0.07/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.14 % 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 0.13/0.35 % Computer : n029.cluster.edu 0.13/0.35 % Model : x86_64 x86_64 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.35 % Memory : 8042.1875MB 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.35 % CPULimit : 1200 0.13/0.35 % WCLimit : 120 0.13/0.35 % DateTime : Tue Jul 13 11:51:10 EDT 2021 0.13/0.35 % CPUTime : 0.13/0.35 % Number of cores: 8 0.13/0.35 % Python version: Python 3.6.8 0.13/0.35 # Version: 2.6rc1-ho 0.13/0.37 # No SInE strategy applied 0.13/0.37 # Trying AutoSched0 for 59 seconds 59.18/59.38 # AutoSched0-Mode selected heuristic G_E___303_C18_F1_URBAN_S0Y 59.18/59.38 # and selection function SelectMaxLComplexAvoidPosPred. 59.18/59.38 # 59.18/59.38 # Preprocessing time : 0.125 s 59.18/59.40 # No success with AutoSched0 59.18/59.40 # Trying AutoSched1 for 26 seconds 85.15/85.44 # AutoSched1-Mode selected heuristic G_E___008_C45_F1_PI_SE_Q4_CS_SP_S4SI 85.15/85.44 # and selection function SelectNewComplexAHPNS. 85.15/85.44 # 85.15/85.44 # Preprocessing time : 0.037 s 85.32/85.57 # No success with AutoSched1 85.32/85.57 # Trying AutoSched2 for 8 seconds 85.32/85.63 # AutoSched2-Mode selected heuristic U_____100_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_ND_S04AN 85.32/85.63 # and selection function SelectComplexExceptUniqMaxHorn. 85.32/85.63 # 85.32/85.63 # Preprocessing time : 0.035 s 85.32/85.63 # Presaturation interreduction done 85.32/85.63 85.32/85.63 # Proof found! 85.32/85.63 # SZS status Theorem 85.32/85.63 # SZS output start CNFRefutation 85.32/85.63 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:$i]:(in @ X3 @ X4&X6 @ X3 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', replAx)). 85.32/85.63 thf(exu, axiom, (exu)=(^[X1:$i > $o]:?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exu)). 85.32/85.63 thf(descrp, axiom, (descrp<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>X1 @ (descr @ (^[X2:$i]:X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', descrp)). 85.32/85.63 thf(exuE1, axiom, (exuE1<=>![X1:$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)). 85.32/85.63 thf(exuE3e, axiom, (exuE3e<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>?[X2:$i]:X1 @ X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuE3e)). 85.32/85.63 thf(nonemptyE1, axiom, (nonemptyE1<=>![X4:$i]:(nonempty @ X4=>?[X2:$i]:in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyE1)). 85.32/85.63 thf(nonempty, axiom, (nonempty)=(^[X2:$i]:(X2)!=(emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonempty)). 85.32/85.63 thf(nonemptyI, axiom, (nonemptyI<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyI)). 85.32/85.63 thf(nonemptyI1, axiom, (nonemptyI1<=>![X4:$i]:(?[X2:$i]:in @ X2 @ X4=>nonempty @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyI1)). 85.32/85.63 thf(exuE2, axiom, (exuE2<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuE2)). 85.32/85.63 thf(nonemptyImpWitness, axiom, (nonemptyImpWitness<=>![X4:$i]:(nonempty @ X4=>?[X2:$i]:(in @ X2 @ X4&$true))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyImpWitness)). 85.32/85.63 thf(exuI1, axiom, (exuI1<=>![X1:$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)). 85.32/85.63 thf(exuI3, axiom, (exuI3<=>![X1:$i > $o]:(?[X2:$i]:X1 @ X2=>(![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3)))=>exu @ (^[X2:$i]:X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuI3)). 85.32/85.63 thf(exuI2, axiom, (exuI2<=>![X1:$i > $o]:(?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2))=>exu @ (^[X2:$i]:X1 @ X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuI2)). 85.32/85.63 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)). 85.32/85.63 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:$i]:X17 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exu__Cong)). 85.32/85.63 thf(exuEu, axiom, (exuEu<=>![X1:$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)). 85.32/85.63 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:$i]:X17 @ X2)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', descr__Cong)). 85.32/85.63 thf(ex1E1, axiom, (ex1E1<=>![X4:$i, X1:$i > $o]:(ex1 @ X4 @ (^[X2:$i]:X1 @ X2)=>?[X2:$i]:(in @ X2 @ X4&X1 @ X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ex1E1)). 85.32/85.63 thf(ex1, axiom, (ex1)=(^[X4:$i, X1:$i > $o]:singleton @ (dsetconstr @ X4 @ (^[X2:$i]:X1 @ X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ex1)). 85.32/85.63 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)). 85.32/85.63 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:$i]:X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ex1I2)). 85.32/85.63 thf(setOfPairsIsBReln, axiom, (setOfPairsIsBReln<=>![X4:$i, X5:$i, X24:$i > $i > $o]:breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:X24 @ X2 @ X3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setOfPairsIsBReln)). 85.32/85.63 thf(breln, axiom, (breln)=(^[X4:$i, X5:$i, X7:$i]:subset @ X7 @ (cartprod @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln)). 85.32/85.63 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)). 85.32/85.63 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)). 85.32/85.63 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)). 85.32/85.63 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)). 85.32/85.63 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)). 85.32/85.63 thf(binunionT_lem, conjecture, (setextAx=>(emptysetAx=>((powersetAx=>(setunionAx=>((omegaSAx=>(omegaIndAx=>(replAx=>(foundationAx=>(wellorderingAx=>(((dsetconstrEL=>(dsetconstrER=>(exuE1=>(prop2setE=>(((notinemptyset=>(exuE3e=>((emptyI=>((setbeta=>(((nonemptyI1=>((emptyinunitempty=>(setadjoinIR=>(setadjoinE=>(setadjoinOr=>(setoftrueEq=>(powersetI=>(((powersetE=>(setunionI=>(setunionE=>(subPowSU=>((((notinsingleton=>(((upairsetE=>((upairsetIR=>(((((quantDeMorgan3=>((prop2setI=>((notdexE=>(notdallE=>((exuI3=>(exuI2=>((in__Cong=>(exuE3u=>((((((((descr__Cong=>(dsetconstr__Cong=>(subsetI1=>(eqimpsubset2=>((subsetI2=>(emptysetsubset=>((subsetE2=>((((((((subset2powerset=>(setextsub=>(subsetemptysetimpeq=>((powersetE1=>(inPowerset=>((sepInPowerset=>(sepSubset=>(binunionIL=>(upairset2IR=>(binunionIR=>(binunionEcases=>(binunionE=>(binunionLsub=>(binunionRsub=>((binintersectSubset5=>(binintersectEL=>(binintersectLsub=>(binintersectSubset2=>(((disjointsetsI1=>(binintersectRsub=>(binintersectSubset4=>(binintersectSubset1=>((setminusI=>(((((setminusELneg=>(setminusILneg=>(setminusIRneg=>(setminusLsub=>((symdiffE=>(symdiffI1=>((symdiffIneg1=>((secondinupair=>((setukpairIR=>(kpairiskpair=>((((singletoninpowunion=>(upairset2E=>(((ubforcartprodlem1=>(ubforcartprodlem2=>(ubforcartprodlem3=>(cartprodpairin=>(cartprodmempair1=>((setunionE2=>(setunionsingleton1=>(((singletonprop=>(ex1E1=>(ex1I=>(ex1I2=>(singletonsuniq=>(setukpairinjL1=>(kfstsingleton=>((((((((((setukpairinjR2=>(((ksndpairEq=>((cartprodsndin=>(cartprodpairmemEL=>(cartprodpairmemER=>(cartprodmempaircEq=>(cartprodfstpairEq=>(cartprodsndpairEq=>(cartprodpairsurjEq=>(dpsetconstrI=>(dpsetconstrSub=>((dpsetconstrERa=>(dpsetconstrEL1=>(dpsetconstrEL2=>((funcImageSingleton=>(((infuncsetfunc=>((funcinfuncset=>(lamProp=>(lamp=>((((ex1E2=>((funcGraphProp3=>((funcextLem=>(funcGraphProp4=>((eqbreln=>(funcext=>(funcext2=>(ap2apEq1=>(ap2apEq2=>(((lam2lamEq=>(((iffalseProp1=>((iftrueProp1=>(iftrueProp2=>(((theeq=>((iffalse=>(iftrueorfalse=>(![X4:$i, X21:$i]:(![X48:$i]:(in @ X48 @ (powerset @ X4)=>in @ (binunion @ X21 @ X48) @ (powerset @ X4))<=in @ X21 @ (powerset @ X4))<=binintersectT_lem)))<=iftrue))<=ifp)<=ifSingleton)))<=iffalseProp2))<=eta2)<=beta2))<=eta1)<=beta1))))))<=subbreln)))<=funcGraphProp2))<=funcGraphProp1))<=brelnall2)<=brelnall1)<=lam2p))))<=ap2p))<=app)<=apProp))<=dpsetconstrER))))<=setOfPairsIsBReln))))))))))<=kpairsurjEq))<=ksndsingleton)<=setukpairinjR))<=upairequniteq)<=setukpairinjR1)<=setukpairinjR12)<=setukpairinjR11)<=setukpairinjL)<=setukpairinjL2)<=cartprodfstin)<=kfstpairEq)<=theprop))))))))<=setunionsingleton)<=setunionsingleton2)))<=cartprodmempair))))))<=upairinpowunion)<=upairsubunion)))<=singletoninpowerset)<=singletonsubset)<=kpairp)))<=setukpairIL))<=symdiffIneg2))<=symdiffI2)))<=setminusSubset1)))))<=setminusERneg)<=setminusSubset2)<=setminusER)<=setminusEL))<=bs114d)))))<=binintersectER)<=binintersectSubset3)))))<=binintersectI))))))))))<=powersetsubset)))<=powersetI1))))<=setadjoinSub2)<=setadjoinSub)<=subsetTrans)<=subsetRefl)<=notequalI2)<=notequalI1)<=notsubsetI))<=subsetE)))<=eqimpsubset1)))))<=exuEu)<=omega__Cong)<=setunion__Cong)<=powerset__Cong)<=setadjoin__Cong)<=emptyset__Cong)<=exu__Cong)))<=inCongP)))<=exuI1)))<=prop2set2propI))<=quantDeMorgan4))<=quantDeMorgan2)<=quantDeMorgan1)<=vacuousDall)<=emptyE1))<=upairsetIL))<=singletonsswitch)<=eqinunit))<=uniqinunit)<=nonemptyImpWitness)<=exuE2)))))<=emptyInPowerset)<=emptyinPowerset)))))))<=setadjoinIL))<=nonemptyI)<=nonemptyE1))<=noeltsimpempty))<=setext)))<=emptysetimpfalse)<=emptysetE)))))<=dsetconstrI)<=descrp))))))<=omega0Ax)))<=setadjoinAx))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionT_lem)). 85.32/85.63 thf(setextAx, axiom, (setextAx<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4<=>in @ X2 @ X5)=>(X4)=(X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setextAx)). 85.32/85.63 thf(emptysetAx, axiom, (emptysetAx<=>![X2:$i]:~(in @ X2 @ emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetAx)). 85.32/85.63 thf(setadjoinAx, axiom, (setadjoinAx<=>![X2:$i, X4:$i, X3:$i]:(in @ X3 @ (setadjoin @ X2 @ X4)<=>((X3)=(X2)|in @ X3 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinAx)). 85.32/85.63 thf(powersetAx, axiom, (powersetAx<=>![X4:$i, X5:$i]:(in @ X5 @ (powerset @ X4)<=>![X2:$i]:(in @ X2 @ X5=>in @ X2 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetAx)). 85.32/85.63 thf(setunionAx, axiom, (setunionAx<=>![X4:$i, X2:$i]:(in @ X2 @ (setunion @ X4)<=>?[X5:$i]:(in @ X2 @ X5&in @ X5 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionAx)). 85.32/85.63 thf(omega0Ax, axiom, (omega0Ax<=>in @ emptyset @ omega), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omega0Ax)). 85.32/85.63 thf(omegaSAx, axiom, (omegaSAx<=>![X2:$i]:(in @ X2 @ omega=>in @ (setadjoin @ X2 @ X2) @ omega)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omegaSAx)). 85.32/85.63 thf(omegaIndAx, axiom, (omegaIndAx<=>![X4:$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)). 85.32/85.63 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)). 85.32/85.63 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:$i]:(in @ X3 @ X9=>in @ X3 @ X8)|in @ X2 @ X9)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', wellorderingAx)). 85.32/85.63 thf(dsetconstrI, axiom, (dsetconstrI<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstrI)). 85.32/85.63 thf(dsetconstrEL, axiom, (dsetconstrEL<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))=>in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstrEL)). 85.32/85.63 thf(dsetconstrER, axiom, (dsetconstrER<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))=>X1 @ X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstrER)). 85.32/85.63 thf(prop2setE, axiom, (prop2setE<=>![X10:$o, X2:$i]:(in @ X2 @ (prop2set @ (X10))=>X10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prop2setE)). 85.32/85.63 thf(emptysetE, axiom, (emptysetE<=>![X2:$i]:(in @ X2 @ emptyset=>![X11:$o]:X11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetE)). 85.32/85.63 thf(emptysetimpfalse, axiom, (emptysetimpfalse<=>![X2:$i]:(in @ X2 @ emptyset=>~$true)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetimpfalse)). 85.32/85.63 thf(notinemptyset, axiom, (notinemptyset<=>![X2:$i]:~(in @ X2 @ emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notinemptyset)). 85.32/85.63 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)). 85.32/85.63 thf(emptyI, axiom, (emptyI<=>![X4:$i]:(![X2:$i]:~(in @ X2 @ X4)=>(X4)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyI)). 85.32/85.63 thf(noeltsimpempty, axiom, (noeltsimpempty<=>![X4:$i]:(![X2:$i]:~(in @ X2 @ X4)=>(X4)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', noeltsimpempty)). 85.32/85.63 thf(setbeta, axiom, (setbeta<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))<=>X1 @ X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setbeta)). 85.32/85.63 thf(setadjoinIL, axiom, (setadjoinIL<=>![X2:$i, X3:$i]:in @ X2 @ (setadjoin @ X2 @ X3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinIL)). 85.32/85.63 thf(emptyinunitempty, axiom, (emptyinunitempty<=>in @ emptyset @ (setadjoin @ emptyset @ emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyinunitempty)). 85.32/85.63 thf(setadjoinIR, axiom, (setadjoinIR<=>![X2:$i, X4:$i, X3:$i]:(in @ X3 @ X4=>in @ X3 @ (setadjoin @ X2 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinIR)). 85.32/85.63 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)). 85.32/85.63 thf(setadjoinOr, axiom, (setadjoinOr<=>![X2:$i, X4:$i, X3:$i]:(in @ X3 @ (setadjoin @ X2 @ X4)=>((X3)=(X2)|in @ X3 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinOr)). 85.32/85.63 thf(setoftrueEq, axiom, (setoftrueEq<=>![X4:$i]:(dsetconstr @ X4 @ (^[X2:$i]:$true))=(X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setoftrueEq)). 85.32/85.63 thf(powersetI, axiom, (powersetI<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X5=>in @ X2 @ X4)=>in @ X5 @ (powerset @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetI)). 85.32/85.63 thf(emptyinPowerset, axiom, (emptyinPowerset<=>![X4:$i]:in @ emptyset @ (powerset @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyinPowerset)). 85.32/85.63 thf(emptyInPowerset, axiom, (emptyInPowerset<=>![X4:$i]:in @ emptyset @ (powerset @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyInPowerset)). 85.32/85.63 thf(powersetE, axiom, (powersetE<=>![X4:$i, X5:$i, X2:$i]:(in @ X5 @ (powerset @ X4)=>(in @ X2 @ X5=>in @ X2 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetE)). 85.32/85.63 thf(setunionI, axiom, (setunionI<=>![X4:$i, X2:$i, X5:$i]:(in @ X2 @ X5=>(in @ X5 @ X4=>in @ X2 @ (setunion @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionI)). 85.32/85.63 thf(setunionE, axiom, (setunionE<=>![X4:$i, X2:$i]:(in @ X2 @ (setunion @ X4)=>![X13:$o]:(![X5:$i]:(in @ X2 @ X5=>(in @ X5 @ X4=>X13))=>X13))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionE)). 85.32/85.63 thf(subPowSU, axiom, (subPowSU<=>![X4:$i, X2:$i]:(in @ X2 @ X4=>in @ X2 @ (powerset @ (setunion @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subPowSU)). 85.32/85.63 thf(uniqinunit, axiom, (uniqinunit<=>![X2:$i, X3:$i]:(in @ X2 @ (setadjoin @ X3 @ emptyset)=>(X2)=(X3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', uniqinunit)). 85.32/85.63 thf(notinsingleton, axiom, (notinsingleton<=>![X2:$i, X3:$i]:((X2)!=(X3)=>~(in @ X3 @ (setadjoin @ X2 @ emptyset)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notinsingleton)). 85.32/85.63 thf(eqinunit, axiom, (eqinunit<=>![X2:$i, X3:$i]:((X2)=(X3)=>in @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqinunit)). 85.32/85.63 thf(singletonsswitch, axiom, (singletonsswitch<=>![X2:$i, X3:$i]:(in @ X2 @ (setadjoin @ X3 @ emptyset)=>in @ X3 @ (setadjoin @ X2 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletonsswitch)). 85.32/85.63 thf(upairsetE, axiom, (upairsetE<=>![X2:$i, X3:$i, X14:$i]:(in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=>((X14)=(X2)|(X14)=(X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsetE)). 85.32/85.63 thf(upairsetIL, axiom, (upairsetIL<=>![X2:$i, X3:$i]:in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsetIL)). 85.32/85.63 thf(upairsetIR, axiom, (upairsetIR<=>![X2:$i, X3:$i]:in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsetIR)). 85.32/85.63 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)). 85.32/85.63 thf(vacuousDall, axiom, (vacuousDall<=>![X1:$i > $o, X2:$i]:(in @ X2 @ emptyset=>X1 @ X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', vacuousDall)). 85.32/85.63 thf(quantDeMorgan1, axiom, (quantDeMorgan1<=>![X4:$i, X1:$i > $o]:(~(![X2:$i]:(in @ X2 @ X4=>X1 @ X2))=>?[X2:$i]:(in @ X2 @ X4&~(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan1)). 85.32/85.63 thf(quantDeMorgan2, axiom, (quantDeMorgan2<=>![X4:$i, X1:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>~(X1 @ X2))=>~(?[X2:$i]:(in @ X2 @ X4&X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan2)). 85.32/85.63 thf(quantDeMorgan3, axiom, (quantDeMorgan3<=>![X4:$i, X1:$i > $o]:(~(?[X2:$i]:(in @ X2 @ X4&X1 @ X2))=>![X2:$i]:(in @ X2 @ X4=>~(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan3)). 85.32/85.63 thf(quantDeMorgan4, axiom, (quantDeMorgan4<=>![X4:$i, X1:$i > $o]:(?[X2:$i]:(in @ X2 @ X4&~(X1 @ X2))=>~(![X2:$i]:(in @ X2 @ X4=>X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan4)). 85.32/85.63 thf(prop2setI, axiom, (prop2setI<=>![X15:$o]:(X15=>in @ emptyset @ (prop2set @ (X15)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prop2setI)). 85.32/85.63 thf(prop2set2propI, axiom, (prop2set2propI<=>![X16:$o]:(X16=>set2prop @ (prop2set @ (X16)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prop2set2propI)). 85.32/85.63 thf(notdexE, axiom, (notdexE<=>![X4:$i, X1:$i > $o]:(~(?[X2:$i]:(in @ X2 @ X4&X1 @ X2))=>![X2:$i]:(in @ X2 @ X4=>~(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notdexE)). 85.32/85.63 thf(notdallE, axiom, (notdallE<=>![X4:$i, X1:$i > $o]:(~(![X2:$i]:(in @ X2 @ X4=>X1 @ X2))=>?[X2:$i]:(in @ X2 @ X4&~(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notdallE)). 85.32/85.63 thf(inCongP, axiom, (inCongP<=>![X4:$i, X5:$i]:((X4)=(X5)=>![X2:$i, X3:$i]:((X2)=(X3)=>(in @ X2 @ X4=>in @ X3 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', inCongP)). 85.32/85.63 thf(in__Cong, axiom, (in__Cong<=>![X4:$i, X5:$i]:((X4)=(X5)=>![X2:$i, X3:$i]:((X2)=(X3)=>(in @ X2 @ X4<=>in @ X3 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', in__Cong)). 85.32/85.63 thf(emptyset__Cong, axiom, (emptyset__Cong<=>(emptyset)=(emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyset__Cong)). 85.32/85.63 thf(setadjoin__Cong, axiom, (setadjoin__Cong<=>![X2:$i, X3:$i]:((X2)=(X3)=>![X14:$i, X18:$i]:((X14)=(X18)=>(setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoin__Cong)). 85.32/85.63 thf(powerset__Cong, axiom, (powerset__Cong<=>![X4:$i, X5:$i]:((X4)=(X5)=>(powerset @ X4)=(powerset @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powerset__Cong)). 85.32/85.63 thf(setunion__Cong, axiom, (setunion__Cong<=>![X4:$i, X5:$i]:((X4)=(X5)=>(setunion @ X4)=(setunion @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunion__Cong)). 85.32/85.63 thf(omega__Cong, axiom, (omega__Cong<=>(omega)=(omega)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omega__Cong)). 85.32/85.63 thf(dsetconstr__Cong, axiom, (dsetconstr__Cong<=>![X4:$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:$i]:X17 @ X2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstr__Cong)). 85.32/85.63 thf(subsetI1, axiom, (subsetI1<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4=>in @ X2 @ X5)=>subset @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetI1)). 85.32/85.63 thf(eqimpsubset2, axiom, (eqimpsubset2<=>![X4:$i, X5:$i]:((X4)=(X5)=>subset @ X5 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqimpsubset2)). 85.32/85.63 thf(eqimpsubset1, axiom, (eqimpsubset1<=>![X4:$i, X5:$i]:((X4)=(X5)=>subset @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqimpsubset1)). 85.32/85.63 thf(subsetI2, axiom, (subsetI2<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4=>in @ X2 @ X5)=>subset @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetI2)). 85.32/85.63 thf(emptysetsubset, axiom, (emptysetsubset<=>![X4:$i]:subset @ emptyset @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetsubset)). 85.32/85.63 thf(subsetE, axiom, (subsetE<=>![X4:$i, X5:$i, X2:$i]:(subset @ X4 @ X5=>(in @ X2 @ X4=>in @ X2 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetE)). 85.32/85.63 thf(subsetE2, axiom, (subsetE2<=>![X4:$i, X5:$i, X2:$i]:(subset @ X4 @ X5=>(~(in @ X2 @ X5)=>~(in @ X2 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetE2)). 85.32/85.63 thf(notsubsetI, axiom, (notsubsetI<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X5)=>~(subset @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notsubsetI)). 85.32/85.63 thf(notequalI1, axiom, (notequalI1<=>![X4:$i, X5:$i]:(~(subset @ X4 @ X5)=>(X4)!=(X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notequalI1)). 85.32/85.63 thf(notequalI2, axiom, (notequalI2<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X5)=>(X4)!=(X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notequalI2)). 85.32/85.63 thf(subsetRefl, axiom, (subsetRefl<=>![X4:$i]:subset @ X4 @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetRefl)). 85.32/85.63 thf(subsetTrans, axiom, (subsetTrans<=>![X4:$i, X5:$i, X7:$i]:(subset @ X4 @ X5=>(subset @ X5 @ X7=>subset @ X4 @ X7))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetTrans)). 85.32/85.63 thf(setadjoinSub, axiom, (setadjoinSub<=>![X2:$i, X4:$i]:subset @ X4 @ (setadjoin @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinSub)). 85.32/85.63 thf(setadjoinSub2, axiom, (setadjoinSub2<=>![X4:$i, X2:$i, X5:$i]:(subset @ X4 @ X5=>subset @ X4 @ (setadjoin @ X2 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinSub2)). 85.32/85.63 thf(subset2powerset, axiom, (subset2powerset<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>in @ X4 @ (powerset @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subset2powerset)). 85.32/85.63 thf(setextsub, axiom, (setextsub<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>(subset @ X5 @ X4=>(X4)=(X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setextsub)). 85.32/85.63 thf(subsetemptysetimpeq, axiom, (subsetemptysetimpeq<=>![X4:$i]:(subset @ X4 @ emptyset=>(X4)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetemptysetimpeq)). 85.32/85.63 thf(powersetI1, axiom, (powersetI1<=>![X4:$i, X5:$i]:(subset @ X5 @ X4=>in @ X5 @ (powerset @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetI1)). 85.32/85.63 thf(powersetE1, axiom, (powersetE1<=>![X4:$i, X5:$i]:(in @ X5 @ (powerset @ X4)=>subset @ X5 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetE1)). 85.32/85.63 thf(inPowerset, axiom, (inPowerset<=>![X4:$i]:in @ X4 @ (powerset @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', inPowerset)). 85.32/85.63 thf(powersetsubset, axiom, (powersetsubset<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>subset @ (powerset @ X4) @ (powerset @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetsubset)). 85.32/85.63 thf(sepInPowerset, axiom, (sepInPowerset<=>![X4:$i, X1:$i > $o]:in @ (dsetconstr @ X4 @ (^[X2:$i]:X1 @ X2)) @ (powerset @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sepInPowerset)). 85.32/85.63 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)). 85.32/85.63 thf(binunionIL, axiom, (binunionIL<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>in @ X2 @ (binunion @ X4 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionIL)). 85.32/85.63 thf(upairset2IR, axiom, (upairset2IR<=>![X2:$i, X3:$i]:in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairset2IR)). 85.32/85.63 thf(binunionIR, axiom, (binunionIR<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X5=>in @ X2 @ (binunion @ X4 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionIR)). 85.32/85.63 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)). 85.32/85.63 thf(binunionE, axiom, (binunionE<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (binunion @ X4 @ X5)=>(in @ X2 @ X4|in @ X2 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionE)). 85.32/85.63 thf(binunionLsub, axiom, (binunionLsub<=>![X4:$i, X5:$i]:subset @ X4 @ (binunion @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionLsub)). 85.32/85.63 thf(binunionRsub, axiom, (binunionRsub<=>![X4:$i, X5:$i]:subset @ X5 @ (binunion @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionRsub)). 85.32/85.63 thf(binintersectI, axiom, (binintersectI<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X5=>in @ X2 @ (binintersect @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectI)). 85.32/85.63 thf(binintersectSubset5, axiom, (binintersectSubset5<=>![X4:$i, X5:$i, X7:$i]:(subset @ X7 @ X4=>(subset @ X7 @ X5=>subset @ X7 @ (binintersect @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset5)). 85.32/85.63 thf(binintersectEL, axiom, (binintersectEL<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (binintersect @ X4 @ X5)=>in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectEL)). 85.32/85.63 thf(binintersectLsub, axiom, (binintersectLsub<=>![X4:$i, X5:$i]:subset @ (binintersect @ X4 @ X5) @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectLsub)). 85.32/85.63 thf(binintersectSubset2, axiom, (binintersectSubset2<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>(binintersect @ X4 @ X5)=(X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset2)). 85.32/85.63 thf(binintersectSubset3, axiom, (binintersectSubset3<=>![X4:$i, X5:$i]:((binintersect @ X4 @ X5)=(X5)=>subset @ X5 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset3)). 85.32/85.63 thf(binintersectER, axiom, (binintersectER<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (binintersect @ X4 @ X5)=>in @ X2 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectER)). 85.32/85.63 thf(disjointsetsI1, axiom, (disjointsetsI1<=>![X4:$i, X5:$i]:(~(?[X2:$i]:(in @ X2 @ X4&in @ X2 @ X5))=>(binintersect @ X4 @ X5)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', disjointsetsI1)). 85.32/85.63 thf(binintersectRsub, axiom, (binintersectRsub<=>![X4:$i, X5:$i]:subset @ (binintersect @ X4 @ X5) @ X5), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectRsub)). 85.32/85.63 thf(binintersectSubset4, axiom, (binintersectSubset4<=>![X4:$i, X5:$i]:(subset @ X5 @ X4=>(binintersect @ X4 @ X5)=(X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset4)). 85.32/85.63 thf(binintersectSubset1, axiom, (binintersectSubset1<=>![X4:$i, X5:$i]:((binintersect @ X4 @ X5)=(X4)=>subset @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset1)). 85.32/85.63 thf(bs114d, axiom, (bs114d<=>![X4:$i, X5:$i, X7:$i]:(binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', bs114d)). 85.32/85.63 thf(setminusI, axiom, (setminusI<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X5)=>in @ X2 @ (setminus @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusI)). 85.32/85.63 thf(setminusEL, axiom, (setminusEL<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (setminus @ X4 @ X5)=>in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusEL)). 85.32/85.63 thf(setminusER, axiom, (setminusER<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (setminus @ X4 @ X5)=>~(in @ X2 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusER)). 85.32/85.63 thf(setminusSubset2, axiom, (setminusSubset2<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>(setminus @ X4 @ X5)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusSubset2)). 85.32/85.63 thf(setminusERneg, axiom, (setminusERneg<=>![X4:$i, X5:$i, X2:$i]:(~(in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4=>in @ X2 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusERneg)). 85.32/85.63 thf(setminusELneg, axiom, (setminusELneg<=>![X4:$i, X5:$i, X2:$i]:(~(in @ X2 @ (setminus @ X4 @ X5))=>(~(in @ X2 @ X5)=>~(in @ X2 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusELneg)). 85.32/85.63 thf(setminusILneg, axiom, (setminusILneg<=>![X4:$i, X5:$i, X2:$i]:(~(in @ X2 @ X4)=>~(in @ X2 @ (setminus @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusILneg)). 85.32/85.63 thf(setminusIRneg, axiom, (setminusIRneg<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X5=>~(in @ X2 @ (setminus @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusIRneg)). 85.32/85.63 thf(setminusLsub, axiom, (setminusLsub<=>![X4:$i, X5:$i]:subset @ (setminus @ X4 @ X5) @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusLsub)). 85.32/85.63 thf(setminusSubset1, axiom, (setminusSubset1<=>![X4:$i, X5:$i]:((setminus @ X4 @ X5)=(emptyset)=>subset @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusSubset1)). 85.32/85.63 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)). 85.32/85.63 thf(symdiffI1, axiom, (symdiffI1<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X5)=>in @ X2 @ (symdiff @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', symdiffI1)). 85.32/85.63 thf(symdiffI2, axiom, (symdiffI2<=>![X4:$i, X5:$i, X2:$i]:(~(in @ X2 @ X4)=>(in @ X2 @ X5=>in @ X2 @ (symdiff @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', symdiffI2)). 85.32/85.63 thf(symdiffIneg1, axiom, (symdiffIneg1<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X5=>~(in @ X2 @ (symdiff @ X4 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', symdiffIneg1)). 85.32/85.63 thf(symdiffIneg2, axiom, (symdiffIneg2<=>![X4:$i, X5:$i, X2:$i]:(~(in @ X2 @ X4)=>(~(in @ X2 @ X5)=>~(in @ X2 @ (symdiff @ X4 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', symdiffIneg2)). 85.32/85.63 thf(secondinupair, axiom, (secondinupair<=>![X2:$i, X3:$i]:in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', secondinupair)). 85.32/85.63 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)). 85.32/85.63 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)). 85.32/85.63 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)). 85.32/85.63 thf(kpairp, axiom, (kpairp<=>![X2:$i, X3:$i]:iskpair @ (kpair @ X2 @ X3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', kpairp)). 85.32/85.63 thf(singletonsubset, axiom, (singletonsubset<=>![X4:$i, X2:$i]:(in @ X2 @ X4=>subset @ (setadjoin @ X2 @ emptyset) @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletonsubset)). 85.32/85.63 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)). 85.32/85.63 thf(singletoninpowunion, axiom, (singletoninpowunion<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletoninpowunion)). 85.32/85.63 thf(upairset2E, axiom, (upairset2E<=>![X2:$i, X3:$i, X14:$i]:(in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=>((X14)=(X2)|(X14)=(X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairset2E)). 85.32/85.63 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)). 85.32/85.63 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)). 85.32/85.63 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)). 85.32/85.63 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)). 85.32/85.63 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)). 85.32/85.63 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)). 85.32/85.63 thf(cartprodmempair1, axiom, (cartprodmempair1<=>![X4:$i, X5:$i, X18:$i]:(in @ X18 @ (cartprod @ X4 @ X5)=>?[X2:$i]:(in @ X2 @ X4&?[X3:$i]:(in @ X3 @ X5&(X18)=(kpair @ X2 @ X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodmempair1)). 85.32/85.63 thf(cartprodmempair, axiom, (cartprodmempair<=>![X4:$i, X5:$i, X18:$i]:(in @ X18 @ (cartprod @ X4 @ X5)=>iskpair @ X18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodmempair)). 85.32/85.63 thf(setunionE2, axiom, (setunionE2<=>![X4:$i, X2:$i]:(in @ X2 @ (setunion @ X4)=>?[X21:$i]:(in @ X21 @ X4&in @ X2 @ X21))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionE2)). 85.32/85.63 thf(setunionsingleton1, axiom, (setunionsingleton1<=>![X4:$i]:subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionsingleton1)). 85.32/85.63 thf(setunionsingleton2, axiom, (setunionsingleton2<=>![X4:$i]:subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionsingleton2)). 85.32/85.63 thf(setunionsingleton, axiom, (setunionsingleton<=>![X2:$i]:(setunion @ (setadjoin @ X2 @ emptyset))=(X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionsingleton)). 85.32/85.63 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:$i]:X1 @ X2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletonprop)). 85.32/85.63 thf(singletonsuniq, axiom, (singletonsuniq<=>![X2:$i, X3:$i]:((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset)=>(X2)=(X3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletonsuniq)). 85.32/85.63 thf(setukpairinjL1, axiom, (setukpairinjL1<=>![X2:$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)). 85.32/85.63 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)). 85.32/85.63 thf(theprop, axiom, (theprop<=>![X21:$i]:(singleton @ X21=>in @ (setunion @ X21) @ X21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', theprop)). 85.32/85.63 thf(kfstpairEq, axiom, (kfstpairEq<=>![X2:$i, X3:$i]:(kfst @ (kpair @ X2 @ X3))=(X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', kfstpairEq)). 85.32/85.63 thf(cartprodfstin, axiom, (cartprodfstin<=>![X4:$i, X5:$i, X18:$i]:(in @ X18 @ (cartprod @ X4 @ X5)=>in @ (kfst @ X18) @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodfstin)). 85.32/85.63 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)). 85.32/85.63 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)). 85.32/85.63 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)). 85.32/85.63 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)). 85.32/85.63 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)). 85.32/85.63 thf(upairequniteq, axiom, (upairequniteq<=>![X2:$i, X3:$i, X14:$i]:((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset)=>(X2)=(X3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairequniteq)). 85.32/85.63 thf(setukpairinjR2, axiom, (setukpairinjR2<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset))=>(X3)=(X18))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairinjR2)). 85.32/85.63 thf(setukpairinjR, axiom, (setukpairinjR<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((kpair @ X2 @ X3)=(kpair @ X14 @ X18)=>(X3)=(X18))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairinjR)). 85.32/85.63 thf(ksndsingleton, axiom, (ksndsingleton<=>![X18:$i]:(iskpair @ X18=>singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(X18)=(kpair @ (kfst @ X18) @ X2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ksndsingleton)). 85.32/85.63 thf(ksndpairEq, axiom, (ksndpairEq<=>![X2:$i, X3:$i]:(ksnd @ (kpair @ X2 @ X3))=(X3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ksndpairEq)). 85.32/85.63 thf(kpairsurjEq, axiom, (kpairsurjEq<=>![X18:$i]:(iskpair @ X18=>(kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', kpairsurjEq)). 85.32/85.63 thf(cartprodsndin, axiom, (cartprodsndin<=>![X4:$i, X5:$i, X18:$i]:(in @ X18 @ (cartprod @ X4 @ X5)=>in @ (ksnd @ X18) @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodsndin)). 85.32/85.63 thf(cartprodpairmemEL, axiom, (cartprodpairmemEL<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5)=>in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodpairmemEL)). 85.32/85.63 thf(cartprodpairmemER, axiom, (cartprodpairmemER<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5)=>in @ X3 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodpairmemER)). 85.32/85.63 thf(cartprodmempaircEq, axiom, (cartprodmempaircEq<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(kpair @ X2 @ X3)=(kpair @ X2 @ X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodmempaircEq)). 85.32/85.63 thf(cartprodfstpairEq, axiom, (cartprodfstpairEq<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodfstpairEq)). 85.32/85.63 thf(cartprodsndpairEq, axiom, (cartprodsndpairEq<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodsndpairEq)). 85.32/85.63 thf(cartprodpairsurjEq, axiom, (cartprodpairsurjEq<=>![X4:$i, X5:$i, X18:$i]:(in @ X18 @ (cartprod @ X4 @ X5)=>(kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodpairsurjEq)). 85.32/85.63 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:$i]:X22 @ X14 @ X18)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dpsetconstrI)). 85.32/85.63 thf(dpsetconstrSub, axiom, (dpsetconstrSub<=>![X4:$i, X5:$i, X23:$i > $i > $o]:subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:X23 @ X2 @ X3)) @ (cartprod @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dpsetconstrSub)). 85.32/85.63 thf(dpsetconstrERa, axiom, (dpsetconstrERa<=>![X4:$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:$i]:X25 @ X14 @ X18))=>X25 @ X2 @ X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dpsetconstrERa)). 85.32/85.63 thf(dpsetconstrEL1, axiom, (dpsetconstrEL1<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:X26 @ X14 @ X18))=>in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dpsetconstrEL1)). 85.32/85.63 thf(dpsetconstrEL2, axiom, (dpsetconstrEL2<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:X27 @ X14 @ X18))=>in @ X3 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dpsetconstrEL2)). 85.32/85.63 thf(dpsetconstrER, axiom, (dpsetconstrER<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:X28 @ X14 @ X18))=>X28 @ X2 @ X3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dpsetconstrER)). 85.32/85.63 thf(funcImageSingleton, axiom, (funcImageSingleton<=>![X4:$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)). 85.32/85.63 thf(apProp, axiom, (apProp<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>![X2:$i]:(in @ X2 @ X4=>in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:in @ (kpair @ X2 @ X3) @ X29))) @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', apProp)). 85.32/85.63 thf(app, axiom, (app<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>![X2:$i]:(in @ X2 @ X4=>in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', app)). 85.32/85.63 thf(infuncsetfunc, axiom, (infuncsetfunc<=>![X4:$i, X5:$i, X29:$i]:(in @ X29 @ (funcSet @ X4 @ X5)=>func @ X4 @ X5 @ X29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', infuncsetfunc)). 85.32/85.63 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)). 85.32/85.63 thf(funcinfuncset, axiom, (funcinfuncset<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>in @ X29 @ (funcSet @ X4 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', funcinfuncset)). 85.32/85.63 thf(lamProp, axiom, (lamProp<=>![X4:$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)). 85.32/85.63 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:$i]:X31 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', lamp)). 85.32/85.63 thf(lam2p, axiom, (lam2p<=>![X4:$i, X5:$i, X32:$i > $i]:(![X2:$i]:(in @ X2 @ X4=>in @ (X32 @ X2) @ X5)=>in @ (lam @ X4 @ X5 @ (^[X2:$i]:X32 @ X2)) @ (funcSet @ X4 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', lam2p)). 85.32/85.63 thf(funcGraphProp1, axiom, (funcGraphProp1<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>![X2:$i]:(in @ X2 @ X4=>in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', funcGraphProp1)). 85.32/85.63 thf(funcGraphProp3, axiom, (funcGraphProp3<=>![X4:$i, X5:$i, X29:$i]:(in @ X29 @ (funcSet @ X4 @ X5)=>![X2:$i]:(in @ X2 @ X4=>in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', funcGraphProp3)). 85.32/85.63 thf(funcGraphProp2, axiom, (funcGraphProp2<=>![X4:$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)). 85.32/85.63 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:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ X34=>in @ (kpair @ X2 @ X3) @ X29))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', funcextLem)). 85.32/85.63 thf(funcGraphProp4, axiom, (funcGraphProp4<=>![X4:$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)). 85.32/85.63 thf(funcext, axiom, (funcext<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>![X34:$i]:(func @ X4 @ X5 @ X34=>(![X2:$i]:(in @ X2 @ X4=>(ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))=>(X29)=(X34))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', funcext)). 85.32/85.63 thf(funcext2, axiom, (funcext2<=>![X4:$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)). 85.32/85.63 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)). 85.32/85.63 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)). 85.32/85.63 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)). 85.32/85.63 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)). 85.32/85.63 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)). 85.32/85.63 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)). 85.32/85.63 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)). 85.32/85.63 thf(iffalseProp1, axiom, (iffalseProp1<=>![X4:$i, X39:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(~(X39)=>in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((X39&(X14)=(X2))|(~(X39)&(X14)=(X3))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', iffalseProp1)). 85.32/85.63 thf(iffalseProp2, axiom, (iffalseProp2<=>![X4:$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)). 85.32/85.63 thf(iftrueProp1, axiom, (iftrueProp1<=>![X4:$i, X41:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(X41=>in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((X41&(X14)=(X2))|(~(X41)&(X14)=(X3))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', iftrueProp1)). 85.32/85.63 thf(iftrueProp2, axiom, (iftrueProp2<=>![X4:$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)). 85.32/85.63 thf(ifSingleton, axiom, (ifSingleton<=>![X4:$i, X43:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((X43&(X14)=(X2))|(~(X43)&(X14)=(X3)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ifSingleton)). 85.32/85.63 thf(ifp, axiom, (ifp<=>![X4:$i, X44:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>in @ (if @ X4 @ (X44) @ X2 @ X3) @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ifp)). 85.32/85.63 thf(theeq, axiom, (theeq<=>![X21:$i]:(singleton @ X21=>![X2:$i]:(in @ X2 @ X21=>(setunion @ X21)=(X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', theeq)). 85.32/85.63 thf(iftrue, axiom, (iftrue<=>![X4:$i, X45:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(X45=>(if @ X4 @ (X45) @ X2 @ X3)=(X2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', iftrue)). 85.32/85.63 thf(iffalse, axiom, (iffalse<=>![X4:$i, X46:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(~(X46)=>(if @ X4 @ (X46) @ X2 @ X3)=(X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', iffalse)). 85.32/85.63 thf(iftrueorfalse, axiom, (iftrueorfalse<=>![X4:$i, X47:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>in @ (if @ X4 @ (X47) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', iftrueorfalse)). 85.32/85.63 thf(binintersectT_lem, axiom, (binintersectT_lem<=>![X4:$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)). 85.32/85.63 thf(c_0_232, axiom, (replAx)=(![X6:$i > $i > $o, X4:$i]:(![X2:$i]:(in @ X2 @ X4=>?[X751:$i]:(X6 @ X2 @ X751&![X753:$i]:(X6 @ X2 @ X753=>(X751)=(X753))))=>?[X5:$i]:![X2:$i]:(in @ X2 @ X5<=>?[X3:$i]:(in @ X3 @ X4&X6 @ X3 @ X2)))), inference(apply_def,[status(thm)],[replAx, exu])). 85.32/85.63 thf(c_0_233, axiom, (descrp)=(![X1:$i > $o]:(?[X754:$i]:(X1 @ X754&![X755:$i]:(X1 @ X755=>(X754)=(X755)))=>X1 @ (descr @ (^[X2:$i]:X1 @ X2)))), inference(apply_def,[status(thm)],[descrp, exu])). 85.32/85.63 thf(c_0_234, axiom, (exuE1)=(![X1:$i > $o]:(?[X756:$i]:(X1 @ X756&![X757:$i]:(X1 @ X757=>(X756)=(X757)))=>?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3))))), inference(apply_def,[status(thm)],[exuE1, exu])). 85.32/85.63 thf(c_0_235, axiom, (exuE3e)=(![X1:$i > $o]:(?[X758:$i]:(X1 @ X758&![X759:$i]:(X1 @ X759=>(X758)=(X759)))=>?[X2:$i]:X1 @ X2)), inference(apply_def,[status(thm)],[exuE3e, exu])). 85.32/85.63 thf(c_0_236, axiom, (nonemptyE1)=(![X4:$i]:((X4)!=(emptyset)=>?[X2:$i]:in @ X2 @ X4)), inference(apply_def,[status(thm)],[nonemptyE1, nonempty])). 85.32/85.63 thf(c_0_237, axiom, (nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>(dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))!=(emptyset)))), inference(apply_def,[status(thm)],[nonemptyI, nonempty])). 85.32/85.63 thf(c_0_238, axiom, (nonemptyI1)=(![X4:$i]:(?[X2:$i]:in @ X2 @ X4=>(X4)!=(emptyset))), inference(apply_def,[status(thm)],[nonemptyI1, nonempty])). 85.32/85.63 thf(c_0_239, axiom, (exuE2)=(![X1:$i > $o]:(?[X760:$i]:(X1 @ X760&![X761:$i]:(X1 @ X761=>(X760)=(X761)))=>?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2)))), inference(apply_def,[status(thm)],[exuE2, exu])). 85.32/85.63 thf(c_0_240, axiom, (nonemptyImpWitness)=(![X4:$i]:((X4)!=(emptyset)=>?[X2:$i]:(in @ X2 @ X4&$true))), inference(apply_def,[status(thm)],[nonemptyImpWitness, nonempty])). 85.32/85.63 thf(c_0_241, axiom, (exuI1)=(![X1:$i > $o]:(?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3)))=>?[X762:$i]:(X1 @ X762&![X763:$i]:(X1 @ X763=>(X762)=(X763))))), inference(apply_def,[status(thm)],[exuI1, exu])). 85.32/85.63 thf(c_0_242, axiom, (exuI3)=(![X1:$i > $o]:(?[X2:$i]:X1 @ X2=>(![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3)))=>?[X764:$i]:(X1 @ X764&![X765:$i]:(X1 @ X765=>(X764)=(X765)))))), inference(apply_def,[status(thm)],[exuI3, exu])). 85.32/85.63 thf(c_0_243, axiom, (exuI2)=(![X1:$i > $o]:(?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2))=>?[X766:$i]:(X1 @ X766&![X767:$i]:(X1 @ X767=>(X766)=(X767))))), inference(apply_def,[status(thm)],[exuI2, exu])). 85.32/85.63 thf(c_0_244, axiom, (exuE3u)=(![X1:$i > $o]:(?[X768:$i]:(X1 @ X768&![X769:$i]:(X1 @ X769=>(X768)=(X769)))=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))), inference(apply_def,[status(thm)],[exuE3u, exu])). 85.32/85.63 thf(c_0_245, axiom, (exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(?[X770:$i]:(X1 @ X770&![X771:$i]:(X1 @ X771=>(X770)=(X771)))<=>?[X772:$i]:(X17 @ X772&![X773:$i]:(X17 @ X773=>(X772)=(X773)))))), inference(apply_def,[status(thm)],[exu__Cong, exu])). 85.32/85.63 thf(c_0_246, axiom, (exuEu)=(![X1:$i > $o]:(?[X774:$i]:(X1 @ X774&![X775:$i]:(X1 @ X775=>(X774)=(X775)))=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))), inference(apply_def,[status(thm)],[exuEu, exu])). 85.32/85.63 thf(c_0_247, axiom, (descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(?[X776:$i]:(X1 @ X776&![X777:$i]:(X1 @ X777=>(X776)=(X777)))=>(?[X778:$i]:(X17 @ X778&![X779:$i]:(X17 @ X779=>(X778)=(X779)))=>(descr @ (^[X2:$i]:X1 @ X2))=(descr @ (^[X2:$i]:X17 @ X2)))))), inference(apply_def,[status(thm)],[descr__Cong, exu])). 85.32/85.63 thf(c_0_248, axiom, (ex1E1)=(![X4:$i, X1:$i > $o]:(singleton @ (dsetconstr @ X4 @ (^[X780:$i]:X1 @ X780))=>?[X2:$i]:(in @ X2 @ X4&X1 @ X2))), inference(apply_def,[status(thm)],[ex1E1, ex1])). 85.32/85.63 thf(c_0_249, axiom, (ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>(![X3:$i]:(in @ X3 @ X4=>(X1 @ X3=>(X3)=(X2)))=>singleton @ (dsetconstr @ X4 @ (^[X781:$i]:X1 @ X781)))))), inference(apply_def,[status(thm)],[ex1I, ex1])). 85.32/85.63 thf(c_0_250, 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 @ (^[X783:$i]:X1 @ X783))))), inference(apply_def,[status(thm)],[ex1I2, ex1])). 85.32/85.63 thf(c_0_251, axiom, (setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:X24 @ X2 @ X3)) @ (cartprod @ X4 @ X5)), inference(apply_def,[status(thm)],[setOfPairsIsBReln, breln])). 85.32/85.63 thf(c_0_252, axiom, (brelnall1)=(![X4:$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])). 85.32/85.63 thf(c_0_253, 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])). 85.32/85.63 thf(c_0_254, axiom, (ex1E2)=(![X4:$i, X1:$i > $o]:(singleton @ (dsetconstr @ X4 @ (^[X784:$i]:X1 @ X784))=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))))), inference(apply_def,[status(thm)],[ex1E2, ex1])). 85.32/85.63 thf(c_0_255, 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])). 85.32/85.63 thf(c_0_256, 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])). 85.32/85.63 thf(c_0_257, plain, ![X3:$i, X1:$i > $o]:(epred1_2 @ X1 @ X3<=>X1 @ X3), introduced(definition)). 85.32/85.63 thf(c_0_258, plain, ![X2:$i, X18:$i]:(epred8_2 @ X18 @ X2<=>(X18)=(kpair @ (kfst @ X18) @ X2)), introduced(definition)). 85.32/85.63 thf(c_0_259, plain, ![X18:$i, X14:$i, X22:$i > $i > $o]:(epred4_3 @ X22 @ X14 @ X18<=>X22 @ X14 @ X18), introduced(definition)). 85.32/85.63 thf(c_0_260, plain, ![X3:$i, X29:$i, X2:$i]:(epred5_3 @ X2 @ X29 @ X3<=>in @ (kpair @ X2 @ X3) @ X29), introduced(definition)). 85.32/85.63 thf(c_0_261, plain, ![X2:$i, X31:$i > $i]:(esk1_2 @ X31 @ X2)=(X31 @ X2), introduced(definition)). 85.32/85.63 thf(c_0_262, plain, ![X14:$i, X2:$i, X39:$o, X3:$i]:(epred7_4 @ X3 @ X39 @ X2 @ X14<=>((X39&(X14)=(X2))|(~X39&(X14)=(X3)))), inference(fof_simplification,[status(thm)],[introduced(definition)])). 85.32/85.63 thf(c_0_263, plain, ![X3:$i, X2:$i, X30:$i > $i]:(epred6_3 @ X30 @ X2 @ X3<=>(X30 @ X2)=(X3)), introduced(definition)). 85.32/85.63 thf(c_0_264, plain, ![X2:$i, X18:$i]:(epred3_2 @ X18 @ X2<=>in @ (setadjoin @ X2 @ emptyset) @ X18), introduced(definition)). 85.32/85.63 thf(c_0_265, plain, ![X2:$i]:epred2_1 @ X2, inference(fof_simplification,[status(thm)],[introduced(definition)])). 85.32/85.63 thf(c_0_266, 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:$i]:(in @ X3 @ X9=>in @ X3 @ X8)|in @ X2 @ X9)))))), introduced(definition)). 85.32/85.63 thf(c_0_267, negated_conjecture, ~((![X4:$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:$i]:(in @ X2 @ X4=>?[X751:$i]:(X6 @ X2 @ X751&![X753:$i]:(X6 @ X2 @ X753=>(X751)=(X753))))=>?[X5:$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 > $o]:(?[X754:$i]:(X1 @ X754&![X755:$i]:(X1 @ X755=>(X754)=(X755)))=>X1 @ (descr @ (epred1_2 @ X1)))=>(![X4:$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 > $o]:(?[X756:$i]:(X1 @ X756&![X757:$i]:(X1 @ X757=>(X756)=(X757)))=>?[X2:$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 > $o]:(?[X758:$i]:(X1 @ X758&![X759:$i]:(X1 @ X759=>(X758)=(X759)))=>?[X2:$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:$i]:(dsetconstr @ X4 @ epred2_1)=(X4)=>(![X4:$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 > $o]:(?[X760:$i]:(X1 @ X760&![X761:$i]:(X1 @ X761=>(X760)=(X761)))=>?[X2:$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:$i]:(X1 @ X3=>(X2)=(X3)))=>?[X762:$i]:(X1 @ X762&![X763:$i]:(X1 @ X763=>(X762)=(X763))))=>(![X1:$i > $o]:(?[X2:$i]:X1 @ X2=>(![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3)))=>?[X764:$i]:(X1 @ X764&![X765:$i]:(X1 @ X765=>(X764)=(X765)))))=>(![X1:$i > $o]:(?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2))=>?[X766:$i]:(X1 @ X766&![X767:$i]:(X1 @ X767=>(X766)=(X767))))=>(![X4:$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 > $o]:(?[X768:$i]:(X1 @ X768&![X769:$i]:(X1 @ X769=>(X768)=(X769)))=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))=>(![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(?[X770:$i]:(X1 @ X770&![X771:$i]:(X1 @ X771=>(X770)=(X771)))<=>?[X772:$i]:(X17 @ X772&![X773:$i]:(X17 @ X773=>(X772)=(X773)))))=>((emptyset)=(emptyset)=>(![X2:$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 > $o]:(?[X774:$i]:(X1 @ X774&![X775:$i]:(X1 @ X775=>(X774)=(X775)))=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))=>(![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(?[X776:$i]:(X1 @ X776&![X777:$i]:(X1 @ X777=>(X776)=(X777)))=>(?[X778:$i]:(X17 @ X778&![X779:$i]:(X17 @ X779=>(X778)=(X779)))=>(descr @ (epred1_2 @ X1))=(descr @ (epred1_2 @ X17)))))=>(![X4:$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 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setunion__Cong]), omega__Cong]), c_0_246]), c_0_247]), 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_248]), c_0_249]), c_0_250]), 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_251]), dpsetconstrERa]), dpsetconstrEL1]), dpsetconstrEL2]), dpsetconstrER]), funcImageSingleton]), apProp]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), lamProp]), lamp]), lam2p]), c_0_252]), c_0_253]), c_0_254]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), c_0_255]), c_0_256]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), beta1]), eta1]), lam2lamEq]), beta2]), eta2]), iffalseProp1]), iffalseProp2]), iftrueProp1]), iftrueProp2]), ifSingleton]), ifp]), theeq]), iftrue]), iffalse]), iftrueorfalse]), binintersectT_lem]), c_0_257]), c_0_257]), c_0_257]), c_0_257]), c_0_258]), c_0_259]), c_0_259]), c_0_260]), c_0_261]), c_0_261]), c_0_261]), c_0_261]), c_0_261]), c_0_262]), c_0_262]), c_0_262]), c_0_262]), c_0_262]), c_0_261]), c_0_261]), c_0_257]), c_0_261]), c_0_263]), c_0_260]), c_0_259]), c_0_259]), c_0_259]), c_0_259]), c_0_259]), c_0_264]), c_0_257]), c_0_257]), c_0_257]), c_0_257]), c_0_257]), c_0_257]), c_0_257]), c_0_257]), c_0_257]), c_0_257]), c_0_265]), c_0_257]), c_0_257]), c_0_257])])]), c_0_266])). 85.32/85.63 thf(c_0_268, negated_conjecture, ![X785:$i, X786:$i, X788:$i, X789:$i, X790:$i, X791:$i, X792:$i, X793:$i, X794:$i, X795:$i, X796:$i, X798:$i, X799:$i, X801:$i, X802:$i, X803:$i, X804:$i, X805:$i, X807:$i, X808:$i > $i > $o, X809:$i, X811:$i, X814:$i, X816:$i, X817:$i, X818:$i, X819:$i, X821:$i, X822:$i > $o, X823:$i, X825:$i, X826:$i > $o, X827:$i, X828:$i, X829:$i > $o, X830:$i, X831:$i, X832:$i > $o, X833:$i, X834:$i > $o, X835:$i, X838:$i, X839:$o, X840:$i, X841:$i, X842:$o, X843:$i, X844:$i, X845:$i > $o, X846:$i, X849:$i, X850:$i, X853:$i, X855:$i, X857:$i, X858:$i > $o, X859:$i, X860:$i, X862:$i, X863:$i > $o, X864:$i, X865:$i, X866:$i, X867:$i, X868:$i, X869:$i, X870:$i, X871:$i, X872:$i, X873:$i, X874:$i, X875:$o, X876:$i, X877:$i, X878:$i, X879:$i, X880:$i, X881:$i, X883:$i, X884:$i, X885:$i, X886:$i, X887:$i, X888:$i, X889:$i, X890:$i, X891:$i, X892:$i, X893:$o, X895:$i, X896:$i, X897:$i > $o, X898:$i, X901:$i, X902:$i, X903:$i, X905:$i, X906:$i, X907:$i, X908:$i, X909:$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 > $o, X922:$i, X923:$i > $o, X924:$i, X925:$i, X926:$i > $o, X927:$i, X929:$i, X930:$i > $o, X932:$i, X933:$i, X934:$i > $o, X936:$i, X937:$i, X938:$i > $o, X939:$i, X941:$o, X942:$o, X943:$i, X944:$i > $o, X946:$i, X947:$i, X948:$i > $o, X949:$i, X951:$i > $o, X952:$i, X955:$i, X956:$i > $o, X957:$i, X961:$i, X962:$i > $o, X963:$i, X966:$i, X967:$i, X968:$i, X969:$i, X970:$i, X971:$i, X972:$i, X973:$i, X974:$i, X975:$i > $o, X976:$i, X978:$i, X979:$i, X980:$i > $o, X981:$i > $o, X984:$i, X987:$i, X988:$i, X991:$i, X992:$i, X993:$i, X994:$i, X995:$i, X996:$i, X997:$i, X998:$i, X999:$i, X1000:$i > $o, X1001:$i, X1003:$i, X1004:$i, X1005:$i > $o, X1006:$i > $o, X1009:$i, X1011:$i, X1013:$i, X1014:$i, X1015:$i > $o, X1016:$i > $o, X1019:$i, X1020:$i, X1022:$i, X1023:$i, X1024:$i, X1025:$i, X1026:$i, X1027:$i, X1029:$i, X1030:$i, X1031:$i, X1032:$i, X1033:$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 > $o, X1067:$i, X1068:$i > $o, X1069:$i, X1070:$i, X1071:$i, X1072:$i, X1073:$i, X1074:$i, X1075:$i, X1076:$i, X1077:$i, X1078:$i, X1079:$i, X1080:$o, X1081:$i, X1082:$i, X1083:$i, X1084:$i, X1085:$i, 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, X1109:$i, X1110:$i, X1111:$i, X1112:$i, X1113:$i, X1114:$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:$i, X1148:$o, X1149:$i, X1150:$i, X1151:$i, X1152:$i, X1153:$i, X1154:$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:$i, X1210:$i, X1211:$i, X1212:$i, X1213:$i, X1214:$i, X1216:$i, X1217:$i, X1218:$i, X1219:$i, X1220:$i > $o, X1223:$i, X1224:$i, X1225:$i > $o, X1227:$i, X1228:$i > $o, X1229:$i, X1231:$i, X1232:$i > $o, X1235:$i, X1236:$i, X1237:$i, X1238:$i, X1239:$i, 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 > $i > $o, X1308:$i, X1309:$i, X1310:$i, X1311:$i, X1312:$i > $i > $o, X1313:$i, X1314:$i, X1315:$i > $i > $o, X1316:$i, X1317:$i, X1318:$i > $i > $o, X1319:$i, X1320:$i, X1321:$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, X1339:$i, X1340:$i, X1341:$i, X1342:$i, X1343:$i, X1344:$i, X1345:$i, X1346:$i, X1347:$i, X1348:$i, X1349:$i, X1350:$i, X1351:$i, X1352:$i, X1353:$i, X1354:$i, X1355:$i, X1356:$i, X1357:$i, X1358:$i, X1359:$i, X1360:$i > $i, X1362:$i, X1363:$i, X1364:$i > $i, X1366:$i, X1367:$i, X1368:$i > $i, X1370:$i, X1371:$i, X1372:$i, X1373:$i > $o, X1376:$i, X1377:$i, X1378:$i, X1379:$i, X1380:$i > $o, X1383:$i, X1384:$i, X1385:$i > $o, X1386:$i, X1387:$i, X1388:$i, X1389:$i, X1390:$i, X1391:$i, X1392:$i, X1393:$i, X1394:$i, X1395:$i, X1396:$i, X1397:$i, X1398:$i, X1399:$i, X1400:$i, X1401:$i, X1402:$i, X1403:$i, X1404:$i, X1406:$i, X1407:$i, X1408:$i, X1409:$i, X1410:$i, X1411:$i, X1412:$i, X1413:$i, X1414:$i, X1415:$i, X1416:$i, X1419:$i, X1420:$i, X1421:$i, X1422:$i, X1427:$i, X1428:$i, X1429:$i, X1430:$i, X1432:$i, X1433:$i, X1434:$i, X1435:$i, X1437:$i, X1438:$i, X1439:$i, X1440:$i, X1441:$i, X1442:$i, X1443:$i, X1444:$i, X1445:$i, X1446:$i, X1447:$i > $i, X1449:$i, X1450:$i, X1451:$i, X1452:$i, X1453:$i, X1454:$i, X1455:$i > $i, X1457:$i, X1458:$i, X1459:$i > $i, X1461:$i, X1462:$i, X1463:$i, X1464:$i, X1465:$i, X1466:$o, X1467:$i, X1468:$i, X1469:$i, X1470:$o, X1471:$i, X1472:$i, X1473:$i, X1474:$o, X1475:$i, X1476:$i, X1477:$i, X1478:$o, X1479:$i, X1480:$i, X1481:$i, X1482:$o, X1483:$i, X1484:$i, X1485:$i, X1486:$o, X1487:$i, X1488:$i, X1489:$i, X1490:$i, X1491:$i, X1492:$o, X1493:$i, X1494:$i, X1495:$i, X1496:$o, X1497:$i, X1498:$i, X1499:$i, X1500:$o, X1501:$i, X1502:$i, X1503:$i, X1504:$i, X1505:$i]:(((~in @ (esk2_2 @ X785 @ X786) @ X785|~in @ (esk2_2 @ X785 @ X786) @ X786|(X785)=(X786))&(in @ (esk2_2 @ X785 @ X786) @ X785|in @ (esk2_2 @ X785 @ X786) @ X786|(X785)=(X786)))&(~in @ X788 @ emptyset&(((~in @ X791 @ (setadjoin @ X789 @ X790)|((X791)=(X789)|in @ X791 @ X790))&(((X791)!=(X789)|in @ X791 @ (setadjoin @ X789 @ X790))&(~in @ X791 @ X790|in @ X791 @ (setadjoin @ X789 @ X790))))&(((~in @ X793 @ (powerset @ X792)|(~in @ X794 @ X793|in @ X794 @ X792))&((in @ (esk3_2 @ X795 @ X796) @ X796|in @ X796 @ (powerset @ X795))&(~in @ (esk3_2 @ X795 @ X796) @ X795|in @ X796 @ (powerset @ X795))))&((((in @ X799 @ (esk4_2 @ X798 @ X799)|~in @ X799 @ (setunion @ X798))&(in @ (esk4_2 @ X798 @ X799) @ X798|~in @ X799 @ (setunion @ X798)))&(~in @ X802 @ X803|~in @ X803 @ X801|in @ X802 @ (setunion @ X801)))&(in @ emptyset @ omega&((~in @ X804 @ omega|in @ (setadjoin @ X804 @ X804) @ omega)&((((in @ (esk5_1 @ X805) @ omega|~in @ emptyset @ X805|(~in @ X807 @ omega|in @ X807 @ X805))&(in @ (esk5_1 @ X805) @ X805|~in @ emptyset @ X805|(~in @ X807 @ omega|in @ X807 @ X805)))&(~in @ (setadjoin @ (esk5_1 @ X805) @ (esk5_1 @ X805)) @ X805|~in @ emptyset @ X805|(~in @ X807 @ omega|in @ X807 @ X805)))&(((((in @ (esk9_3 @ X808 @ X809 @ X814) @ X809|~in @ X814 @ (esk8_2 @ X808 @ X809)|in @ (esk6_2 @ X808 @ X809) @ X809)&(X808 @ (esk9_3 @ X808 @ X809 @ X814) @ X814|~in @ X814 @ (esk8_2 @ X808 @ X809)|in @ (esk6_2 @ X808 @ X809) @ X809))&(~in @ X817 @ X809|~X808 @ X817 @ X816|in @ X816 @ (esk8_2 @ X808 @ X809)|in @ (esk6_2 @ X808 @ X809) @ X809))&((((in @ (esk9_3 @ X808 @ X809 @ X814) @ X809|~in @ X814 @ (esk8_2 @ X808 @ X809)|(X808 @ (esk6_2 @ X808 @ X809) @ (esk7_3 @ X808 @ X809 @ X811)|~X808 @ (esk6_2 @ X808 @ X809) @ X811))&(X808 @ (esk9_3 @ X808 @ X809 @ X814) @ X814|~in @ X814 @ (esk8_2 @ X808 @ X809)|(X808 @ (esk6_2 @ X808 @ X809) @ (esk7_3 @ X808 @ X809 @ X811)|~X808 @ (esk6_2 @ X808 @ X809) @ X811)))&(~in @ X817 @ X809|~X808 @ X817 @ X816|in @ X816 @ (esk8_2 @ X808 @ X809)|(X808 @ (esk6_2 @ X808 @ X809) @ (esk7_3 @ X808 @ X809 @ X811)|~X808 @ (esk6_2 @ X808 @ X809) @ X811)))&(((in @ (esk9_3 @ X808 @ X809 @ X814) @ X809|~in @ X814 @ (esk8_2 @ X808 @ X809)|((X811)!=(esk7_3 @ X808 @ X809 @ X811)|~X808 @ (esk6_2 @ X808 @ X809) @ X811))&(X808 @ (esk9_3 @ X808 @ X809 @ X814) @ X814|~in @ X814 @ (esk8_2 @ X808 @ X809)|((X811)!=(esk7_3 @ X808 @ X809 @ X811)|~X808 @ (esk6_2 @ X808 @ X809) @ X811)))&(~in @ X817 @ X809|~X808 @ X817 @ X816|in @ X816 @ (esk8_2 @ X808 @ X809)|((X811)!=(esk7_3 @ X808 @ X809 @ X811)|~X808 @ (esk6_2 @ X808 @ X809) @ X811)))))&(((in @ (esk10_1 @ X818) @ X818|~in @ X819 @ X818)&(~in @ X821 @ (esk10_1 @ X818)|~in @ X821 @ X818|~in @ X819 @ X818))&(epred9_0&(((X822 @ (esk11_2 @ X822 @ X823)|~X822 @ X823|X822 @ (descr @ (epred1_2 @ X822)))&((X823)!=(esk11_2 @ X822 @ X823)|~X822 @ X823|X822 @ (descr @ (epred1_2 @ X822))))&((~in @ X827 @ X825|(~X826 @ X827|in @ X827 @ (dsetconstr @ X825 @ (epred1_2 @ X826))))&((~in @ X830 @ (dsetconstr @ X828 @ (epred1_2 @ X829))|in @ X830 @ X828)&((~in @ X833 @ (dsetconstr @ X831 @ (epred1_2 @ X832))|X832 @ X833)&((((X834 @ (esk13_1 @ X834)|(X834 @ (esk12_2 @ X834 @ X835)|~X834 @ X835))&(~X834 @ X838|(esk13_1 @ X834)=(X838)|(X834 @ (esk12_2 @ X834 @ X835)|~X834 @ X835)))&((X834 @ (esk13_1 @ X834)|((X835)!=(esk12_2 @ X834 @ X835)|~X834 @ X835))&(~X834 @ X838|(esk13_1 @ X834)=(X838)|((X835)!=(esk12_2 @ X834 @ X835)|~X834 @ X835))))&((((~X839|X839|X839)&(~in @ X840 @ (prop2set @ $false)|X839|X839))&((~X839|~in @ X840 @ (prop2set @ $true)|X839)&(~in @ X840 @ (prop2set @ $false)|~in @ X840 @ (prop2set @ $true)|X839)))&((~in @ X841 @ emptyset|X842)&(~in @ X843 @ emptyset&(~in @ X844 @ emptyset&(((X845 @ (esk14_2 @ X845 @ X846)|~X845 @ X846|X845 @ (esk15_1 @ X845))&((X846)!=(esk14_2 @ X845 @ X846)|~X845 @ X846|X845 @ (esk15_1 @ X845)))&((((in @ (esk17_2 @ X849 @ X850) @ X850|(X849)=(X850)|in @ (esk16_2 @ X849 @ X850) @ X849)&(~in @ (esk17_2 @ X849 @ X850) @ X849|(X849)=(X850)|in @ (esk16_2 @ X849 @ X850) @ X849))&((in @ (esk17_2 @ X849 @ X850) @ X850|(X849)=(X850)|~in @ (esk16_2 @ X849 @ X850) @ X850)&(~in @ (esk17_2 @ X849 @ X850) @ X849|(X849)=(X850)|~in @ (esk16_2 @ X849 @ X850) @ X850)))&((in @ (esk18_1 @ X853) @ X853|(X853)=(emptyset))&((in @ (esk19_1 @ X855) @ X855|(X855)=(emptyset))&(((~in @ X859 @ (dsetconstr @ X857 @ (epred1_2 @ X858))|X858 @ X859|~in @ X859 @ X857)&(~X858 @ X859|in @ X859 @ (dsetconstr @ X857 @ (epred1_2 @ X858))|~in @ X859 @ X857))&(((X860)=(emptyset)|in @ (esk20_1 @ X860) @ X860)&((~in @ X864 @ X862|(~X863 @ X864|(dsetconstr @ X862 @ (epred1_2 @ X863))!=(emptyset)))&((~in @ X866 @ X865|(X865)!=(emptyset))&(in @ X867 @ (setadjoin @ X867 @ X868)&(in @ emptyset @ (setadjoin @ emptyset @ emptyset)&((~in @ X871 @ X870|in @ X871 @ (setadjoin @ X869 @ X870))&((((in @ X874 @ X873|X875|(X874)=(X872)|~in @ X874 @ (setadjoin @ X872 @ X873))&(~X875|X875|(X874)=(X872)|~in @ X874 @ (setadjoin @ X872 @ X873)))&((in @ X874 @ X873|X875|~X875|~in @ X874 @ (setadjoin @ X872 @ X873))&(~X875|X875|~X875|~in @ X874 @ (setadjoin @ X872 @ X873))))&((~in @ X878 @ (setadjoin @ X876 @ X877)|((X878)=(X876)|in @ X878 @ X877))&((dsetconstr @ X879 @ epred2_1)=(X879)&(((in @ (esk21_2 @ X880 @ X881) @ X881|in @ X881 @ (powerset @ X880))&(~in @ (esk21_2 @ X880 @ X881) @ X880|in @ X881 @ (powerset @ X880)))&(in @ emptyset @ (powerset @ X883)&(in @ emptyset @ (powerset @ X884)&((~in @ X886 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(setadjoin @ X912 @ emptyset)|in @ X912 @ (setadjoin @ X911 @ emptyset))&((~in @ X915 @ (setadjoin @ X913 @ (setadjoin @ X914 @ emptyset))|((X915)=(X913)|(X915)=(X914)))&(in @ X916 @ (setadjoin @ X916 @ (setadjoin @ X917 @ emptyset))&(in @ X919 @ (setadjoin @ X918 @ (setadjoin @ X919 @ emptyset))&((~in @ X922 @ X920|~X921 @ X922|(dsetconstr @ X920 @ (epred1_2 @ X921))!=(emptyset))&((~in @ X924 @ emptyset|X923 @ X924)&(((in @ (esk26_2 @ X925 @ X926) @ X925|(~in @ X927 @ X925|X926 @ X927))&(~X926 @ (esk26_2 @ X925 @ X926)|(~in @ X927 @ X925|X926 @ X927)))&(((in @ (esk27_2 @ X929 @ X930) @ X929|(~in @ X932 @ X929|~X930 @ X932))&(X930 @ (esk27_2 @ X929 @ X930)|(~in @ X932 @ X929|~X930 @ X932)))&(((in @ (esk28_2 @ X933 @ X934) @ X933|(~in @ X936 @ X933|~X934 @ X936))&(X934 @ (esk28_2 @ X933 @ X934)|(~in @ X936 @ X933|~X934 @ X936)))&(((in @ (esk29_2 @ X937 @ X938) @ X937|(~in @ X939 @ X937|X938 @ X939))&(~X938 @ (esk29_2 @ X937 @ X938)|(~in @ X939 @ X937|X938 @ X939)))&(((~X941|in @ 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X979|(X978)=(X979)))))&((((((X981 @ (esk43_2 @ X980 @ X981)|(X980 @ (esk42_3 @ X980 @ X981 @ X984)|~X980 @ X984)|(esk40_2 @ X980 @ X981)=(esk41_2 @ X980 @ X981))&(~X981 @ X987|(esk43_2 @ X980 @ X981)=(X987)|(X980 @ (esk42_3 @ X980 @ X981 @ X984)|~X980 @ X984)|(esk40_2 @ X980 @ X981)=(esk41_2 @ X980 @ X981)))&((X981 @ (esk43_2 @ X980 @ X981)|((X984)!=(esk42_3 @ X980 @ X981 @ X984)|~X980 @ X984)|(esk40_2 @ X980 @ X981)=(esk41_2 @ X980 @ X981))&(~X981 @ X987|(esk43_2 @ X980 @ X981)=(X987)|((X984)!=(esk42_3 @ X980 @ X981 @ X984)|~X980 @ X984)|(esk40_2 @ X980 @ X981)=(esk41_2 @ X980 @ X981))))&(((X980 @ (esk45_2 @ X980 @ X981)|(X981 @ (esk44_3 @ X980 @ X981 @ X988)|~X981 @ X988)|(esk40_2 @ X980 @ X981)=(esk41_2 @ X980 @ X981))&(~X980 @ X991|(esk45_2 @ X980 @ X981)=(X991)|(X981 @ (esk44_3 @ X980 @ X981 @ X988)|~X981 @ X988)|(esk40_2 @ X980 @ X981)=(esk41_2 @ X980 @ X981)))&((X980 @ (esk45_2 @ X980 @ X981)|((X988)!=(esk44_3 @ X980 @ X981 @ X988)|~X981 @ X988)|(esk40_2 @ X980 @ X981)=(esk41_2 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X1015))=(dsetconstr @ X1014 @ (epred1_2 @ X1016))|(X1013)!=(X1014))))))&(((in @ (esk53_2 @ X1019 @ X1020) @ X1019|subset @ X1019 @ X1020)&(~in @ (esk53_2 @ X1019 @ X1020) @ X1020|subset @ X1019 @ X1020))&(((X1022)!=(X1023)|subset @ X1023 @ X1022)&(((X1024)!=(X1025)|subset @ X1024 @ X1025)&(((in @ (esk54_2 @ X1026 @ X1027) @ X1026|subset @ X1026 @ X1027)&(~in @ (esk54_2 @ X1026 @ X1027) @ X1027|subset @ X1026 @ X1027))&(subset @ emptyset @ X1029&((~subset @ X1030 @ X1031|(~in @ X1032 @ X1030|in @ X1032 @ X1031))&((~subset @ X1033 @ X1034|(in @ X1035 @ X1034|~in @ X1035 @ X1033))&((~in @ X1038 @ X1036|(in @ X1038 @ X1037|~subset @ X1036 @ X1037))&((subset @ X1039 @ X1040|(X1039)!=(X1040))&((~in @ X1043 @ X1041|(in @ X1043 @ X1042|(X1041)!=(X1042)))&(subset @ X1044 @ X1044&((~subset @ X1045 @ X1046|(~subset @ X1046 @ X1047|subset @ X1045 @ X1047))&(subset @ X1049 @ (setadjoin @ X1048 @ X1049)&((~subset @ X1050 @ X1052|subset @ X1050 @ (setadjoin @ X1051 @ X1052))&((~subset @ X1053 @ X1054|in @ X1053 @ (powerset @ X1054))&((~subset @ X1055 @ X1056|(~subset @ X1056 @ X1055|(X1055)=(X1056)))&((~subset @ X1057 @ emptyset|(X1057)=(emptyset))&((~subset @ X1059 @ X1058|in @ X1059 @ (powerset @ X1058))&((~in @ X1061 @ (powerset @ X1060)|subset @ X1061 @ X1060)&(in @ X1062 @ (powerset @ X1062)&((~subset @ X1063 @ X1064|subset @ (powerset @ X1063) @ (powerset @ X1064))&(in @ (dsetconstr @ X1065 @ (epred1_2 @ X1066)) @ (powerset @ X1065)&(subset @ (dsetconstr @ X1067 @ (epred1_2 @ X1068)) @ X1067&((~in @ X1071 @ X1069|in @ X1071 @ (binunion @ X1069 @ X1070))&(in @ X1073 @ (setadjoin @ X1072 @ (setadjoin @ X1073 @ emptyset))&((~in @ X1076 @ X1075|in @ X1076 @ (binunion @ X1074 @ X1075))&((((in @ X1079 @ X1078|X1080|in @ X1079 @ X1077|~in @ X1079 @ (binunion @ X1077 @ X1078))&(~X1080|X1080|in @ X1079 @ X1077|~in @ X1079 @ (binunion @ X1077 @ X1078)))&((in @ X1079 @ X1078|X1080|~X1080|~in @ X1079 @ (binunion @ X1077 @ X1078))&(~X1080|X1080|~X1080|~in @ X1079 @ (binunion @ X1077 @ X1078))))&((~in @ X1083 @ (binunion @ X1081 @ X1082)|(in @ X1083 @ X1081|in @ X1083 @ X1082))&(subset @ X1084 @ (binunion @ X1084 @ X1085)&(subset @ X1087 @ (binunion @ X1086 @ X1087)&((~in @ X1090 @ X1088|(~in @ X1090 @ X1089|in @ X1090 @ (binintersect @ X1088 @ X1089)))&((~subset @ X1093 @ X1091|(~subset @ X1093 @ X1092|subset @ X1093 @ (binintersect @ X1091 @ X1092)))&((~in @ X1096 @ (binintersect @ X1094 @ X1095)|in @ X1096 @ X1094)&(subset @ (binintersect @ X1097 @ X1098) @ X1097&((~subset @ X1099 @ X1100|(binintersect @ X1099 @ X1100)=(X1099))&(((binintersect @ X1101 @ X1102)!=(X1102)|subset @ X1102 @ X1101)&((~in @ X1105 @ (binintersect @ X1103 @ X1104)|in @ X1105 @ X1104)&(((in @ (esk55_2 @ X1106 @ X1107) @ X1106|(binintersect @ X1106 @ X1107)=(emptyset))&(in @ (esk55_2 @ X1106 @ X1107) @ X1107|(binintersect @ X1106 @ X1107)=(emptyset)))&(subset @ (binintersect @ X1109 @ X1110) @ X1110&((~subset @ X1112 @ X1111|(binintersect @ X1111 @ X1112)=(X1112))&(((binintersect @ X1113 @ X1114)!=(X1113)|subset @ X1113 @ X1114)&((binintersect @ X1115 @ (binunion @ X1116 @ X1117))=(binunion @ (binintersect @ X1115 @ X1116) @ (binintersect @ X1115 @ X1117))&((~in @ X1120 @ X1118|(in @ X1120 @ X1119|in @ X1120 @ (setminus @ X1118 @ X1119)))&((~in @ X1123 @ (setminus @ X1121 @ X1122)|in @ X1123 @ X1121)&((~in @ X1126 @ (setminus @ X1124 @ X1125)|~in @ X1126 @ X1125)&((~subset @ X1127 @ X1128|(setminus @ X1127 @ X1128)=(emptyset))&((in @ X1131 @ (setminus @ X1129 @ X1130)|(~in @ X1131 @ X1129|in @ X1131 @ X1130))&((in @ X1134 @ (setminus @ X1132 @ X1133)|(in @ X1134 @ X1133|~in @ X1134 @ X1132))&((in @ X1137 @ X1135|~in @ X1137 @ (setminus @ X1135 @ X1136))&((~in @ X1140 @ X1139|~in @ X1140 @ (setminus @ X1138 @ X1139))&(subset @ (setminus @ X1141 @ X1142) @ X1141&(((setminus @ X1143 @ X1144)!=(emptyset)|subset @ X1143 @ X1144)&((((~in @ X1147 @ X1145|X1148|in @ X1147 @ X1145|~in @ X1147 @ (symdiff @ X1145 @ X1146))&((in @ X1147 @ X1146|X1148|in @ X1147 @ X1145|~in @ X1147 @ (symdiff @ X1145 @ X1146))&(~X1148|X1148|in @ X1147 @ X1145|~in @ X1147 @ (symdiff @ X1145 @ X1146))))&(((~in @ X1147 @ X1145|X1148|~in @ X1147 @ X1146|~in @ X1147 @ (symdiff @ X1145 @ X1146))&((in @ X1147 @ X1146|X1148|~in @ X1147 @ X1146|~in @ X1147 @ (symdiff @ X1145 @ X1146))&(~X1148|X1148|~in @ X1147 @ X1146|~in @ X1147 @ (symdiff @ X1145 @ X1146))))&((~in @ X1147 @ X1145|X1148|~X1148|~in @ X1147 @ (symdiff @ X1145 @ X1146))&((in @ X1147 @ X1146|X1148|~X1148|~in @ X1147 @ (symdiff @ X1145 @ X1146))&(~X1148|X1148|~X1148|~in @ X1147 @ (symdiff @ X1145 @ X1146))))))&((~in @ X1151 @ X1149|(in @ X1151 @ X1150|in @ X1151 @ (symdiff @ X1149 @ X1150)))&((in @ X1154 @ X1152|(~in @ X1154 @ X1153|in @ X1154 @ (symdiff @ X1152 @ X1153)))&((~in @ X1157 @ X1155|(~in @ X1157 @ X1156|~in @ X1157 @ (symdiff @ X1155 @ X1156)))&((in @ X1160 @ X1158|(in @ X1160 @ X1159|~in @ X1160 @ (symdiff @ X1158 @ X1159)))&(in @ X1162 @ (setadjoin @ X1161 @ (setadjoin @ X1162 @ emptyset))&(in @ X1163 @ (setunion 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X1220))))&((esk59_2 @ X1219 @ X1220)!=(esk60_2 @ X1219 @ X1220)|(~in @ X1223 @ X1219|~X1220 @ X1223|singleton @ (dsetconstr @ X1219 @ (epred1_2 @ X1220))))))))&(((in @ (esk61_2 @ X1224 @ X1225) @ X1224|~singleton @ (dsetconstr @ X1224 @ (epred1_2 @ X1225)))&(X1225 @ (esk61_2 @ X1224 @ X1225)|~singleton @ (dsetconstr @ X1224 @ (epred1_2 @ X1225))))&(((in @ (esk62_3 @ X1227 @ X1228 @ X1229) @ X1227|singleton @ (dsetconstr @ X1227 @ (epred1_2 @ X1228))|~X1228 @ X1229|~in @ X1229 @ X1227)&((X1228 @ (esk62_3 @ X1227 @ X1228 @ X1229)|singleton @ (dsetconstr @ X1227 @ (epred1_2 @ X1228))|~X1228 @ X1229|~in @ X1229 @ X1227)&((esk62_3 @ X1227 @ X1228 @ X1229)!=(X1229)|singleton @ (dsetconstr @ X1227 @ (epred1_2 @ X1228))|~X1228 @ X1229|~in @ X1229 @ X1227)))&(((in @ (esk63_2 @ X1231 @ X1232) @ X1231|(~in @ X1235 @ X1231|~X1232 @ X1235|singleton @ (dsetconstr @ X1231 @ (epred1_2 @ X1232))))&((in @ (esk64_2 @ X1231 @ X1232) @ X1231|(~in @ X1235 @ X1231|~X1232 @ X1235|singleton @ (dsetconstr @ X1231 @ (epred1_2 @ X1232))))&((X1232 @ (esk63_2 @ X1231 @ X1232)|(~in @ X1235 @ X1231|~X1232 @ X1235|singleton @ (dsetconstr @ X1231 @ (epred1_2 @ X1232))))&((X1232 @ (esk64_2 @ X1231 @ X1232)|(~in @ X1235 @ X1231|~X1232 @ X1235|singleton @ (dsetconstr @ X1231 @ (epred1_2 @ X1232))))&((esk63_2 @ X1231 @ X1232)!=(esk64_2 @ X1231 @ X1232)|(~in @ X1235 @ X1231|~X1232 @ X1235|singleton @ (dsetconstr @ X1231 @ (epred1_2 @ X1232))))))))&(((setadjoin @ X1236 @ emptyset)!=(setadjoin @ X1237 @ emptyset)|(X1236)=(X1237))&((~in @ (setadjoin @ X1240 @ emptyset) @ (setadjoin @ (setadjoin @ X1238 @ emptyset) @ (setadjoin @ (setadjoin @ X1238 @ (setadjoin @ X1239 @ emptyset)) @ emptyset))|(X1238)=(X1240))&((~iskpair @ X1241|singleton @ (dsetconstr @ (setunion @ X1241) @ (epred3_2 @ X1241)))&((~singleton @ X1242|in @ (setunion @ X1242) @ X1242)&((kfst @ (kpair @ X1243 @ X1244))=(X1243)&((~in @ X1247 @ (cartprod @ X1245 @ X1246)|in @ (kfst @ X1247) @ X1245)&(((setadjoin @ (setadjoin @ X1248 @ 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X1298|(~in @ X1301 @ X1299|(ksnd @ (kpair @ X1300 @ X1301))=(X1301)))&((~in @ X1304 @ (cartprod @ X1302 @ X1303)|(kpair @ (kfst @ X1304) @ (ksnd @ X1304))=(X1304))&((~in @ X1308 @ X1305|(~in @ X1309 @ X1306|(~X1307 @ X1308 @ X1309|in @ (kpair @ X1308 @ X1309) @ (dpsetconstr @ X1305 @ X1306 @ (epred4_3 @ X1307)))))&(subset @ (dpsetconstr @ X1310 @ X1311 @ (epred4_3 @ X1312)) @ (cartprod @ X1310 @ X1311)&(subset @ (dpsetconstr @ X1313 @ X1314 @ (epred4_3 @ X1315)) @ (cartprod @ X1313 @ X1314)&((~in @ X1319 @ X1316|(~in @ X1320 @ X1317|(~in @ (kpair @ X1319 @ X1320) @ (dpsetconstr @ X1316 @ X1317 @ (epred4_3 @ X1318))|X1318 @ X1319 @ X1320)))&((~in @ (kpair @ X1324 @ X1325) @ (dpsetconstr @ X1321 @ X1322 @ (epred4_3 @ X1323))|in @ X1324 @ X1321)&((~in @ (kpair @ X1329 @ X1330) @ (dpsetconstr @ X1326 @ X1327 @ (epred4_3 @ X1328))|in @ X1330 @ X1327)&((~in @ (kpair @ X1334 @ X1335) @ (dpsetconstr @ X1331 @ X1332 @ (epred4_3 @ X1333))|X1333 @ X1334 @ X1335)&((~func @ X1336 @ X1337 @ 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@ X1371)))))&(((in @ (esk70_4 @ X1377 @ X1378 @ X1379 @ X1380) @ X1377|(~in @ X1383 @ X1379|X1380 @ X1383)|~subset @ X1379 @ (cartprod @ X1377 @ X1378))&((in @ (esk71_4 @ X1377 @ X1378 @ X1379 @ X1380) @ X1378|(~in @ X1383 @ X1379|X1380 @ X1383)|~subset @ X1379 @ (cartprod @ X1377 @ X1378))&((in @ (kpair @ (esk70_4 @ X1377 @ X1378 @ X1379 @ X1380) @ (esk71_4 @ X1377 @ X1378 @ X1379 @ X1380)) @ X1379|(~in @ X1383 @ X1379|X1380 @ X1383)|~subset @ X1379 @ (cartprod @ X1377 @ X1378))&(~X1380 @ (kpair @ (esk70_4 @ X1377 @ X1378 @ X1379 @ X1380) @ (esk71_4 @ X1377 @ X1378 @ X1379 @ X1380))|(~in @ X1383 @ X1379|X1380 @ X1383)|~subset @ X1379 @ (cartprod @ X1377 @ X1378)))))&((~singleton @ (dsetconstr @ X1384 @ (epred1_2 @ X1385))|(~in @ X1386 @ X1384|(~in @ X1387 @ X1384|(~X1385 @ X1386|(~X1385 @ X1387|(X1386)=(X1387))))))&((~func @ X1388 @ X1389 @ X1390|(~in @ X1391 @ X1388|in @ (kpair @ X1391 @ (ap @ X1388 @ X1389 @ X1390 @ X1391)) @ X1390))&((~in @ X1394 @ (funcSet @ X1392 @ X1393)|(~in @ X1395 @ X1392|in @ (kpair @ X1395 @ (ap @ X1392 @ X1393 @ X1394 @ X1395)) @ X1394))&((~func @ X1396 @ X1397 @ X1398|(~in @ X1399 @ X1396|(~in @ X1400 @ X1397|(~in @ (kpair @ X1399 @ X1400) @ X1398|(ap @ X1396 @ X1397 @ X1398 @ X1399)=(X1400)))))&(((in @ (esk72_4 @ X1401 @ X1402 @ X1403 @ X1404) @ X1401|(~in @ X1406 @ X1401|(~in @ X1407 @ X1402|(~in @ (kpair @ X1406 @ X1407) @ X1404|in @ (kpair @ X1406 @ X1407) @ X1403)))|~func @ X1401 @ X1402 @ X1404|~func @ X1401 @ X1402 @ X1403)&((ap @ X1401 @ X1402 @ X1403 @ (esk72_4 @ X1401 @ X1402 @ X1403 @ X1404))!=(ap @ X1401 @ X1402 @ X1404 @ (esk72_4 @ X1401 @ X1402 @ X1403 @ X1404))|(~in @ X1406 @ X1401|(~in @ X1407 @ X1402|(~in @ (kpair @ X1406 @ X1407) @ X1404|in @ (kpair @ X1406 @ X1407) @ X1403)))|~func @ X1401 @ X1402 @ X1404|~func @ X1401 @ X1402 @ X1403))&((~in @ X1410 @ (funcSet @ X1408 @ X1409)|(~in @ X1411 @ X1408|(~in @ X1412 @ X1409|(~in @ (kpair @ X1411 @ X1412) @ X1410|(ap @ X1408 @ X1409 @ X1410 @ X1411)=(X1412)))))&(((in @ (esk73_4 @ X1413 @ X1414 @ X1415 @ X1416) @ X1413|subset @ X1415 @ X1416|~subset @ X1416 @ (cartprod @ X1413 @ X1414)|~subset @ X1415 @ (cartprod @ X1413 @ X1414))&((in @ (esk74_4 @ X1413 @ X1414 @ X1415 @ X1416) @ X1414|subset @ X1415 @ X1416|~subset @ X1416 @ (cartprod @ X1413 @ X1414)|~subset @ X1415 @ (cartprod @ X1413 @ X1414))&((in @ (kpair @ (esk73_4 @ X1413 @ X1414 @ X1415 @ X1416) @ (esk74_4 @ X1413 @ X1414 @ X1415 @ X1416)) @ X1415|subset @ X1415 @ X1416|~subset @ X1416 @ (cartprod @ X1413 @ X1414)|~subset @ X1415 @ (cartprod @ X1413 @ X1414))&(~in @ (kpair @ (esk73_4 @ X1413 @ X1414 @ X1415 @ X1416) @ (esk74_4 @ X1413 @ X1414 @ X1415 @ X1416)) @ X1416|subset @ X1415 @ X1416|~subset @ X1416 @ (cartprod @ X1413 @ X1414)|~subset @ X1415 @ (cartprod @ X1413 @ X1414)))))&((((in @ (esk77_4 @ X1419 @ X1420 @ X1421 @ X1422) @ X1419|(X1421)=(X1422)|in @ (esk75_4 @ X1419 @ X1420 @ X1421 @ X1422) @ X1419|~subset @ X1422 @ (cartprod @ X1419 @ X1420)|~subset @ X1421 @ (cartprod @ X1419 @ X1420))&((in @ (esk78_4 @ X1419 @ X1420 @ X1421 @ X1422) @ X1420|(X1421)=(X1422)|in @ (esk75_4 @ X1419 @ X1420 @ X1421 @ X1422) @ X1419|~subset @ X1422 @ (cartprod @ X1419 @ X1420)|~subset @ X1421 @ (cartprod @ X1419 @ X1420))&((in @ (kpair @ (esk77_4 @ X1419 @ X1420 @ X1421 @ X1422) @ (esk78_4 @ X1419 @ X1420 @ X1421 @ X1422)) @ X1422|(X1421)=(X1422)|in @ (esk75_4 @ X1419 @ X1420 @ X1421 @ X1422) @ X1419|~subset @ X1422 @ (cartprod @ X1419 @ X1420)|~subset @ X1421 @ (cartprod @ X1419 @ X1420))&(~in @ (kpair @ (esk77_4 @ X1419 @ X1420 @ X1421 @ X1422) @ (esk78_4 @ X1419 @ X1420 @ X1421 @ X1422)) @ X1421|(X1421)=(X1422)|in @ (esk75_4 @ X1419 @ X1420 @ X1421 @ X1422) @ X1419|~subset @ X1422 @ (cartprod @ X1419 @ X1420)|~subset @ X1421 @ (cartprod @ X1419 @ X1420)))))&(((in @ (esk77_4 @ X1419 @ X1420 @ X1421 @ X1422) @ X1419|(X1421)=(X1422)|in @ (esk76_4 @ X1419 @ X1420 @ X1421 @ X1422) @ X1420|~subset @ X1422 @ (cartprod @ X1419 @ X1420)|~subset @ X1421 @ (cartprod @ X1419 @ X1420))&((in @ (esk78_4 @ X1419 @ X1420 @ X1421 @ X1422) @ X1420|(X1421)=(X1422)|in @ (esk76_4 @ X1419 @ X1420 @ X1421 @ X1422) @ X1420|~subset @ X1422 @ (cartprod @ X1419 @ X1420)|~subset @ X1421 @ (cartprod @ X1419 @ X1420))&((in @ (kpair @ (esk77_4 @ X1419 @ X1420 @ X1421 @ X1422) @ (esk78_4 @ X1419 @ X1420 @ X1421 @ X1422)) @ X1422|(X1421)=(X1422)|in @ (esk76_4 @ X1419 @ X1420 @ X1421 @ X1422) @ X1420|~subset @ X1422 @ (cartprod @ X1419 @ X1420)|~subset @ X1421 @ (cartprod @ X1419 @ X1420))&(~in @ (kpair @ (esk77_4 @ X1419 @ X1420 @ X1421 @ X1422) @ (esk78_4 @ X1419 @ X1420 @ X1421 @ X1422)) @ X1421|(X1421)=(X1422)|in @ (esk76_4 @ X1419 @ X1420 @ X1421 @ X1422) @ X1420|~subset @ X1422 @ (cartprod @ X1419 @ X1420)|~subset @ X1421 @ (cartprod @ X1419 @ X1420)))))&(((in @ (esk77_4 @ X1419 @ X1420 @ X1421 @ X1422) @ X1419|(X1421)=(X1422)|in @ (kpair @ (esk75_4 @ X1419 @ X1420 @ X1421 @ X1422) @ (esk76_4 @ X1419 @ X1420 @ X1421 @ X1422)) @ X1421|~subset @ X1422 @ (cartprod @ X1419 @ X1420)|~subset @ X1421 @ (cartprod @ X1419 @ X1420))&((in @ (esk78_4 @ X1419 @ X1420 @ X1421 @ X1422) @ X1420|(X1421)=(X1422)|in @ (kpair @ (esk75_4 @ X1419 @ X1420 @ X1421 @ X1422) @ (esk76_4 @ X1419 @ X1420 @ X1421 @ X1422)) @ X1421|~subset @ X1422 @ (cartprod @ X1419 @ X1420)|~subset @ X1421 @ (cartprod @ X1419 @ X1420))&((in @ (kpair @ (esk77_4 @ X1419 @ X1420 @ X1421 @ X1422) @ (esk78_4 @ X1419 @ X1420 @ X1421 @ X1422)) @ X1422|(X1421)=(X1422)|in @ (kpair @ (esk75_4 @ X1419 @ X1420 @ X1421 @ X1422) @ (esk76_4 @ X1419 @ X1420 @ X1421 @ X1422)) @ X1421|~subset @ X1422 @ (cartprod @ X1419 @ X1420)|~subset @ X1421 @ (cartprod @ X1419 @ X1420))&(~in @ (kpair @ (esk77_4 @ X1419 @ X1420 @ X1421 @ X1422) @ (esk78_4 @ X1419 @ X1420 @ X1421 @ X1422)) @ X1421|(X1421)=(X1422)|in @ (kpair @ (esk75_4 @ X1419 @ X1420 @ X1421 @ X1422) @ (esk76_4 @ X1419 @ X1420 @ X1421 @ X1422)) @ X1421|~subset @ X1422 @ (cartprod @ X1419 @ X1420)|~subset @ X1421 @ (cartprod @ X1419 @ X1420)))))&((in @ (esk77_4 @ X1419 @ X1420 @ X1421 @ X1422) @ X1419|(X1421)=(X1422)|~in @ (kpair @ (esk75_4 @ X1419 @ X1420 @ X1421 @ X1422) @ (esk76_4 @ X1419 @ X1420 @ X1421 @ X1422)) @ X1422|~subset @ X1422 @ (cartprod @ X1419 @ X1420)|~subset @ X1421 @ (cartprod @ X1419 @ X1420))&((in @ (esk78_4 @ X1419 @ X1420 @ X1421 @ X1422) @ X1420|(X1421)=(X1422)|~in @ (kpair @ (esk75_4 @ X1419 @ X1420 @ X1421 @ X1422) @ (esk76_4 @ X1419 @ X1420 @ X1421 @ X1422)) @ X1422|~subset @ X1422 @ (cartprod @ X1419 @ X1420)|~subset @ X1421 @ (cartprod @ X1419 @ X1420))&((in @ (kpair @ (esk77_4 @ X1419 @ X1420 @ X1421 @ X1422) @ (esk78_4 @ X1419 @ X1420 @ X1421 @ X1422)) @ X1422|(X1421)=(X1422)|~in @ (kpair @ (esk75_4 @ X1419 @ X1420 @ X1421 @ X1422) @ (esk76_4 @ X1419 @ X1420 @ X1421 @ X1422)) @ X1422|~subset @ X1422 @ (cartprod @ X1419 @ X1420)|~subset @ X1421 @ (cartprod @ X1419 @ X1420))&(~in @ (kpair @ (esk77_4 @ X1419 @ X1420 @ X1421 @ X1422) @ (esk78_4 @ X1419 @ X1420 @ X1421 @ X1422)) @ X1421|(X1421)=(X1422)|~in @ (kpair @ (esk75_4 @ X1419 @ X1420 @ X1421 @ X1422) @ (esk76_4 @ X1419 @ X1420 @ X1421 @ X1422)) @ X1422|~subset @ X1422 @ (cartprod @ X1419 @ X1420)|~subset @ X1421 @ (cartprod @ X1419 @ X1420))))))))&(((in @ (esk79_4 @ X1427 @ X1428 @ X1429 @ X1430) @ X1427|(X1429)=(X1430)|~func @ X1427 @ X1428 @ X1430|~func @ X1427 @ X1428 @ X1429)&((ap @ X1427 @ X1428 @ X1429 @ (esk79_4 @ X1427 @ X1428 @ X1429 @ X1430))!=(ap @ X1427 @ X1428 @ X1430 @ (esk79_4 @ X1427 @ X1428 @ X1429 @ X1430))|(X1429)=(X1430)|~func @ X1427 @ X1428 @ X1430|~func @ X1427 @ X1428 @ X1429))&(((in @ (esk80_4 @ X1432 @ X1433 @ X1434 @ X1435) @ X1432|(X1434)=(X1435)|~in @ X1435 @ (funcSet @ X1432 @ X1433)|~in @ X1434 @ (funcSet @ X1432 @ X1433))&((ap @ X1432 @ X1433 @ X1434 @ (esk80_4 @ X1432 @ X1433 @ X1434 @ X1435))!=(ap @ X1432 @ X1433 @ X1435 @ (esk80_4 @ X1432 @ X1433 @ X1434 @ X1435))|(X1434)=(X1435)|~in @ X1435 @ (funcSet @ X1432 @ X1433)|~in @ X1434 @ (funcSet @ X1432 @ X1433)))&((~in @ X1439 @ (funcSet @ X1437 @ X1438)|(~in @ X1440 @ X1437|(ap @ X1437 @ X1438 @ X1439 @ X1440)=(ap @ X1437 @ X1438 @ X1439 @ X1440)))&((~func @ X1441 @ X1442 @ X1443|(~in @ X1444 @ X1441|(ap @ X1441 @ X1442 @ X1443 @ X1444)=(ap @ X1441 @ X1442 @ X1443 @ X1444)))&(((in @ (esk81_3 @ X1445 @ X1446 @ X1447) @ X1445|(~in @ X1449 @ X1445|(ap @ X1445 @ X1446 @ (lam @ X1445 @ X1446 @ (esk1_2 @ X1447)) @ X1449)=(X1447 @ X1449)))&(~in @ (X1447 @ (esk81_3 @ X1445 @ X1446 @ X1447)) @ X1446|(~in @ X1449 @ X1445|(ap @ X1445 @ X1446 @ (lam @ X1445 @ X1446 @ (esk1_2 @ X1447)) @ X1449)=(X1447 @ X1449))))&((~func @ X1450 @ X1451 @ X1452|(lam @ X1450 @ X1451 @ (esk1_2 @ (ap @ X1450 @ X1451 @ X1452)))=(X1452))&(((in @ (esk82_3 @ X1453 @ X1454 @ X1455) @ X1453|(lam @ X1453 @ X1454 @ (esk1_2 @ X1455))=(lam @ X1453 @ X1454 @ (esk1_2 @ X1455)))&(~in @ (X1455 @ (esk82_3 @ X1453 @ X1454 @ X1455)) @ X1454|(lam @ X1453 @ X1454 @ (esk1_2 @ X1455))=(lam @ X1453 @ X1454 @ (esk1_2 @ X1455))))&(((in @ (esk83_3 @ X1457 @ X1458 @ X1459) @ X1457|(~in @ X1461 @ X1457|(ap @ X1457 @ X1458 @ (lam @ X1457 @ X1458 @ (esk1_2 @ X1459)) @ X1461)=(X1459 @ X1461)))&(~in @ (X1459 @ (esk83_3 @ X1457 @ X1458 @ X1459)) @ X1458|(~in @ X1461 @ X1457|(ap @ X1457 @ X1458 @ (lam @ X1457 @ X1458 @ (esk1_2 @ X1459)) @ X1461)=(X1459 @ X1461))))&((~in @ X1464 @ (funcSet @ X1462 @ X1463)|(lam @ X1462 @ X1463 @ (esk1_2 @ (ap @ X1462 @ X1463 @ X1464)))=(X1464))&((~in @ X1467 @ X1465|(~in @ X1468 @ X1465|(X1466|in @ X1468 @ (dsetconstr @ X1465 @ (epred7_4 @ X1468 @ X1466 @ X1467)))))&((~in @ X1471 @ X1469|(~in @ X1472 @ X1469|(X1470|(dsetconstr @ X1469 @ (epred7_4 @ X1472 @ X1470 @ X1471))=(setadjoin @ X1472 @ emptyset))))&((~in @ X1475 @ X1473|(~in @ X1476 @ X1473|(~X1474|in @ X1475 @ (dsetconstr @ X1473 @ (epred7_4 @ X1476 @ X1474 @ X1475)))))&((~in @ X1479 @ X1477|(~in @ X1480 @ X1477|(~X1478|(dsetconstr @ X1477 @ (epred7_4 @ X1480 @ X1478 @ X1479))=(setadjoin @ X1479 @ emptyset))))&((~in @ X1483 @ X1481|(~in @ X1484 @ X1481|singleton @ (dsetconstr @ X1481 @ (epred7_4 @ X1484 @ X1482 @ X1483))))&(((~X1486|in @ (if @ X1485 @ $true @ X1487 @ X1488) @ X1485|~in @ X1488 @ X1485|~in @ X1487 @ X1485)&(X1486|in @ (if @ X1485 @ $false @ X1487 @ X1488) @ X1485|~in @ X1488 @ X1485|~in @ X1487 @ X1485))&((~singleton @ X1489|(~in @ X1490 @ X1489|(setunion @ X1489)=(X1490)))&(((~X1492|(if @ X1491 @ $true @ X1493 @ X1494)=(X1493)|~X1492|~in @ X1494 @ X1491|~in @ X1493 @ X1491)&(X1492|(if @ X1491 @ $false @ X1493 @ X1494)=(X1493)|~X1492|~in @ X1494 @ X1491|~in @ X1493 @ X1491))&(((~X1496|(if @ X1495 @ $true @ X1497 @ X1498)=(X1498)|X1496|~in @ X1498 @ X1495|~in @ X1497 @ X1495)&(X1496|(if @ X1495 @ $false @ X1497 @ X1498)=(X1498)|X1496|~in @ X1498 @ X1495|~in @ X1497 @ X1495))&(((~X1500|in @ (if @ X1499 @ $true @ X1501 @ X1502) @ (setadjoin @ X1501 @ (setadjoin @ X1502 @ emptyset))|~in @ X1502 @ X1499|~in @ X1501 @ X1499)&(X1500|in @ (if @ X1499 @ $false @ X1501 @ X1502) @ (setadjoin @ X1501 @ (setadjoin @ X1502 @ emptyset))|~in @ X1502 @ X1499|~in @ X1501 @ X1499))&((~in @ X1504 @ (powerset @ X1503)|(~in @ X1505 @ (powerset @ X1503)|in @ (binintersect @ X1504 @ X1505) @ (powerset @ X1503)))&(in @ esk85_0 @ (powerset @ esk84_0)&(in @ esk86_0 @ (powerset @ esk84_0)&~in @ (binunion @ esk85_0 @ esk86_0) @ (powerset @ esk84_0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_267])])])])])])). 85.32/85.63 thf(c_0_269, negated_conjecture, ![X2:$i, X3:$i]:(subset @ X2 @ X3|~in @ X2 @ (powerset @ X3)), inference(split_conjunct,[status(thm)],[c_0_268])). 85.32/85.63 thf(c_0_270, negated_conjecture, in @ esk86_0 @ (powerset @ esk84_0), inference(split_conjunct,[status(thm)],[c_0_268])). 85.32/85.63 thf(c_0_271, negated_conjecture, ![X2:$i, X3:$i]:((binintersect @ X3 @ X2)=(X2)|~subset @ X2 @ X3), inference(split_conjunct,[status(thm)],[c_0_268])). 85.32/85.63 thf(c_0_272, negated_conjecture, subset @ esk86_0 @ esk84_0, inference(spm,[status(thm)],[c_0_269, c_0_270])). 85.32/85.63 thf(c_0_273, negated_conjecture, in @ esk85_0 @ (powerset @ esk84_0), inference(split_conjunct,[status(thm)],[c_0_268])). 85.32/85.63 thf(c_0_274, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(binintersect @ X2 @ (binunion @ X3 @ X4))=(binunion @ (binintersect @ X2 @ X3) @ (binintersect @ X2 @ X4)), inference(split_conjunct,[status(thm)],[c_0_268])). 85.32/85.63 thf(c_0_275, negated_conjecture, (binintersect @ esk84_0 @ esk86_0)=(esk86_0), inference(spm,[status(thm)],[c_0_271, c_0_272])). 85.32/85.63 thf(c_0_276, negated_conjecture, subset @ esk85_0 @ esk84_0, inference(spm,[status(thm)],[c_0_269, c_0_273])). 85.32/85.63 thf(c_0_277, negated_conjecture, ![X2:$i]:(binunion @ (binintersect @ esk84_0 @ X2) @ esk86_0)=(binintersect @ esk84_0 @ (binunion @ X2 @ esk86_0)), inference(spm,[status(thm)],[c_0_274, c_0_275])). 85.32/85.63 thf(c_0_278, negated_conjecture, (binintersect @ esk84_0 @ esk85_0)=(esk85_0), inference(spm,[status(thm)],[c_0_271, c_0_276])). 85.32/85.63 thf(c_0_279, negated_conjecture, ![X3:$i, X2:$i]:subset @ (binintersect @ X2 @ X3) @ X2, inference(split_conjunct,[status(thm)],[c_0_268])). 85.32/85.63 thf(c_0_280, negated_conjecture, (binintersect @ esk84_0 @ (binunion @ esk85_0 @ esk86_0))=(binunion @ esk85_0 @ esk86_0), inference(spm,[status(thm)],[c_0_277, c_0_278])). 85.32/85.63 thf(c_0_281, negated_conjecture, ~in @ (binunion @ esk85_0 @ esk86_0) @ (powerset @ esk84_0), inference(split_conjunct,[status(thm)],[c_0_268])). 85.32/85.63 thf(c_0_282, negated_conjecture, ![X2:$i, X3:$i]:(in @ X2 @ (powerset @ X3)|~subset @ X2 @ X3), inference(split_conjunct,[status(thm)],[c_0_268])). 85.32/85.63 thf(c_0_283, negated_conjecture, subset @ (binunion @ esk85_0 @ esk86_0) @ esk84_0, inference(spm,[status(thm)],[c_0_279, c_0_280])). 85.32/85.63 thf(c_0_284, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_281, c_0_282]), c_0_283])]), ['proof']). 85.32/85.63 # SZS output end CNFRefutation 85.32/85.63 # Proof object total steps : 285 85.32/85.63 # Proof object clause steps : 16 85.32/85.63 # Proof object formula steps : 269 85.32/85.63 # Proof object conjectures : 19 85.32/85.63 # Proof object clause conjectures : 16 85.32/85.63 # Proof object formula conjectures : 3 85.32/85.63 # Proof object initial clauses used : 8 85.32/85.63 # Proof object initial formulas used : 232 85.32/85.63 # Proof object generating inferences : 8 85.32/85.63 # Proof object simplifying inferences : 2 85.32/85.63 # Training examples: 0 positive, 0 negative 85.32/85.63 # Parsed axioms : 497 85.32/85.63 # Removed by relevancy pruning/SinE : 0 85.32/85.63 # Initial clauses : 692 85.32/85.63 # Removed in clause preprocessing : 300 85.32/85.63 # Initial clauses in saturation : 392 85.32/85.63 # Processed clauses : 578 85.32/85.63 # ...of these trivial : 8 85.32/85.63 # ...subsumed : 42 85.32/85.63 # ...remaining for further processing : 528 85.32/85.63 # Other redundant clauses eliminated : 28 85.32/85.63 # Clauses deleted for lack of memory : 0 85.32/85.63 # Backward-subsumed : 0 85.32/85.63 # Backward-rewritten : 5 85.32/85.63 # Generated clauses : 636 85.32/85.63 # ...of the previous two non-trivial : 245 85.32/85.63 # Contextual simplify-reflections : 0 85.32/85.63 # Paramodulations : 287 85.32/85.63 # Factorizations : 0 85.32/85.63 # NegExts : 10 85.32/85.63 # Equation resolutions : 29 85.32/85.63 # Propositional unsat checks : 0 85.32/85.63 # Propositional check models : 0 85.32/85.63 # Propositional check unsatisfiable : 0 85.32/85.63 # Propositional clauses : 0 85.32/85.63 # Propositional clauses after purity: 0 85.32/85.63 # Propositional unsat core size : 0 85.32/85.63 # Propositional preprocessing time : 0.000 85.32/85.63 # Propositional encoding time : 0.000 85.32/85.63 # Propositional solver time : 0.000 85.32/85.63 # Success case prop preproc time : 0.000 85.32/85.63 # Success case prop encoding time : 0.000 85.32/85.63 # Success case prop solver time : 0.000 85.32/85.63 # Current number of processed clauses : 155 85.32/85.63 # Positive orientable unit clauses : 85 85.32/85.63 # Positive unorientable unit clauses: 0 85.32/85.63 # Negative unit clauses : 3 85.32/85.63 # Non-unit-clauses : 67 85.32/85.63 # Current number of unprocessed clauses: 405 85.32/85.63 # ...number of literals in the above : 1183 85.32/85.63 # Current number of archived formulas : 0 85.32/85.63 # Current number of archived clauses : 355 85.32/85.63 # Clause-clause subsumption calls (NU) : 22478 85.32/85.63 # Rec. Clause-clause subsumption calls : 8389 85.32/85.63 # Non-unit clause-clause subsumptions : 27 85.32/85.63 # Unit Clause-clause subsumption calls : 317 85.32/85.63 # Rewrite failures with RHS unbound : 0 85.32/85.63 # BW rewrite match attempts : 75 85.32/85.63 # BW rewrite match successes : 3 85.32/85.63 # Condensation attempts : 0 85.32/85.63 # Condensation successes : 0 85.32/85.63 # Termbank termtop insertions : 71552 85.32/85.63 85.32/85.63 # ------------------------------------------------- 85.32/85.63 # User time : 84.033 s 85.32/85.63 # System time : 1.188 s 85.32/85.63 # Total time : 85.221 s 85.32/85.63 # Maximum resident set size: 2200 pages 85.32/85.64 EOF