0.06/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.12 % 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 0.10/0.33 % Computer : n011.cluster.edu 0.10/0.33 % Model : x86_64 x86_64 0.10/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.33 % Memory : 8042.1875MB 0.10/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.33 % CPULimit : 1200 0.10/0.33 % WCLimit : 120 0.10/0.33 % DateTime : Tue Jul 13 14:30:40 EDT 2021 0.10/0.33 % CPUTime : 0.10/0.33 % Number of cores: 8 0.10/0.33 % Python version: Python 3.6.8 0.10/0.33 # Version: 2.6rc1-ho 0.18/0.34 # No SInE strategy applied 0.18/0.34 # Trying AutoSched0 for 59 seconds 0.98/1.23 # AutoSched0-Mode selected heuristic G_E___208_C18AMC_F1_SE_CS_SP_PS_S5PRR_RG_S04AN 0.98/1.23 # and selection function SelectComplexExceptUniqMaxHorn. 0.98/1.23 # 0.98/1.23 # Preprocessing time : 0.046 s 0.98/1.23 # Presaturation interreduction done 0.98/1.23 0.98/1.23 # Proof found! 0.98/1.23 # SZS status Theorem 0.98/1.23 # SZS output start CNFRefutation 0.98/1.23 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:$i]:(in @ X3 @ X4&X6 @ X3 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', replAx)). 0.98/1.23 thf(exu, axiom, (exu)=(^[X1:$i > $o]:?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exu)). 0.98/1.23 thf(descrp, axiom, (descrp<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>X1 @ (descr @ (^[X2:$i]:X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', descrp)). 0.98/1.23 thf(exuE1, axiom, (exuE1<=>![X1:$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)). 0.98/1.23 thf(exuE3e, axiom, (exuE3e<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>?[X2:$i]:X1 @ X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuE3e)). 0.98/1.23 thf(nonemptyE1, axiom, (nonemptyE1<=>![X4:$i]:(nonempty @ X4=>?[X2:$i]:in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyE1)). 0.98/1.23 thf(nonempty, axiom, (nonempty)=(^[X2:$i]:(X2)!=(emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonempty)). 0.98/1.23 thf(nonemptyI, axiom, (nonemptyI<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyI)). 0.98/1.23 thf(nonemptyI1, axiom, (nonemptyI1<=>![X4:$i]:(?[X2:$i]:in @ X2 @ X4=>nonempty @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyI1)). 0.98/1.23 thf(exuE2, axiom, (exuE2<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuE2)). 0.98/1.23 thf(nonemptyImpWitness, axiom, (nonemptyImpWitness<=>![X4:$i]:(nonempty @ X4=>?[X2:$i]:(in @ X2 @ X4&$true))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyImpWitness)). 0.98/1.23 thf(exuI1, axiom, (exuI1<=>![X1:$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)). 0.98/1.23 thf(exuI3, axiom, (exuI3<=>![X1:$i > $o]:(?[X2:$i]:X1 @ X2=>(![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3)))=>exu @ (^[X2:$i]:X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuI3)). 0.98/1.23 thf(exuI2, axiom, (exuI2<=>![X1:$i > $o]:(?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2))=>exu @ (^[X2:$i]:X1 @ X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuI2)). 0.98/1.23 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)). 0.98/1.23 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:$i]:X17 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exu__Cong)). 0.98/1.23 thf(exuEu, axiom, (exuEu<=>![X1:$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)). 0.98/1.23 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:$i]:X17 @ X2)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', descr__Cong)). 0.98/1.23 thf(binintersectLsub, conjecture, (((setadjoinAx=>((((((replAx=>(((descrp=>(((((prop2setE=>((emptysetimpfalse=>(notinemptyset=>(exuE3e=>(setext=>(emptyI=>((((nonemptyI=>((setadjoinIL=>(emptyinunitempty=>((setadjoinE=>((setoftrueEq=>(powersetI=>(emptyinPowerset=>((powersetE=>(setunionI=>(setunionE=>((exuE2=>((uniqinunit=>((eqinunit=>((upairsetE=>(((emptyE1=>((((((((notdexE=>(notdallE=>((exuI3=>(exuI2=>(((exuE3u=>(exu__Cong=>((setadjoin__Cong=>(powerset__Cong=>(setunion__Cong=>(((((subsetI1=>(((subsetI2=>(emptysetsubset=>(subsetE=>((notsubsetI=>(notequalI1=>(notequalI2=>((((setadjoinSub2=>(subset2powerset=>(setextsub=>(((powersetE1=>((powersetsubset=>((sepSubset=>(binunionIL=>(((((binunionLsub=>(binunionRsub=>(binintersectI=>(binintersectSubset5=>(![X4:$i, X5:$i]:subset @ (binintersect @ X4 @ X5) @ X4<=binintersectEL)))))<=binunionE)<=binunionEcases)<=binunionIR)<=upairset2IR)))<=sepInPowerset))<=inPowerset))<=powersetI1)<=subsetemptysetimpeq))))<=setadjoinSub)<=subsetTrans)<=subsetRefl))))<=subsetE2))))<=eqimpsubset1)<=eqimpsubset2))<=dsetconstr__Cong)<=descr__Cong)<=exuEu)<=omega__Cong))))<=emptyset__Cong)))<=in__Cong)<=inCongP)))<=exuI1)))<=prop2set2propI)<=prop2setI)<=quantDeMorgan4)<=quantDeMorgan3)<=quantDeMorgan2)<=quantDeMorgan1)<=vacuousDall))<=upairsetIR)<=upairsetIL))<=singletonsswitch))<=notinsingleton))<=nonemptyImpWitness))<=subPowSU))))<=emptyInPowerset))))<=setadjoinOr))<=setadjoinIR)))<=nonemptyI1))<=nonemptyE1)<=setbeta)<=noeltsimpempty))))))<=emptysetE))<=exuE1)<=dsetconstrER)<=dsetconstrEL)<=dsetconstrI))<=wellorderingAx)<=foundationAx))<=omegaIndAx)<=omegaSAx)<=omega0Ax)<=setunionAx)<=powersetAx))<=emptysetAx)<=setextAx), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectLsub)). 0.98/1.23 thf(setextAx, axiom, (setextAx<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4<=>in @ X2 @ X5)=>(X4)=(X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setextAx)). 0.98/1.23 thf(emptysetAx, axiom, (emptysetAx<=>![X2:$i]:~(in @ X2 @ emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetAx)). 0.98/1.23 thf(setadjoinAx, axiom, (setadjoinAx<=>![X2:$i, X4:$i, X3:$i]:(in @ X3 @ (setadjoin @ X2 @ X4)<=>((X3)=(X2)|in @ X3 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinAx)). 0.98/1.23 thf(powersetAx, axiom, (powersetAx<=>![X4:$i, X5:$i]:(in @ X5 @ (powerset @ X4)<=>![X2:$i]:(in @ X2 @ X5=>in @ X2 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetAx)). 0.98/1.23 thf(setunionAx, axiom, (setunionAx<=>![X4:$i, X2:$i]:(in @ X2 @ (setunion @ X4)<=>?[X5:$i]:(in @ X2 @ X5&in @ X5 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionAx)). 0.98/1.23 thf(omega0Ax, axiom, (omega0Ax<=>in @ emptyset @ omega), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omega0Ax)). 0.98/1.23 thf(omegaSAx, axiom, (omegaSAx<=>![X2:$i]:(in @ X2 @ omega=>in @ (setadjoin @ X2 @ X2) @ omega)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omegaSAx)). 0.98/1.23 thf(omegaIndAx, axiom, (omegaIndAx<=>![X4:$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)). 0.98/1.23 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)). 0.98/1.23 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:$i]:(in @ X3 @ X9=>in @ X3 @ X8)|in @ X2 @ X9)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', wellorderingAx)). 0.98/1.23 thf(dsetconstrI, axiom, (dsetconstrI<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstrI)). 0.98/1.23 thf(dsetconstrEL, axiom, (dsetconstrEL<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))=>in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstrEL)). 0.98/1.23 thf(dsetconstrER, axiom, (dsetconstrER<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))=>X1 @ X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstrER)). 0.98/1.23 thf(prop2setE, axiom, (prop2setE<=>![X10:$o, X2:$i]:(in @ X2 @ (prop2set @ (X10))=>X10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prop2setE)). 0.98/1.23 thf(emptysetE, axiom, (emptysetE<=>![X2:$i]:(in @ X2 @ emptyset=>![X11:$o]:X11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetE)). 0.98/1.23 thf(emptysetimpfalse, axiom, (emptysetimpfalse<=>![X2:$i]:(in @ X2 @ emptyset=>~$true)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetimpfalse)). 0.98/1.23 thf(notinemptyset, axiom, (notinemptyset<=>![X2:$i]:~(in @ X2 @ emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notinemptyset)). 0.98/1.23 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)). 0.98/1.23 thf(emptyI, axiom, (emptyI<=>![X4:$i]:(![X2:$i]:~(in @ X2 @ X4)=>(X4)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyI)). 0.98/1.23 thf(noeltsimpempty, axiom, (noeltsimpempty<=>![X4:$i]:(![X2:$i]:~(in @ X2 @ X4)=>(X4)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', noeltsimpempty)). 0.98/1.23 thf(setbeta, axiom, (setbeta<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))<=>X1 @ X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setbeta)). 0.98/1.23 thf(setadjoinIL, axiom, (setadjoinIL<=>![X2:$i, X3:$i]:in @ X2 @ (setadjoin @ X2 @ X3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinIL)). 0.98/1.23 thf(emptyinunitempty, axiom, (emptyinunitempty<=>in @ emptyset @ (setadjoin @ emptyset @ emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyinunitempty)). 0.98/1.23 thf(setadjoinIR, axiom, (setadjoinIR<=>![X2:$i, X4:$i, X3:$i]:(in @ X3 @ X4=>in @ X3 @ (setadjoin @ X2 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinIR)). 0.98/1.23 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)). 0.98/1.23 thf(setadjoinOr, axiom, (setadjoinOr<=>![X2:$i, X4:$i, X3:$i]:(in @ X3 @ (setadjoin @ X2 @ X4)=>((X3)=(X2)|in @ X3 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinOr)). 0.98/1.23 thf(setoftrueEq, axiom, (setoftrueEq<=>![X4:$i]:(dsetconstr @ X4 @ (^[X2:$i]:$true))=(X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setoftrueEq)). 0.98/1.23 thf(powersetI, axiom, (powersetI<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X5=>in @ X2 @ X4)=>in @ X5 @ (powerset @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetI)). 0.98/1.23 thf(emptyinPowerset, axiom, (emptyinPowerset<=>![X4:$i]:in @ emptyset @ (powerset @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyinPowerset)). 0.98/1.23 thf(emptyInPowerset, axiom, (emptyInPowerset<=>![X4:$i]:in @ emptyset @ (powerset @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyInPowerset)). 0.98/1.23 thf(powersetE, axiom, (powersetE<=>![X4:$i, X5:$i, X2:$i]:(in @ X5 @ (powerset @ X4)=>(in @ X2 @ X5=>in @ X2 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetE)). 0.98/1.23 thf(setunionI, axiom, (setunionI<=>![X4:$i, X2:$i, X5:$i]:(in @ X2 @ X5=>(in @ X5 @ X4=>in @ X2 @ (setunion @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionI)). 0.98/1.23 thf(setunionE, axiom, (setunionE<=>![X4:$i, X2:$i]:(in @ X2 @ (setunion @ X4)=>![X13:$o]:(![X5:$i]:(in @ X2 @ X5=>(in @ X5 @ X4=>X13))=>X13))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionE)). 0.98/1.23 thf(subPowSU, axiom, (subPowSU<=>![X4:$i, X2:$i]:(in @ X2 @ X4=>in @ X2 @ (powerset @ (setunion @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subPowSU)). 0.98/1.23 thf(uniqinunit, axiom, (uniqinunit<=>![X2:$i, X3:$i]:(in @ X2 @ (setadjoin @ X3 @ emptyset)=>(X2)=(X3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', uniqinunit)). 0.98/1.23 thf(notinsingleton, axiom, (notinsingleton<=>![X2:$i, X3:$i]:((X2)!=(X3)=>~(in @ X3 @ (setadjoin @ X2 @ emptyset)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notinsingleton)). 0.98/1.23 thf(eqinunit, axiom, (eqinunit<=>![X2:$i, X3:$i]:((X2)=(X3)=>in @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqinunit)). 0.98/1.23 thf(singletonsswitch, axiom, (singletonsswitch<=>![X2:$i, X3:$i]:(in @ X2 @ (setadjoin @ X3 @ emptyset)=>in @ X3 @ (setadjoin @ X2 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletonsswitch)). 0.98/1.23 thf(upairsetE, axiom, (upairsetE<=>![X2:$i, X3:$i, X14:$i]:(in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=>((X14)=(X2)|(X14)=(X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsetE)). 0.98/1.23 thf(upairsetIL, axiom, (upairsetIL<=>![X2:$i, X3:$i]:in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsetIL)). 0.98/1.23 thf(upairsetIR, axiom, (upairsetIR<=>![X2:$i, X3:$i]:in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsetIR)). 0.98/1.23 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)). 0.98/1.23 thf(vacuousDall, axiom, (vacuousDall<=>![X1:$i > $o, X2:$i]:(in @ X2 @ emptyset=>X1 @ X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', vacuousDall)). 0.98/1.23 thf(quantDeMorgan1, axiom, (quantDeMorgan1<=>![X4:$i, X1:$i > $o]:(~(![X2:$i]:(in @ X2 @ X4=>X1 @ X2))=>?[X2:$i]:(in @ X2 @ X4&~(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan1)). 0.98/1.23 thf(quantDeMorgan2, axiom, (quantDeMorgan2<=>![X4:$i, X1:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>~(X1 @ X2))=>~(?[X2:$i]:(in @ X2 @ X4&X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan2)). 0.98/1.23 thf(quantDeMorgan3, axiom, (quantDeMorgan3<=>![X4:$i, X1:$i > $o]:(~(?[X2:$i]:(in @ X2 @ X4&X1 @ X2))=>![X2:$i]:(in @ X2 @ X4=>~(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan3)). 0.98/1.23 thf(quantDeMorgan4, axiom, (quantDeMorgan4<=>![X4:$i, X1:$i > $o]:(?[X2:$i]:(in @ X2 @ X4&~(X1 @ X2))=>~(![X2:$i]:(in @ X2 @ X4=>X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan4)). 0.98/1.23 thf(prop2setI, axiom, (prop2setI<=>![X15:$o]:(X15=>in @ emptyset @ (prop2set @ (X15)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prop2setI)). 0.98/1.23 thf(prop2set2propI, axiom, (prop2set2propI<=>![X16:$o]:(X16=>set2prop @ (prop2set @ (X16)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prop2set2propI)). 0.98/1.23 thf(notdexE, axiom, (notdexE<=>![X4:$i, X1:$i > $o]:(~(?[X2:$i]:(in @ X2 @ X4&X1 @ X2))=>![X2:$i]:(in @ X2 @ X4=>~(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notdexE)). 0.98/1.23 thf(notdallE, axiom, (notdallE<=>![X4:$i, X1:$i > $o]:(~(![X2:$i]:(in @ X2 @ X4=>X1 @ X2))=>?[X2:$i]:(in @ X2 @ X4&~(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notdallE)). 0.98/1.23 thf(inCongP, axiom, (inCongP<=>![X4:$i, X5:$i]:((X4)=(X5)=>![X2:$i, X3:$i]:((X2)=(X3)=>(in @ X2 @ X4=>in @ X3 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', inCongP)). 0.98/1.23 thf(in__Cong, axiom, (in__Cong<=>![X4:$i, X5:$i]:((X4)=(X5)=>![X2:$i, X3:$i]:((X2)=(X3)=>(in @ X2 @ X4<=>in @ X3 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', in__Cong)). 0.98/1.23 thf(emptyset__Cong, axiom, (emptyset__Cong<=>(emptyset)=(emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyset__Cong)). 0.98/1.23 thf(setadjoin__Cong, axiom, (setadjoin__Cong<=>![X2:$i, X3:$i]:((X2)=(X3)=>![X14:$i, X18:$i]:((X14)=(X18)=>(setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoin__Cong)). 0.98/1.23 thf(powerset__Cong, axiom, (powerset__Cong<=>![X4:$i, X5:$i]:((X4)=(X5)=>(powerset @ X4)=(powerset @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powerset__Cong)). 0.98/1.23 thf(setunion__Cong, axiom, (setunion__Cong<=>![X4:$i, X5:$i]:((X4)=(X5)=>(setunion @ X4)=(setunion @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunion__Cong)). 0.98/1.23 thf(omega__Cong, axiom, (omega__Cong<=>(omega)=(omega)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omega__Cong)). 0.98/1.23 thf(dsetconstr__Cong, axiom, (dsetconstr__Cong<=>![X4:$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:$i]:X17 @ X2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstr__Cong)). 0.98/1.23 thf(subsetI1, axiom, (subsetI1<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4=>in @ X2 @ X5)=>subset @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetI1)). 0.98/1.23 thf(eqimpsubset2, axiom, (eqimpsubset2<=>![X4:$i, X5:$i]:((X4)=(X5)=>subset @ X5 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqimpsubset2)). 0.98/1.23 thf(eqimpsubset1, axiom, (eqimpsubset1<=>![X4:$i, X5:$i]:((X4)=(X5)=>subset @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqimpsubset1)). 0.98/1.23 thf(subsetI2, axiom, (subsetI2<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4=>in @ X2 @ X5)=>subset @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetI2)). 0.98/1.23 thf(emptysetsubset, axiom, (emptysetsubset<=>![X4:$i]:subset @ emptyset @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetsubset)). 0.98/1.23 thf(subsetE, axiom, (subsetE<=>![X4:$i, X5:$i, X2:$i]:(subset @ X4 @ X5=>(in @ X2 @ X4=>in @ X2 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetE)). 0.98/1.23 thf(subsetE2, axiom, (subsetE2<=>![X4:$i, X5:$i, X2:$i]:(subset @ X4 @ X5=>(~(in @ X2 @ X5)=>~(in @ X2 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetE2)). 0.98/1.23 thf(notsubsetI, axiom, (notsubsetI<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X5)=>~(subset @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notsubsetI)). 0.98/1.23 thf(notequalI1, axiom, (notequalI1<=>![X4:$i, X5:$i]:(~(subset @ X4 @ X5)=>(X4)!=(X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notequalI1)). 0.98/1.23 thf(notequalI2, axiom, (notequalI2<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X5)=>(X4)!=(X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notequalI2)). 0.98/1.23 thf(subsetRefl, axiom, (subsetRefl<=>![X4:$i]:subset @ X4 @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetRefl)). 0.98/1.23 thf(subsetTrans, axiom, (subsetTrans<=>![X4:$i, X5:$i, X7:$i]:(subset @ X4 @ X5=>(subset @ X5 @ X7=>subset @ X4 @ X7))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetTrans)). 0.98/1.23 thf(setadjoinSub, axiom, (setadjoinSub<=>![X2:$i, X4:$i]:subset @ X4 @ (setadjoin @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinSub)). 0.98/1.23 thf(setadjoinSub2, axiom, (setadjoinSub2<=>![X4:$i, X2:$i, X5:$i]:(subset @ X4 @ X5=>subset @ X4 @ (setadjoin @ X2 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinSub2)). 0.98/1.23 thf(subset2powerset, axiom, (subset2powerset<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>in @ X4 @ (powerset @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subset2powerset)). 0.98/1.23 thf(setextsub, axiom, (setextsub<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>(subset @ X5 @ X4=>(X4)=(X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setextsub)). 0.98/1.23 thf(subsetemptysetimpeq, axiom, (subsetemptysetimpeq<=>![X4:$i]:(subset @ X4 @ emptyset=>(X4)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetemptysetimpeq)). 0.98/1.23 thf(powersetI1, axiom, (powersetI1<=>![X4:$i, X5:$i]:(subset @ X5 @ X4=>in @ X5 @ (powerset @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetI1)). 0.98/1.23 thf(powersetE1, axiom, (powersetE1<=>![X4:$i, X5:$i]:(in @ X5 @ (powerset @ X4)=>subset @ X5 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetE1)). 0.98/1.23 thf(inPowerset, axiom, (inPowerset<=>![X4:$i]:in @ X4 @ (powerset @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', inPowerset)). 0.98/1.23 thf(powersetsubset, axiom, (powersetsubset<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>subset @ (powerset @ X4) @ (powerset @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetsubset)). 0.98/1.23 thf(sepInPowerset, axiom, (sepInPowerset<=>![X4:$i, X1:$i > $o]:in @ (dsetconstr @ X4 @ (^[X2:$i]:X1 @ X2)) @ (powerset @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sepInPowerset)). 0.98/1.23 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)). 0.98/1.23 thf(binunionIL, axiom, (binunionIL<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>in @ X2 @ (binunion @ X4 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionIL)). 0.98/1.23 thf(upairset2IR, axiom, (upairset2IR<=>![X2:$i, X3:$i]:in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairset2IR)). 0.98/1.23 thf(binunionIR, axiom, (binunionIR<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X5=>in @ X2 @ (binunion @ X4 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionIR)). 0.98/1.23 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)). 0.98/1.23 thf(binunionE, axiom, (binunionE<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (binunion @ X4 @ X5)=>(in @ X2 @ X4|in @ X2 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionE)). 0.98/1.23 thf(binunionLsub, axiom, (binunionLsub<=>![X4:$i, X5:$i]:subset @ X4 @ (binunion @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionLsub)). 0.98/1.23 thf(binunionRsub, axiom, (binunionRsub<=>![X4:$i, X5:$i]:subset @ X5 @ (binunion @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionRsub)). 0.98/1.23 thf(binintersectI, axiom, (binintersectI<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X5=>in @ X2 @ (binintersect @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectI)). 0.98/1.23 thf(binintersectSubset5, axiom, (binintersectSubset5<=>![X4:$i, X5:$i, X7:$i]:(subset @ X7 @ X4=>(subset @ X7 @ X5=>subset @ X7 @ (binintersect @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset5)). 0.98/1.23 thf(binintersectEL, axiom, (binintersectEL<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (binintersect @ X4 @ X5)=>in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectEL)). 0.98/1.23 thf(c_0_111, axiom, (replAx)=(![X6:$i > $i > $o, X4:$i]:(![X2:$i]:(in @ X2 @ X4=>?[X312:$i]:(X6 @ X2 @ X312&![X314:$i]:(X6 @ X2 @ X314=>(X312)=(X314))))=>?[X5:$i]:![X2:$i]:(in @ X2 @ X5<=>?[X3:$i]:(in @ X3 @ X4&X6 @ X3 @ X2)))), inference(apply_def,[status(thm)],[replAx, exu])). 0.98/1.23 thf(c_0_112, axiom, (descrp)=(![X1:$i > $o]:(?[X315:$i]:(X1 @ X315&![X316:$i]:(X1 @ X316=>(X315)=(X316)))=>X1 @ (descr @ (^[X2:$i]:X1 @ X2)))), inference(apply_def,[status(thm)],[descrp, exu])). 0.98/1.23 thf(c_0_113, axiom, (exuE1)=(![X1:$i > $o]:(?[X317:$i]:(X1 @ X317&![X318:$i]:(X1 @ X318=>(X317)=(X318)))=>?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3))))), inference(apply_def,[status(thm)],[exuE1, exu])). 0.98/1.23 thf(c_0_114, axiom, (exuE3e)=(![X1:$i > $o]:(?[X319:$i]:(X1 @ X319&![X320:$i]:(X1 @ X320=>(X319)=(X320)))=>?[X2:$i]:X1 @ X2)), inference(apply_def,[status(thm)],[exuE3e, exu])). 0.98/1.23 thf(c_0_115, axiom, (nonemptyE1)=(![X4:$i]:((X4)!=(emptyset)=>?[X2:$i]:in @ X2 @ X4)), inference(apply_def,[status(thm)],[nonemptyE1, nonempty])). 0.98/1.23 thf(c_0_116, axiom, (nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>(dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))!=(emptyset)))), inference(apply_def,[status(thm)],[nonemptyI, nonempty])). 0.98/1.23 thf(c_0_117, axiom, (nonemptyI1)=(![X4:$i]:(?[X2:$i]:in @ X2 @ X4=>(X4)!=(emptyset))), inference(apply_def,[status(thm)],[nonemptyI1, nonempty])). 0.98/1.23 thf(c_0_118, axiom, (exuE2)=(![X1:$i > $o]:(?[X321:$i]:(X1 @ X321&![X322:$i]:(X1 @ X322=>(X321)=(X322)))=>?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2)))), inference(apply_def,[status(thm)],[exuE2, exu])). 0.98/1.23 thf(c_0_119, axiom, (nonemptyImpWitness)=(![X4:$i]:((X4)!=(emptyset)=>?[X2:$i]:(in @ X2 @ X4&$true))), inference(apply_def,[status(thm)],[nonemptyImpWitness, nonempty])). 0.98/1.23 thf(c_0_120, axiom, (exuI1)=(![X1:$i > $o]:(?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3)))=>?[X323:$i]:(X1 @ X323&![X324:$i]:(X1 @ X324=>(X323)=(X324))))), inference(apply_def,[status(thm)],[exuI1, exu])). 0.98/1.23 thf(c_0_121, axiom, (exuI3)=(![X1:$i > $o]:(?[X2:$i]:X1 @ X2=>(![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3)))=>?[X325:$i]:(X1 @ X325&![X326:$i]:(X1 @ X326=>(X325)=(X326)))))), inference(apply_def,[status(thm)],[exuI3, exu])). 0.98/1.23 thf(c_0_122, axiom, (exuI2)=(![X1:$i > $o]:(?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2))=>?[X327:$i]:(X1 @ X327&![X328:$i]:(X1 @ X328=>(X327)=(X328))))), inference(apply_def,[status(thm)],[exuI2, exu])). 0.98/1.23 thf(c_0_123, axiom, (exuE3u)=(![X1:$i > $o]:(?[X329:$i]:(X1 @ X329&![X330:$i]:(X1 @ X330=>(X329)=(X330)))=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))), inference(apply_def,[status(thm)],[exuE3u, exu])). 0.98/1.23 thf(c_0_124, axiom, (exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(?[X331:$i]:(X1 @ X331&![X332:$i]:(X1 @ X332=>(X331)=(X332)))<=>?[X333:$i]:(X17 @ X333&![X334:$i]:(X17 @ X334=>(X333)=(X334)))))), inference(apply_def,[status(thm)],[exu__Cong, exu])). 0.98/1.23 thf(c_0_125, axiom, (exuEu)=(![X1:$i > $o]:(?[X335:$i]:(X1 @ X335&![X336:$i]:(X1 @ X336=>(X335)=(X336)))=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))), inference(apply_def,[status(thm)],[exuEu, exu])). 0.98/1.23 thf(c_0_126, axiom, (descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(?[X337:$i]:(X1 @ X337&![X338:$i]:(X1 @ X338=>(X337)=(X338)))=>(?[X339:$i]:(X17 @ X339&![X340:$i]:(X17 @ X340=>(X339)=(X340)))=>(descr @ (^[X2:$i]:X1 @ X2))=(descr @ (^[X2:$i]:X17 @ X2)))))), inference(apply_def,[status(thm)],[descr__Cong, exu])). 0.98/1.23 thf(c_0_127, plain, ![X2:$i, X1:$i > $o]:(epred2_2 @ X1 @ X2<=>X1 @ X2), introduced(definition)). 0.98/1.23 thf(c_0_128, plain, ![X2:$i]:epred3_1 @ X2, inference(fof_simplification,[status(thm)],[introduced(definition)])). 0.98/1.23 thf(c_0_129, plain, (epred4_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:$i]:(in @ X3 @ X9=>in @ X3 @ X8)|in @ X2 @ X9)))))), introduced(definition)). 0.98/1.23 thf(c_0_130, negated_conjecture, ~((![X4:$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:$i]:(in @ X2 @ X4=>?[X312:$i]:(X6 @ X2 @ X312&![X314:$i]:(X6 @ X2 @ X314=>(X312)=(X314))))=>?[X5:$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))))=>(epred4_0=>(![X1:$i > $o]:(?[X315:$i]:(X1 @ X315&![X316:$i]:(X1 @ X316=>(X315)=(X316)))=>X1 @ (descr @ (epred2_2 @ X1)))=>(![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>in @ X2 @ (dsetconstr @ X4 @ (epred2_2 @ X1))))=>(![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ (dsetconstr @ X4 @ (epred2_2 @ X1))=>in @ X2 @ X4)=>(![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ (dsetconstr @ X4 @ (epred2_2 @ X1))=>X1 @ X2)=>(![X1:$i > $o]:(?[X317:$i]:(X1 @ X317&![X318:$i]:(X1 @ X318=>(X317)=(X318)))=>?[X2:$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 > $o]:(?[X319:$i]:(X1 @ X319&![X320:$i]:(X1 @ X320=>(X319)=(X320)))=>?[X2:$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 @ (epred2_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 @ (epred2_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:$i]:(dsetconstr @ X4 @ epred3_1)=(X4)=>(![X4:$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 > $o]:(?[X321:$i]:(X1 @ X321&![X322:$i]:(X1 @ X322=>(X321)=(X322)))=>?[X2:$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 @ (epred2_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:$i]:(X1 @ X3=>(X2)=(X3)))=>?[X323:$i]:(X1 @ X323&![X324:$i]:(X1 @ X324=>(X323)=(X324))))=>(![X1:$i > $o]:(?[X2:$i]:X1 @ X2=>(![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3)))=>?[X325:$i]:(X1 @ X325&![X326:$i]:(X1 @ X326=>(X325)=(X326)))))=>(![X1:$i > $o]:(?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2))=>?[X327:$i]:(X1 @ X327&![X328:$i]:(X1 @ X328=>(X327)=(X328))))=>(![X4:$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 > $o]:(?[X329:$i]:(X1 @ X329&![X330:$i]:(X1 @ X330=>(X329)=(X330)))=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))=>(![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(?[X331:$i]:(X1 @ X331&![X332:$i]:(X1 @ X332=>(X331)=(X332)))<=>?[X333:$i]:(X17 @ X333&![X334:$i]:(X17 @ X334=>(X333)=(X334)))))=>((emptyset)=(emptyset)=>(![X2:$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 > $o]:(?[X335:$i]:(X1 @ X335&![X336:$i]:(X1 @ X336=>(X335)=(X336)))=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))=>(![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(?[X337:$i]:(X1 @ X337&![X338:$i]:(X1 @ X338=>(X337)=(X338)))=>(?[X339:$i]:(X17 @ X339&![X340:$i]:(X17 @ X340=>(X339)=(X340)))=>(descr @ (epred2_2 @ X1))=(descr @ (epred2_2 @ X17)))))=>(![X4:$i, X5:$i]:((X4)=(X5)=>![X1:$i > $o, X17:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))))=>(dsetconstr @ X4 @ (epred2_2 @ X1))=(dsetconstr @ X5 @ (epred2_2 @ X17))))=>(![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4=>in @ X2 @ X5)=>subset @ X4 @ X5)=>(![X4:$i, X5:$i]:((X4)=(X5)=>subset @ X5 @ X4)=>(![X4:$i, X5:$i]:((X4)=(X5)=>subset @ X4 @ X5)=>(![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4=>in @ X2 @ X5)=>subset @ X4 @ X5)=>(![X4:$i]:subset @ emptyset @ X4=>(![X4:$i, X5:$i, X2:$i]:(subset @ X4 @ X5=>(in @ X2 @ X4=>in @ X2 @ X5))=>(![X4:$i, X5:$i, X2:$i]:(subset @ X4 @ X5=>(~in @ X2 @ X5=>~in @ X2 @ X4))=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~in @ X2 @ X5=>~subset @ X4 @ X5))=>(![X4:$i, X5:$i]:(~subset @ X4 @ X5=>(X4)!=(X5))=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~in @ X2 @ X5=>(X4)!=(X5)))=>(![X4:$i]:subset @ X4 @ X4=>(![X4:$i, X5:$i, X7:$i]:(subset @ X4 @ X5=>(subset @ X5 @ X7=>subset @ X4 @ X7))=>(![X2:$i, X4:$i]:subset @ X4 @ (setadjoin @ X2 @ X4)=>(![X4:$i, X2:$i, X5:$i]:(subset @ X4 @ X5=>subset @ X4 @ (setadjoin @ X2 @ X5))=>(![X4:$i, X5:$i]:(subset @ X4 @ X5=>in @ X4 @ (powerset @ X5))=>(![X4:$i, X5:$i]:(subset @ X4 @ X5=>(subset @ X5 @ X4=>(X4)=(X5)))=>(![X4:$i]:(subset @ X4 @ emptyset=>(X4)=(emptyset))=>(![X4:$i, X5:$i]:(subset @ X5 @ X4=>in @ X5 @ (powerset @ X4))=>(![X4:$i, X5:$i]:(in @ X5 @ (powerset @ X4)=>subset @ X5 @ X4)=>(![X4:$i]:in @ X4 @ (powerset @ X4)=>(![X4:$i, X5:$i]:(subset @ X4 @ X5=>subset @ (powerset @ X4) @ (powerset @ X5))=>(![X4:$i, X1:$i > $o]:in @ (dsetconstr @ X4 @ (epred2_2 @ X1)) @ (powerset @ X4)=>(![X4:$i, X1:$i > $o]:subset @ (dsetconstr @ X4 @ (epred2_2 @ X1)) @ X4=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>in @ X2 @ (binunion @ X4 @ X5))=>(![X2:$i, X3:$i]:in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X5=>in @ X2 @ (binunion @ X4 @ X5))=>(![X4:$i, X5:$i, X2:$i, X19:$o]:(in @ X2 @ (binunion @ X4 @ X5)=>((in @ X2 @ X4=>X19)=>((in @ X2 @ X5=>X19)=>X19)))=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (binunion @ X4 @ X5)=>(in @ X2 @ X4|in @ X2 @ X5))=>(![X4:$i, X5:$i]:subset @ X4 @ (binunion @ X4 @ X5)=>(![X4:$i, X5:$i]:subset @ X5 @ (binunion @ X4 @ X5)=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X5=>in @ X2 @ (binintersect @ X4 @ X5)))=>(![X4:$i, X5:$i, X7:$i]:(subset @ X7 @ X4=>(subset @ X7 @ X5=>subset @ X7 @ (binintersect @ X4 @ X5)))=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (binintersect @ X4 @ X5)=>in @ X2 @ X4)=>![X4:$i, X5:$i]:subset @ (binintersect @ X4 @ X5) @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[binintersectLsub]), setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_111]), foundationAx]), wellorderingAx]), c_0_112]), dsetconstrI]), dsetconstrEL]), dsetconstrER]), c_0_113]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_114]), setext]), emptyI]), noeltsimpempty]), setbeta]), c_0_115]), c_0_116]), c_0_117]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), setoftrueEq]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_118]), c_0_119]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), emptyE1]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_120]), c_0_121]), c_0_122]), inCongP]), in__Cong]), c_0_123]), c_0_124]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_125]), c_0_126]), 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]), c_0_127]), c_0_127]), c_0_127]), c_0_127]), c_0_127]), c_0_127]), c_0_127]), c_0_127]), c_0_127]), c_0_127]), c_0_127]), c_0_128]), c_0_127]), c_0_127])])]), c_0_129])). 0.98/1.23 thf(c_0_131, negated_conjecture, ![X344:$i, X345:$i, X347:$i, X348:$i, X349:$i, X350:$i, X351:$i, X352:$i, X353:$i, X354:$i, X355:$i, X357:$i, X358:$i, X360:$i, X361:$i, X362:$i, X363:$i, X364:$i, X366:$i, X367:$i > $i > $o, X368:$i, X370:$i, X373:$i, X375:$i, X376:$i, X377:$i, X378:$i, X380:$i, X381:$i > $o, X382:$i, X384:$i, X385:$i > $o, X386:$i, X387:$i, X388:$i > $o, X389:$i, X390:$i, X391:$i > $o, X392:$i, X393:$i > $o, X394:$i, X397:$i, X398:$o, X399:$i, X400:$i, X401:$o, X402:$i, X403:$i, X404:$i > $o, X405:$i, X408:$i, X409:$i, X412:$i, X414:$i, X416:$i, X417:$i > $o, X418:$i, X419:$i, X421:$i, X422:$i > $o, X423:$i, X424:$i, X425:$i, X426:$i, X427:$i, X428:$i, X429:$i, X430:$i, X431:$i, X432:$i, X433:$i, X434:$o, X435:$i, X436:$i, X437:$i, X438:$i, X439:$i, X440:$i, X442:$i, X443:$i, X444:$i, X445:$i, X446:$i, X447:$i, X448:$i, X449:$i, X450:$i, X451:$i, X452:$o, X454:$i, X455:$i, X456:$i > $o, X457:$i, X460:$i, X461:$i, X462:$i, X464:$i, X465:$i, X466:$i, X467:$i, X468:$i, X469:$i, X470:$i, X471:$i, X472:$i, X473:$i, X474:$i, X475:$i, X476:$i, X477:$i, X478:$i, X479:$i, X480:$i > $o, X481:$i, X482:$i > $o, X483:$i, X484:$i, X485:$i > $o, X486:$i, X488:$i, X489:$i > $o, X491:$i, X492:$i, X493:$i > $o, X495:$i, X496:$i, X497:$i > $o, X498:$i, X500:$o, X501:$o, X502:$i, X503:$i > $o, X505:$i, X506:$i, X507:$i > $o, X508:$i, X510:$i > $o, X511:$i, X514:$i, X515:$i > $o, X516:$i, X520:$i, X521:$i > $o, X522:$i, X525:$i, X526:$i, X527:$i, X528:$i, X529:$i, X530:$i, X531:$i, X532:$i, X533:$i, X534:$i > $o, X535:$i, X537:$i, X538:$i, X539:$i > $o, X540:$i > $o, X543:$i, X546:$i, X547:$i, X550:$i, X551:$i, X552:$i, X553:$i, X554:$i, X555:$i, X556:$i, X557:$i, X558:$i, X559:$i > $o, X560:$i, X562:$i, X563:$i, X564:$i > $o, X565:$i > $o, X568:$i, X570:$i, X572:$i, X573:$i, X574:$i > $o, X575:$i > $o, X578:$i, X579:$i, X581:$i, X582:$i, X583:$i, X584:$i, X585:$i, X586:$i, X588:$i, X589:$i, X590:$i, X591:$i, X592:$i, X593:$i, X594:$i, X595:$i, X596:$i, X597:$i, X598:$i, X599:$i, X600:$i, X601:$i, X602:$i, X603:$i, X604:$i, X605:$i, X606:$i, X607:$i, X608:$i, X609:$i, X610:$i, X611:$i, X612:$i, X613:$i, X614:$i, X615:$i, X616:$i, X617:$i, X618:$i, X619:$i, X620:$i, X621:$i, X622:$i, X623:$i, X624:$i, X625:$i > $o, X626:$i, X627:$i > $o, X628:$i, X629:$i, X630:$i, X631:$i, X632:$i, X633:$i, X634:$i, X635:$i, X636:$i, X637:$i, X638:$i, X639:$o, X640:$i, X641:$i, X642:$i, X643:$i, X644:$i, X645:$i, X646:$i, X647:$i, X648:$i, X649:$i, X650:$i, X651:$i, X652:$i, X653:$i, X654:$i, X655:$i]:(((~in @ (esk1_2 @ X344 @ X345) @ X344|~in @ (esk1_2 @ X344 @ X345) @ X345|(X344)=(X345))&(in @ (esk1_2 @ X344 @ X345) @ X344|in @ (esk1_2 @ X344 @ X345) @ X345|(X344)=(X345)))&(~in @ X347 @ emptyset&(((~in @ X350 @ (setadjoin @ X348 @ X349)|((X350)=(X348)|in @ X350 @ X349))&(((X350)!=(X348)|in @ X350 @ (setadjoin @ X348 @ X349))&(~in @ X350 @ X349|in @ X350 @ (setadjoin @ X348 @ X349))))&(((~in @ X352 @ (powerset @ X351)|(~in @ X353 @ X352|in @ X353 @ X351))&((in @ (esk2_2 @ X354 @ X355) @ X355|in @ X355 @ (powerset @ X354))&(~in @ (esk2_2 @ X354 @ X355) @ X354|in @ X355 @ (powerset @ X354))))&((((in @ X358 @ (esk3_2 @ X357 @ X358)|~in @ X358 @ (setunion @ X357))&(in @ (esk3_2 @ X357 @ X358) @ X357|~in @ X358 @ (setunion @ X357)))&(~in @ X361 @ X362|~in @ X362 @ X360|in @ X361 @ (setunion @ X360)))&(in @ emptyset @ omega&((~in @ X363 @ omega|in @ (setadjoin @ X363 @ X363) @ omega)&((((in @ (esk4_1 @ X364) @ omega|~in @ emptyset @ X364|(~in @ X366 @ omega|in @ X366 @ X364))&(in @ (esk4_1 @ X364) @ X364|~in @ emptyset @ X364|(~in @ X366 @ omega|in @ X366 @ X364)))&(~in @ (setadjoin @ (esk4_1 @ X364) @ (esk4_1 @ X364)) @ X364|~in @ emptyset @ X364|(~in @ X366 @ omega|in @ X366 @ X364)))&(((((in @ (esk8_3 @ X367 @ X368 @ X373) @ X368|~in @ X373 @ (esk7_2 @ X367 @ X368)|in @ (esk5_2 @ X367 @ X368) @ X368)&(X367 @ (esk8_3 @ X367 @ X368 @ X373) @ X373|~in @ X373 @ (esk7_2 @ X367 @ X368)|in @ (esk5_2 @ X367 @ X368) @ X368))&(~in @ X376 @ X368|~X367 @ X376 @ X375|in @ X375 @ (esk7_2 @ X367 @ X368)|in @ (esk5_2 @ X367 @ X368) @ X368))&((((in @ (esk8_3 @ X367 @ X368 @ X373) @ X368|~in @ X373 @ (esk7_2 @ X367 @ X368)|(X367 @ (esk5_2 @ X367 @ X368) @ (esk6_3 @ X367 @ X368 @ X370)|~X367 @ (esk5_2 @ X367 @ X368) @ X370))&(X367 @ (esk8_3 @ X367 @ X368 @ X373) @ X373|~in @ X373 @ (esk7_2 @ X367 @ X368)|(X367 @ (esk5_2 @ X367 @ X368) @ (esk6_3 @ X367 @ X368 @ X370)|~X367 @ (esk5_2 @ X367 @ X368) @ X370)))&(~in @ X376 @ X368|~X367 @ X376 @ X375|in @ X375 @ (esk7_2 @ X367 @ X368)|(X367 @ (esk5_2 @ X367 @ X368) @ (esk6_3 @ X367 @ X368 @ X370)|~X367 @ (esk5_2 @ X367 @ X368) @ X370)))&(((in @ (esk8_3 @ X367 @ X368 @ X373) @ X368|~in @ X373 @ (esk7_2 @ X367 @ X368)|((X370)!=(esk6_3 @ X367 @ X368 @ X370)|~X367 @ (esk5_2 @ X367 @ X368) @ X370))&(X367 @ (esk8_3 @ X367 @ X368 @ X373) @ X373|~in @ X373 @ (esk7_2 @ X367 @ X368)|((X370)!=(esk6_3 @ X367 @ X368 @ X370)|~X367 @ (esk5_2 @ X367 @ X368) @ X370)))&(~in @ X376 @ X368|~X367 @ X376 @ X375|in @ X375 @ (esk7_2 @ X367 @ X368)|((X370)!=(esk6_3 @ X367 @ X368 @ X370)|~X367 @ (esk5_2 @ X367 @ X368) @ X370)))))&(((in @ (esk9_1 @ X377) @ X377|~in @ X378 @ X377)&(~in @ X380 @ (esk9_1 @ X377)|~in @ X380 @ X377|~in @ X378 @ X377))&(epred4_0&(((X381 @ (esk10_2 @ X381 @ X382)|~X381 @ X382|X381 @ (descr @ (epred2_2 @ X381)))&((X382)!=(esk10_2 @ X381 @ X382)|~X381 @ X382|X381 @ (descr @ (epred2_2 @ X381))))&((~in @ X386 @ X384|(~X385 @ X386|in @ X386 @ (dsetconstr @ X384 @ (epred2_2 @ X385))))&((~in @ X389 @ (dsetconstr @ X387 @ (epred2_2 @ X388))|in @ X389 @ X387)&((~in @ X392 @ (dsetconstr @ X390 @ (epred2_2 @ X391))|X391 @ X392)&((((X393 @ (esk12_1 @ X393)|(X393 @ (esk11_2 @ X393 @ X394)|~X393 @ X394))&(~X393 @ X397|(esk12_1 @ X393)=(X397)|(X393 @ (esk11_2 @ X393 @ X394)|~X393 @ X394)))&((X393 @ (esk12_1 @ X393)|((X394)!=(esk11_2 @ X393 @ X394)|~X393 @ X394))&(~X393 @ X397|(esk12_1 @ X393)=(X397)|((X394)!=(esk11_2 @ X393 @ X394)|~X393 @ X394))))&((((~X398|X398|X398)&(~in @ X399 @ (prop2set @ $false)|X398|X398))&((~X398|~in @ X399 @ (prop2set @ $true)|X398)&(~in @ X399 @ (prop2set @ $false)|~in @ X399 @ (prop2set @ $true)|X398)))&((~in @ X400 @ emptyset|X401)&(~in @ X402 @ emptyset&(~in @ X403 @ emptyset&(((X404 @ (esk13_2 @ X404 @ X405)|~X404 @ X405|X404 @ (esk14_1 @ X404))&((X405)!=(esk13_2 @ X404 @ X405)|~X404 @ X405|X404 @ (esk14_1 @ X404)))&((((in @ (esk16_2 @ X408 @ X409) @ X409|(X408)=(X409)|in @ (esk15_2 @ X408 @ X409) @ X408)&(~in @ (esk16_2 @ X408 @ X409) @ X408|(X408)=(X409)|in @ (esk15_2 @ X408 @ X409) @ X408))&((in @ (esk16_2 @ X408 @ X409) @ X409|(X408)=(X409)|~in @ (esk15_2 @ X408 @ X409) @ X409)&(~in @ (esk16_2 @ X408 @ X409) @ X408|(X408)=(X409)|~in @ (esk15_2 @ X408 @ X409) @ X409)))&((in @ (esk17_1 @ X412) @ X412|(X412)=(emptyset))&((in @ (esk18_1 @ X414) @ X414|(X414)=(emptyset))&(((~in @ X418 @ (dsetconstr @ X416 @ (epred2_2 @ X417))|X417 @ X418|~in @ X418 @ X416)&(~X417 @ X418|in @ X418 @ (dsetconstr @ X416 @ (epred2_2 @ X417))|~in @ X418 @ X416))&(((X419)=(emptyset)|in @ (esk19_1 @ X419) @ X419)&((~in @ X423 @ X421|(~X422 @ X423|(dsetconstr @ X421 @ (epred2_2 @ X422))!=(emptyset)))&((~in @ X425 @ X424|(X424)!=(emptyset))&(in @ X426 @ (setadjoin @ X426 @ X427)&(in @ emptyset @ (setadjoin @ emptyset @ emptyset)&((~in @ X430 @ X429|in @ X430 @ (setadjoin @ X428 @ X429))&((((in @ X433 @ X432|X434|(X433)=(X431)|~in @ X433 @ (setadjoin @ X431 @ X432))&(~X434|X434|(X433)=(X431)|~in @ X433 @ (setadjoin @ X431 @ X432)))&((in @ X433 @ X432|X434|~X434|~in @ X433 @ (setadjoin @ X431 @ X432))&(~X434|X434|~X434|~in @ X433 @ (setadjoin @ X431 @ X432))))&((~in @ X437 @ (setadjoin @ X435 @ X436)|((X437)=(X435)|in @ X437 @ X436))&((dsetconstr @ X438 @ epred3_1)=(X438)&(((in @ (esk20_2 @ X439 @ X440) @ X440|in @ X440 @ (powerset @ X439))&(~in @ (esk20_2 @ X439 @ X440) @ X439|in @ X440 @ (powerset @ X439)))&(in @ emptyset @ (powerset @ X442)&(in @ emptyset @ (powerset @ X443)&((~in @ X445 @ (powerset @ X444)|(~in @ X446 @ X445|in @ X446 @ X444))&((~in @ X448 @ X449|(~in @ X449 @ X447|in @ X448 @ (setunion @ X447)))&(((in @ X451 @ (esk21_3 @ X450 @ X451 @ X452)|X452|~in @ X451 @ (setunion @ X450))&((in @ (esk21_3 @ X450 @ X451 @ X452) @ X450|X452|~in @ X451 @ (setunion @ X450))&(~X452|X452|~in @ X451 @ (setunion @ X450))))&((~in @ X455 @ X454|in @ X455 @ (powerset @ (setunion @ X454)))&((((~X456 @ X460|(X460)=(esk23_1 @ X456)|(X456 @ (esk22_2 @ X456 @ X457)|~X456 @ X457))&((X461)!=(esk23_1 @ X456)|X456 @ X461|(X456 @ (esk22_2 @ X456 @ X457)|~X456 @ X457)))&((~X456 @ X460|(X460)=(esk23_1 @ X456)|((X457)!=(esk22_2 @ X456 @ X457)|~X456 @ X457))&((X461)!=(esk23_1 @ X456)|X456 @ X461|((X457)!=(esk22_2 @ X456 @ X457)|~X456 @ X457))))&(((X462)=(emptyset)|in @ (esk24_1 @ X462) @ X462)&((~in @ X464 @ (setadjoin @ X465 @ emptyset)|(X464)=(X465))&(((X466)=(X467)|~in @ X467 @ (setadjoin @ X466 @ emptyset))&(((X468)!=(X469)|in @ X468 @ (setadjoin @ X469 @ emptyset))&((~in @ X470 @ (setadjoin @ X471 @ emptyset)|in @ X471 @ (setadjoin @ X470 @ emptyset))&((~in @ X474 @ (setadjoin @ X472 @ (setadjoin @ X473 @ emptyset))|((X474)=(X472)|(X474)=(X473)))&(in @ X475 @ (setadjoin @ X475 @ (setadjoin @ X476 @ emptyset))&(in @ X478 @ (setadjoin @ X477 @ (setadjoin @ X478 @ emptyset))&((~in @ X481 @ X479|~X480 @ X481|(dsetconstr @ X479 @ (epred2_2 @ X480))!=(emptyset))&((~in @ X483 @ emptyset|X482 @ X483)&(((in @ (esk25_2 @ X484 @ X485) @ X484|(~in @ X486 @ X484|X485 @ X486))&(~X485 @ (esk25_2 @ X484 @ X485)|(~in @ X486 @ X484|X485 @ X486)))&(((in @ (esk26_2 @ X488 @ X489) @ X488|(~in @ X491 @ X488|~X489 @ X491))&(X489 @ (esk26_2 @ X488 @ X489)|(~in @ X491 @ X488|~X489 @ X491)))&(((in @ (esk27_2 @ X492 @ X493) @ X492|(~in @ X495 @ X492|~X493 @ X495))&(X493 @ (esk27_2 @ X492 @ X493)|(~in @ X495 @ X492|~X493 @ X495)))&(((in @ (esk28_2 @ X496 @ X497) @ X496|(~in @ X498 @ X496|X497 @ X498))&(~X497 @ (esk28_2 @ X496 @ X497)|(~in @ X498 @ X496|X497 @ X498)))&(((~X500|in @ emptyset @ (prop2set @ $true)|~X500)&(X500|in @ emptyset @ (prop2set @ $false)|~X500))&(((~X501|set2prop @ (prop2set @ $true)|~X501)&(X501|set2prop @ (prop2set @ $false)|~X501))&(((in @ (esk29_2 @ X502 @ X503) @ X502|(~in @ X505 @ X502|~X503 @ X505))&(X503 @ (esk29_2 @ X502 @ X503)|(~in @ X505 @ X502|~X503 @ X505)))&(((in @ (esk30_2 @ X506 @ X507) @ X506|(~in @ X508 @ X506|X507 @ X508))&(~X507 @ (esk30_2 @ X506 @ X507)|(~in @ X508 @ X506|X507 @ X508)))&((((X510 @ (esk32_1 @ X510)|(X510 @ (esk31_2 @ X510 @ X511)|~X510 @ X511))&(~X510 @ X514|(esk32_1 @ X510)=(X514)|(X510 @ (esk31_2 @ X510 @ X511)|~X510 @ X511)))&((X510 @ (esk32_1 @ X510)|((X511)!=(esk31_2 @ X510 @ X511)|~X510 @ X511))&(~X510 @ X514|(esk32_1 @ X510)=(X514)|((X511)!=(esk31_2 @ X510 @ X511)|~X510 @ X511))))&((((X515 @ (esk35_1 @ X515)|X515 @ (esk33_1 @ X515)|~X515 @ X516)&(~X515 @ X520|(esk35_1 @ X515)=(X520)|X515 @ (esk33_1 @ X515)|~X515 @ X516))&(((X515 @ (esk35_1 @ X515)|X515 @ (esk34_1 @ X515)|~X515 @ X516)&(~X515 @ X520|(esk35_1 @ X515)=(X520)|X515 @ (esk34_1 @ X515)|~X515 @ X516))&((X515 @ (esk35_1 @ X515)|(esk33_1 @ X515)!=(esk34_1 @ X515)|~X515 @ X516)&(~X515 @ X520|(esk35_1 @ X515)=(X520)|(esk33_1 @ X515)!=(esk34_1 @ X515)|~X515 @ X516))))&((((X521 @ (esk37_1 @ X521)|(~X521 @ (esk36_2 @ X521 @ X522)|(esk36_2 @ X521 @ X522)!=(X522)))&(~X521 @ X525|(esk37_1 @ X521)=(X525)|(~X521 @ (esk36_2 @ X521 @ X522)|(esk36_2 @ X521 @ X522)!=(X522))))&((X521 @ (esk37_1 @ X521)|(X521 @ (esk36_2 @ X521 @ X522)|(esk36_2 @ X521 @ X522)=(X522)))&(~X521 @ X525|(esk37_1 @ X521)=(X525)|(X521 @ (esk36_2 @ X521 @ X522)|(esk36_2 @ X521 @ X522)=(X522)))))&(((X526)!=(X527)|((X528)!=(X529)|(~in @ X528 @ X526|in @ X529 @ X527)))&(((~in @ X532 @ X530|in @ X533 @ X531|(X532)!=(X533)|(X530)!=(X531))&(~in @ X533 @ X531|in @ X532 @ X530|(X532)!=(X533)|(X530)!=(X531)))&(((X534 @ (esk38_2 @ X534 @ X535)|~X534 @ X535|(~X534 @ X537|(~X534 @ X538|(X537)=(X538))))&((X535)!=(esk38_2 @ X534 @ X535)|~X534 @ X535|(~X534 @ X537|(~X534 @ X538|(X537)=(X538)))))&((((((X540 @ (esk42_2 @ X539 @ X540)|(X539 @ (esk41_3 @ X539 @ X540 @ X543)|~X539 @ X543)|(esk39_2 @ X539 @ X540)=(esk40_2 @ X539 @ X540))&(~X540 @ X546|(esk42_2 @ X539 @ X540)=(X546)|(X539 @ (esk41_3 @ X539 @ X540 @ X543)|~X539 @ X543)|(esk39_2 @ X539 @ X540)=(esk40_2 @ X539 @ X540)))&((X540 @ (esk42_2 @ X539 @ X540)|((X543)!=(esk41_3 @ X539 @ X540 @ X543)|~X539 @ X543)|(esk39_2 @ X539 @ X540)=(esk40_2 @ X539 @ X540))&(~X540 @ X546|(esk42_2 @ X539 @ X540)=(X546)|((X543)!=(esk41_3 @ X539 @ X540 @ X543)|~X539 @ X543)|(esk39_2 @ X539 @ X540)=(esk40_2 @ X539 @ X540))))&(((X539 @ (esk44_2 @ X539 @ X540)|(X540 @ (esk43_3 @ X539 @ X540 @ X547)|~X540 @ X547)|(esk39_2 @ X539 @ X540)=(esk40_2 @ X539 @ X540))&(~X539 @ X550|(esk44_2 @ X539 @ X540)=(X550)|(X540 @ (esk43_3 @ X539 @ X540 @ X547)|~X540 @ X547)|(esk39_2 @ X539 @ X540)=(esk40_2 @ X539 @ X540)))&((X539 @ (esk44_2 @ X539 @ X540)|((X547)!=(esk43_3 @ X539 @ X540 @ X547)|~X540 @ X547)|(esk39_2 @ X539 @ X540)=(esk40_2 @ X539 @ X540))&(~X539 @ X550|(esk44_2 @ X539 @ X540)=(X550)|((X547)!=(esk43_3 @ X539 @ X540 @ X547)|~X540 @ X547)|(esk39_2 @ X539 @ X540)=(esk40_2 @ X539 @ X540)))))&(((((X540 @ (esk42_2 @ X539 @ X540)|(X539 @ (esk41_3 @ X539 @ X540 @ X543)|~X539 @ X543)|(~X539 @ (esk39_2 @ X539 @ X540)|~X540 @ (esk40_2 @ X539 @ X540)))&(~X540 @ X546|(esk42_2 @ X539 @ X540)=(X546)|(X539 @ (esk41_3 @ X539 @ X540 @ X543)|~X539 @ X543)|(~X539 @ (esk39_2 @ X539 @ X540)|~X540 @ (esk40_2 @ X539 @ X540))))&((X540 @ (esk42_2 @ X539 @ X540)|((X543)!=(esk41_3 @ X539 @ X540 @ X543)|~X539 @ X543)|(~X539 @ (esk39_2 @ X539 @ X540)|~X540 @ (esk40_2 @ X539 @ X540)))&(~X540 @ X546|(esk42_2 @ X539 @ X540)=(X546)|((X543)!=(esk41_3 @ X539 @ X540 @ X543)|~X539 @ X543)|(~X539 @ (esk39_2 @ X539 @ X540)|~X540 @ (esk40_2 @ X539 @ X540)))))&(((X539 @ (esk44_2 @ X539 @ X540)|(X540 @ (esk43_3 @ X539 @ X540 @ X547)|~X540 @ X547)|(~X539 @ (esk39_2 @ X539 @ X540)|~X540 @ (esk40_2 @ X539 @ X540)))&(~X539 @ X550|(esk44_2 @ X539 @ X540)=(X550)|(X540 @ (esk43_3 @ X539 @ X540 @ X547)|~X540 @ X547)|(~X539 @ (esk39_2 @ X539 @ X540)|~X540 @ (esk40_2 @ X539 @ X540))))&((X539 @ (esk44_2 @ X539 @ X540)|((X547)!=(esk43_3 @ X539 @ X540 @ X547)|~X540 @ X547)|(~X539 @ (esk39_2 @ X539 @ X540)|~X540 @ (esk40_2 @ X539 @ X540)))&(~X539 @ X550|(esk44_2 @ X539 @ X540)=(X550)|((X547)!=(esk43_3 @ X539 @ X540 @ X547)|~X540 @ X547)|(~X539 @ (esk39_2 @ X539 @ X540)|~X540 @ (esk40_2 @ X539 @ X540))))))&((((X540 @ (esk42_2 @ X539 @ X540)|(X539 @ (esk41_3 @ X539 @ X540 @ X543)|~X539 @ X543)|(X539 @ (esk39_2 @ X539 @ X540)|X540 @ (esk40_2 @ X539 @ X540)))&(~X540 @ X546|(esk42_2 @ X539 @ X540)=(X546)|(X539 @ (esk41_3 @ X539 @ X540 @ X543)|~X539 @ X543)|(X539 @ (esk39_2 @ X539 @ X540)|X540 @ (esk40_2 @ X539 @ X540))))&((X540 @ (esk42_2 @ X539 @ X540)|((X543)!=(esk41_3 @ X539 @ X540 @ X543)|~X539 @ X543)|(X539 @ (esk39_2 @ X539 @ X540)|X540 @ (esk40_2 @ X539 @ X540)))&(~X540 @ X546|(esk42_2 @ X539 @ X540)=(X546)|((X543)!=(esk41_3 @ X539 @ X540 @ X543)|~X539 @ X543)|(X539 @ (esk39_2 @ X539 @ X540)|X540 @ (esk40_2 @ X539 @ X540)))))&(((X539 @ (esk44_2 @ X539 @ X540)|(X540 @ (esk43_3 @ X539 @ X540 @ X547)|~X540 @ X547)|(X539 @ (esk39_2 @ X539 @ X540)|X540 @ (esk40_2 @ X539 @ X540)))&(~X539 @ X550|(esk44_2 @ X539 @ X540)=(X550)|(X540 @ (esk43_3 @ X539 @ X540 @ X547)|~X540 @ X547)|(X539 @ (esk39_2 @ X539 @ X540)|X540 @ (esk40_2 @ X539 @ X540))))&((X539 @ (esk44_2 @ X539 @ X540)|((X547)!=(esk43_3 @ X539 @ X540 @ X547)|~X540 @ X547)|(X539 @ (esk39_2 @ X539 @ X540)|X540 @ (esk40_2 @ X539 @ X540)))&(~X539 @ X550|(esk44_2 @ X539 @ X540)=(X550)|((X547)!=(esk43_3 @ X539 @ X540 @ X547)|~X540 @ X547)|(X539 @ (esk39_2 @ X539 @ X540)|X540 @ (esk40_2 @ X539 @ X540))))))))&((emptyset)=(emptyset)&(((X551)!=(X552)|((X553)!=(X554)|(setadjoin @ X551 @ X553)=(setadjoin @ X552 @ X554)))&(((X555)!=(X556)|(powerset @ X555)=(powerset @ X556))&(((X557)!=(X558)|(setunion @ X557)=(setunion @ X558))&((omega)=(omega)&(((X559 @ (esk45_2 @ X559 @ X560)|~X559 @ X560|(~X559 @ X562|(~X559 @ X563|(X562)=(X563))))&((X560)!=(esk45_2 @ X559 @ X560)|~X559 @ X560|(~X559 @ X562|(~X559 @ X563|(X562)=(X563)))))&(((((X565 @ (esk49_3 @ X564 @ X565 @ X570)|~X565 @ X570|(descr @ (epred2_2 @ X564))=(descr @ (epred2_2 @ X565))|(X564 @ (esk48_3 @ X564 @ X565 @ X568)|~X564 @ X568)|(esk46_2 @ X564 @ X565)=(esk47_2 @ X564 @ X565))&((X570)!=(esk49_3 @ X564 @ X565 @ X570)|~X565 @ X570|(descr @ (epred2_2 @ X564))=(descr @ (epred2_2 @ X565))|(X564 @ (esk48_3 @ X564 @ X565 @ X568)|~X564 @ X568)|(esk46_2 @ X564 @ X565)=(esk47_2 @ X564 @ X565)))&((X565 @ (esk49_3 @ X564 @ X565 @ X570)|~X565 @ X570|(descr @ (epred2_2 @ X564))=(descr @ (epred2_2 @ X565))|((X568)!=(esk48_3 @ X564 @ X565 @ X568)|~X564 @ X568)|(esk46_2 @ X564 @ X565)=(esk47_2 @ X564 @ X565))&((X570)!=(esk49_3 @ X564 @ X565 @ X570)|~X565 @ X570|(descr @ (epred2_2 @ X564))=(descr @ (epred2_2 @ X565))|((X568)!=(esk48_3 @ X564 @ X565 @ X568)|~X564 @ X568)|(esk46_2 @ X564 @ X565)=(esk47_2 @ X564 @ X565))))&((((X565 @ (esk49_3 @ X564 @ X565 @ X570)|~X565 @ X570|(descr @ (epred2_2 @ X564))=(descr @ (epred2_2 @ X565))|(X564 @ (esk48_3 @ X564 @ X565 @ X568)|~X564 @ X568)|(~X564 @ (esk46_2 @ X564 @ X565)|~X565 @ (esk47_2 @ X564 @ X565)))&((X570)!=(esk49_3 @ X564 @ X565 @ X570)|~X565 @ X570|(descr @ (epred2_2 @ X564))=(descr @ (epred2_2 @ X565))|(X564 @ (esk48_3 @ X564 @ X565 @ X568)|~X564 @ X568)|(~X564 @ (esk46_2 @ X564 @ X565)|~X565 @ (esk47_2 @ X564 @ X565))))&((X565 @ (esk49_3 @ X564 @ X565 @ X570)|~X565 @ X570|(descr @ (epred2_2 @ X564))=(descr @ (epred2_2 @ X565))|((X568)!=(esk48_3 @ X564 @ X565 @ X568)|~X564 @ X568)|(~X564 @ (esk46_2 @ X564 @ X565)|~X565 @ (esk47_2 @ X564 @ X565)))&((X570)!=(esk49_3 @ X564 @ X565 @ X570)|~X565 @ X570|(descr @ (epred2_2 @ X564))=(descr @ (epred2_2 @ X565))|((X568)!=(esk48_3 @ X564 @ X565 @ X568)|~X564 @ X568)|(~X564 @ (esk46_2 @ X564 @ X565)|~X565 @ (esk47_2 @ X564 @ X565)))))&(((X565 @ (esk49_3 @ X564 @ X565 @ X570)|~X565 @ X570|(descr @ (epred2_2 @ X564))=(descr @ (epred2_2 @ X565))|(X564 @ (esk48_3 @ X564 @ X565 @ X568)|~X564 @ X568)|(X564 @ (esk46_2 @ X564 @ X565)|X565 @ (esk47_2 @ X564 @ X565)))&((X570)!=(esk49_3 @ X564 @ X565 @ X570)|~X565 @ X570|(descr @ (epred2_2 @ X564))=(descr @ (epred2_2 @ X565))|(X564 @ (esk48_3 @ X564 @ X565 @ X568)|~X564 @ X568)|(X564 @ (esk46_2 @ X564 @ X565)|X565 @ (esk47_2 @ X564 @ X565))))&((X565 @ (esk49_3 @ X564 @ X565 @ X570)|~X565 @ X570|(descr @ (epred2_2 @ X564))=(descr @ (epred2_2 @ X565))|((X568)!=(esk48_3 @ X564 @ X565 @ X568)|~X564 @ X568)|(X564 @ (esk46_2 @ X564 @ X565)|X565 @ (esk47_2 @ X564 @ X565)))&((X570)!=(esk49_3 @ X564 @ X565 @ X570)|~X565 @ X570|(descr @ (epred2_2 @ X564))=(descr @ (epred2_2 @ X565))|((X568)!=(esk48_3 @ X564 @ X565 @ X568)|~X564 @ X568)|(X564 @ (esk46_2 @ X564 @ X565)|X565 @ (esk47_2 @ X564 @ X565)))))))&(((in @ (esk50_4 @ X572 @ X573 @ X574 @ X575) @ X572|(dsetconstr @ X572 @ (epred2_2 @ X574))=(dsetconstr @ X573 @ (epred2_2 @ X575))|(X572)!=(X573))&((in @ (esk51_4 @ X572 @ X573 @ X574 @ X575) @ X573|(dsetconstr @ X572 @ (epred2_2 @ X574))=(dsetconstr @ X573 @ (epred2_2 @ X575))|(X572)!=(X573))&(((esk50_4 @ X572 @ X573 @ X574 @ X575)=(esk51_4 @ X572 @ X573 @ X574 @ X575)|(dsetconstr @ X572 @ (epred2_2 @ X574))=(dsetconstr @ X573 @ (epred2_2 @ X575))|(X572)!=(X573))&((~X574 @ (esk50_4 @ X572 @ X573 @ X574 @ X575)|~X575 @ (esk51_4 @ X572 @ X573 @ X574 @ X575)|(dsetconstr @ X572 @ (epred2_2 @ X574))=(dsetconstr @ X573 @ (epred2_2 @ X575))|(X572)!=(X573))&(X574 @ (esk50_4 @ X572 @ X573 @ X574 @ X575)|X575 @ (esk51_4 @ X572 @ X573 @ X574 @ X575)|(dsetconstr @ X572 @ (epred2_2 @ X574))=(dsetconstr @ X573 @ (epred2_2 @ X575))|(X572)!=(X573))))))&(((in @ (esk52_2 @ X578 @ X579) @ X578|subset @ X578 @ X579)&(~in @ (esk52_2 @ X578 @ X579) @ X579|subset @ X578 @ X579))&(((X581)!=(X582)|subset @ X582 @ X581)&(((X583)!=(X584)|subset @ X583 @ X584)&(((in @ (esk53_2 @ X585 @ X586) @ X585|subset @ X585 @ X586)&(~in @ (esk53_2 @ X585 @ X586) @ X586|subset @ X585 @ X586))&(subset @ emptyset @ X588&((~subset @ X589 @ X590|(~in @ X591 @ X589|in @ X591 @ X590))&((~subset @ X592 @ X593|(in @ X594 @ X593|~in @ X594 @ X592))&((~in @ X597 @ X595|(in @ X597 @ X596|~subset @ X595 @ X596))&((subset @ X598 @ X599|(X598)!=(X599))&((~in @ X602 @ X600|(in @ X602 @ X601|(X600)!=(X601)))&(subset @ X603 @ X603&((~subset @ X604 @ X605|(~subset @ X605 @ X606|subset @ X604 @ X606))&(subset @ X608 @ (setadjoin @ X607 @ X608)&((~subset @ X609 @ X611|subset @ X609 @ (setadjoin @ X610 @ X611))&((~subset @ X612 @ X613|in @ X612 @ (powerset @ X613))&((~subset @ X614 @ X615|(~subset @ X615 @ X614|(X614)=(X615)))&((~subset @ X616 @ emptyset|(X616)=(emptyset))&((~subset @ X618 @ X617|in @ X618 @ (powerset @ X617))&((~in @ X620 @ (powerset @ X619)|subset @ X620 @ X619)&(in @ X621 @ (powerset @ X621)&((~subset @ X622 @ X623|subset @ (powerset @ X622) @ (powerset @ X623))&(in @ (dsetconstr @ X624 @ (epred2_2 @ X625)) @ (powerset @ X624)&(subset @ (dsetconstr @ X626 @ (epred2_2 @ X627)) @ X626&((~in @ X630 @ X628|in @ X630 @ (binunion @ X628 @ X629))&(in @ X632 @ (setadjoin @ X631 @ (setadjoin @ X632 @ emptyset))&((~in @ X635 @ X634|in @ X635 @ (binunion @ X633 @ X634))&((((in @ X638 @ X637|X639|in @ X638 @ X636|~in @ X638 @ (binunion @ X636 @ X637))&(~X639|X639|in @ X638 @ X636|~in @ X638 @ (binunion @ X636 @ X637)))&((in @ X638 @ X637|X639|~X639|~in @ X638 @ (binunion @ X636 @ X637))&(~X639|X639|~X639|~in @ X638 @ (binunion @ X636 @ X637))))&((~in @ X642 @ (binunion @ X640 @ X641)|(in @ X642 @ X640|in @ X642 @ X641))&(subset @ X643 @ (binunion @ X643 @ X644)&(subset @ X646 @ (binunion @ X645 @ X646)&((~in @ X649 @ X647|(~in @ X649 @ X648|in @ X649 @ (binintersect @ X647 @ X648)))&((~subset @ X652 @ X650|(~subset @ X652 @ X651|subset @ X652 @ (binintersect @ X650 @ X651)))&((~in @ X655 @ (binintersect @ X653 @ X654)|in @ X655 @ X653)&~subset @ (binintersect @ esk54_0 @ esk55_0) @ esk54_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_130])])])])])])). 0.98/1.24 thf(c_0_132, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(in @ X2 @ X3|~in @ X2 @ (binintersect @ X3 @ X4)), inference(split_conjunct,[status(thm)],[c_0_131])). 0.98/1.24 thf(c_0_133, negated_conjecture, ![X2:$i, X3:$i]:(in @ (esk52_2 @ X2 @ X3) @ X2|subset @ X2 @ X3), inference(split_conjunct,[status(thm)],[c_0_131])). 0.98/1.24 thf(c_0_134, negated_conjecture, ![X2:$i, X3:$i]:(subset @ X2 @ X3|~in @ (esk52_2 @ X2 @ X3) @ X3), inference(split_conjunct,[status(thm)],[c_0_131])). 0.98/1.24 thf(c_0_135, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(in @ (esk52_2 @ (binintersect @ X2 @ X3) @ X4) @ X2|subset @ (binintersect @ X2 @ X3) @ X4), inference(spm,[status(thm)],[c_0_132, c_0_133])). 0.98/1.24 thf(c_0_136, negated_conjecture, ~subset @ (binintersect @ esk54_0 @ esk55_0) @ esk54_0, inference(split_conjunct,[status(thm)],[c_0_131])). 0.98/1.24 thf(c_0_137, negated_conjecture, ![X3:$i, X2:$i]:subset @ (binintersect @ X2 @ X3) @ X2, inference(spm,[status(thm)],[c_0_134, c_0_135])). 0.98/1.24 thf(c_0_138, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_136, c_0_137])]), ['proof']). 0.98/1.24 # SZS output end CNFRefutation 0.98/1.24 # Proof object total steps : 139 0.98/1.24 # Proof object clause steps : 7 0.98/1.24 # Proof object formula steps : 132 0.98/1.24 # Proof object conjectures : 10 0.98/1.24 # Proof object clause conjectures : 7 0.98/1.24 # Proof object formula conjectures : 3 0.98/1.24 # Proof object initial clauses used : 4 0.98/1.24 # Proof object initial formulas used : 111 0.98/1.24 # Proof object generating inferences : 2 0.98/1.24 # Proof object simplifying inferences : 2 0.98/1.24 # Training examples: 0 positive, 0 negative 0.98/1.24 # Parsed axioms : 237 0.98/1.24 # Removed by relevancy pruning/SinE : 0 0.98/1.24 # Initial clauses : 357 0.98/1.24 # Removed in clause preprocessing : 145 0.98/1.24 # Initial clauses in saturation : 212 0.98/1.24 # Processed clauses : 2603 0.98/1.24 # ...of these trivial : 145 0.98/1.24 # ...subsumed : 974 0.98/1.24 # ...remaining for further processing : 1484 0.98/1.24 # Other redundant clauses eliminated : 4302 0.98/1.24 # Clauses deleted for lack of memory : 0 0.98/1.24 # Backward-subsumed : 43 0.98/1.24 # Backward-rewritten : 57 0.98/1.24 # Generated clauses : 47911 0.98/1.24 # ...of the previous two non-trivial : 41087 0.98/1.24 # Contextual simplify-reflections : 0 0.98/1.24 # Paramodulations : 37066 0.98/1.24 # Factorizations : 2 0.98/1.24 # NegExts : 35 0.98/1.24 # Equation resolutions : 4302 0.98/1.24 # Propositional unsat checks : 0 0.98/1.24 # Propositional check models : 0 0.98/1.24 # Propositional check unsatisfiable : 0 0.98/1.24 # Propositional clauses : 0 0.98/1.24 # Propositional clauses after purity: 0 0.98/1.24 # Propositional unsat core size : 0 0.98/1.24 # Propositional preprocessing time : 0.000 0.98/1.24 # Propositional encoding time : 0.000 0.98/1.24 # Propositional solver time : 0.000 0.98/1.24 # Success case prop preproc time : 0.000 0.98/1.24 # Success case prop encoding time : 0.000 0.98/1.24 # Success case prop solver time : 0.000 0.98/1.24 # Current number of processed clauses : 1186 0.98/1.24 # Positive orientable unit clauses : 67 0.98/1.24 # Positive unorientable unit clauses: 0 0.98/1.24 # Negative unit clauses : 176 0.98/1.24 # Non-unit-clauses : 943 0.98/1.24 # Current number of unprocessed clauses: 38405 0.98/1.24 # ...number of literals in the above : 142419 0.98/1.24 # Current number of archived formulas : 0 0.98/1.24 # Current number of archived clauses : 285 0.98/1.24 # Clause-clause subsumption calls (NU) : 80405 0.98/1.24 # Rec. Clause-clause subsumption calls : 52281 0.98/1.24 # Non-unit clause-clause subsumptions : 695 0.98/1.24 # Unit Clause-clause subsumption calls : 24030 0.98/1.24 # Rewrite failures with RHS unbound : 0 0.98/1.24 # BW rewrite match attempts : 108 0.98/1.24 # BW rewrite match successes : 56 0.98/1.24 # Condensation attempts : 0 0.98/1.24 # Condensation successes : 0 0.98/1.24 # Termbank termtop insertions : 821926 0.98/1.24 0.98/1.24 # ------------------------------------------------- 0.98/1.24 # User time : 0.877 s 0.98/1.24 # System time : 0.028 s 0.98/1.24 # Total time : 0.905 s 0.98/1.24 # Maximum resident set size: 1884 pages 0.98/1.24 EOF