsetIR=>(emptyE1=>((((quantDeMorgan3=>((((notdexE=>(notdallE=>(((((in__Cong=>(((emptyset__Cong=>(setadjoin__Cong=>((((exuEu=>((dsetconstr__Cong=>(((eqimpsubset1=>(subsetI2=>(((subsetE2=>((notequalI1=>(notequalI2=>((((setadjoinSub2=>(subset2powerset=>(setextsub=>(((powersetE1=>(inPowerset=>(powersetsubset=>((((((binunionEcases=>((binunionLsub=>((binintersectI=>((binintersectEL=>(binintersectLsub=>(binintersectSubset2=>(binintersectSubset3=>((disjointsetsI1=>(binintersectRsub=>(((bs114d=>(setminusI=>(setminusEL=>(((setminusERneg=>(((((setminusSubset1=>(symdiffE=>(symdiffI1=>((((secondinupair=>((((((singletoninpowerset=>((upairset2E=>(upairsubunion=>(upairinpowunion=>(ubforcartprodlem1=>((ubforcartprodlem3=>((((setunionE2=>(setunionsingleton1=>(setunionsingleton2=>((singletonprop=>(ex1E1=>((((setukpairinjL1=>(((kfstpairEq=>(((setukpairinjL=>(setukpairinjR11=>(setukpairinjR12=>(setukpairinjR1=>((setukpairinjR2=>(setukpairinjR=>((ksndpairEq=>(kpairsurjEq=>((cartprodpairmemEL=>((((cartprodsndpairEq=>(cartprodpairsurjEq=>(dpsetconstrI=>(dpsetconstrSub=>(setOfPairsIsBReln=>(((dpsetconstrEL2=>(dpsetconstrER=>(funcImageSingleton=>(apProp=>(((ap2p=>(((((brelnall1=>(brelnall2=>((funcGraphProp1=>(funcGraphProp3=>(funcGraphProp2=>(funcextLem=>(funcGraphProp4=>(subbreln=>(eqbreln=>((funcext2=>((ap2apEq2=>(beta1=>((lam2lamEq=>(beta2=>(((iffalseProp2=>(iftrueProp1=>(iftrueProp2=>(ifSingleton=>(ifp=>(theeq=>(iftrue=>((((binunionT_lem=>(powersetT_lem=>![X4:$i, X21:$i]:(![X48:$i]:(in @ (setminus @ X21 @ X48) @ (powerset @ X4)<=in @ X48 @ (powerset @ X4))<=in @ X21 @ (powerset @ X4))))<=binintersectT_lem)<=iftrueorfalse)<=iffalse))))))))<=iffalseProp1)<=eta2)))<=eta1)))<=ap2apEq1))<=funcext))))))))<=ex1E2)))<=lam2p)<=lamp)<=lamProp)<=funcinfuncset))<=infuncsetfunc)<=app)))))<=dpsetconstrEL1)<=dpsetconstrERa))))))<=cartprodfstpairEq)<=cartprodmempaircEq)<=cartprodpairmemER))<=cartprodsndin)))<=ksndsingleton)))<=upairequniteq)))))<=setukpairinjL2)<=cartprodfstin))<=theprop)<=kfstsingleton))<=singletonsuniq)<=ex1I2)<=ex1I)))<=setunionsingleton))))<=cartprodmempair)<=cartprodmempair1)<=cartprodpairin))<=ubforcartprodlem2)))))<=singletoninpowunion))<=singletonsubset)<=kpairp)<=kpairiskpair)<=setukpairIR)<=setukpairIL))<=symdiffIneg2)<=symdiffIneg1)<=symdiffI2))))<=setminusLsub)<=setminusIRneg)<=setminusILneg)<=setminusELneg))<=setminusSubset2)<=setminusER))))<=binintersectSubset1)<=binintersectSubset4)))<=binintersectER)))))<=binintersectSubset5))<=binunionRsub))<=binunionE))<=binunionIR)<=upairset2IR)<=binunionIL)<=sepSubset)<=sepInPowerset))))<=powersetI1)<=subsetemptysetimpeq))))<=setadjoinSub)<=subsetTrans)<=subsetRefl)))<=notsubsetI))<=subsetE)<=emptysetsubset)))<=eqimpsubset2)<=subsetI1))<=descr__Cong))<=omega__Cong)<=setunion__Cong)<=powerset__Cong)))<=exu__Cong)<=exuE3u))<=inCongP)<=exuI2)<=exuI3)<=exuI1)))<=prop2set2propI)<=prop2setI)<=quantDeMorgan4))<=quantDeMorgan2)<=quantDeMorgan1)<=vacuousDall)))))))))<=nonemptyImpWitness))))<=setunionI)))))<=setoftrueEq))<=setadjoinE))<=emptyinunitempty)<=setadjoinIL))))<=setbeta)<=noeltsimpempty)))))<=emptysetimpfalse)<=emptysetE))<=exuE1)<=dsetconstrER))))))))))))<=setadjoinAx))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusT_lem)).
85.30/85.71	thf(setextAx, axiom, (setextAx<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4<=>in @ X2 @ X5)=>(X4)=(X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setextAx)).
85.30/85.71	thf(emptysetAx, axiom, (emptysetAx<=>![X2:$i]:~(in @ X2 @ emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetAx)).
85.30/85.71	thf(setadjoinAx, axiom, (setadjoinAx<=>![X2:$i, X4:$i, X3:$i]:(in @ X3 @ (setadjoin @ X2 @ X4)<=>((X3)=(X2)|in @ X3 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinAx)).
85.30/85.71	thf(powersetAx, axiom, (powersetAx<=>![X4:$i, X5:$i]:(in @ X5 @ (powerset @ X4)<=>![X2:$i]:(in @ X2 @ X5=>in @ X2 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetAx)).
85.30/85.71	thf(setunionAx, axiom, (setunionAx<=>![X4:$i, X2:$i]:(in @ X2 @ (setunion @ X4)<=>?[X5:$i]:(in @ X2 @ X5&in @ X5 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionAx)).
85.30/85.71	thf(omega0Ax, axiom, (omega0Ax<=>in @ emptyset @ omega), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omega0Ax)).
85.30/85.71	thf(omegaSAx, axiom, (omegaSAx<=>![X2:$i]:(in @ X2 @ omega=>in @ (setadjoin @ X2 @ X2) @ omega)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omegaSAx)).
85.30/85.71	thf(omegaIndAx, axiom, (omegaIndAx<=>![X4:$i]:((in @ emptyset @ X4&![X2:$i]:((in @ X2 @ omega&in @ X2 @ X4)=>in @ (setadjoin @ X2 @ X2) @ X4))=>![X2:$i]:(in @ X2 @ omega=>in @ X2 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omegaIndAx)).
85.30/85.71	thf(foundationAx, axiom, (foundationAx<=>![X4:$i]:(?[X2:$i]:in @ X2 @ X4=>?[X5:$i]:(in @ X5 @ X4&~(?[X2:$i]:(in @ X2 @ X5&in @ X2 @ X4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', foundationAx)).
85.30/85.71	thf(wellorderingAx, axiom, (wellorderingAx<=>![X4:$i]:?[X5:$i]:(((![X7:$i]:(in @ X7 @ X5=>![X2:$i]:(in @ X2 @ X7=>in @ X2 @ X4))&![X2:$i, X3:$i]:((in @ X2 @ X4&in @ X3 @ X4)=>(![X7:$i]:(in @ X7 @ X5=>(in @ X2 @ X7<=>in @ X3 @ X7))=>(X2)=(X3))))&![X7:$i, X8:$i]:((in @ X7 @ X5&in @ X8 @ X5)=>(![X2:$i]:(in @ X2 @ X7=>in @ X2 @ X8)|![X2:$i]:(in @ X2 @ X8=>in @ X2 @ X7))))&![X7:$i]:((![X2:$i]:(in @ X2 @ X7=>in @ X2 @ X4)&?[X2:$i]:in @ X2 @ X7)=>?[X8:$i, X2:$i]:(((in @ X8 @ X5&in @ X2 @ X7)&~(?[X3:$i]:(in @ X3 @ X8&in @ X3 @ X7)))&![X9:$i]:(in @ X9 @ X5=>(![X3:$i]:(in @ X3 @ X9=>in @ X3 @ X8)|in @ X2 @ X9)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', wellorderingAx)).
85.30/85.71	thf(dsetconstrI, axiom, (dsetconstrI<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstrI)).
85.30/85.71	thf(dsetconstrEL, axiom, (dsetconstrEL<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))=>in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstrEL)).
85.30/85.71	thf(dsetconstrER, axiom, (dsetconstrER<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))=>X1 @ X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstrER)).
85.30/85.71	thf(prop2setE, axiom, (prop2setE<=>![X10:$o, X2:$i]:(in @ X2 @ (prop2set @ (X10))=>X10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prop2setE)).
85.30/85.71	thf(emptysetE, axiom, (emptysetE<=>![X2:$i]:(in @ X2 @ emptyset=>![X11:$o]:X11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetE)).
85.30/85.71	thf(emptysetimpfalse, axiom, (emptysetimpfalse<=>![X2:$i]:(in @ X2 @ emptyset=>~$true)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetimpfalse)).
85.30/85.71	thf(notinemptyset, axiom, (notinemptyset<=>![X2:$i]:~(in @ X2 @ emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notinemptyset)).
85.30/85.71	thf(setext, axiom, (setext<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4=>in @ X2 @ X5)=>(![X2:$i]:(in @ X2 @ X5=>in @ X2 @ X4)=>(X4)=(X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setext)).
85.30/85.71	thf(emptyI, axiom, (emptyI<=>![X4:$i]:(![X2:$i]:~(in @ X2 @ X4)=>(X4)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyI)).
85.30/85.71	thf(noeltsimpempty, axiom, (noeltsimpempty<=>![X4:$i]:(![X2:$i]:~(in @ X2 @ X4)=>(X4)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', noeltsimpempty)).
85.30/85.71	thf(setbeta, axiom, (setbeta<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))<=>X1 @ X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setbeta)).
85.30/85.71	thf(setadjoinIL, axiom, (setadjoinIL<=>![X2:$i, X3:$i]:in @ X2 @ (setadjoin @ X2 @ X3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinIL)).
85.30/85.71	thf(emptyinunitempty, axiom, (emptyinunitempty<=>in @ emptyset @ (setadjoin @ emptyset @ emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyinunitempty)).
85.30/85.71	thf(setadjoinIR, axiom, (setadjoinIR<=>![X2:$i, X4:$i, X3:$i]:(in @ X3 @ X4=>in @ X3 @ (setadjoin @ X2 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinIR)).
85.30/85.71	thf(setadjoinE, axiom, (setadjoinE<=>![X2:$i, X4:$i, X3:$i]:(in @ X3 @ (setadjoin @ X2 @ X4)=>![X12:$o]:(((X3)=(X2)=>X12)=>((in @ X3 @ X4=>X12)=>X12)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinE)).
85.30/85.71	thf(setadjoinOr, axiom, (setadjoinOr<=>![X2:$i, X4:$i, X3:$i]:(in @ X3 @ (setadjoin @ X2 @ X4)=>((X3)=(X2)|in @ X3 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinOr)).
85.30/85.71	thf(setoftrueEq, axiom, (setoftrueEq<=>![X4:$i]:(dsetconstr @ X4 @ (^[X2:$i]:$true))=(X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setoftrueEq)).
85.30/85.71	thf(powersetI, axiom, (powersetI<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X5=>in @ X2 @ X4)=>in @ X5 @ (powerset @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetI)).
85.30/85.71	thf(emptyinPowerset, axiom, (emptyinPowerset<=>![X4:$i]:in @ emptyset @ (powerset @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyinPowerset)).
85.30/85.71	thf(emptyInPowerset, axiom, (emptyInPowerset<=>![X4:$i]:in @ emptyset @ (powerset @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyInPowerset)).
85.30/85.71	thf(powersetE, axiom, (powersetE<=>![X4:$i, X5:$i, X2:$i]:(in @ X5 @ (powerset @ X4)=>(in @ X2 @ X5=>in @ X2 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetE)).
85.30/85.71	thf(setunionI, axiom, (setunionI<=>![X4:$i, X2:$i, X5:$i]:(in @ X2 @ X5=>(in @ X5 @ X4=>in @ X2 @ (setunion @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionI)).
85.30/85.71	thf(setunionE, axiom, (setunionE<=>![X4:$i, X2:$i]:(in @ X2 @ (setunion @ X4)=>![X13:$o]:(![X5:$i]:(in @ X2 @ X5=>(in @ X5 @ X4=>X13))=>X13))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionE)).
85.30/85.71	thf(subPowSU, axiom, (subPowSU<=>![X4:$i, X2:$i]:(in @ X2 @ X4=>in @ X2 @ (powerset @ (setunion @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subPowSU)).
85.30/85.71	thf(uniqinunit, axiom, (uniqinunit<=>![X2:$i, X3:$i]:(in @ X2 @ (setadjoin @ X3 @ emptyset)=>(X2)=(X3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', uniqinunit)).
85.30/85.71	thf(notinsingleton, axiom, (notinsingleton<=>![X2:$i, X3:$i]:((X2)!=(X3)=>~(in @ X3 @ (setadjoin @ X2 @ emptyset)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notinsingleton)).
85.30/85.71	thf(eqinunit, axiom, (eqinunit<=>![X2:$i, X3:$i]:((X2)=(X3)=>in @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqinunit)).
85.30/85.71	thf(singletonsswitch, axiom, (singletonsswitch<=>![X2:$i, X3:$i]:(in @ X2 @ (setadjoin @ X3 @ emptyset)=>in @ X3 @ (setadjoin @ X2 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletonsswitch)).
85.30/85.71	thf(upairsetE, axiom, (upairsetE<=>![X2:$i, X3:$i, X14:$i]:(in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=>((X14)=(X2)|(X14)=(X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsetE)).
85.30/85.71	thf(upairsetIL, axiom, (upairsetIL<=>![X2:$i, X3:$i]:in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsetIL)).
85.30/85.71	thf(upairsetIR, axiom, (upairsetIR<=>![X2:$i, X3:$i]:in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsetIR)).
85.30/85.71	thf(emptyE1, axiom, (emptyE1<=>![X4:$i, X1:$i > $o]:(?[X2:$i]:(in @ X2 @ X4&X1 @ X2)=>((dsetconstr @ X4 @ (^[X2:$i]:X1 @ X2))=(emptyset)=>~$true))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyE1)).
85.30/85.71	thf(vacuousDall, axiom, (vacuousDall<=>![X1:$i > $o, X2:$i]:(in @ X2 @ emptyset=>X1 @ X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', vacuousDall)).
85.30/85.71	thf(quantDeMorgan1, axiom, (quantDeMorgan1<=>![X4:$i, X1:$i > $o]:(~(![X2:$i]:(in @ X2 @ X4=>X1 @ X2))=>?[X2:$i]:(in @ X2 @ X4&~(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan1)).
85.30/85.71	thf(quantDeMorgan2, axiom, (quantDeMorgan2<=>![X4:$i, X1:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>~(X1 @ X2))=>~(?[X2:$i]:(in @ X2 @ X4&X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan2)).
85.30/85.71	thf(quantDeMorgan3, axiom, (quantDeMorgan3<=>![X4:$i, X1:$i > $o]:(~(?[X2:$i]:(in @ X2 @ X4&X1 @ X2))=>![X2:$i]:(in @ X2 @ X4=>~(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan3)).
85.30/85.71	thf(quantDeMorgan4, axiom, (quantDeMorgan4<=>![X4:$i, X1:$i > $o]:(?[X2:$i]:(in @ X2 @ X4&~(X1 @ X2))=>~(![X2:$i]:(in @ X2 @ X4=>X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan4)).
85.30/85.71	thf(prop2setI, axiom, (prop2setI<=>![X15:$o]:(X15=>in @ emptyset @ (prop2set @ (X15)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prop2setI)).
85.30/85.71	thf(prop2set2propI, axiom, (prop2set2propI<=>![X16:$o]:(X16=>set2prop @ (prop2set @ (X16)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prop2set2propI)).
85.30/85.71	thf(notdexE, axiom, (notdexE<=>![X4:$i, X1:$i > $o]:(~(?[X2:$i]:(in @ X2 @ X4&X1 @ X2))=>![X2:$i]:(in @ X2 @ X4=>~(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notdexE)).
85.30/85.71	thf(notdallE, axiom, (notdallE<=>![X4:$i, X1:$i > $o]:(~(![X2:$i]:(in @ X2 @ X4=>X1 @ X2))=>?[X2:$i]:(in @ X2 @ X4&~(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notdallE)).
85.30/85.71	thf(inCongP, axiom, (inCongP<=>![X4:$i, X5:$i]:((X4)=(X5)=>![X2:$i, X3:$i]:((X2)=(X3)=>(in @ X2 @ X4=>in @ X3 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', inCongP)).
85.30/85.71	thf(in__Cong, axiom, (in__Cong<=>![X4:$i, X5:$i]:((X4)=(X5)=>![X2:$i, X3:$i]:((X2)=(X3)=>(in @ X2 @ X4<=>in @ X3 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', in__Cong)).
85.30/85.71	thf(emptyset__Cong, axiom, (emptyset__Cong<=>(emptyset)=(emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyset__Cong)).
85.30/85.71	thf(setadjoin__Cong, axiom, (setadjoin__Cong<=>![X2:$i, X3:$i]:((X2)=(X3)=>![X14:$i, X18:$i]:((X14)=(X18)=>(setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoin__Cong)).
85.30/85.71	thf(powerset__Cong, axiom, (powerset__Cong<=>![X4:$i, X5:$i]:((X4)=(X5)=>(powerset @ X4)=(powerset @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powerset__Cong)).
85.30/85.71	thf(setunion__Cong, axiom, (setunion__Cong<=>![X4:$i, X5:$i]:((X4)=(X5)=>(setunion @ X4)=(setunion @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunion__Cong)).
85.30/85.71	thf(omega__Cong, axiom, (omega__Cong<=>(omega)=(omega)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omega__Cong)).
85.30/85.71	thf(dsetconstr__Cong, axiom, (dsetconstr__Cong<=>![X4:$i, X5:$i]:((X4)=(X5)=>![X1:$i > $o, X17:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))))=>(dsetconstr @ X4 @ (^[X2:$i]:X1 @ X2))=(dsetconstr @ X5 @ (^[X2:$i]:X17 @ X2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstr__Cong)).
85.30/85.71	thf(subsetI1, axiom, (subsetI1<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4=>in @ X2 @ X5)=>subset @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetI1)).
85.30/85.71	thf(eqimpsubset2, axiom, (eqimpsubset2<=>![X4:$i, X5:$i]:((X4)=(X5)=>subset @ X5 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqimpsubset2)).
85.30/85.71	thf(eqimpsubset1, axiom, (eqimpsubset1<=>![X4:$i, X5:$i]:((X4)=(X5)=>subset @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqimpsubset1)).
85.30/85.71	thf(subsetI2, axiom, (subsetI2<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4=>in @ X2 @ X5)=>subset @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetI2)).
85.30/85.71	thf(emptysetsubset, axiom, (emptysetsubset<=>![X4:$i]:subset @ emptyset @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetsubset)).
85.30/85.71	thf(subsetE, axiom, (subsetE<=>![X4:$i, X5:$i, X2:$i]:(subset @ X4 @ X5=>(in @ X2 @ X4=>in @ X2 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetE)).
85.30/85.71	thf(subsetE2, axiom, (subsetE2<=>![X4:$i, X5:$i, X2:$i]:(subset @ X4 @ X5=>(~(in @ X2 @ X5)=>~(in @ X2 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetE2)).
85.30/85.71	thf(notsubsetI, axiom, (notsubsetI<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X5)=>~(subset @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notsubsetI)).
85.30/85.71	thf(notequalI1, axiom, (notequalI1<=>![X4:$i, X5:$i]:(~(subset @ X4 @ X5)=>(X4)!=(X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notequalI1)).
85.30/85.71	thf(notequalI2, axiom, (notequalI2<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X5)=>(X4)!=(X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notequalI2)).
85.30/85.71	thf(subsetRefl, axiom, (subsetRefl<=>![X4:$i]:subset @ X4 @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetRefl)).
85.30/85.71	thf(subsetTrans, axiom, (subsetTrans<=>![X4:$i, X5:$i, X7:$i]:(subset @ X4 @ X5=>(subset @ X5 @ X7=>subset @ X4 @ X7))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetTrans)).
85.30/85.71	thf(setadjoinSub, axiom, (setadjoinSub<=>![X2:$i, X4:$i]:subset @ X4 @ (setadjoin @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinSub)).
85.30/85.71	thf(setadjoinSub2, axiom, (setadjoinSub2<=>![X4:$i, X2:$i, X5:$i]:(subset @ X4 @ X5=>subset @ X4 @ (setadjoin @ X2 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinSub2)).
85.30/85.71	thf(subset2powerset, axiom, (subset2powerset<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>in @ X4 @ (powerset @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subset2powerset)).
85.30/85.71	thf(setextsub, axiom, (setextsub<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>(subset @ X5 @ X4=>(X4)=(X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setextsub)).
85.30/85.71	thf(subsetemptysetimpeq, axiom, (subsetemptysetimpeq<=>![X4:$i]:(subset @ X4 @ emptyset=>(X4)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetemptysetimpeq)).
85.30/85.71	thf(powersetI1, axiom, (powersetI1<=>![X4:$i, X5:$i]:(subset @ X5 @ X4=>in @ X5 @ (powerset @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetI1)).
85.30/85.71	thf(powersetE1, axiom, (powersetE1<=>![X4:$i, X5:$i]:(in @ X5 @ (powerset @ X4)=>subset @ X5 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetE1)).
85.30/85.71	thf(inPowerset, axiom, (inPowerset<=>![X4:$i]:in @ X4 @ (powerset @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', inPowerset)).
85.30/85.71	thf(powersetsubset, axiom, (powersetsubset<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>subset @ (powerset @ X4) @ (powerset @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetsubset)).
85.30/85.71	thf(sepInPowerset, axiom, (sepInPowerset<=>![X4:$i, X1:$i > $o]:in @ (dsetconstr @ X4 @ (^[X2:$i]:X1 @ X2)) @ (powerset @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sepInPowerset)).
85.30/85.71	thf(sepSubset, axiom, (sepSubset<=>![X4:$i, X1:$i > $o]:subset @ (dsetconstr @ X4 @ (^[X2:$i]:X1 @ X2)) @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sepSubset)).
85.30/85.71	thf(binunionIL, axiom, (binunionIL<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>in @ X2 @ (binunion @ X4 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionIL)).
85.30/85.71	thf(upairset2IR, axiom, (upairset2IR<=>![X2:$i, X3:$i]:in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairset2IR)).
85.30/85.71	thf(binunionIR, axiom, (binunionIR<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X5=>in @ X2 @ (binunion @ X4 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionIR)).
85.30/85.71	thf(binunionEcases, axiom, (binunionEcases<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(in @ X2 @ (binunion @ X4 @ X5)=>((in @ X2 @ X4=>X19)=>((in @ X2 @ X5=>X19)=>X19)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionEcases)).
85.30/85.71	thf(binunionE, axiom, (binunionE<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (binunion @ X4 @ X5)=>(in @ X2 @ X4|in @ X2 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionE)).
85.30/85.71	thf(binunionLsub, axiom, (binunionLsub<=>![X4:$i, X5:$i]:subset @ X4 @ (binunion @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionLsub)).
85.30/85.71	thf(binunionRsub, axiom, (binunionRsub<=>![X4:$i, X5:$i]:subset @ X5 @ (binunion @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionRsub)).
85.30/85.71	thf(binintersectI, axiom, (binintersectI<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X5=>in @ X2 @ (binintersect @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectI)).
85.30/85.71	thf(binintersectSubset5, axiom, (binintersectSubset5<=>![X4:$i, X5:$i, X7:$i]:(subset @ X7 @ X4=>(subset @ X7 @ X5=>subset @ X7 @ (binintersect @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset5)).
85.30/85.71	thf(binintersectEL, axiom, (binintersectEL<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (binintersect @ X4 @ X5)=>in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectEL)).
85.30/85.71	thf(binintersectLsub, axiom, (binintersectLsub<=>![X4:$i, X5:$i]:subset @ (binintersect @ X4 @ X5) @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectLsub)).
85.30/85.71	thf(binintersectSubset2, axiom, (binintersectSubset2<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>(binintersect @ X4 @ X5)=(X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset2)).
85.30/85.71	thf(binintersectSubset3, axiom, (binintersectSubset3<=>![X4:$i, X5:$i]:((binintersect @ X4 @ X5)=(X5)=>subset @ X5 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset3)).
85.30/85.71	thf(binintersectER, axiom, (binintersectER<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (binintersect @ X4 @ X5)=>in @ X2 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectER)).
85.30/85.71	thf(disjointsetsI1, axiom, (disjointsetsI1<=>![X4:$i, X5:$i]:(~(?[X2:$i]:(in @ X2 @ X4&in @ X2 @ X5))=>(binintersect @ X4 @ X5)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', disjointsetsI1)).
85.30/85.71	thf(binintersectRsub, axiom, (binintersectRsub<=>![X4:$i, X5:$i]:subset @ (binintersect @ X4 @ X5) @ X5), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectRsub)).
85.30/85.71	thf(binintersectSubset4, axiom, (binintersectSubset4<=>![X4:$i, X5:$i]:(subset @ X5 @ X4=>(binintersect @ X4 @ X5)=(X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset4)).
85.30/85.71	thf(binintersectSubset1, axiom, (binintersectSubset1<=>![X4:$i, X5:$i]:((binintersect @ X4 @ X5)=(X4)=>subset @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset1)).
85.30/85.71	thf(bs114d, axiom, (bs114d<=>![X4:$i, X5:$i, X7:$i]:(binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', bs114d)).
85.30/85.71	thf(setminusI, axiom, (setminusI<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X5)=>in @ X2 @ (setminus @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusI)).
85.30/85.71	thf(setminusEL, axiom, (setminusEL<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (setminus @ X4 @ X5)=>in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusEL)).
85.30/85.71	thf(setminusER, axiom, (setminusER<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (setminus @ X4 @ X5)=>~(in @ X2 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusER)).
85.30/85.71	thf(setminusSubset2, axiom, (setminusSubset2<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>(setminus @ X4 @ X5)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusSubset2)).
85.30/85.71	thf(setminusERneg, axiom, (setminusERneg<=>![X4:$i, X5:$i, X2:$i]:(~(in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4=>in @ X2 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusERneg)).
85.30/85.71	thf(setminusELneg, axiom, (setminusELneg<=>![X4:$i, X5:$i, X2:$i]:(~(in @ X2 @ (setminus @ X4 @ X5))=>(~(in @ X2 @ X5)=>~(in @ X2 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusELneg)).
85.30/85.71	thf(setminusILneg, axiom, (setminusILneg<=>![X4:$i, X5:$i, X2:$i]:(~(in @ X2 @ X4)=>~(in @ X2 @ (setminus @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusILneg)).
85.30/85.71	thf(setminusIRneg, axiom, (setminusIRneg<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X5=>~(in @ X2 @ (setminus @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusIRneg)).
85.30/85.71	thf(setminusLsub, axiom, (setminusLsub<=>![X4:$i, X5:$i]:subset @ (setminus @ X4 @ X5) @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusLsub)).
85.30/85.71	thf(setminusSubset1, axiom, (setminusSubset1<=>![X4:$i, X5:$i]:((setminus @ X4 @ X5)=(emptyset)=>subset @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusSubset1)).
85.30/85.71	thf(symdiffE, axiom, (symdiffE<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (symdiff @ X4 @ X5)=>![X20:$o]:((in @ X2 @ X4=>(~(in @ X2 @ X5)=>X20))=>((~(in @ X2 @ X4)=>(in @ X2 @ X5=>X20))=>X20)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', symdiffE)).
85.30/85.71	thf(symdiffI1, axiom, (symdiffI1<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X5)=>in @ X2 @ (symdiff @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', symdiffI1)).
85.30/85.71	thf(symdiffI2, axiom, (symdiffI2<=>![X4:$i, X5:$i, X2:$i]:(~(in @ X2 @ X4)=>(in @ X2 @ X5=>in @ X2 @ (symdiff @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', symdiffI2)).
85.30/85.71	thf(symdiffIneg1, axiom, (symdiffIneg1<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X5=>~(in @ X2 @ (symdiff @ X4 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', symdiffIneg1)).
85.30/85.71	thf(symdiffIneg2, axiom, (symdiffIneg2<=>![X4:$i, X5:$i, X2:$i]:(~(in @ X2 @ X4)=>(~(in @ X2 @ X5)=>~(in @ X2 @ (symdiff @ X4 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', symdiffIneg2)).
85.30/85.71	thf(secondinupair, axiom, (secondinupair<=>![X2:$i, X3:$i]:in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', secondinupair)).
85.30/85.71	thf(setukpairIL, axiom, (setukpairIL<=>![X2:$i, X3:$i]:in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairIL)).
85.30/85.71	thf(setukpairIR, axiom, (setukpairIR<=>![X2:$i, X3:$i]:in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairIR)).
85.30/85.71	thf(kpairiskpair, axiom, (kpairiskpair<=>![X2:$i, X3:$i]:iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', kpairiskpair)).
85.30/85.71	thf(kpairp, axiom, (kpairp<=>![X2:$i, X3:$i]:iskpair @ (kpair @ X2 @ X3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', kpairp)).
85.30/85.71	thf(singletonsubset, axiom, (singletonsubset<=>![X4:$i, X2:$i]:(in @ X2 @ X4=>subset @ (setadjoin @ X2 @ emptyset) @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletonsubset)).
85.30/85.71	thf(singletoninpowerset, axiom, (singletoninpowerset<=>![X4:$i, X2:$i]:(in @ X2 @ X4=>in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletoninpowerset)).
85.30/85.71	thf(singletoninpowunion, axiom, (singletoninpowunion<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletoninpowunion)).
85.30/85.71	thf(upairset2E, axiom, (upairset2E<=>![X2:$i, X3:$i, X14:$i]:(in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=>((X14)=(X2)|(X14)=(X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairset2E)).
85.30/85.71	thf(upairsubunion, axiom, (upairsubunion<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsubunion)).
85.30/85.71	thf(upairinpowunion, axiom, (upairinpowunion<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairinpowunion)).
85.30/85.71	thf(ubforcartprodlem1, axiom, (ubforcartprodlem1<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ubforcartprodlem1)).
85.30/85.71	thf(ubforcartprodlem2, axiom, (ubforcartprodlem2<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ubforcartprodlem2)).
85.30/85.71	thf(ubforcartprodlem3, axiom, (ubforcartprodlem3<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ubforcartprodlem3)).
85.30/85.71	thf(cartprodpairin, axiom, (cartprodpairin<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodpairin)).
85.30/85.71	thf(cartprodmempair1, axiom, (cartprodmempair1<=>![X4:$i, X5:$i, X18:$i]:(in @ X18 @ (cartprod @ X4 @ X5)=>?[X2:$i]:(in @ X2 @ X4&?[X3:$i]:(in @ X3 @ X5&(X18)=(kpair @ X2 @ X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodmempair1)).
85.30/85.71	thf(cartprodmempair, axiom, (cartprodmempair<=>![X4:$i, X5:$i, X18:$i]:(in @ X18 @ (cartprod @ X4 @ X5)=>iskpair @ X18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodmempair)).
85.30/85.71	thf(setunionE2, axiom, (setunionE2<=>![X4:$i, X2:$i]:(in @ X2 @ (setunion @ X4)=>?[X21:$i]:(in @ X21 @ X4&in @ X2 @ X21))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionE2)).
85.30/85.71	thf(setunionsingleton1, axiom, (setunionsingleton1<=>![X4:$i]:subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionsingleton1)).
85.30/85.71	thf(setunionsingleton2, axiom, (setunionsingleton2<=>![X4:$i]:subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionsingleton2)).
85.30/85.71	thf(setunionsingleton, axiom, (setunionsingleton<=>![X2:$i]:(setunion @ (setadjoin @ X2 @ emptyset))=(X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionsingleton)).
85.30/85.71	thf(singletonprop, axiom, (singletonprop<=>![X4:$i, X1:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(X1 @ X2=>(X1 @ X3=>(X2)=(X3)))))=>(?[X2:$i]:(in @ X2 @ X4&X1 @ X2)=>singleton @ (dsetconstr @ X4 @ (^[X2:$i]:X1 @ X2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletonprop)).
85.30/85.71	thf(singletonsuniq, axiom, (singletonsuniq<=>![X2:$i, X3:$i]:((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset)=>(X2)=(X3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletonsuniq)).
85.30/85.71	thf(setukpairinjL1, axiom, (setukpairinjL1<=>![X2:$i, X3:$i, X14:$i]:(in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=>(X2)=(X14))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairinjL1)).
85.30/85.71	thf(kfstsingleton, axiom, (kfstsingleton<=>![X18:$i]:(iskpair @ X18=>singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:in @ (setadjoin @ X2 @ emptyset) @ X18)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', kfstsingleton)).
85.30/85.71	thf(theprop, axiom, (theprop<=>![X21:$i]:(singleton @ X21=>in @ (setunion @ X21) @ X21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', theprop)).
85.30/85.71	thf(kfstpairEq, axiom, (kfstpairEq<=>![X2:$i, X3:$i]:(kfst @ (kpair @ X2 @ X3))=(X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', kfstpairEq)).
85.30/85.71	thf(cartprodfstin, axiom, (cartprodfstin<=>![X4:$i, X5:$i, X18:$i]:(in @ X18 @ (cartprod @ X4 @ X5)=>in @ (kfst @ X18) @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodfstin)).
85.30/85.71	thf(setukpairinjL2, axiom, (setukpairinjL2<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset))=>(X2)=(X14))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairinjL2)).
85.30/85.71	thf(setukpairinjL, axiom, (setukpairinjL<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((kpair @ X2 @ X3)=(kpair @ X14 @ X18)=>(X2)=(X14))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairinjL)).
85.30/85.71	thf(setukpairinjR11, axiom, (setukpairinjR11<=>![X2:$i, X3:$i]:((X2)=(X3)=>(setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairinjR11)).
85.30/85.71	thf(setukpairinjR12, axiom, (setukpairinjR12<=>![X2:$i, X3:$i]:((X2)=(X3)=>(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairinjR12)).
85.30/85.71	thf(setukpairinjR1, axiom, (setukpairinjR1<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset))=>((X14)=(X18)=>(X3)=(X18)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairinjR1)).
85.30/85.71	thf(upairequniteq, axiom, (upairequniteq<=>![X2:$i, X3:$i, X14:$i]:((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset)=>(X2)=(X3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairequniteq)).
85.30/85.71	thf(setukpairinjR2, axiom, (setukpairinjR2<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset))=>(X3)=(X18))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairinjR2)).
85.30/85.71	thf(setukpairinjR, axiom, (setukpairinjR<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((kpair @ X2 @ X3)=(kpair @ X14 @ X18)=>(X3)=(X18))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairinjR)).
85.30/85.71	thf(ksndsingleton, axiom, (ksndsingleton<=>![X18:$i]:(iskpair @ X18=>singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(X18)=(kpair @ (kfst @ X18) @ X2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ksndsingleton)).
85.30/85.71	thf(ksndpairEq, axiom, (ksndpairEq<=>![X2:$i, X3:$i]:(ksnd @ (kpair @ X2 @ X3))=(X3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ksndpairEq)).
85.30/85.71	thf(kpairsurjEq, axiom, (kpairsurjEq<=>![X18:$i]:(iskpair @ X18=>(kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', kpairsurjEq)).
85.30/85.71	thf(cartprodsndin, axiom, (cartprodsndin<=>![X4:$i, X5:$i, X18:$i]:(in @ X18 @ (cartprod @ X4 @ X5)=>in @ (ksnd @ X18) @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodsndin)).
85.30/85.71	thf(cartprodpairmemEL, axiom, (cartprodpairmemEL<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5)=>in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodpairmemEL)).
85.30/85.71	thf(cartprodpairmemER, axiom, (cartprodpairmemER<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5)=>in @ X3 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodpairmemER)).
85.30/85.71	thf(cartprodmempaircEq, axiom, (cartprodmempaircEq<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(kpair @ X2 @ X3)=(kpair @ X2 @ X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodmempaircEq)).
85.30/85.71	thf(cartprodfstpairEq, axiom, (cartprodfstpairEq<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodfstpairEq)).
85.30/85.71	thf(cartprodsndpairEq, axiom, (cartprodsndpairEq<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodsndpairEq)).
85.30/85.71	thf(cartprodpairsurjEq, axiom, (cartprodpairsurjEq<=>![X4:$i, X5:$i, X18:$i]:(in @ X18 @ (cartprod @ X4 @ X5)=>(kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodpairsurjEq)).
85.30/85.71	thf(dpsetconstrI, axiom, (dpsetconstrI<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(X22 @ X2 @ X3=>in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:X22 @ X14 @ X18)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dpsetconstrI)).
85.30/85.71	thf(dpsetconstrSub, axiom, (dpsetconstrSub<=>![X4:$i, X5:$i, X23:$i > $i > $o]:subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:X23 @ X2 @ X3)) @ (cartprod @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dpsetconstrSub)).
85.30/85.71	thf(dpsetconstrERa, axiom, (dpsetconstrERa<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:X25 @ X14 @ X18))=>X25 @ X2 @ X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dpsetconstrERa)).
85.30/85.71	thf(dpsetconstrEL1, axiom, (dpsetconstrEL1<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:X26 @ X14 @ X18))=>in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dpsetconstrEL1)).
85.30/85.71	thf(dpsetconstrEL2, axiom, (dpsetconstrEL2<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:X27 @ X14 @ X18))=>in @ X3 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dpsetconstrEL2)).
85.30/85.71	thf(dpsetconstrER, axiom, (dpsetconstrER<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:X28 @ X14 @ X18))=>X28 @ X2 @ X3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dpsetconstrER)).
85.30/85.71	thf(funcImageSingleton, axiom, (funcImageSingleton<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>![X2:$i]:(in @ X2 @ X4=>singleton @ (dsetconstr @ X5 @ (^[X3:$i]:in @ (kpair @ X2 @ X3) @ X29))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', funcImageSingleton)).
85.30/85.71	thf(apProp, axiom, (apProp<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>![X2:$i]:(in @ X2 @ X4=>in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:in @ (kpair @ X2 @ X3) @ X29))) @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', apProp)).
85.30/85.71	thf(app, axiom, (app<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>![X2:$i]:(in @ X2 @ X4=>in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', app)).
85.30/85.71	thf(infuncsetfunc, axiom, (infuncsetfunc<=>![X4:$i, X5:$i, X29:$i]:(in @ X29 @ (funcSet @ X4 @ X5)=>func @ X4 @ X5 @ X29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', infuncsetfunc)).
85.30/85.71	thf(ap2p, axiom, (ap2p<=>![X4:$i, X5:$i, X29:$i]:(in @ X29 @ (funcSet @ X4 @ X5)=>![X2:$i]:(in @ X2 @ X4=>in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ap2p)).
85.30/85.71	thf(funcinfuncset, axiom, (funcinfuncset<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>in @ X29 @ (funcSet @ X4 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', funcinfuncset)).
85.30/85.71	thf(lamProp, axiom, (lamProp<=>![X4:$i, X5:$i, X30:$i > $i]:(![X2:$i]:(in @ X2 @ X4=>in @ (X30 @ X2) @ X5)=>func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(X30 @ X2)=(X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', lamProp)).
85.30/85.71	thf(lamp, axiom, (lamp<=>![X4:$i, X5:$i, X31:$i > $i]:(![X2:$i]:(in @ X2 @ X4=>in @ (X31 @ X2) @ X5)=>func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:X31 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', lamp)).
85.30/85.71	thf(lam2p, axiom, (lam2p<=>![X4:$i, X5:$i, X32:$i > $i]:(![X2:$i]:(in @ X2 @ X4=>in @ (X32 @ X2) @ X5)=>in @ (lam @ X4 @ X5 @ (^[X2:$i]:X32 @ X2)) @ (funcSet @ X4 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', lam2p)).
85.30/85.71	thf(funcGraphProp1, axiom, (funcGraphProp1<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>![X2:$i]:(in @ X2 @ X4=>in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', funcGraphProp1)).
85.30/85.71	thf(funcGraphProp3, axiom, (funcGraphProp3<=>![X4:$i, X5:$i, X29:$i]:(in @ X29 @ (funcSet @ X4 @ X5)=>![X2:$i]:(in @ X2 @ X4=>in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', funcGraphProp3)).
85.30/85.71	thf(funcGraphProp2, axiom, (funcGraphProp2<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ X29=>(ap @ X4 @ X5 @ X29 @ X2)=(X3)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', funcGraphProp2)).
85.30/85.71	thf(funcextLem, axiom, (funcextLem<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>![X34:$i]:(func @ X4 @ X5 @ X34=>(![X2:$i]:(in @ X2 @ X4=>(ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ X34=>in @ (kpair @ X2 @ X3) @ X29))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', funcextLem)).
85.30/85.71	thf(funcGraphProp4, axiom, (funcGraphProp4<=>![X4:$i, X5:$i, X29:$i]:(in @ X29 @ (funcSet @ X4 @ X5)=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ X29=>(ap @ X4 @ X5 @ X29 @ X2)=(X3)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', funcGraphProp4)).
85.30/85.71	thf(funcext, axiom, (funcext<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>![X34:$i]:(func @ X4 @ X5 @ X34=>(![X2:$i]:(in @ X2 @ X4=>(ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))=>(X29)=(X34))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', funcext)).
85.30/85.71	thf(funcext2, axiom, (funcext2<=>![X4:$i, X5:$i, X29:$i]:(in @ X29 @ (funcSet @ X4 @ X5)=>![X34:$i]:(in @ X34 @ (funcSet @ X4 @ X5)=>(![X2:$i]:(in @ X2 @ X4=>(ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))=>(X29)=(X34))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', funcext2)).
85.30/85.71	thf(ap2apEq1, axiom, (ap2apEq1<=>![X4:$i, X5:$i, X29:$i]:(in @ X29 @ (funcSet @ X4 @ X5)=>![X2:$i]:(in @ X2 @ X4=>(ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ap2apEq1)).
85.30/85.71	thf(ap2apEq2, axiom, (ap2apEq2<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>![X2:$i]:(in @ X2 @ X4=>(ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ap2apEq2)).
85.30/85.71	thf(beta1, axiom, (beta1<=>![X4:$i, X5:$i, X36:$i > $i]:(![X2:$i]:(in @ X2 @ X4=>in @ (X36 @ X2) @ X5)=>![X2:$i]:(in @ X2 @ X4=>(ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:X36 @ X3)) @ X2)=(X36 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', beta1)).
85.30/85.71	thf(eta1, axiom, (eta1<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>(lam @ X4 @ X5 @ (^[X2:$i]:ap @ X4 @ X5 @ X29 @ X2))=(X29))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eta1)).
85.30/85.71	thf(lam2lamEq, axiom, (lam2lamEq<=>![X4:$i, X5:$i, X37:$i > $i]:(![X2:$i]:(in @ X2 @ X4=>in @ (X37 @ X2) @ X5)=>(lam @ X4 @ X5 @ (^[X2:$i]:X37 @ X2))=(lam @ X4 @ X5 @ (^[X2:$i]:X37 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', lam2lamEq)).
85.30/85.71	thf(beta2, axiom, (beta2<=>![X4:$i, X5:$i, X38:$i > $i]:(![X2:$i]:(in @ X2 @ X4=>in @ (X38 @ X2) @ X5)=>![X2:$i]:(in @ X2 @ X4=>(ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:X38 @ X3)) @ X2)=(X38 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', beta2)).
85.30/85.71	thf(eta2, axiom, (eta2<=>![X4:$i, X5:$i, X29:$i]:(in @ X29 @ (funcSet @ X4 @ X5)=>(lam @ X4 @ X5 @ (^[X2:$i]:ap @ X4 @ X5 @ X29 @ X2))=(X29))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eta2)).
85.30/85.71	thf(iffalseProp1, axiom, (iffalseProp1<=>![X4:$i, X39:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(~(X39)=>in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((X39&(X14)=(X2))|(~(X39)&(X14)=(X3))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', iffalseProp1)).
85.30/85.71	thf(iffalseProp2, axiom, (iffalseProp2<=>![X4:$i, X40:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(~(X40)=>(dsetconstr @ X4 @ (^[X14:$i]:((X40&(X14)=(X2))|(~(X40)&(X14)=(X3)))))=(setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', iffalseProp2)).
85.30/85.71	thf(iftrueProp1, axiom, (iftrueProp1<=>![X4:$i, X41:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(X41=>in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((X41&(X14)=(X2))|(~(X41)&(X14)=(X3))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', iftrueProp1)).
85.30/85.71	thf(iftrueProp2, axiom, (iftrueProp2<=>![X4:$i, X42:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(X42=>(dsetconstr @ X4 @ (^[X14:$i]:((X42&(X14)=(X2))|(~(X42)&(X14)=(X3)))))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', iftrueProp2)).
85.30/85.71	thf(ifSingleton, axiom, (ifSingleton<=>![X4:$i, X43:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((X43&(X14)=(X2))|(~(X43)&(X14)=(X3)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ifSingleton)).
85.30/85.71	thf(ifp, axiom, (ifp<=>![X4:$i, X44:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>in @ (if @ X4 @ (X44) @ X2 @ X3) @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ifp)).
85.30/85.71	thf(theeq, axiom, (theeq<=>![X21:$i]:(singleton @ X21=>![X2:$i]:(in @ X2 @ X21=>(setunion @ X21)=(X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', theeq)).
85.30/85.71	thf(iftrue, axiom, (iftrue<=>![X4:$i, X45:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(X45=>(if @ X4 @ (X45) @ X2 @ X3)=(X2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', iftrue)).
85.30/85.71	thf(iffalse, axiom, (iffalse<=>![X4:$i, X46:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(~(X46)=>(if @ X4 @ (X46) @ X2 @ X3)=(X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', iffalse)).
85.30/85.71	thf(iftrueorfalse, axiom, (iftrueorfalse<=>![X4:$i, X47:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>in @ (if @ X4 @ (X47) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', iftrueorfalse)).
85.30/85.71	thf(binintersectT_lem, axiom, (binintersectT_lem<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>in @ (binintersect @ X21 @ X48) @ (powerset @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectT_lem)).
85.30/85.71	thf(binunionT_lem, axiom, (binunionT_lem<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>in @ (binunion @ X21 @ X48) @ (powerset @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionT_lem)).
85.30/85.71	thf(powersetT_lem, axiom, (powersetT_lem<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetT_lem)).
85.30/85.71	thf(c_0_234, axiom, (replAx)=(![X6:$i > $i > $o, X4:$i]:(![X2:$i]:(in @ X2 @ X4=>?[X756:$i]:(X6 @ X2 @ X756&![X758:$i]:(X6 @ X2 @ X758=>(X756)=(X758))))=>?[X5:$i]:![X2:$i]:(in @ X2 @ X5<=>?[X3:$i]:(in @ X3 @ X4&X6 @ X3 @ X2)))), inference(apply_def,[status(thm)],[replAx, exu])).
85.30/85.71	thf(c_0_235, axiom, (descrp)=(![X1:$i > $o]:(?[X759:$i]:(X1 @ X759&![X760:$i]:(X1 @ X760=>(X759)=(X760)))=>X1 @ (descr @ (^[X2:$i]:X1 @ X2)))), inference(apply_def,[status(thm)],[descrp, exu])).
85.30/85.71	thf(c_0_236, axiom, (exuE1)=(![X1:$i > $o]:(?[X761:$i]:(X1 @ X761&![X762:$i]:(X1 @ X762=>(X761)=(X762)))=>?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3))))), inference(apply_def,[status(thm)],[exuE1, exu])).
85.30/85.71	thf(c_0_237, axiom, (exuE3e)=(![X1:$i > $o]:(?[X763:$i]:(X1 @ X763&![X764:$i]:(X1 @ X764=>(X763)=(X764)))=>?[X2:$i]:X1 @ X2)), inference(apply_def,[status(thm)],[exuE3e, exu])).
85.30/85.71	thf(c_0_238, axiom, (nonemptyE1)=(![X4:$i]:((X4)!=(emptyset)=>?[X2:$i]:in @ X2 @ X4)), inference(apply_def,[status(thm)],[nonemptyE1, nonempty])).
85.30/85.71	thf(c_0_239, axiom, (nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>(dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))!=(emptyset)))), inference(apply_def,[status(thm)],[nonemptyI, nonempty])).
85.30/85.71	thf(c_0_240, axiom, (nonemptyI1)=(![X4:$i]:(?[X2:$i]:in @ X2 @ X4=>(X4)!=(emptyset))), inference(apply_def,[status(thm)],[nonemptyI1, nonempty])).
85.30/85.71	thf(c_0_241, axiom, (exuE2)=(![X1:$i > $o]:(?[X765:$i]:(X1 @ X765&![X766:$i]:(X1 @ X766=>(X765)=(X766)))=>?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2)))), inference(apply_def,[status(thm)],[exuE2, exu])).
85.30/85.71	thf(c_0_242, axiom, (nonemptyImpWitness)=(![X4:$i]:((X4)!=(emptyset)=>?[X2:$i]:(in @ X2 @ X4&$true))), inference(apply_def,[status(thm)],[nonemptyImpWitness, nonempty])).
85.30/85.71	thf(c_0_243, axiom, (exuI1)=(![X1:$i > $o]:(?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3)))=>?[X767:$i]:(X1 @ X767&![X768:$i]:(X1 @ X768=>(X767)=(X768))))), inference(apply_def,[status(thm)],[exuI1, exu])).
85.30/85.71	thf(c_0_244, axiom, (exuI3)=(![X1:$i > $o]:(?[X2:$i]:X1 @ X2=>(![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3)))=>?[X769:$i]:(X1 @ X769&![X770:$i]:(X1 @ X770=>(X769)=(X770)))))), inference(apply_def,[status(thm)],[exuI3, exu])).
85.30/85.71	thf(c_0_245, axiom, (exuI2)=(![X1:$i > $o]:(?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2))=>?[X771:$i]:(X1 @ X771&![X772:$i]:(X1 @ X772=>(X771)=(X772))))), inference(apply_def,[status(thm)],[exuI2, exu])).
85.30/85.71	thf(c_0_246, axiom, (exuE3u)=(![X1:$i > $o]:(?[X773:$i]:(X1 @ X773&![X774:$i]:(X1 @ X774=>(X773)=(X774)))=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))), inference(apply_def,[status(thm)],[exuE3u, exu])).
85.30/85.71	thf(c_0_247, axiom, (exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(?[X775:$i]:(X1 @ X775&![X776:$i]:(X1 @ X776=>(X775)=(X776)))<=>?[X777:$i]:(X17 @ X777&![X778:$i]:(X17 @ X778=>(X777)=(X778)))))), inference(apply_def,[status(thm)],[exu__Cong, exu])).
85.30/85.71	thf(c_0_248, axiom, (exuEu)=(![X1:$i > $o]:(?[X779:$i]:(X1 @ X779&![X780:$i]:(X1 @ X780=>(X779)=(X780)))=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))), inference(apply_def,[status(thm)],[exuEu, exu])).
85.30/85.71	thf(c_0_249, axiom, (descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(?[X781:$i]:(X1 @ X781&![X782:$i]:(X1 @ X782=>(X781)=(X782)))=>(?[X783:$i]:(X17 @ X783&![X784:$i]:(X17 @ X784=>(X783)=(X784)))=>(descr @ (^[X2:$i]:X1 @ X2))=(descr @ (^[X2:$i]:X17 @ X2)))))), inference(apply_def,[status(thm)],[descr__Cong, exu])).
85.30/85.71	thf(c_0_250, axiom, (ex1E1)=(![X4:$i, X1:$i > $o]:(singleton @ (dsetconstr @ X4 @ (^[X785:$i]:X1 @ X785))=>?[X2:$i]:(in @ X2 @ X4&X1 @ X2))), inference(apply_def,[status(thm)],[ex1E1, ex1])).
85.30/85.71	thf(c_0_251, axiom, (ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>(![X3:$i]:(in @ X3 @ X4=>(X1 @ X3=>(X3)=(X2)))=>singleton @ (dsetconstr @ X4 @ (^[X786:$i]:X1 @ X786)))))), inference(apply_def,[status(thm)],[ex1I, ex1])).
85.30/85.71	thf(c_0_252, axiom, (ex1I2)=(![X4:$i, X1:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(X1 @ X2=>(X1 @ X3=>(X2)=(X3)))))=>(?[X2:$i]:(in @ X2 @ X4&X1 @ X2)=>singleton @ (dsetconstr @ X4 @ (^[X788:$i]:X1 @ X788))))), inference(apply_def,[status(thm)],[ex1I2, ex1])).
85.30/85.71	thf(c_0_253, axiom, (setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:X24 @ X2 @ X3)) @ (cartprod @ X4 @ X5)), inference(apply_def,[status(thm)],[setOfPairsIsBReln, breln])).
85.30/85.71	thf(c_0_254, axiom, (brelnall1)=(![X4:$i, X5:$i, X33:$i]:(subset @ X33 @ (cartprod @ X4 @ X5)=>![X1:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ X33=>X1 @ (kpair @ X2 @ X3))))=>![X2:$i]:(in @ X2 @ X33=>X1 @ X2)))), inference(apply_def,[status(thm)],[brelnall1, breln])).
85.30/85.71	thf(c_0_255, axiom, (brelnall2)=(![X4:$i, X5:$i, X33:$i]:(subset @ X33 @ (cartprod @ X4 @ X5)=>![X1:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ X33=>X1 @ (kpair @ X2 @ X3))))=>![X2:$i]:(in @ X2 @ X33=>X1 @ X2)))), inference(apply_def,[status(thm)],[brelnall2, breln])).
85.30/85.71	thf(c_0_256, axiom, (ex1E2)=(![X4:$i, X1:$i > $o]:(singleton @ (dsetconstr @ X4 @ (^[X789:$i]:X1 @ X789))=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))))), inference(apply_def,[status(thm)],[ex1E2, ex1])).
85.30/85.71	thf(c_0_257, axiom, (subbreln)=(![X4:$i, X5:$i, X33:$i]:(subset @ X33 @ (cartprod @ X4 @ X5)=>![X35:$i]:(subset @ X35 @ (cartprod @ X4 @ X5)=>(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ X33=>in @ (kpair @ X2 @ X3) @ X35)))=>subset @ X33 @ X35)))), inference(apply_def,[status(thm)],[subbreln, breln])).
85.30/85.71	thf(c_0_258, axiom, (eqbreln)=(![X4:$i, X5:$i, X33:$i]:(subset @ X33 @ (cartprod @ X4 @ X5)=>![X35:$i]:(subset @ X35 @ (cartprod @ X4 @ X5)=>(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ X33=>in @ (kpair @ X2 @ X3) @ X35)))=>(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ X35=>in @ (kpair @ X2 @ X3) @ X33)))=>(X33)=(X35)))))), inference(apply_def,[status(thm)],[eqbreln, breln])).
85.30/85.71	thf(c_0_259, plain, ![X2:$i, X1:$i > $o]:(epred1_2 @ X1 @ X2<=>X1 @ X2), introduced(definition)).
85.30/85.71	thf(c_0_260, plain, ![X2:$i]:epred8_1 @ X2, inference(fof_simplification,[status(thm)],[introduced(definition)])).
85.30/85.71	thf(c_0_261, plain, ![X2:$i, X18:$i]:(epred7_2 @ X18 @ X2<=>in @ (setadjoin @ X2 @ emptyset) @ X18), introduced(definition)).
85.30/85.71	thf(c_0_262, plain, ![X2:$i, X18:$i]:(epred6_2 @ X18 @ X2<=>(X18)=(kpair @ (kfst @ X18) @ X2)), introduced(definition)).
85.30/85.71	thf(c_0_263, plain, ![X18:$i, X14:$i, X22:$i > $i > $o]:(epred2_3 @ X22 @ X14 @ X18<=>X22 @ X14 @ X18), introduced(definition)).
85.30/85.71	thf(c_0_264, plain, ![X3:$i, X2:$i, X30:$i > $i]:(epred5_3 @ X30 @ X2 @ X3<=>(X30 @ X2)=(X3)), introduced(definition)).
85.30/85.71	thf(c_0_265, plain, ![X3:$i, X36:$i > $i]:(esk1_2 @ X36 @ X3)=(X36 @ X3), introduced(definition)).
85.30/85.71	thf(c_0_266, plain, ![X14:$i, X2:$i, X40:$o, X3:$i]:(epred4_4 @ X3 @ X40 @ X2 @ X14<=>((X40&(X14)=(X2))|(~X40&(X14)=(X3)))), inference(fof_simplification,[status(thm)],[introduced(definition)])).
85.30/85.71	thf(c_0_267, plain, ![X3:$i, X29:$i, X2:$i]:(epred3_3 @ X2 @ X29 @ X3<=>in @ (kpair @ X2 @ X3) @ X29), introduced(definition)).
85.30/85.71	thf(c_0_268, plain, (epred9_0<=>![X4:$i]:?[X5:$i]:(((![X7:$i]:(in @ X7 @ X5=>![X2:$i]:(in @ X2 @ X7=>in @ X2 @ X4))&![X2:$i, X3:$i]:((in @ X2 @ X4&in @ X3 @ X4)=>(![X7:$i]:(in @ X7 @ X5=>(in @ X2 @ X7<=>in @ X3 @ X7))=>(X2)=(X3))))&![X7:$i, X8:$i]:((in @ X7 @ X5&in @ X8 @ X5)=>(![X2:$i]:(in @ X2 @ X7=>in @ X2 @ X8)|![X2:$i]:(in @ X2 @ X8=>in @ X2 @ X7))))&![X7:$i]:((![X2:$i]:(in @ X2 @ X7=>in @ X2 @ X4)&?[X2:$i]:in @ X2 @ X7)=>?[X8:$i, X2:$i]:(((in @ X8 @ X5&in @ X2 @ X7)&~(?[X3:$i]:(in @ X3 @ X8&in @ X3 @ X7)))&![X9:$i]:(in @ X9 @ X5=>(![X3:$i]:(in @ X3 @ X9=>in @ X3 @ X8)|in @ X2 @ X9)))))), introduced(definition)).
85.30/85.71	thf(c_0_269, negated_conjecture, ~((![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4<=>in @ X2 @ X5)=>(X4)=(X5))=>(![X2:$i]:~in @ X2 @ emptyset=>(![X2:$i, X4:$i, X3:$i]:(in @ X3 @ (setadjoin @ X2 @ X4)<=>((X3)=(X2)|in @ X3 @ X4))=>(![X4:$i, X5:$i]:(in @ X5 @ (powerset @ X4)<=>![X2:$i]:(in @ X2 @ X5=>in @ X2 @ X4))=>(![X4:$i, X2:$i]:(in @ X2 @ (setunion @ X4)<=>?[X5:$i]:(in @ X2 @ X5&in @ X5 @ X4))=>(in @ emptyset @ omega=>(![X2:$i]:(in @ X2 @ omega=>in @ (setadjoin @ X2 @ X2) @ omega)=>(![X4:$i]:((in @ emptyset @ X4&![X2:$i]:((in @ X2 @ omega&in @ X2 @ X4)=>in @ (setadjoin @ X2 @ X2) @ X4))=>![X2:$i]:(in @ X2 @ omega=>in @ X2 @ X4))=>(![X6:$i > $i > $o, X4:$i]:(![X2:$i]:(in @ X2 @ X4=>?[X756:$i]:(X6 @ X2 @ X756&![X758:$i]:(X6 @ X2 @ X758=>(X756)=(X758))))=>?[X5:$i]:![X2:$i]:(in @ X2 @ X5<=>?[X3:$i]:(in @ X3 @ X4&X6 @ X3 @ X2)))=>(![X4:$i]:(?[X2:$i]:in @ X2 @ X4=>?[X5:$i]:(in @ X5 @ X4&~(?[X2:$i]:(in @ X2 @ X5&in @ X2 @ X4))))=>(epred9_0=>(![X1:$i > $o]:(?[X759:$i]:(X1 @ X759&![X760:$i]:(X1 @ X760=>(X759)=(X760)))=>X1 @ (descr @ (epred1_2 @ X1)))=>(![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>in @ X2 @ (dsetconstr @ X4 @ (epred1_2 @ X1))))=>(![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ (dsetconstr @ X4 @ (epred1_2 @ X1))=>in @ X2 @ X4)=>(![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ (dsetconstr @ X4 @ (epred1_2 @ X1))=>X1 @ X2)=>(![X1:$i > $o]:(?[X761:$i]:(X1 @ X761&![X762:$i]:(X1 @ X762=>(X761)=(X762)))=>?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3))))=>(![X10:$o, X2:$i]:(((~X10|in @ X2 @ (prop2set @ $true))&(X10|in @ X2 @ (prop2set @ $false)))=>X10)=>(![X2:$i]:(in @ X2 @ emptyset=>![X11:$o]:X11)=>(![X2:$i]:~in @ X2 @ emptyset=>(![X2:$i]:~in @ X2 @ emptyset=>(![X1:$i > $o]:(?[X763:$i]:(X1 @ X763&![X764:$i]:(X1 @ X764=>(X763)=(X764)))=>?[X2:$i]:X1 @ X2)=>(![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4=>in @ X2 @ X5)=>(![X2:$i]:(in @ X2 @ X5=>in @ X2 @ X4)=>(X4)=(X5)))=>(![X4:$i]:(![X2:$i]:~in @ X2 @ X4=>(X4)=(emptyset))=>(![X4:$i]:(![X2:$i]:~in @ X2 @ X4=>(X4)=(emptyset))=>(![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (dsetconstr @ X4 @ (epred1_2 @ X1))<=>X1 @ X2))=>(![X4:$i]:((X4)!=(emptyset)=>?[X2:$i]:in @ X2 @ X4)=>(![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>(dsetconstr @ X4 @ (epred1_2 @ X1))!=(emptyset)))=>(![X4:$i]:(?[X2:$i]:in @ X2 @ X4=>(X4)!=(emptyset))=>(![X2:$i, X3:$i]:in @ X2 @ (setadjoin @ X2 @ X3)=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset)=>(![X2:$i, X4:$i, X3:$i]:(in @ X3 @ X4=>in @ X3 @ (setadjoin @ X2 @ X4))=>(![X2:$i, X4:$i, X3:$i]:(in @ X3 @ (setadjoin @ X2 @ X4)=>![X12:$o]:(((X3)=(X2)=>X12)=>((in @ X3 @ X4=>X12)=>X12)))=>(![X2:$i, X4:$i, X3:$i]:(in @ X3 @ (setadjoin @ X2 @ X4)=>((X3)=(X2)|in @ X3 @ X4))=>(![X4:$i]:(dsetconstr @ X4 @ epred8_1)=(X4)=>(![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X5=>in @ X2 @ X4)=>in @ X5 @ (powerset @ X4))=>(![X4:$i]:in @ emptyset @ (powerset @ X4)=>(![X4:$i]:in @ emptyset @ (powerset @ X4)=>(![X4:$i, X5:$i, X2:$i]:(in @ X5 @ (powerset @ X4)=>(in @ X2 @ X5=>in @ X2 @ X4))=>(![X4:$i, X2:$i, X5:$i]:(in @ X2 @ X5=>(in @ X5 @ X4=>in @ X2 @ (setunion @ X4)))=>(![X4:$i, X2:$i]:(in @ X2 @ (setunion @ X4)=>![X13:$o]:(![X5:$i]:(in @ X2 @ X5=>(in @ X5 @ X4=>X13))=>X13))=>(![X4:$i, X2:$i]:(in @ X2 @ X4=>in @ X2 @ (powerset @ (setunion @ X4)))=>(![X1:$i > $o]:(?[X765:$i]:(X1 @ X765&![X766:$i]:(X1 @ X766=>(X765)=(X766)))=>?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2)))=>(![X4:$i]:((X4)!=(emptyset)=>?[X2:$i]:in @ X2 @ X4)=>(![X2:$i, X3:$i]:(in @ X2 @ (setadjoin @ X3 @ emptyset)=>(X2)=(X3))=>(![X2:$i, X3:$i]:((X2)!=(X3)=>~in @ X3 @ (setadjoin @ X2 @ emptyset))=>(![X2:$i, X3:$i]:((X2)=(X3)=>in @ X2 @ (setadjoin @ X3 @ emptyset))=>(![X2:$i, X3:$i]:(in @ X2 @ (setadjoin @ X3 @ emptyset)=>in @ X3 @ (setadjoin @ X2 @ emptyset))=>(![X2:$i, X3:$i, X14:$i]:(in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=>((X14)=(X2)|(X14)=(X3)))=>(![X2:$i, X3:$i]:in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=>(![X2:$i, X3:$i]:in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=>(![X4:$i, X1:$i > $o]:(?[X2:$i]:(in @ X2 @ X4&X1 @ X2)=>(dsetconstr @ X4 @ (epred1_2 @ X1))!=(emptyset))=>(![X1:$i > $o, X2:$i]:(in @ X2 @ emptyset=>X1 @ X2)=>(![X4:$i, X1:$i > $o]:(~(![X2:$i]:(in @ X2 @ X4=>X1 @ X2))=>?[X2:$i]:(in @ X2 @ X4&~X1 @ X2))=>(![X4:$i, X1:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>~X1 @ X2)=>~(?[X2:$i]:(in @ X2 @ X4&X1 @ X2)))=>(![X4:$i, X1:$i > $o]:(~(?[X2:$i]:(in @ X2 @ X4&X1 @ X2))=>![X2:$i]:(in @ X2 @ X4=>~X1 @ X2))=>(![X4:$i, X1:$i > $o]:(?[X2:$i]:(in @ X2 @ X4&~X1 @ X2)=>~(![X2:$i]:(in @ X2 @ X4=>X1 @ X2)))=>(![X15:$o]:(X15=>((~X15|in @ emptyset @ (prop2set @ $true))&(X15|in @ emptyset @ (prop2set @ $false))))=>(![X16:$o]:(X16=>((~X16|set2prop @ (prop2set @ $true))&(X16|set2prop @ (prop2set @ $false))))=>(![X4:$i, X1:$i > $o]:(~(?[X2:$i]:(in @ X2 @ X4&X1 @ X2))=>![X2:$i]:(in @ X2 @ X4=>~X1 @ X2))=>(![X4:$i, X1:$i > $o]:(~(![X2:$i]:(in @ X2 @ X4=>X1 @ X2))=>?[X2:$i]:(in @ X2 @ X4&~X1 @ X2))=>(![X1:$i > $o]:(?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3)))=>?[X767:$i]:(X1 @ X767&![X768:$i]:(X1 @ X768=>(X767)=(X768))))=>(![X1:$i > $o]:(?[X2:$i]:X1 @ X2=>(![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3)))=>?[X769:$i]:(X1 @ X769&![X770:$i]:(X1 @ X770=>(X769)=(X770)))))=>(![X1:$i > $o]:(?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2))=>?[X771:$i]:(X1 @ X771&![X772:$i]:(X1 @ X772=>(X771)=(X772))))=>(![X4:$i, X5:$i]:((X4)=(X5)=>![X2:$i, X3:$i]:((X2)=(X3)=>(in @ X2 @ X4=>in @ X3 @ X5)))=>(![X4:$i, X5:$i]:((X4)=(X5)=>![X2:$i, X3:$i]:((X2)=(X3)=>(in @ X2 @ X4<=>in @ X3 @ X5)))=>(![X1:$i > $o]:(?[X773:$i]:(X1 @ X773&![X774:$i]:(X1 @ X774=>(X773)=(X774)))=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))=>(![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(?[X775:$i]:(X1 @ X775&![X776:$i]:(X1 @ X776=>(X775)=(X776)))<=>?[X777:$i]:(X17 @ X777&![X778:$i]:(X17 @ X778=>(X777)=(X778)))))=>((emptyset)=(emptyset)=>(![X2:$i, X3:$i]:((X2)=(X3)=>![X14:$i, X18:$i]:((X14)=(X18)=>(setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18)))=>(![X4:$i, X5:$i]:((X4)=(X5)=>(powerset @ X4)=(powerset @ X5))=>(![X4:$i, X5:$i]:((X4)=(X5)=>(setunion @ X4)=(setunion @ X5))=>((omega)=(omega)=>(![X1:$i > $o]:(?[X779:$i]:(X1 @ X779&![X780:$i]:(X1 @ X780=>(X779)=(X780)))=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))=>(![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(?[X781:$i]:(X1 @ X781&![X782:$i]:(X1 @ X782=>(X781)=(X782)))=>(?[X783:$i]:(X17 @ X783&![X784:$i]:(X17 @ X784=>(X783)=(X784)))=>(descr @ (epred1_2 @ X1))=(descr @ (epred1_2 @ X17)))))=>(![X4:$i, X5:$i]:((X4)=(X5)=>![X1:$i > $o, X17:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))))=>(dsetconstr @ X4 @ (epred1_2 @ X1))=(dsetconstr @ X5 @ (epred1_2 @ X17))))=>(![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4=>in @ X2 @ X5)=>subset @ X4 @ X5)=>(![X4:$i, X5:$i]:((X4)=(X5)=>subset @ X5 @ X4)=>(![X4:$i, X5:$i]:((X4)=(X5)=>subset @ X4 @ X5)=>(![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4=>in @ X2 @ X5)=>subset @ X4 @ X5)=>(![X4:$i]:subset @ emptyset @ X4=>(![X4:$i, X5:$i, X2:$i]:(subset @ X4 @ X5=>(in @ X2 @ X4=>in @ X2 @ X5))=>(![X4:$i, X5:$i, X2:$i]:(subset @ X4 @ X5=>(~in @ X2 @ X5=>~in @ X2 @ X4))=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~in @ X2 @ X5=>~subset @ X4 @ X5))=>(![X4:$i, X5:$i]:(~subset @ X4 @ X5=>(X4)!=(X5))=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~in @ X2 @ X5=>(X4)!=(X5)))=>(![X4:$i]:subset @ X4 @ X4=>(![X4:$i, X5:$i, X7:$i]:(subset @ X4 @ X5=>(subset @ X5 @ X7=>subset @ X4 @ X7))=>(![X2:$i, X4:$i]:subset @ X4 @ (setadjoin @ X2 @ X4)=>(![X4:$i, X2:$i, X5:$i]:(subset @ X4 @ X5=>subset @ X4 @ (setadjoin @ X2 @ X5))=>(![X4:$i, X5:$i]:(subset @ X4 @ X5=>in @ X4 @ (powerset @ X5))=>(![X4:$i, X5:$i]:(subset @ X4 @ X5=>(subset @ X5 @ X4=>(X4)=(X5)))=>(![X4:$i]:(subset @ X4 @ emptyset=>(X4)=(emptyset))=>(![X4:$i, X5:$i]:(subset @ X5 @ X4=>in @ X5 @ (powerset @ X4))=>(![X4:$i, X5:$i]:(in @ X5 @ (powerset @ X4)=>subset @ X5 @ X4)=>(![X4:$i]:in @ X4 @ (powerset @ X4)=>(![X4:$i, X5:$i]:(subset @ X4 @ X5=>subset @ (powerset @ X4) @ (powerset @ X5))=>(![X4:$i, X1:$i > $o]:in @ (dsetconstr @ X4 @ (epred1_2 @ X1)) @ (powerset @ X4)=>(![X4:$i, X1:$i > $o]:subset @ (dsetconstr @ X4 @ (epred1_2 @ X1)) @ X4=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>in @ X2 @ (binunion @ X4 @ X5))=>(![X2:$i, X3:$i]:in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X5=>in @ X2 @ (binunion @ X4 @ X5))=>(![X4:$i, X5:$i, X2:$i, X19:$o]:(in @ X2 @ (binunion @ X4 @ X5)=>((in @ X2 @ X4=>X19)=>((in @ X2 @ X5=>X19)=>X19)))=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (binunion @ X4 @ X5)=>(in @ X2 @ X4|in @ X2 @ X5))=>(![X4:$i, X5:$i]:subset @ X4 @ (binunion @ X4 @ X5)=>(![X4:$i, X5:$i]:subset @ X5 @ (binunion @ X4 @ X5)=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X5=>in @ X2 @ (binintersect @ X4 @ X5)))=>(![X4:$i, X5:$i, X7:$i]:(subset @ X7 @ X4=>(subset @ X7 @ X5=>subset @ X7 @ (binintersect @ X4 @ X5)))=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (binintersect @ X4 @ X5)=>in @ X2 @ X4)=>(![X4:$i, X5:$i]:subset @ (binintersect @ X4 @ X5) @ X4=>(![X4:$i, X5:$i]:(subset @ X4 @ X5=>(binintersect @ X4 @ X5)=(X4))=>(![X4:$i, X5:$i]:((binintersect @ X4 @ X5)=(X5)=>subset @ X5 @ X4)=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (binintersect @ X4 @ X5)=>in @ X2 @ X5)=>(![X4:$i, X5:$i]:(~(?[X2:$i]:(in @ X2 @ X4&in @ X2 @ X5))=>(binintersect @ X4 @ X5)=(emptyset))=>(![X4:$i, X5:$i]:subset @ (binintersect @ X4 @ X5) @ X5=>(![X4:$i, X5:$i]:(subset @ X5 @ X4=>(binintersect @ X4 @ X5)=(X5))=>(![X4:$i, X5:$i]:((binintersect @ X4 @ X5)=(X4)=>subset @ X4 @ X5)=>(![X4:$i, X5:$i, X7:$i]:(binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~in @ X2 @ X5=>in @ X2 @ (setminus @ X4 @ X5)))=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (setminus @ X4 @ X5)=>in @ X2 @ X4)=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (setminus @ X4 @ X5)=>~in @ X2 @ X5)=>(![X4:$i, X5:$i]:(subset @ X4 @ X5=>(setminus @ X4 @ X5)=(emptyset))=>(![X4:$i, X5:$i, X2:$i]:(~in @ X2 @ (setminus @ X4 @ X5)=>(in @ X2 @ X4=>in @ X2 @ X5))=>(![X4:$i, X5:$i, X2:$i]:(~in @ X2 @ (setminus @ X4 @ X5)=>(~in @ X2 @ X5=>~in @ X2 @ X4))=>(![X4:$i, X5:$i, X2:$i]:(~in @ X2 @ X4=>~in @ X2 @ (setminus @ X4 @ X5))=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X5=>~in @ X2 @ (setminus @ X4 @ X5))=>(![X4:$i, X5:$i]:subset @ (setminus @ X4 @ X5) @ X4=>(![X4:$i, X5:$i]:((setminus @ X4 @ X5)=(emptyset)=>subset @ X4 @ X5)=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (symdiff @ X4 @ X5)=>![X20:$o]:((in @ X2 @ X4=>(~in @ X2 @ X5=>X20))=>((~in @ X2 @ X4=>(in @ X2 @ X5=>X20))=>X20)))=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~in @ X2 @ X5=>in @ X2 @ (symdiff @ X4 @ X5)))=>(![X4:$i, X5:$i, X2:$i]:(~in @ X2 @ X4=>(in @ X2 @ X5=>in @ X2 @ (symdiff @ X4 @ X5)))=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X5=>~in @ X2 @ (symdiff @ X4 @ X5)))=>(![X4:$i, X5:$i, X2:$i]:(~in @ X2 @ X4=>(~in @ X2 @ X5=>~in @ X2 @ (symdiff @ X4 @ X5)))=>(![X2:$i, X3:$i]:in @ 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X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>in @ (binintersect @ X21 @ X48) @ (powerset @ X4)))=>(![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>in @ (binunion @ X21 @ X48) @ (powerset @ X4)))=>(![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_234]), foundationAx]), wellorderingAx]), c_0_235]), dsetconstrI]), dsetconstrEL]), dsetconstrER]), c_0_236]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_237]), setext]), emptyI]), noeltsimpempty]), setbeta]), c_0_238]), c_0_239]), c_0_240]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), setoftrueEq]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_241]), c_0_242]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), emptyE1]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_243]), c_0_244]), c_0_245]), inCongP]), in__Cong]), c_0_246]), c_0_247]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_248]), c_0_249]), 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]), c_0_250]), c_0_251]), c_0_252]), 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]), dpsetconstrSub]), c_0_253]), dpsetconstrERa]), dpsetconstrEL1]), dpsetconstrEL2]), dpsetconstrER]), funcImageSingleton]), apProp]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), lamProp]), lamp]), lam2p]), c_0_254]), c_0_255]), c_0_256]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), c_0_257]), c_0_258]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), beta1]), eta1]), lam2lamEq]), beta2]), eta2]), iffalseProp1]), iffalseProp2]), iftrueProp1]), iftrueProp2]), ifSingleton]), ifp]), theeq]), iftrue]), iffalse]), iftrueorfalse]), binintersectT_lem]), binunionT_lem]), powersetT_lem]), c_0_259]), c_0_259]), c_0_260]), c_0_259]), c_0_259]), c_0_259]), c_0_259]), c_0_259]), c_0_259]), c_0_261]), c_0_262]), c_0_263]), c_0_263]), c_0_264]), c_0_265]), c_0_265]), c_0_259]), c_0_265]), c_0_265]), c_0_266]), c_0_266]), c_0_266]), c_0_266]), c_0_266]), c_0_265]), c_0_265]), c_0_265]), c_0_265]), c_0_267]), c_0_267]), c_0_263]), c_0_263]), c_0_263]), c_0_263]), c_0_263]), c_0_259]), c_0_259]), c_0_259]), c_0_259]), c_0_259]), c_0_259]), c_0_259]), c_0_259]), c_0_259])])]), c_0_268])).
85.30/85.71	thf(c_0_270, negated_conjecture, ![X790:$i, X791:$i, X793:$i, X794:$i, X795:$i, X796:$i, X797:$i, X798:$i, X799:$i, X800:$i, X801:$i, X803:$i, X804:$i, X806:$i, X807:$i, X808:$i, X809:$i, X810:$i, X812:$i, X813:$i > $i > $o, X814:$i, X816:$i, X819:$i, X821:$i, X822:$i, X823:$i, X824:$i, X826:$i, X827:$i > $o, X828:$i, X830:$i, X831:$i > $o, X832:$i, X833:$i, X834:$i > $o, X835:$i, X836:$i, X837:$i > $o, X838:$i, X839:$i > $o, X840:$i, X843:$i, X844:$o, X845:$i, X846:$i, X847:$o, X848:$i, X849:$i, X850:$i > $o, X851:$i, X854:$i, X855:$i, X858:$i, X860:$i, X862:$i, X863:$i > $o, X864:$i, X865:$i, X867:$i, X868:$i > $o, X869:$i, X870:$i, X871:$i, X872:$i, X873:$i, X874:$i, X875:$i, X876:$i, X877:$i, X878:$i, X879:$i, X880:$o, X881:$i, X882:$i, X883:$i, X884:$i, X885:$i, X886:$i, X888:$i, X889:$i, X890:$i, X891:$i, X892:$i, X893:$i, X894:$i, X895:$i, X896:$i, X897:$i, X898:$o, X900:$i, X901:$i, X902:$i > $o, X903:$i, X906:$i, X907:$i, X908:$i, X910:$i, X911:$i, X912:$i, X913:$i, X914:$i, X915:$i, X916:$i, X917:$i, X918:$i, X919:$i, X920:$i, X921:$i, X922:$i, X923:$i, X924:$i, X925:$i, X926:$i > $o, X927:$i, X928:$i > $o, X929:$i, X930:$i, X931:$i > $o, X932:$i, X934:$i, X935:$i > $o, X937:$i, X938:$i, X939:$i > $o, X941:$i, X942:$i, X943:$i > $o, X944:$i, X946:$o, X947:$o, X948:$i, X949:$i > $o, X951:$i, X952:$i, X953:$i > $o, X954:$i, X956:$i > $o, X957:$i, X960:$i, X961:$i > $o, X962:$i, X966:$i, X967:$i > $o, X968:$i, X971:$i, X972:$i, X973:$i, X974:$i, X975:$i, X976:$i, X977:$i, X978:$i, X979:$i, X980:$i > $o, X981:$i, X983:$i, X984:$i, X985:$i > $o, X986:$i > $o, X989:$i, X992:$i, X993:$i, X996:$i, X997:$i, X998:$i, X999:$i, X1000:$i, X1001:$i, X1002:$i, X1003:$i, X1004:$i, X1005:$i > $o, X1006:$i, X1008:$i, X1009:$i, X1010:$i > $o, X1011:$i > $o, X1014:$i, X1016:$i, X1018:$i, X1019:$i, X1020:$i > $o, X1021:$i > $o, X1024:$i, X1025:$i, X1027:$i, X1028:$i, X1029:$i, X1030:$i, X1031:$i, X1032:$i, X1034:$i, X1035:$i, X1036:$i, X1037:$i, X1038:$i, X1039:$i, X1040:$i, X1041:$i, X1042:$i, X1043:$i, X1044:$i, X1045:$i, X1046:$i, X1047:$i, X1048:$i, X1049:$i, X1050:$i, X1051:$i, X1052:$i, X1053:$i, X1054:$i, X1055:$i, X1056:$i, X1057:$i, X1058:$i, X1059:$i, X1060:$i, X1061:$i, X1062:$i, X1063:$i, X1064:$i, X1065:$i, X1066:$i, X1067:$i, X1068:$i, X1069:$i, X1070:$i, X1071:$i > $o, X1072:$i, X1073:$i > $o, X1074:$i, X1075:$i, X1076:$i, X1077:$i, X1078:$i, X1079:$i, X1080:$i, X1081:$i, X1082:$i, X1083:$i, X1084:$i, X1085:$o, X1086:$i, X1087:$i, X1088:$i, X1089:$i, X1090:$i, X1091:$i, X1092:$i, X1093:$i, X1094:$i, X1095:$i, X1096:$i, X1097:$i, X1098:$i, X1099:$i, X1100:$i, X1101:$i, X1102:$i, X1103:$i, X1104:$i, X1105:$i, X1106:$i, X1107:$i, X1108:$i, X1109:$i, X1110:$i, X1111:$i, X1112:$i, X1114:$i, X1115:$i, X1116:$i, X1117:$i, X1118:$i, X1119:$i, X1120:$i, X1121:$i, X1122:$i, X1123:$i, X1124:$i, X1125:$i, X1126:$i, X1127:$i, X1128:$i, X1129:$i, X1130:$i, X1131:$i, X1132:$i, X1133:$i, X1134:$i, X1135:$i, X1136:$i, X1137:$i, X1138:$i, X1139:$i, X1140:$i, X1141:$i, X1142:$i, X1143:$i, X1144:$i, X1145:$i, X1146:$i, X1147:$i, X1148:$i, X1149:$i, X1150:$i, X1151:$i, X1152:$i, X1153:$o, X1154:$i, X1155:$i, X1156:$i, X1157:$i, X1158:$i, X1159:$i, X1160:$i, X1161:$i, X1162:$i, X1163:$i, X1164:$i, X1165:$i, X1166:$i, X1167:$i, X1168:$i, X1169:$i, X1170:$i, X1171:$i, X1172:$i, X1173:$i, X1174:$i, X1175:$i, X1176:$i, X1177:$i, X1178:$i, X1179:$i, X1180:$i, X1181:$i, X1182:$i, X1183:$i, X1184:$i, X1185:$i, X1186:$i, X1187:$i, X1188:$i, X1189:$i, X1190:$i, X1191:$i, X1192:$i, X1193:$i, X1194:$i, X1195:$i, X1196:$i, X1197:$i, X1198:$i, X1199:$i, X1200:$i, X1201:$i, X1202:$i, X1203:$i, X1204:$i, X1205:$i, X1206:$i, X1207:$i, X1208:$i, X1209:$i, X1210:$i, X1211:$i, X1212:$i, X1215:$i, X1216:$i, X1217:$i, X1218:$i, X1219:$i, X1221:$i, X1222:$i, X1223:$i, X1224:$i, X1225:$i > $o, X1228:$i, X1229:$i, X1230:$i > $o, X1232:$i, X1233:$i > $o, X1234:$i, X1236:$i, X1237:$i > $o, X1240:$i, X1241:$i, X1242:$i, X1243:$i, X1244:$i, X1245:$i, X1246:$i, X1247:$i, X1248:$i, X1249:$i, X1250:$i, X1251:$i, X1252:$i, X1253:$i, X1254:$i, X1255:$i, X1256:$i, X1257:$i, X1258:$i, X1259:$i, X1260:$i, X1261:$i, X1262:$i, X1263:$i, X1264:$i, X1265:$i, X1266:$i, X1267:$i, X1268:$i, X1269:$i, X1270:$i, X1271:$i, X1272:$i, X1273:$i, X1274:$i, X1275:$i, X1276:$i, X1277:$i, X1278:$i, X1279:$i, X1280:$i, X1281:$i, X1282:$i, X1283:$i, X1284:$i, X1285:$i, X1286:$i, X1287:$i, X1288:$i, X1289:$i, X1290:$i, X1291:$i, X1292:$i, X1293:$i, X1294:$i, X1295:$i, X1296:$i, X1297:$i, X1298:$i, X1299:$i, X1300:$i, X1301:$i, X1302:$i, X1303:$i, X1304:$i, X1305:$i, X1306:$i, X1307:$i, X1308:$i, X1309:$i, X1310:$i, X1311:$i, X1312:$i > $i > $o, X1313:$i, X1314:$i, X1315:$i, X1316:$i, X1317:$i > $i > $o, X1318:$i, X1319:$i, X1320:$i > $i > $o, X1321:$i, X1322:$i, X1323:$i > $i > $o, X1324:$i, X1325:$i, X1326:$i, X1327:$i, X1328:$i > $i > $o, X1329:$i, X1330:$i, X1331:$i, X1332:$i, X1333:$i > $i > $o, X1334:$i, X1335:$i, X1336:$i, X1337:$i, X1338:$i > $i > $o, 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X984|(X983)=(X984))))&((X981)!=(esk39_2 @ X980 @ X981)|~X980 @ X981|(~X980 @ X983|(~X980 @ X984|(X983)=(X984)))))&((((((X986 @ (esk43_2 @ X985 @ X986)|(X985 @ (esk42_3 @ X985 @ X986 @ X989)|~X985 @ X989)|(esk40_2 @ X985 @ X986)=(esk41_2 @ X985 @ X986))&(~X986 @ X992|(esk43_2 @ X985 @ X986)=(X992)|(X985 @ (esk42_3 @ X985 @ X986 @ X989)|~X985 @ X989)|(esk40_2 @ X985 @ X986)=(esk41_2 @ X985 @ X986)))&((X986 @ (esk43_2 @ X985 @ X986)|((X989)!=(esk42_3 @ X985 @ X986 @ X989)|~X985 @ X989)|(esk40_2 @ X985 @ X986)=(esk41_2 @ X985 @ X986))&(~X986 @ X992|(esk43_2 @ X985 @ X986)=(X992)|((X989)!=(esk42_3 @ X985 @ X986 @ X989)|~X985 @ X989)|(esk40_2 @ X985 @ X986)=(esk41_2 @ X985 @ X986))))&(((X985 @ (esk45_2 @ X985 @ X986)|(X986 @ (esk44_3 @ X985 @ X986 @ X993)|~X986 @ X993)|(esk40_2 @ X985 @ X986)=(esk41_2 @ X985 @ X986))&(~X985 @ X996|(esk45_2 @ X985 @ X986)=(X996)|(X986 @ (esk44_3 @ X985 @ X986 @ X993)|~X986 @ X993)|(esk40_2 @ X985 @ X986)=(esk41_2 @ X985 @ X986)))&((X985 @ (esk45_2 @ X985 @ X986)|((X993)!=(esk44_3 @ X985 @ X986 @ X993)|~X986 @ X993)|(esk40_2 @ X985 @ X986)=(esk41_2 @ X985 @ X986))&(~X985 @ X996|(esk45_2 @ X985 @ X986)=(X996)|((X993)!=(esk44_3 @ X985 @ X986 @ X993)|~X986 @ X993)|(esk40_2 @ X985 @ X986)=(esk41_2 @ X985 @ X986)))))&(((((X986 @ (esk43_2 @ X985 @ X986)|(X985 @ (esk42_3 @ X985 @ X986 @ X989)|~X985 @ X989)|(~X985 @ (esk40_2 @ X985 @ X986)|~X986 @ (esk41_2 @ X985 @ X986)))&(~X986 @ X992|(esk43_2 @ X985 @ X986)=(X992)|(X985 @ (esk42_3 @ X985 @ X986 @ X989)|~X985 @ X989)|(~X985 @ (esk40_2 @ X985 @ X986)|~X986 @ (esk41_2 @ X985 @ X986))))&((X986 @ (esk43_2 @ X985 @ X986)|((X989)!=(esk42_3 @ X985 @ X986 @ X989)|~X985 @ X989)|(~X985 @ (esk40_2 @ X985 @ X986)|~X986 @ (esk41_2 @ X985 @ X986)))&(~X986 @ X992|(esk43_2 @ X985 @ X986)=(X992)|((X989)!=(esk42_3 @ X985 @ X986 @ X989)|~X985 @ X989)|(~X985 @ (esk40_2 @ X985 @ X986)|~X986 @ (esk41_2 @ X985 @ X986)))))&(((X985 @ (esk45_2 @ X985 @ X986)|(X986 @ (esk44_3 @ X985 @ X986 @ X993)|~X986 @ X993)|(~X985 @ (esk40_2 @ X985 @ X986)|~X986 @ (esk41_2 @ X985 @ X986)))&(~X985 @ X996|(esk45_2 @ X985 @ X986)=(X996)|(X986 @ (esk44_3 @ X985 @ X986 @ X993)|~X986 @ X993)|(~X985 @ (esk40_2 @ X985 @ X986)|~X986 @ (esk41_2 @ X985 @ X986))))&((X985 @ (esk45_2 @ X985 @ X986)|((X993)!=(esk44_3 @ X985 @ X986 @ X993)|~X986 @ X993)|(~X985 @ (esk40_2 @ X985 @ X986)|~X986 @ (esk41_2 @ X985 @ X986)))&(~X985 @ X996|(esk45_2 @ X985 @ X986)=(X996)|((X993)!=(esk44_3 @ X985 @ X986 @ X993)|~X986 @ X993)|(~X985 @ (esk40_2 @ X985 @ X986)|~X986 @ (esk41_2 @ X985 @ X986))))))&((((X986 @ (esk43_2 @ X985 @ X986)|(X985 @ (esk42_3 @ X985 @ X986 @ X989)|~X985 @ X989)|(X985 @ (esk40_2 @ X985 @ X986)|X986 @ (esk41_2 @ X985 @ X986)))&(~X986 @ X992|(esk43_2 @ X985 @ X986)=(X992)|(X985 @ (esk42_3 @ X985 @ X986 @ X989)|~X985 @ X989)|(X985 @ (esk40_2 @ X985 @ X986)|X986 @ (esk41_2 @ X985 @ X986))))&((X986 @ (esk43_2 @ X985 @ X986)|((X989)!=(esk42_3 @ X985 @ X986 @ X989)|~X985 @ X989)|(X985 @ (esk40_2 @ X985 @ X986)|X986 @ (esk41_2 @ X985 @ X986)))&(~X986 @ X992|(esk43_2 @ X985 @ X986)=(X992)|((X989)!=(esk42_3 @ X985 @ X986 @ X989)|~X985 @ X989)|(X985 @ (esk40_2 @ X985 @ X986)|X986 @ (esk41_2 @ X985 @ X986)))))&(((X985 @ (esk45_2 @ X985 @ X986)|(X986 @ (esk44_3 @ X985 @ X986 @ X993)|~X986 @ X993)|(X985 @ (esk40_2 @ X985 @ X986)|X986 @ (esk41_2 @ X985 @ X986)))&(~X985 @ X996|(esk45_2 @ X985 @ X986)=(X996)|(X986 @ (esk44_3 @ X985 @ X986 @ X993)|~X986 @ X993)|(X985 @ (esk40_2 @ X985 @ X986)|X986 @ (esk41_2 @ X985 @ X986))))&((X985 @ (esk45_2 @ X985 @ X986)|((X993)!=(esk44_3 @ X985 @ X986 @ X993)|~X986 @ X993)|(X985 @ (esk40_2 @ X985 @ X986)|X986 @ (esk41_2 @ X985 @ X986)))&(~X985 @ X996|(esk45_2 @ X985 @ X986)=(X996)|((X993)!=(esk44_3 @ X985 @ X986 @ X993)|~X986 @ X993)|(X985 @ (esk40_2 @ X985 @ X986)|X986 @ (esk41_2 @ X985 @ X986))))))))&((emptyset)=(emptyset)&(((X997)!=(X998)|((X999)!=(X1000)|(setadjoin @ X997 @ X999)=(setadjoin @ X998 @ X1000)))&(((X1001)!=(X1002)|(powerset @ X1001)=(powerset @ X1002))&(((X1003)!=(X1004)|(setunion @ X1003)=(setunion @ X1004))&((omega)=(omega)&(((X1005 @ (esk46_2 @ X1005 @ X1006)|~X1005 @ X1006|(~X1005 @ X1008|(~X1005 @ X1009|(X1008)=(X1009))))&((X1006)!=(esk46_2 @ X1005 @ X1006)|~X1005 @ X1006|(~X1005 @ X1008|(~X1005 @ X1009|(X1008)=(X1009)))))&(((((X1011 @ (esk50_3 @ X1010 @ X1011 @ X1016)|~X1011 @ X1016|(descr @ (epred1_2 @ X1010))=(descr @ (epred1_2 @ X1011))|(X1010 @ (esk49_3 @ X1010 @ X1011 @ X1014)|~X1010 @ X1014)|(esk47_2 @ X1010 @ X1011)=(esk48_2 @ X1010 @ X1011))&((X1016)!=(esk50_3 @ X1010 @ X1011 @ X1016)|~X1011 @ X1016|(descr @ (epred1_2 @ X1010))=(descr @ (epred1_2 @ X1011))|(X1010 @ (esk49_3 @ X1010 @ X1011 @ X1014)|~X1010 @ X1014)|(esk47_2 @ X1010 @ X1011)=(esk48_2 @ X1010 @ X1011)))&((X1011 @ (esk50_3 @ X1010 @ X1011 @ X1016)|~X1011 @ X1016|(descr @ (epred1_2 @ X1010))=(descr @ (epred1_2 @ X1011))|((X1014)!=(esk49_3 @ X1010 @ X1011 @ X1014)|~X1010 @ X1014)|(esk47_2 @ X1010 @ X1011)=(esk48_2 @ X1010 @ X1011))&((X1016)!=(esk50_3 @ X1010 @ X1011 @ X1016)|~X1011 @ X1016|(descr @ (epred1_2 @ X1010))=(descr @ (epred1_2 @ X1011))|((X1014)!=(esk49_3 @ X1010 @ X1011 @ X1014)|~X1010 @ X1014)|(esk47_2 @ X1010 @ X1011)=(esk48_2 @ X1010 @ X1011))))&((((X1011 @ (esk50_3 @ X1010 @ X1011 @ X1016)|~X1011 @ X1016|(descr @ (epred1_2 @ X1010))=(descr @ (epred1_2 @ X1011))|(X1010 @ (esk49_3 @ X1010 @ X1011 @ X1014)|~X1010 @ X1014)|(~X1010 @ (esk47_2 @ X1010 @ X1011)|~X1011 @ (esk48_2 @ X1010 @ X1011)))&((X1016)!=(esk50_3 @ X1010 @ X1011 @ X1016)|~X1011 @ X1016|(descr @ (epred1_2 @ X1010))=(descr @ (epred1_2 @ X1011))|(X1010 @ (esk49_3 @ X1010 @ X1011 @ X1014)|~X1010 @ X1014)|(~X1010 @ (esk47_2 @ X1010 @ X1011)|~X1011 @ (esk48_2 @ X1010 @ X1011))))&((X1011 @ (esk50_3 @ X1010 @ X1011 @ X1016)|~X1011 @ X1016|(descr @ (epred1_2 @ X1010))=(descr @ (epred1_2 @ X1011))|((X1014)!=(esk49_3 @ X1010 @ X1011 @ X1014)|~X1010 @ X1014)|(~X1010 @ (esk47_2 @ X1010 @ X1011)|~X1011 @ (esk48_2 @ X1010 @ X1011)))&((X1016)!=(esk50_3 @ X1010 @ X1011 @ 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X1083))&(~X1085|X1085|~X1085|~in @ X1084 @ (binunion @ X1082 @ X1083))))&((~in @ X1088 @ (binunion @ X1086 @ X1087)|(in @ X1088 @ X1086|in @ X1088 @ X1087))&(subset @ X1089 @ (binunion @ X1089 @ X1090)&(subset @ X1092 @ (binunion @ X1091 @ X1092)&((~in @ X1095 @ X1093|(~in @ X1095 @ X1094|in @ X1095 @ (binintersect @ X1093 @ X1094)))&((~subset @ X1098 @ X1096|(~subset @ X1098 @ X1097|subset @ X1098 @ (binintersect @ X1096 @ X1097)))&((~in @ X1101 @ (binintersect @ X1099 @ X1100)|in @ X1101 @ X1099)&(subset @ (binintersect @ X1102 @ X1103) @ X1102&((~subset @ X1104 @ X1105|(binintersect @ X1104 @ X1105)=(X1104))&(((binintersect @ X1106 @ X1107)!=(X1107)|subset @ X1107 @ X1106)&((~in @ X1110 @ (binintersect @ X1108 @ X1109)|in @ X1110 @ X1109)&(((in @ (esk55_2 @ X1111 @ X1112) @ X1111|(binintersect @ X1111 @ X1112)=(emptyset))&(in @ (esk55_2 @ X1111 @ X1112) @ X1112|(binintersect @ X1111 @ X1112)=(emptyset)))&(subset @ (binintersect @ X1114 @ X1115) @ X1115&((~subset @ X1117 @ 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@ X1186 @ X1187)))&((~in @ X1192 @ X1190|(~in @ X1193 @ X1191|in @ (setadjoin @ X1192 @ (setadjoin @ X1193 @ emptyset)) @ (powerset @ (binunion @ X1190 @ X1191))))&((~in @ X1196 @ X1194|(~in @ X1197 @ X1195|subset @ (setadjoin @ (setadjoin @ X1196 @ emptyset) @ (setadjoin @ (setadjoin @ X1196 @ (setadjoin @ X1197 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X1194 @ X1195))))&((~in @ X1200 @ X1198|(~in @ X1201 @ X1199|in @ (setadjoin @ (setadjoin @ X1200 @ emptyset) @ (setadjoin @ (setadjoin @ X1200 @ (setadjoin @ X1201 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1198 @ X1199)))))&((~in @ X1204 @ X1202|(~in @ X1205 @ X1203|in @ (kpair @ X1204 @ X1205) @ (powerset @ (powerset @ (binunion @ X1202 @ X1203)))))&((~in @ X1208 @ X1206|(~in @ X1209 @ X1207|in @ (kpair @ X1208 @ X1209) @ (cartprod @ X1206 @ X1207)))&(((in @ (esk56_3 @ X1210 @ X1211 @ X1212) @ X1210|~in @ X1212 @ (cartprod @ X1210 @ X1211))&((in @ (esk57_3 @ X1210 @ X1211 @ X1212) @ X1211|~in @ X1212 @ (cartprod @ X1210 @ X1211))&((X1212)=(kpair @ (esk56_3 @ X1210 @ X1211 @ X1212) @ (esk57_3 @ X1210 @ X1211 @ X1212))|~in @ X1212 @ (cartprod @ X1210 @ X1211))))&((~in @ X1217 @ (cartprod @ X1215 @ X1216)|iskpair @ X1217)&(((in @ (esk58_2 @ X1218 @ X1219) @ X1218|~in @ X1219 @ (setunion @ X1218))&(in @ X1219 @ (esk58_2 @ X1218 @ X1219)|~in @ X1219 @ (setunion @ X1218)))&(subset @ (setunion @ (setadjoin @ X1221 @ emptyset)) @ X1221&(subset @ X1222 @ (setunion @ (setadjoin @ X1222 @ emptyset))&((setunion @ (setadjoin @ X1223 @ emptyset))=(X1223)&(((in @ (esk59_2 @ X1224 @ X1225) @ X1224|(~in @ X1228 @ X1224|~X1225 @ X1228|singleton @ (dsetconstr @ X1224 @ (epred1_2 @ X1225))))&((in @ (esk60_2 @ X1224 @ X1225) @ X1224|(~in @ X1228 @ X1224|~X1225 @ X1228|singleton @ (dsetconstr @ X1224 @ (epred1_2 @ X1225))))&((X1225 @ (esk59_2 @ X1224 @ X1225)|(~in @ X1228 @ X1224|~X1225 @ X1228|singleton @ (dsetconstr @ X1224 @ (epred1_2 @ X1225))))&((X1225 @ (esk60_2 @ X1224 @ X1225)|(~in @ X1228 @ X1224|~X1225 @ X1228|singleton @ (dsetconstr @ X1224 @ (epred1_2 @ X1225))))&((esk59_2 @ X1224 @ X1225)!=(esk60_2 @ X1224 @ X1225)|(~in @ X1228 @ X1224|~X1225 @ X1228|singleton @ (dsetconstr @ X1224 @ (epred1_2 @ X1225))))))))&(((in @ (esk61_2 @ X1229 @ X1230) @ X1229|~singleton @ (dsetconstr @ X1229 @ (epred1_2 @ X1230)))&(X1230 @ (esk61_2 @ X1229 @ X1230)|~singleton @ (dsetconstr @ X1229 @ (epred1_2 @ X1230))))&(((in @ (esk62_3 @ X1232 @ X1233 @ X1234) @ X1232|singleton @ (dsetconstr @ X1232 @ (epred1_2 @ X1233))|~X1233 @ X1234|~in @ X1234 @ X1232)&((X1233 @ (esk62_3 @ X1232 @ X1233 @ X1234)|singleton @ (dsetconstr @ X1232 @ (epred1_2 @ X1233))|~X1233 @ X1234|~in @ X1234 @ X1232)&((esk62_3 @ X1232 @ X1233 @ X1234)!=(X1234)|singleton @ (dsetconstr @ X1232 @ (epred1_2 @ X1233))|~X1233 @ X1234|~in @ X1234 @ X1232)))&(((in @ (esk63_2 @ X1236 @ X1237) @ X1236|(~in @ X1240 @ X1236|~X1237 @ X1240|singleton @ (dsetconstr @ X1236 @ (epred1_2 @ X1237))))&((in @ (esk64_2 @ X1236 @ X1237) @ X1236|(~in @ X1240 @ X1236|~X1237 @ X1240|singleton @ (dsetconstr @ X1236 @ (epred1_2 @ X1237))))&((X1237 @ (esk63_2 @ X1236 @ X1237)|(~in @ X1240 @ X1236|~X1237 @ X1240|singleton @ (dsetconstr @ X1236 @ (epred1_2 @ X1237))))&((X1237 @ (esk64_2 @ X1236 @ X1237)|(~in @ X1240 @ X1236|~X1237 @ X1240|singleton @ (dsetconstr @ X1236 @ (epred1_2 @ X1237))))&((esk63_2 @ X1236 @ X1237)!=(esk64_2 @ X1236 @ X1237)|(~in @ X1240 @ X1236|~X1237 @ X1240|singleton @ (dsetconstr @ X1236 @ (epred1_2 @ X1237))))))))&(((setadjoin @ X1241 @ emptyset)!=(setadjoin @ X1242 @ emptyset)|(X1241)=(X1242))&((~in @ (setadjoin @ X1245 @ emptyset) @ (setadjoin @ (setadjoin @ X1243 @ emptyset) @ (setadjoin @ (setadjoin @ X1243 @ (setadjoin @ X1244 @ emptyset)) @ emptyset))|(X1243)=(X1245))&((~iskpair @ X1246|singleton @ (dsetconstr @ (setunion @ X1246) @ (epred7_2 @ X1246)))&((~singleton @ X1247|in @ (setunion @ X1247) @ X1247)&((kfst @ (kpair @ X1248 @ X1249))=(X1248)&((~in @ X1252 @ (cartprod @ X1250 @ X1251)|in @ 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X1302))=(X1301)))&((~in @ X1305 @ X1303|(~in @ X1306 @ X1304|(ksnd @ (kpair @ X1305 @ X1306))=(X1306)))&((~in @ X1309 @ (cartprod @ X1307 @ X1308)|(kpair @ (kfst @ X1309) @ (ksnd @ X1309))=(X1309))&((~in @ X1313 @ X1310|(~in @ X1314 @ X1311|(~X1312 @ X1313 @ X1314|in @ (kpair @ X1313 @ X1314) @ (dpsetconstr @ X1310 @ X1311 @ (epred2_3 @ X1312)))))&(subset @ (dpsetconstr @ X1315 @ X1316 @ (epred2_3 @ X1317)) @ (cartprod @ X1315 @ X1316)&(subset @ (dpsetconstr @ X1318 @ X1319 @ (epred2_3 @ X1320)) @ (cartprod @ X1318 @ X1319)&((~in @ X1324 @ X1321|(~in @ X1325 @ X1322|(~in @ (kpair @ X1324 @ X1325) @ (dpsetconstr @ X1321 @ X1322 @ (epred2_3 @ X1323))|X1323 @ X1324 @ X1325)))&((~in @ (kpair @ X1329 @ X1330) @ (dpsetconstr @ X1326 @ X1327 @ (epred2_3 @ X1328))|in @ X1329 @ X1326)&((~in @ (kpair @ X1334 @ X1335) @ (dpsetconstr @ X1331 @ X1332 @ (epred2_3 @ X1333))|in @ X1335 @ X1332)&((~in @ (kpair @ X1339 @ X1340) @ (dpsetconstr @ X1336 @ X1337 @ (epred2_3 @ X1338))|X1338 @ X1339 @ 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@ X1377 @ (cartprod @ X1375 @ X1376)))))&(((in @ (esk70_4 @ X1382 @ X1383 @ X1384 @ X1385) @ X1382|(~in @ X1388 @ X1384|X1385 @ X1388)|~subset @ X1384 @ (cartprod @ X1382 @ X1383))&((in @ (esk71_4 @ X1382 @ X1383 @ X1384 @ X1385) @ X1383|(~in @ X1388 @ X1384|X1385 @ X1388)|~subset @ X1384 @ (cartprod @ X1382 @ X1383))&((in @ (kpair @ (esk70_4 @ X1382 @ X1383 @ X1384 @ X1385) @ (esk71_4 @ X1382 @ X1383 @ X1384 @ X1385)) @ X1384|(~in @ X1388 @ X1384|X1385 @ X1388)|~subset @ X1384 @ (cartprod @ X1382 @ X1383))&(~X1385 @ (kpair @ (esk70_4 @ X1382 @ X1383 @ X1384 @ X1385) @ (esk71_4 @ X1382 @ X1383 @ X1384 @ X1385))|(~in @ X1388 @ X1384|X1385 @ X1388)|~subset @ X1384 @ (cartprod @ X1382 @ X1383)))))&((~singleton @ (dsetconstr @ X1389 @ (epred1_2 @ X1390))|(~in @ X1391 @ X1389|(~in @ X1392 @ X1389|(~X1390 @ X1391|(~X1390 @ X1392|(X1391)=(X1392))))))&((~func @ X1393 @ X1394 @ X1395|(~in @ X1396 @ X1393|in @ (kpair @ X1396 @ (ap @ X1393 @ X1394 @ X1395 @ X1396)) @ X1395))&((~in @ X1399 @ (funcSet @ X1397 @ X1398)|(~in @ X1400 @ X1397|in @ (kpair @ X1400 @ (ap @ X1397 @ X1398 @ X1399 @ X1400)) @ X1399))&((~func @ X1401 @ X1402 @ X1403|(~in @ X1404 @ X1401|(~in @ X1405 @ X1402|(~in @ (kpair @ X1404 @ X1405) @ X1403|(ap @ X1401 @ X1402 @ X1403 @ X1404)=(X1405)))))&(((in @ (esk72_4 @ X1406 @ X1407 @ X1408 @ X1409) @ X1406|(~in @ X1411 @ X1406|(~in @ X1412 @ X1407|(~in @ (kpair @ X1411 @ X1412) @ X1409|in @ (kpair @ X1411 @ X1412) @ X1408)))|~func @ X1406 @ X1407 @ X1409|~func @ X1406 @ X1407 @ X1408)&((ap @ X1406 @ X1407 @ X1408 @ (esk72_4 @ X1406 @ X1407 @ X1408 @ X1409))!=(ap @ X1406 @ X1407 @ X1409 @ (esk72_4 @ X1406 @ X1407 @ X1408 @ X1409))|(~in @ X1411 @ X1406|(~in @ X1412 @ X1407|(~in @ (kpair @ X1411 @ X1412) @ X1409|in @ (kpair @ X1411 @ X1412) @ X1408)))|~func @ X1406 @ X1407 @ X1409|~func @ X1406 @ X1407 @ X1408))&((~in @ X1415 @ (funcSet @ X1413 @ X1414)|(~in @ X1416 @ X1413|(~in @ X1417 @ X1414|(~in @ (kpair @ X1416 @ X1417) @ X1415|(ap @ X1413 @ X1414 @ X1415 @ X1416)=(X1417)))))&(((in @ (esk73_4 @ X1418 @ X1419 @ X1420 @ X1421) @ X1418|subset @ X1420 @ X1421|~subset @ X1421 @ (cartprod @ X1418 @ X1419)|~subset @ X1420 @ (cartprod @ X1418 @ X1419))&((in @ (esk74_4 @ X1418 @ X1419 @ X1420 @ X1421) @ X1419|subset @ X1420 @ X1421|~subset @ X1421 @ (cartprod @ X1418 @ X1419)|~subset @ X1420 @ (cartprod @ X1418 @ X1419))&((in @ (kpair @ (esk73_4 @ X1418 @ X1419 @ X1420 @ X1421) @ (esk74_4 @ X1418 @ X1419 @ X1420 @ X1421)) @ X1420|subset @ X1420 @ X1421|~subset @ X1421 @ (cartprod @ X1418 @ X1419)|~subset @ X1420 @ (cartprod @ X1418 @ X1419))&(~in @ (kpair @ (esk73_4 @ X1418 @ X1419 @ X1420 @ X1421) @ (esk74_4 @ X1418 @ X1419 @ X1420 @ X1421)) @ X1421|subset @ X1420 @ X1421|~subset @ X1421 @ (cartprod @ X1418 @ X1419)|~subset @ X1420 @ (cartprod @ X1418 @ X1419)))))&((((in @ (esk77_4 @ X1424 @ X1425 @ X1426 @ X1427) @ X1424|(X1426)=(X1427)|in @ (esk75_4 @ X1424 @ X1425 @ X1426 @ X1427) @ X1424|~subset @ X1427 @ (cartprod @ X1424 @ X1425)|~subset @ X1426 @ (cartprod @ X1424 @ X1425))&((in @ (esk78_4 @ X1424 @ X1425 @ X1426 @ X1427) @ X1425|(X1426)=(X1427)|in @ (esk75_4 @ X1424 @ X1425 @ X1426 @ X1427) @ X1424|~subset @ X1427 @ (cartprod @ X1424 @ X1425)|~subset @ X1426 @ (cartprod @ X1424 @ X1425))&((in @ (kpair @ (esk77_4 @ X1424 @ X1425 @ X1426 @ X1427) @ (esk78_4 @ X1424 @ X1425 @ X1426 @ X1427)) @ X1427|(X1426)=(X1427)|in @ (esk75_4 @ X1424 @ X1425 @ X1426 @ X1427) @ X1424|~subset @ X1427 @ (cartprod @ X1424 @ X1425)|~subset @ X1426 @ (cartprod @ X1424 @ X1425))&(~in @ (kpair @ (esk77_4 @ X1424 @ X1425 @ X1426 @ X1427) @ (esk78_4 @ X1424 @ X1425 @ X1426 @ X1427)) @ X1426|(X1426)=(X1427)|in @ (esk75_4 @ X1424 @ X1425 @ X1426 @ X1427) @ X1424|~subset @ X1427 @ (cartprod @ X1424 @ X1425)|~subset @ X1426 @ (cartprod @ X1424 @ X1425)))))&(((in @ (esk77_4 @ X1424 @ X1425 @ X1426 @ X1427) @ X1424|(X1426)=(X1427)|in @ (esk76_4 @ X1424 @ X1425 @ X1426 @ X1427) @ X1425|~subset @ X1427 @ (cartprod @ X1424 @ X1425)|~subset @ X1426 @ (cartprod @ X1424 @ X1425))&((in @ (esk78_4 @ X1424 @ X1425 @ X1426 @ X1427) @ X1425|(X1426)=(X1427)|in @ (esk76_4 @ X1424 @ X1425 @ X1426 @ X1427) @ X1425|~subset @ X1427 @ (cartprod @ X1424 @ X1425)|~subset @ X1426 @ (cartprod @ X1424 @ X1425))&((in @ (kpair @ (esk77_4 @ X1424 @ X1425 @ X1426 @ X1427) @ (esk78_4 @ X1424 @ X1425 @ X1426 @ X1427)) @ X1427|(X1426)=(X1427)|in @ (esk76_4 @ X1424 @ X1425 @ X1426 @ X1427) @ X1425|~subset @ X1427 @ (cartprod @ X1424 @ X1425)|~subset @ X1426 @ (cartprod @ X1424 @ X1425))&(~in @ (kpair @ (esk77_4 @ X1424 @ X1425 @ X1426 @ X1427) @ (esk78_4 @ X1424 @ X1425 @ X1426 @ X1427)) @ X1426|(X1426)=(X1427)|in @ (esk76_4 @ X1424 @ X1425 @ X1426 @ X1427) @ X1425|~subset @ X1427 @ (cartprod @ X1424 @ X1425)|~subset @ X1426 @ (cartprod @ X1424 @ X1425)))))&(((in @ (esk77_4 @ X1424 @ X1425 @ X1426 @ X1427) @ X1424|(X1426)=(X1427)|in @ (kpair @ (esk75_4 @ X1424 @ X1425 @ X1426 @ X1427) @ (esk76_4 @ X1424 @ X1425 @ X1426 @ X1427)) @ X1426|~subset @ X1427 @ (cartprod @ X1424 @ X1425)|~subset @ X1426 @ (cartprod @ X1424 @ X1425))&((in @ (esk78_4 @ X1424 @ X1425 @ X1426 @ X1427) @ X1425|(X1426)=(X1427)|in @ (kpair @ (esk75_4 @ X1424 @ X1425 @ X1426 @ X1427) @ (esk76_4 @ X1424 @ X1425 @ X1426 @ X1427)) @ X1426|~subset @ X1427 @ (cartprod @ X1424 @ X1425)|~subset @ X1426 @ (cartprod @ X1424 @ X1425))&((in @ (kpair @ (esk77_4 @ X1424 @ X1425 @ X1426 @ X1427) @ (esk78_4 @ X1424 @ X1425 @ X1426 @ X1427)) @ X1427|(X1426)=(X1427)|in @ (kpair @ (esk75_4 @ X1424 @ X1425 @ X1426 @ X1427) @ (esk76_4 @ X1424 @ X1425 @ X1426 @ X1427)) @ X1426|~subset @ X1427 @ (cartprod @ X1424 @ X1425)|~subset @ X1426 @ (cartprod @ X1424 @ X1425))&(~in @ (kpair @ (esk77_4 @ X1424 @ X1425 @ X1426 @ X1427) @ (esk78_4 @ X1424 @ X1425 @ X1426 @ X1427)) @ X1426|(X1426)=(X1427)|in @ (kpair @ (esk75_4 @ X1424 @ X1425 @ X1426 @ X1427) @ (esk76_4 @ X1424 @ X1425 @ X1426 @ X1427)) @ X1426|~subset @ X1427 @ (cartprod @ X1424 @ X1425)|~subset @ X1426 @ (cartprod @ X1424 @ X1425)))))&((in @ (esk77_4 @ X1424 @ X1425 @ X1426 @ X1427) @ X1424|(X1426)=(X1427)|~in @ (kpair @ (esk75_4 @ X1424 @ X1425 @ X1426 @ X1427) @ (esk76_4 @ X1424 @ X1425 @ X1426 @ X1427)) @ X1427|~subset @ X1427 @ (cartprod @ X1424 @ X1425)|~subset @ X1426 @ (cartprod @ X1424 @ X1425))&((in @ (esk78_4 @ X1424 @ X1425 @ X1426 @ X1427) @ X1425|(X1426)=(X1427)|~in @ (kpair @ (esk75_4 @ X1424 @ X1425 @ X1426 @ X1427) @ (esk76_4 @ X1424 @ X1425 @ X1426 @ X1427)) @ X1427|~subset @ X1427 @ (cartprod @ X1424 @ X1425)|~subset @ X1426 @ (cartprod @ X1424 @ X1425))&((in @ (kpair @ (esk77_4 @ X1424 @ X1425 @ X1426 @ X1427) @ (esk78_4 @ X1424 @ X1425 @ X1426 @ X1427)) @ X1427|(X1426)=(X1427)|~in @ (kpair @ (esk75_4 @ X1424 @ X1425 @ X1426 @ X1427) @ (esk76_4 @ X1424 @ X1425 @ X1426 @ X1427)) @ X1427|~subset @ X1427 @ (cartprod @ X1424 @ X1425)|~subset @ X1426 @ (cartprod @ X1424 @ X1425))&(~in @ (kpair @ (esk77_4 @ X1424 @ X1425 @ X1426 @ X1427) @ (esk78_4 @ X1424 @ X1425 @ X1426 @ X1427)) @ X1426|(X1426)=(X1427)|~in @ (kpair @ (esk75_4 @ X1424 @ X1425 @ X1426 @ X1427) @ (esk76_4 @ X1424 @ X1425 @ X1426 @ X1427)) @ X1427|~subset @ X1427 @ (cartprod @ X1424 @ X1425)|~subset @ X1426 @ (cartprod @ X1424 @ X1425))))))))&(((in @ (esk79_4 @ X1432 @ X1433 @ X1434 @ X1435) @ X1432|(X1434)=(X1435)|~func @ X1432 @ X1433 @ X1435|~func @ X1432 @ X1433 @ X1434)&((ap @ X1432 @ X1433 @ X1434 @ (esk79_4 @ X1432 @ X1433 @ X1434 @ X1435))!=(ap @ X1432 @ X1433 @ X1435 @ (esk79_4 @ X1432 @ X1433 @ X1434 @ X1435))|(X1434)=(X1435)|~func @ X1432 @ X1433 @ X1435|~func @ X1432 @ X1433 @ X1434))&(((in @ (esk80_4 @ X1437 @ X1438 @ X1439 @ X1440) @ X1437|(X1439)=(X1440)|~in @ X1440 @ (funcSet @ X1437 @ X1438)|~in @ X1439 @ (funcSet @ X1437 @ X1438))&((ap @ X1437 @ X1438 @ X1439 @ (esk80_4 @ X1437 @ X1438 @ X1439 @ X1440))!=(ap @ X1437 @ X1438 @ X1440 @ (esk80_4 @ X1437 @ X1438 @ X1439 @ X1440))|(X1439)=(X1440)|~in @ X1440 @ (funcSet @ X1437 @ X1438)|~in @ X1439 @ (funcSet @ X1437 @ X1438)))&((~in @ X1444 @ (funcSet @ X1442 @ X1443)|(~in @ X1445 @ X1442|(ap @ X1442 @ X1443 @ X1444 @ X1445)=(ap @ X1442 @ X1443 @ X1444 @ X1445)))&((~func @ X1446 @ X1447 @ X1448|(~in @ X1449 @ X1446|(ap @ X1446 @ X1447 @ X1448 @ X1449)=(ap @ X1446 @ X1447 @ X1448 @ X1449)))&(((in @ (esk81_3 @ X1450 @ X1451 @ X1452) @ X1450|(~in @ X1454 @ X1450|(ap @ X1450 @ X1451 @ (lam @ X1450 @ X1451 @ (esk1_2 @ X1452)) @ X1454)=(X1452 @ X1454)))&(~in @ (X1452 @ (esk81_3 @ X1450 @ X1451 @ X1452)) @ X1451|(~in @ X1454 @ X1450|(ap @ X1450 @ X1451 @ (lam @ X1450 @ X1451 @ (esk1_2 @ X1452)) @ X1454)=(X1452 @ X1454))))&((~func @ X1455 @ X1456 @ X1457|(lam @ X1455 @ X1456 @ (esk1_2 @ (ap @ X1455 @ X1456 @ X1457)))=(X1457))&(((in @ (esk82_3 @ X1458 @ X1459 @ X1460) @ X1458|(lam @ X1458 @ X1459 @ (esk1_2 @ X1460))=(lam @ X1458 @ X1459 @ (esk1_2 @ X1460)))&(~in @ (X1460 @ (esk82_3 @ X1458 @ X1459 @ X1460)) @ X1459|(lam @ X1458 @ X1459 @ (esk1_2 @ X1460))=(lam @ X1458 @ X1459 @ (esk1_2 @ X1460))))&(((in @ (esk83_3 @ X1462 @ X1463 @ X1464) @ X1462|(~in @ X1466 @ X1462|(ap @ X1462 @ X1463 @ (lam @ X1462 @ X1463 @ (esk1_2 @ X1464)) @ X1466)=(X1464 @ X1466)))&(~in @ (X1464 @ (esk83_3 @ X1462 @ X1463 @ X1464)) @ X1463|(~in @ X1466 @ X1462|(ap @ X1462 @ X1463 @ (lam @ X1462 @ X1463 @ (esk1_2 @ X1464)) @ X1466)=(X1464 @ X1466))))&((~in @ X1469 @ (funcSet @ X1467 @ X1468)|(lam @ X1467 @ X1468 @ (esk1_2 @ (ap @ X1467 @ X1468 @ X1469)))=(X1469))&((~in @ X1472 @ X1470|(~in @ X1473 @ X1470|(X1471|in @ X1473 @ (dsetconstr @ X1470 @ (epred4_4 @ X1473 @ X1471 @ X1472)))))&((~in @ X1476 @ X1474|(~in @ X1477 @ X1474|(X1475|(dsetconstr @ X1474 @ (epred4_4 @ X1477 @ X1475 @ X1476))=(setadjoin @ X1477 @ emptyset))))&((~in @ X1480 @ X1478|(~in @ X1481 @ X1478|(~X1479|in @ X1480 @ (dsetconstr @ X1478 @ (epred4_4 @ X1481 @ X1479 @ X1480)))))&((~in @ X1484 @ X1482|(~in @ X1485 @ X1482|(~X1483|(dsetconstr @ X1482 @ (epred4_4 @ X1485 @ X1483 @ X1484))=(setadjoin @ X1484 @ emptyset))))&((~in @ X1488 @ X1486|(~in @ X1489 @ X1486|singleton @ (dsetconstr @ X1486 @ (epred4_4 @ X1489 @ X1487 @ X1488))))&(((~X1491|in @ (if @ X1490 @ $true @ X1492 @ X1493) @ X1490|~in @ X1493 @ X1490|~in @ X1492 @ X1490)&(X1491|in @ (if @ X1490 @ $false @ X1492 @ X1493) @ X1490|~in @ X1493 @ X1490|~in @ X1492 @ X1490))&((~singleton @ X1494|(~in @ X1495 @ X1494|(setunion @ X1494)=(X1495)))&(((~X1497|(if @ X1496 @ $true @ X1498 @ X1499)=(X1498)|~X1497|~in @ X1499 @ X1496|~in @ X1498 @ X1496)&(X1497|(if @ X1496 @ $false @ X1498 @ X1499)=(X1498)|~X1497|~in @ X1499 @ X1496|~in @ X1498 @ X1496))&(((~X1501|(if @ X1500 @ $true @ X1502 @ X1503)=(X1503)|X1501|~in @ X1503 @ X1500|~in @ X1502 @ X1500)&(X1501|(if @ X1500 @ $false @ X1502 @ X1503)=(X1503)|X1501|~in @ X1503 @ X1500|~in @ X1502 @ X1500))&(((~X1505|in @ (if @ X1504 @ $true @ X1506 @ X1507) @ (setadjoin @ X1506 @ (setadjoin @ X1507 @ emptyset))|~in @ X1507 @ X1504|~in @ X1506 @ X1504)&(X1505|in @ (if @ X1504 @ $false @ X1506 @ X1507) @ (setadjoin @ X1506 @ (setadjoin @ X1507 @ emptyset))|~in @ X1507 @ X1504|~in @ X1506 @ X1504))&((~in @ X1509 @ (powerset @ X1508)|(~in @ X1510 @ (powerset @ X1508)|in @ (binintersect @ X1509 @ X1510) @ (powerset @ X1508)))&((~in @ X1512 @ (powerset @ X1511)|(~in @ X1513 @ (powerset @ X1511)|in @ (binunion @ X1512 @ X1513) @ (powerset @ X1511)))&((~in @ X1515 @ (powerset @ X1514)|in @ (powerset @ X1515) @ (powerset @ (powerset @ X1514)))&(in @ esk85_0 @ (powerset @ esk84_0)&(in @ esk86_0 @ (powerset @ esk84_0)&~in @ (setminus @ esk85_0 @ esk86_0) @ (powerset @ esk84_0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_269])])])])])])).
85.30/85.71	thf(c_0_271, negated_conjecture, ![X2:$i, X3:$i]:(subset @ X2 @ X3|~in @ X2 @ (powerset @ X3)), inference(split_conjunct,[status(thm)],[c_0_270])).
85.30/85.71	thf(c_0_272, negated_conjecture, in @ esk85_0 @ (powerset @ esk84_0), inference(split_conjunct,[status(thm)],[c_0_270])).
85.30/85.71	thf(c_0_273, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(subset @ X2 @ X4|~subset @ X2 @ X3|~subset @ X3 @ X4), inference(split_conjunct,[status(thm)],[c_0_270])).
85.30/85.71	thf(c_0_274, negated_conjecture, subset @ esk85_0 @ esk84_0, inference(spm,[status(thm)],[c_0_271, c_0_272])).
85.30/85.71	thf(c_0_275, negated_conjecture, ~in @ (setminus @ esk85_0 @ esk86_0) @ (powerset @ esk84_0), inference(split_conjunct,[status(thm)],[c_0_270])).
85.30/85.71	thf(c_0_276, negated_conjecture, ![X2:$i, X3:$i]:(in @ X2 @ (powerset @ X3)|~subset @ X2 @ X3), inference(split_conjunct,[status(thm)],[c_0_270])).
85.30/85.71	thf(c_0_277, negated_conjecture, ![X2:$i]:(subset @ X2 @ esk84_0|~subset @ X2 @ esk85_0), inference(spm,[status(thm)],[c_0_273, c_0_274])).
85.30/85.71	thf(c_0_278, negated_conjecture, ![X3:$i, X2:$i]:subset @ (setminus @ X2 @ X3) @ X2, inference(split_conjunct,[status(thm)],[c_0_270])).
85.30/85.71	thf(c_0_279, negated_conjecture, ~subset @ (setminus @ esk85_0 @ esk86_0) @ esk84_0, inference(spm,[status(thm)],[c_0_275, c_0_276])).
85.30/85.71	thf(c_0_280, negated_conjecture, ![X2:$i]:subset @ (setminus @ esk85_0 @ X2) @ esk84_0, inference(spm,[status(thm)],[c_0_277, c_0_278])).
85.30/85.71	thf(c_0_281, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_279, c_0_280])]), ['proof']).
85.30/85.71	# SZS output end CNFRefutation
85.30/85.71	# Proof object total steps             : 282
85.30/85.71	# Proof object clause steps            : 11
85.30/85.71	# Proof object formula steps           : 271
85.30/85.71	# Proof object conjectures             : 14
85.30/85.71	# Proof object clause conjectures      : 11
85.30/85.71	# Proof object formula conjectures     : 3
85.30/85.71	# Proof object initial clauses used    : 6
85.30/85.71	# Proof object initial formulas used   : 234
85.30/85.71	# Proof object generating inferences   : 4
85.30/85.71	# Proof object simplifying inferences  : 2
85.30/85.71	# Training examples: 0 positive, 0 negative
85.30/85.71	# Parsed axioms                        : 501
85.30/85.71	# Removed by relevancy pruning/SinE    : 0
85.30/85.71	# Initial clauses                      : 696
85.30/85.71	# Removed in clause preprocessing      : 302
85.30/85.71	# Initial clauses in saturation        : 394
85.30/85.71	# Processed clauses                    : 1869
85.30/85.71	# ...of these trivial                  : 21
85.30/85.71	# ...subsumed                          : 609
85.30/85.71	# ...remaining for further processing  : 1239
85.30/85.71	# Other redundant clauses eliminated   : 85
85.30/85.71	# Clauses deleted for lack of memory   : 0
85.30/85.71	# Backward-subsumed                    : 9
85.30/85.71	# Backward-rewritten                   : 23
85.30/85.71	# Generated clauses                    : 9772
85.30/85.71	# ...of the previous two non-trivial   : 8297
85.30/85.71	# Contextual simplify-reflections      : 0
85.30/85.71	# Paramodulations                      : 9170
85.30/85.71	# Factorizations                       : 2
85.30/85.71	# NegExts                              : 64
85.30/85.71	# Equation resolutions                 : 88
85.30/85.71	# Propositional unsat checks           : 0
85.30/85.71	#    Propositional check models        : 0
85.30/85.71	#    Propositional check unsatisfiable : 0
85.30/85.71	#    Propositional clauses             : 0
85.30/85.71	#    Propositional clauses after purity: 0
85.30/85.71	#    Propositional unsat core size     : 0
85.30/85.71	#    Propositional preprocessing time  : 0.000
85.30/85.71	#    Propositional encoding time       : 0.000
85.30/85.71	#    Propositional solver time         : 0.000
85.30/85.71	#    Success case prop preproc time    : 0.000
85.30/85.71	#    Success case prop encoding time   : 0.000
85.30/85.71	#    Success case prop solver time     : 0.000
85.30/85.71	# Current number of processed clauses  : 815
85.30/85.71	#    Positive orientable unit clauses  : 213
85.30/85.71	#    Positive unorientable unit clauses: 0
85.30/85.71	#    Negative unit clauses             : 23
85.30/85.71	#    Non-unit-clauses                  : 579
85.30/85.71	# Current number of unprocessed clauses: 7135
85.30/85.71	# ...number of literals in the above   : 19908
85.30/85.71	# Current number of archived formulas  : 0
85.30/85.71	# Current number of archived clauses   : 406
85.30/85.71	# Clause-clause subsumption calls (NU) : 43970
85.30/85.71	# Rec. Clause-clause subsumption calls : 26165
85.30/85.71	# Non-unit clause-clause subsumptions  : 358
85.30/85.71	# Unit Clause-clause subsumption calls : 2911
85.30/85.71	# Rewrite failures with RHS unbound    : 0
85.30/85.71	# BW rewrite match attempts            : 336
85.30/85.71	# BW rewrite match successes           : 14
85.30/85.71	# Condensation attempts                : 0
85.30/85.71	# Condensation successes               : 0
85.30/85.71	# Termbank termtop insertions          : 193599
85.30/85.71	
85.30/85.71	# -------------------------------------------------
85.30/85.71	# User time                : 84.056 s
85.30/85.71	# System time              : 1.215 s
85.30/85.71	# Total time               : 85.272 s
85.30/85.71	# Maximum resident set size: 2204 pages
85.30/85.72	EOF