0.03/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.12 % 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 0.11/0.32 % Computer : n005.cluster.edu 0.11/0.32 % Model : x86_64 x86_64 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.32 % Memory : 8042.1875MB 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.32 % CPULimit : 1200 0.11/0.32 % WCLimit : 120 0.11/0.33 % DateTime : Tue Jul 13 15:59:48 EDT 2021 0.11/0.33 % CPUTime : 0.11/0.33 % Number of cores: 8 0.11/0.33 % Python version: Python 3.6.8 0.11/0.33 # Version: 2.6rc1-ho 0.11/0.34 # No SInE strategy applied 0.11/0.34 # Trying AutoSched0 for 59 seconds 0.17/0.39 # AutoSched0-Mode selected heuristic G_E___302_C18_F1_URBAN_S0Y 0.17/0.39 # and selection function SelectMaxLComplexAvoidPosPred. 0.17/0.39 # 0.17/0.39 # Preprocessing time : 0.050 s 0.17/0.39 0.17/0.39 # Proof found! 0.17/0.39 # SZS status Theorem 0.17/0.39 # SZS output start CNFRefutation 0.17/0.39 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:$i]:(in @ X3 @ X4&X6 @ X3 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', replAx)). 0.17/0.39 thf(exu, axiom, (exu)=(^[X1:$i > $o]:?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exu)). 0.17/0.39 thf(descrp, axiom, (descrp<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>X1 @ (descr @ (^[X2:$i]:X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', descrp)). 0.17/0.39 thf(exuE1, axiom, (exuE1<=>![X1:$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)). 0.17/0.39 thf(exuE3e, axiom, (exuE3e<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>?[X2:$i]:X1 @ X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuE3e)). 0.17/0.39 thf(nonemptyE1, axiom, (nonemptyE1<=>![X4:$i]:(nonempty @ X4=>?[X2:$i]:in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyE1)). 0.17/0.39 thf(nonempty, axiom, (nonempty)=(^[X2:$i]:(X2)!=(emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonempty)). 0.17/0.39 thf(nonemptyI, axiom, (nonemptyI<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyI)). 0.17/0.39 thf(nonemptyI1, axiom, (nonemptyI1<=>![X4:$i]:(?[X2:$i]:in @ X2 @ X4=>nonempty @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyI1)). 0.17/0.39 thf(exuE2, axiom, (exuE2<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuE2)). 0.17/0.39 thf(nonemptyImpWitness, axiom, (nonemptyImpWitness<=>![X4:$i]:(nonempty @ X4=>?[X2:$i]:(in @ X2 @ X4&$true))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyImpWitness)). 0.17/0.39 thf(exuI1, axiom, (exuI1<=>![X1:$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)). 0.17/0.39 thf(exuI3, axiom, (exuI3<=>![X1:$i > $o]:(?[X2:$i]:X1 @ X2=>(![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3)))=>exu @ (^[X2:$i]:X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuI3)). 0.17/0.39 thf(exuI2, axiom, (exuI2<=>![X1:$i > $o]:(?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2))=>exu @ (^[X2:$i]:X1 @ X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuI2)). 0.17/0.39 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)). 0.17/0.39 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:$i]:X17 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exu__Cong)). 0.17/0.39 thf(exuEu, axiom, (exuEu<=>![X1:$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)). 0.17/0.39 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:$i]:X17 @ X2)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', descr__Cong)). 0.17/0.39 thf(binintersectSubset3, conjecture, (setextAx=>(emptysetAx=>(setadjoinAx=>(((omega0Ax=>(omegaSAx=>(omegaIndAx=>((foundationAx=>((((dsetconstrEL=>(dsetconstrER=>(exuE1=>((emptysetE=>(emptysetimpfalse=>((((((((nonemptyI=>(nonemptyI1=>(((setadjoinIR=>(setadjoinE=>((((((powersetE=>((setunionE=>(((((notinsingleton=>(eqinunit=>((upairsetE=>((((((quantDeMorgan2=>(((((notdexE=>((exuI1=>(exuI3=>((inCongP=>(in__Cong=>(exuE3u=>(exu__Cong=>(((powerset__Cong=>(setunion__Cong=>(omega__Cong=>(exuEu=>(((subsetI1=>((eqimpsubset1=>(((subsetE=>((notsubsetI=>(notequalI1=>((subsetRefl=>((setadjoinSub=>(((((powersetI1=>((inPowerset=>(((sepSubset=>(binunionIL=>((((binunionE=>(binunionLsub=>(binunionRsub=>((((binintersectLsub=>(binintersectSubset2=>![X4:$i, X5:$i]:(subset @ X5 @ X4<=(binintersect @ X4 @ X5)=(X5))))<=binintersectEL)<=binintersectSubset5)<=binintersectI))))<=binunionEcases)<=binunionIR)<=upairset2IR)))<=sepInPowerset)<=powersetsubset))<=powersetE1))<=subsetemptysetimpeq)<=setextsub)<=subset2powerset)<=setadjoinSub2))<=subsetTrans))<=notequalI2)))<=subsetE2))<=emptysetsubset)<=subsetI2))<=eqimpsubset2))<=dsetconstr__Cong)<=descr__Cong)))))<=setadjoin__Cong)<=emptyset__Cong)))))<=exuI2)))<=notdallE))<=prop2set2propI)<=prop2setI)<=quantDeMorgan4)<=quantDeMorgan3))<=quantDeMorgan1)<=vacuousDall)<=emptyE1)<=upairsetIR)<=upairsetIL))<=singletonsswitch)))<=uniqinunit)<=nonemptyImpWitness)<=exuE2)<=subPowSU))<=setunionI))<=emptyInPowerset)<=emptyinPowerset)<=powersetI)<=setoftrueEq)<=setadjoinOr)))<=emptyinunitempty)<=setadjoinIL)))<=nonemptyE1)<=setbeta)<=noeltsimpempty)<=emptyI)<=setext)<=exuE3e)<=notinemptyset)))<=prop2setE))))<=dsetconstrI)<=descrp)<=wellorderingAx))<=replAx))))<=setunionAx)<=powersetAx)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset3)). 0.17/0.39 thf(setextAx, axiom, (setextAx<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4<=>in @ X2 @ X5)=>(X4)=(X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setextAx)). 0.17/0.39 thf(emptysetAx, axiom, (emptysetAx<=>![X2:$i]:~(in @ X2 @ emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetAx)). 0.17/0.39 thf(setadjoinAx, axiom, (setadjoinAx<=>![X2:$i, X4:$i, X3:$i]:(in @ X3 @ (setadjoin @ X2 @ X4)<=>((X3)=(X2)|in @ X3 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinAx)). 0.17/0.39 thf(powersetAx, axiom, (powersetAx<=>![X4:$i, X5:$i]:(in @ X5 @ (powerset @ X4)<=>![X2:$i]:(in @ X2 @ X5=>in @ X2 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetAx)). 0.17/0.39 thf(setunionAx, axiom, (setunionAx<=>![X4:$i, X2:$i]:(in @ X2 @ (setunion @ X4)<=>?[X5:$i]:(in @ X2 @ X5&in @ X5 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionAx)). 0.17/0.39 thf(omega0Ax, axiom, (omega0Ax<=>in @ emptyset @ omega), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omega0Ax)). 0.17/0.39 thf(omegaSAx, axiom, (omegaSAx<=>![X2:$i]:(in @ X2 @ omega=>in @ (setadjoin @ X2 @ X2) @ omega)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omegaSAx)). 0.17/0.39 thf(omegaIndAx, axiom, (omegaIndAx<=>![X4:$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)). 0.17/0.39 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)). 0.17/0.39 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:$i]:(in @ X3 @ X9=>in @ X3 @ X8)|in @ X2 @ X9)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', wellorderingAx)). 0.17/0.39 thf(dsetconstrI, axiom, (dsetconstrI<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstrI)). 0.17/0.39 thf(dsetconstrEL, axiom, (dsetconstrEL<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))=>in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstrEL)). 0.17/0.39 thf(dsetconstrER, axiom, (dsetconstrER<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))=>X1 @ X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstrER)). 0.17/0.39 thf(prop2setE, axiom, (prop2setE<=>![X10:$o, X2:$i]:(in @ X2 @ (prop2set @ (X10))=>X10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prop2setE)). 0.17/0.39 thf(emptysetE, axiom, (emptysetE<=>![X2:$i]:(in @ X2 @ emptyset=>![X11:$o]:X11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetE)). 0.17/0.39 thf(emptysetimpfalse, axiom, (emptysetimpfalse<=>![X2:$i]:(in @ X2 @ emptyset=>~$true)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetimpfalse)). 0.17/0.39 thf(notinemptyset, axiom, (notinemptyset<=>![X2:$i]:~(in @ X2 @ emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notinemptyset)). 0.17/0.39 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)). 0.17/0.39 thf(emptyI, axiom, (emptyI<=>![X4:$i]:(![X2:$i]:~(in @ X2 @ X4)=>(X4)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyI)). 0.17/0.39 thf(noeltsimpempty, axiom, (noeltsimpempty<=>![X4:$i]:(![X2:$i]:~(in @ X2 @ X4)=>(X4)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', noeltsimpempty)). 0.17/0.39 thf(setbeta, axiom, (setbeta<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))<=>X1 @ X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setbeta)). 0.17/0.39 thf(setadjoinIL, axiom, (setadjoinIL<=>![X2:$i, X3:$i]:in @ X2 @ (setadjoin @ X2 @ X3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinIL)). 0.17/0.39 thf(emptyinunitempty, axiom, (emptyinunitempty<=>in @ emptyset @ (setadjoin @ emptyset @ emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyinunitempty)). 0.17/0.39 thf(setadjoinIR, axiom, (setadjoinIR<=>![X2:$i, X4:$i, X3:$i]:(in @ X3 @ X4=>in @ X3 @ (setadjoin @ X2 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinIR)). 0.17/0.39 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)). 0.17/0.39 thf(setadjoinOr, axiom, (setadjoinOr<=>![X2:$i, X4:$i, X3:$i]:(in @ X3 @ (setadjoin @ X2 @ X4)=>((X3)=(X2)|in @ X3 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinOr)). 0.17/0.39 thf(setoftrueEq, axiom, (setoftrueEq<=>![X4:$i]:(dsetconstr @ X4 @ (^[X2:$i]:$true))=(X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setoftrueEq)). 0.17/0.39 thf(powersetI, axiom, (powersetI<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X5=>in @ X2 @ X4)=>in @ X5 @ (powerset @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetI)). 0.17/0.39 thf(emptyinPowerset, axiom, (emptyinPowerset<=>![X4:$i]:in @ emptyset @ (powerset @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyinPowerset)). 0.17/0.39 thf(emptyInPowerset, axiom, (emptyInPowerset<=>![X4:$i]:in @ emptyset @ (powerset @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyInPowerset)). 0.17/0.39 thf(powersetE, axiom, (powersetE<=>![X4:$i, X5:$i, X2:$i]:(in @ X5 @ (powerset @ X4)=>(in @ X2 @ X5=>in @ X2 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetE)). 0.17/0.39 thf(setunionI, axiom, (setunionI<=>![X4:$i, X2:$i, X5:$i]:(in @ X2 @ X5=>(in @ X5 @ X4=>in @ X2 @ (setunion @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionI)). 0.17/0.39 thf(setunionE, axiom, (setunionE<=>![X4:$i, X2:$i]:(in @ X2 @ (setunion @ X4)=>![X13:$o]:(![X5:$i]:(in @ X2 @ X5=>(in @ X5 @ X4=>X13))=>X13))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionE)). 0.17/0.39 thf(subPowSU, axiom, (subPowSU<=>![X4:$i, X2:$i]:(in @ X2 @ X4=>in @ X2 @ (powerset @ (setunion @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subPowSU)). 0.17/0.39 thf(uniqinunit, axiom, (uniqinunit<=>![X2:$i, X3:$i]:(in @ X2 @ (setadjoin @ X3 @ emptyset)=>(X2)=(X3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', uniqinunit)). 0.17/0.39 thf(notinsingleton, axiom, (notinsingleton<=>![X2:$i, X3:$i]:((X2)!=(X3)=>~(in @ X3 @ (setadjoin @ X2 @ emptyset)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notinsingleton)). 0.17/0.39 thf(eqinunit, axiom, (eqinunit<=>![X2:$i, X3:$i]:((X2)=(X3)=>in @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqinunit)). 0.17/0.39 thf(singletonsswitch, axiom, (singletonsswitch<=>![X2:$i, X3:$i]:(in @ X2 @ (setadjoin @ X3 @ emptyset)=>in @ X3 @ (setadjoin @ X2 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletonsswitch)). 0.17/0.39 thf(upairsetE, axiom, (upairsetE<=>![X2:$i, X3:$i, X14:$i]:(in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=>((X14)=(X2)|(X14)=(X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsetE)). 0.17/0.39 thf(upairsetIL, axiom, (upairsetIL<=>![X2:$i, X3:$i]:in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsetIL)). 0.17/0.39 thf(upairsetIR, axiom, (upairsetIR<=>![X2:$i, X3:$i]:in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsetIR)). 0.17/0.39 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)). 0.17/0.39 thf(vacuousDall, axiom, (vacuousDall<=>![X1:$i > $o, X2:$i]:(in @ X2 @ emptyset=>X1 @ X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', vacuousDall)). 0.17/0.39 thf(quantDeMorgan1, axiom, (quantDeMorgan1<=>![X4:$i, X1:$i > $o]:(~(![X2:$i]:(in @ X2 @ X4=>X1 @ X2))=>?[X2:$i]:(in @ X2 @ X4&~(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan1)). 0.17/0.39 thf(quantDeMorgan2, axiom, (quantDeMorgan2<=>![X4:$i, X1:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>~(X1 @ X2))=>~(?[X2:$i]:(in @ X2 @ X4&X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan2)). 0.17/0.39 thf(quantDeMorgan3, axiom, (quantDeMorgan3<=>![X4:$i, X1:$i > $o]:(~(?[X2:$i]:(in @ X2 @ X4&X1 @ X2))=>![X2:$i]:(in @ X2 @ X4=>~(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan3)). 0.17/0.39 thf(quantDeMorgan4, axiom, (quantDeMorgan4<=>![X4:$i, X1:$i > $o]:(?[X2:$i]:(in @ X2 @ X4&~(X1 @ X2))=>~(![X2:$i]:(in @ X2 @ X4=>X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan4)). 0.17/0.39 thf(prop2setI, axiom, (prop2setI<=>![X15:$o]:(X15=>in @ emptyset @ (prop2set @ (X15)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prop2setI)). 0.17/0.39 thf(prop2set2propI, axiom, (prop2set2propI<=>![X16:$o]:(X16=>set2prop @ (prop2set @ (X16)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prop2set2propI)). 0.17/0.39 thf(notdexE, axiom, (notdexE<=>![X4:$i, X1:$i > $o]:(~(?[X2:$i]:(in @ X2 @ X4&X1 @ X2))=>![X2:$i]:(in @ X2 @ X4=>~(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notdexE)). 0.17/0.39 thf(notdallE, axiom, (notdallE<=>![X4:$i, X1:$i > $o]:(~(![X2:$i]:(in @ X2 @ X4=>X1 @ X2))=>?[X2:$i]:(in @ X2 @ X4&~(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notdallE)). 0.17/0.39 thf(inCongP, axiom, (inCongP<=>![X4:$i, X5:$i]:((X4)=(X5)=>![X2:$i, X3:$i]:((X2)=(X3)=>(in @ X2 @ X4=>in @ X3 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', inCongP)). 0.17/0.39 thf(in__Cong, axiom, (in__Cong<=>![X4:$i, X5:$i]:((X4)=(X5)=>![X2:$i, X3:$i]:((X2)=(X3)=>(in @ X2 @ X4<=>in @ X3 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', in__Cong)). 0.17/0.39 thf(emptyset__Cong, axiom, (emptyset__Cong<=>(emptyset)=(emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyset__Cong)). 0.17/0.39 thf(setadjoin__Cong, axiom, (setadjoin__Cong<=>![X2:$i, X3:$i]:((X2)=(X3)=>![X14:$i, X18:$i]:((X14)=(X18)=>(setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoin__Cong)). 0.17/0.39 thf(powerset__Cong, axiom, (powerset__Cong<=>![X4:$i, X5:$i]:((X4)=(X5)=>(powerset @ X4)=(powerset @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powerset__Cong)). 0.17/0.39 thf(setunion__Cong, axiom, (setunion__Cong<=>![X4:$i, X5:$i]:((X4)=(X5)=>(setunion @ X4)=(setunion @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunion__Cong)). 0.17/0.39 thf(omega__Cong, axiom, (omega__Cong<=>(omega)=(omega)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omega__Cong)). 0.17/0.39 thf(dsetconstr__Cong, axiom, (dsetconstr__Cong<=>![X4:$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:$i]:X17 @ X2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstr__Cong)). 0.17/0.39 thf(subsetI1, axiom, (subsetI1<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4=>in @ X2 @ X5)=>subset @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetI1)). 0.17/0.39 thf(eqimpsubset2, axiom, (eqimpsubset2<=>![X4:$i, X5:$i]:((X4)=(X5)=>subset @ X5 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqimpsubset2)). 0.17/0.39 thf(eqimpsubset1, axiom, (eqimpsubset1<=>![X4:$i, X5:$i]:((X4)=(X5)=>subset @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqimpsubset1)). 0.17/0.39 thf(subsetI2, axiom, (subsetI2<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4=>in @ X2 @ X5)=>subset @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetI2)). 0.17/0.39 thf(emptysetsubset, axiom, (emptysetsubset<=>![X4:$i]:subset @ emptyset @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetsubset)). 0.17/0.39 thf(subsetE, axiom, (subsetE<=>![X4:$i, X5:$i, X2:$i]:(subset @ X4 @ X5=>(in @ X2 @ X4=>in @ X2 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetE)). 0.17/0.39 thf(subsetE2, axiom, (subsetE2<=>![X4:$i, X5:$i, X2:$i]:(subset @ X4 @ X5=>(~(in @ X2 @ X5)=>~(in @ X2 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetE2)). 0.17/0.39 thf(notsubsetI, axiom, (notsubsetI<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X5)=>~(subset @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notsubsetI)). 0.17/0.39 thf(notequalI1, axiom, (notequalI1<=>![X4:$i, X5:$i]:(~(subset @ X4 @ X5)=>(X4)!=(X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notequalI1)). 0.17/0.39 thf(notequalI2, axiom, (notequalI2<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X5)=>(X4)!=(X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notequalI2)). 0.17/0.39 thf(subsetRefl, axiom, (subsetRefl<=>![X4:$i]:subset @ X4 @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetRefl)). 0.17/0.39 thf(subsetTrans, axiom, (subsetTrans<=>![X4:$i, X5:$i, X7:$i]:(subset @ X4 @ X5=>(subset @ X5 @ X7=>subset @ X4 @ X7))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetTrans)). 0.17/0.39 thf(setadjoinSub, axiom, (setadjoinSub<=>![X2:$i, X4:$i]:subset @ X4 @ (setadjoin @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinSub)). 0.17/0.39 thf(setadjoinSub2, axiom, (setadjoinSub2<=>![X4:$i, X2:$i, X5:$i]:(subset @ X4 @ X5=>subset @ X4 @ (setadjoin @ X2 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinSub2)). 0.17/0.39 thf(subset2powerset, axiom, (subset2powerset<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>in @ X4 @ (powerset @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subset2powerset)). 0.17/0.39 thf(setextsub, axiom, (setextsub<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>(subset @ X5 @ X4=>(X4)=(X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setextsub)). 0.17/0.39 thf(subsetemptysetimpeq, axiom, (subsetemptysetimpeq<=>![X4:$i]:(subset @ X4 @ emptyset=>(X4)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetemptysetimpeq)). 0.17/0.39 thf(powersetI1, axiom, (powersetI1<=>![X4:$i, X5:$i]:(subset @ X5 @ X4=>in @ X5 @ (powerset @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetI1)). 0.17/0.39 thf(powersetE1, axiom, (powersetE1<=>![X4:$i, X5:$i]:(in @ X5 @ (powerset @ X4)=>subset @ X5 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetE1)). 0.17/0.39 thf(inPowerset, axiom, (inPowerset<=>![X4:$i]:in @ X4 @ (powerset @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', inPowerset)). 0.17/0.39 thf(powersetsubset, axiom, (powersetsubset<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>subset @ (powerset @ X4) @ (powerset @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetsubset)). 0.17/0.39 thf(sepInPowerset, axiom, (sepInPowerset<=>![X4:$i, X1:$i > $o]:in @ (dsetconstr @ X4 @ (^[X2:$i]:X1 @ X2)) @ (powerset @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sepInPowerset)). 0.17/0.39 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)). 0.17/0.39 thf(binunionIL, axiom, (binunionIL<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>in @ X2 @ (binunion @ X4 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionIL)). 0.17/0.39 thf(upairset2IR, axiom, (upairset2IR<=>![X2:$i, X3:$i]:in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairset2IR)). 0.17/0.39 thf(binunionIR, axiom, (binunionIR<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X5=>in @ X2 @ (binunion @ X4 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionIR)). 0.17/0.39 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)). 0.17/0.39 thf(binunionE, axiom, (binunionE<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (binunion @ X4 @ X5)=>(in @ X2 @ X4|in @ X2 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionE)). 0.17/0.39 thf(binunionLsub, axiom, (binunionLsub<=>![X4:$i, X5:$i]:subset @ X4 @ (binunion @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionLsub)). 0.17/0.39 thf(binunionRsub, axiom, (binunionRsub<=>![X4:$i, X5:$i]:subset @ X5 @ (binunion @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionRsub)). 0.17/0.39 thf(binintersectI, axiom, (binintersectI<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X5=>in @ X2 @ (binintersect @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectI)). 0.17/0.39 thf(binintersectSubset5, axiom, (binintersectSubset5<=>![X4:$i, X5:$i, X7:$i]:(subset @ X7 @ X4=>(subset @ X7 @ X5=>subset @ X7 @ (binintersect @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset5)). 0.17/0.39 thf(binintersectEL, axiom, (binintersectEL<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (binintersect @ X4 @ X5)=>in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectEL)). 0.17/0.39 thf(binintersectLsub, axiom, (binintersectLsub<=>![X4:$i, X5:$i]:subset @ (binintersect @ X4 @ X5) @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectLsub)). 0.17/0.39 thf(binintersectSubset2, axiom, (binintersectSubset2<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>(binintersect @ X4 @ X5)=(X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset2)). 0.17/0.39 thf(c_0_113, axiom, (replAx)=(![X6:$i > $i > $o, X4:$i]:(![X2:$i]:(in @ X2 @ X4=>?[X316:$i]:(X6 @ X2 @ X316&![X318:$i]:(X6 @ X2 @ X318=>(X316)=(X318))))=>?[X5:$i]:![X2:$i]:(in @ X2 @ X5<=>?[X3:$i]:(in @ X3 @ X4&X6 @ X3 @ X2)))), inference(apply_def,[status(thm)],[replAx, exu])). 0.17/0.39 thf(c_0_114, axiom, (descrp)=(![X1:$i > $o]:(?[X319:$i]:(X1 @ X319&![X320:$i]:(X1 @ X320=>(X319)=(X320)))=>X1 @ (descr @ (^[X2:$i]:X1 @ X2)))), inference(apply_def,[status(thm)],[descrp, exu])). 0.17/0.39 thf(c_0_115, axiom, (exuE1)=(![X1:$i > $o]:(?[X321:$i]:(X1 @ X321&![X322:$i]:(X1 @ X322=>(X321)=(X322)))=>?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3))))), inference(apply_def,[status(thm)],[exuE1, exu])). 0.17/0.39 thf(c_0_116, axiom, (exuE3e)=(![X1:$i > $o]:(?[X323:$i]:(X1 @ X323&![X324:$i]:(X1 @ X324=>(X323)=(X324)))=>?[X2:$i]:X1 @ X2)), inference(apply_def,[status(thm)],[exuE3e, exu])). 0.17/0.39 thf(c_0_117, axiom, (nonemptyE1)=(![X4:$i]:((X4)!=(emptyset)=>?[X2:$i]:in @ X2 @ X4)), inference(apply_def,[status(thm)],[nonemptyE1, nonempty])). 0.17/0.39 thf(c_0_118, axiom, (nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>(dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))!=(emptyset)))), inference(apply_def,[status(thm)],[nonemptyI, nonempty])). 0.17/0.39 thf(c_0_119, axiom, (nonemptyI1)=(![X4:$i]:(?[X2:$i]:in @ X2 @ X4=>(X4)!=(emptyset))), inference(apply_def,[status(thm)],[nonemptyI1, nonempty])). 0.17/0.39 thf(c_0_120, axiom, (exuE2)=(![X1:$i > $o]:(?[X325:$i]:(X1 @ X325&![X326:$i]:(X1 @ X326=>(X325)=(X326)))=>?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2)))), inference(apply_def,[status(thm)],[exuE2, exu])). 0.17/0.39 thf(c_0_121, axiom, (nonemptyImpWitness)=(![X4:$i]:((X4)!=(emptyset)=>?[X2:$i]:(in @ X2 @ X4&$true))), inference(apply_def,[status(thm)],[nonemptyImpWitness, nonempty])). 0.17/0.39 thf(c_0_122, axiom, (exuI1)=(![X1:$i > $o]:(?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3)))=>?[X327:$i]:(X1 @ X327&![X328:$i]:(X1 @ X328=>(X327)=(X328))))), inference(apply_def,[status(thm)],[exuI1, exu])). 0.17/0.39 thf(c_0_123, axiom, (exuI3)=(![X1:$i > $o]:(?[X2:$i]:X1 @ X2=>(![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3)))=>?[X329:$i]:(X1 @ X329&![X330:$i]:(X1 @ X330=>(X329)=(X330)))))), inference(apply_def,[status(thm)],[exuI3, exu])). 0.17/0.39 thf(c_0_124, axiom, (exuI2)=(![X1:$i > $o]:(?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2))=>?[X331:$i]:(X1 @ X331&![X332:$i]:(X1 @ X332=>(X331)=(X332))))), inference(apply_def,[status(thm)],[exuI2, exu])). 0.17/0.39 thf(c_0_125, axiom, (exuE3u)=(![X1:$i > $o]:(?[X333:$i]:(X1 @ X333&![X334:$i]:(X1 @ X334=>(X333)=(X334)))=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))), inference(apply_def,[status(thm)],[exuE3u, exu])). 0.17/0.39 thf(c_0_126, axiom, (exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(?[X335:$i]:(X1 @ X335&![X336:$i]:(X1 @ X336=>(X335)=(X336)))<=>?[X337:$i]:(X17 @ X337&![X338:$i]:(X17 @ X338=>(X337)=(X338)))))), inference(apply_def,[status(thm)],[exu__Cong, exu])). 0.17/0.39 thf(c_0_127, axiom, (exuEu)=(![X1:$i > $o]:(?[X339:$i]:(X1 @ X339&![X340:$i]:(X1 @ X340=>(X339)=(X340)))=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))), inference(apply_def,[status(thm)],[exuEu, exu])). 0.17/0.39 thf(c_0_128, axiom, (descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(?[X341:$i]:(X1 @ X341&![X342:$i]:(X1 @ X342=>(X341)=(X342)))=>(?[X343:$i]:(X17 @ X343&![X344:$i]:(X17 @ X344=>(X343)=(X344)))=>(descr @ (^[X2:$i]:X1 @ X2))=(descr @ (^[X2:$i]:X17 @ X2)))))), inference(apply_def,[status(thm)],[descr__Cong, exu])). 0.17/0.39 thf(c_0_129, plain, ![X3:$i, X1:$i > $o]:(epred2_2 @ X1 @ X3<=>X1 @ X3), introduced(definition)). 0.17/0.39 thf(c_0_130, plain, ![X2:$i]:epred3_1 @ X2, inference(fof_simplification,[status(thm)],[introduced(definition)])). 0.17/0.39 thf(c_0_131, 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:$i]:(in @ X3 @ X9=>in @ X3 @ X8)|in @ X2 @ X9)))))), introduced(definition)). 0.17/0.39 thf(c_0_132, negated_conjecture, ~((![X4:$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:$i]:(in @ X2 @ X4=>?[X316:$i]:(X6 @ X2 @ X316&![X318:$i]:(X6 @ X2 @ X318=>(X316)=(X318))))=>?[X5:$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 > $o]:(?[X319:$i]:(X1 @ X319&![X320:$i]:(X1 @ X320=>(X319)=(X320)))=>X1 @ (descr @ (epred2_2 @ X1)))=>(![X4:$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 > $o]:(?[X321:$i]:(X1 @ X321&![X322:$i]:(X1 @ X322=>(X321)=(X322)))=>?[X2:$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 > $o]:(?[X323:$i]:(X1 @ X323&![X324:$i]:(X1 @ X324=>(X323)=(X324)))=>?[X2:$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 > $o]:(?[X325:$i]:(X1 @ X325&![X326:$i]:(X1 @ X326=>(X325)=(X326)))=>?[X2:$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:$i]:(X1 @ X3=>(X2)=(X3)))=>?[X327:$i]:(X1 @ X327&![X328:$i]:(X1 @ X328=>(X327)=(X328))))=>(![X1:$i > $o]:(?[X2:$i]:X1 @ X2=>(![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3)))=>?[X329:$i]:(X1 @ X329&![X330:$i]:(X1 @ X330=>(X329)=(X330)))))=>(![X1:$i > $o]:(?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2))=>?[X331:$i]:(X1 @ X331&![X332:$i]:(X1 @ X332=>(X331)=(X332))))=>(![X4:$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 > $o]:(?[X333:$i]:(X1 @ X333&![X334:$i]:(X1 @ X334=>(X333)=(X334)))=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))=>(![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(?[X335:$i]:(X1 @ X335&![X336:$i]:(X1 @ X336=>(X335)=(X336)))<=>?[X337:$i]:(X17 @ X337&![X338:$i]:(X17 @ X338=>(X337)=(X338)))))=>((emptyset)=(emptyset)=>(![X2:$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 > $o]:(?[X339:$i]:(X1 @ X339&![X340:$i]:(X1 @ X340=>(X339)=(X340)))=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))=>(![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(?[X341:$i]:(X1 @ X341&![X342:$i]:(X1 @ X342=>(X341)=(X342)))=>(?[X343:$i]:(X17 @ X343&![X344:$i]:(X17 @ X344=>(X343)=(X344)))=>(descr @ (epred2_2 @ X1))=(descr @ (epred2_2 @ X17)))))=>(![X4:$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:$i]:subset @ (binintersect @ X4 @ X5) @ X4=>(![X4:$i, X5:$i]:(subset @ X4 @ X5=>(binintersect @ X4 @ X5)=(X4))=>![X4:$i, X5:$i]:((binintersect @ X4 @ X5)=(X5)=>subset @ 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(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[binintersectSubset3]), setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_113]), foundationAx]), wellorderingAx]), c_0_114]), dsetconstrI]), dsetconstrEL]), dsetconstrER]), c_0_115]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_116]), setext]), emptyI]), noeltsimpempty]), setbeta]), c_0_117]), c_0_118]), c_0_119]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), setoftrueEq]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_120]), c_0_121]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), emptyE1]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_122]), c_0_123]), c_0_124]), inCongP]), in__Cong]), c_0_125]), c_0_126]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_127]), c_0_128]), 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]), c_0_129]), c_0_129]), c_0_129]), c_0_130]), c_0_129]), c_0_129]), c_0_129]), c_0_129]), c_0_129]), c_0_129]), c_0_129]), c_0_129]), c_0_129]), c_0_129])])]), c_0_131])). 0.17/0.39 thf(c_0_133, negated_conjecture, ![X348:$i, X349:$i, X351:$i, X352:$i, X353:$i, X354:$i, X355:$i, X356:$i, X357:$i, X358:$i, X359:$i, X361:$i, X362:$i, X364:$i, X365:$i, X366:$i, X367:$i, X368:$i, X370:$i, X371:$i > $i > $o, X372:$i, X374:$i, X377:$i, X379:$i, X380:$i, X381:$i, X382:$i, X384:$i, X385:$i > $o, X386:$i, X388:$i, X389:$i > $o, X390:$i, X391:$i, X392:$i > $o, X393:$i, X394:$i, X395:$i > $o, X396:$i, X397:$i > $o, X398:$i, X401:$i, X402:$o, X403:$i, X404:$i, X405:$o, X406:$i, X407:$i, X408:$i > $o, X409:$i, X412:$i, X413:$i, X416:$i, X418:$i, X420:$i, X421:$i > $o, X422:$i, X423:$i, X425:$i, X426:$i > $o, X427:$i, X428:$i, X429:$i, X430:$i, X431:$i, X432:$i, X433:$i, X434:$i, X435:$i, X436:$i, X437:$i, X438:$o, X439:$i, X440:$i, X441:$i, X442:$i, X443:$i, X444:$i, X446:$i, X447:$i, X448:$i, X449:$i, X450:$i, X451:$i, X452:$i, X453:$i, X454:$i, X455:$i, X456:$o, X458:$i, X459:$i, X460:$i > $o, X461:$i, X464:$i, X465:$i, X466:$i, X468:$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, X481:$i, X482:$i, X483:$i, X484:$i > $o, X485:$i, X486:$i > $o, X487:$i, X488:$i, X489:$i > $o, X490:$i, X492:$i, X493:$i > $o, X495:$i, X496:$i, X497:$i > $o, X499:$i, X500:$i, X501:$i > $o, X502:$i, X504:$o, X505:$o, X506:$i, X507:$i > $o, X509:$i, X510:$i, X511:$i > $o, X512:$i, X514:$i > $o, X515:$i, X518:$i, X519:$i > $o, X520:$i, X524:$i, X525:$i > $o, X526:$i, X529:$i, X530:$i, X531:$i, X532:$i, X533:$i, X534:$i, X535:$i, X536:$i, X537:$i, X538:$i > $o, X539:$i, X541:$i, X542:$i, X543:$i > $o, X544:$i > $o, X547:$i, X550:$i, X551:$i, X554:$i, X555:$i, X556:$i, X557:$i, X558:$i, X559:$i, X560:$i, X561:$i, X562:$i, X563:$i > $o, X564:$i, X566:$i, X567:$i, X568:$i > $o, X569:$i > $o, X572:$i, X574:$i, X576:$i, X577:$i, X578:$i > $o, X579:$i > $o, X582:$i, X583:$i, X585:$i, X586:$i, X587:$i, X588:$i, X589:$i, X590:$i, X592:$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:$i, X626:$i, X627:$i, X628:$i, X629:$i > $o, X630:$i, X631:$i > $o, X632:$i, X633:$i, X634:$i, X635:$i, X636:$i, X637:$i, X638:$i, X639:$i, X640:$i, X641:$i, X642:$i, X643:$o, X644:$i, X645:$i, X646:$i, X647:$i, X648:$i, X649:$i, X650:$i, X651:$i, X652:$i, X653:$i, X654:$i, X655:$i, X656:$i, X657:$i, X658:$i, X659:$i, X660:$i, X661:$i, X662:$i, X663:$i]:(((~in @ (esk1_2 @ X348 @ X349) @ X348|~in @ (esk1_2 @ X348 @ X349) @ X349|(X348)=(X349))&(in @ (esk1_2 @ X348 @ X349) @ X348|in @ (esk1_2 @ X348 @ X349) @ X349|(X348)=(X349)))&(~in @ X351 @ emptyset&(((~in @ X354 @ (setadjoin @ X352 @ X353)|((X354)=(X352)|in @ X354 @ X353))&(((X354)!=(X352)|in @ X354 @ (setadjoin @ X352 @ X353))&(~in @ X354 @ X353|in @ X354 @ (setadjoin @ X352 @ X353))))&(((~in @ X356 @ (powerset @ X355)|(~in @ X357 @ X356|in @ X357 @ X355))&((in @ (esk2_2 @ X358 @ X359) @ X359|in @ X359 @ (powerset @ X358))&(~in @ (esk2_2 @ X358 @ X359) @ X358|in @ X359 @ (powerset @ X358))))&((((in @ X362 @ (esk3_2 @ X361 @ X362)|~in @ X362 @ (setunion @ X361))&(in @ (esk3_2 @ X361 @ X362) @ X361|~in @ X362 @ (setunion @ X361)))&(~in @ X365 @ X366|~in @ X366 @ X364|in @ X365 @ (setunion @ X364)))&(in @ emptyset @ omega&((~in @ X367 @ omega|in @ (setadjoin @ X367 @ X367) @ omega)&((((in @ (esk4_1 @ X368) @ omega|~in @ emptyset @ X368|(~in @ X370 @ omega|in @ X370 @ X368))&(in @ (esk4_1 @ X368) @ X368|~in @ emptyset @ X368|(~in @ X370 @ omega|in @ X370 @ X368)))&(~in @ (setadjoin @ (esk4_1 @ X368) @ (esk4_1 @ X368)) @ X368|~in @ emptyset @ X368|(~in @ X370 @ omega|in @ X370 @ X368)))&(((((in @ (esk8_3 @ X371 @ X372 @ X377) @ X372|~in @ X377 @ (esk7_2 @ X371 @ X372)|in @ (esk5_2 @ X371 @ X372) @ X372)&(X371 @ (esk8_3 @ X371 @ X372 @ X377) @ X377|~in @ X377 @ (esk7_2 @ X371 @ X372)|in @ (esk5_2 @ X371 @ X372) @ X372))&(~in @ X380 @ X372|~X371 @ X380 @ X379|in @ X379 @ (esk7_2 @ X371 @ X372)|in @ (esk5_2 @ X371 @ X372) @ X372))&((((in @ (esk8_3 @ X371 @ X372 @ X377) @ X372|~in @ X377 @ (esk7_2 @ X371 @ X372)|(X371 @ (esk5_2 @ X371 @ X372) @ (esk6_3 @ X371 @ X372 @ X374)|~X371 @ (esk5_2 @ X371 @ X372) @ X374))&(X371 @ (esk8_3 @ X371 @ X372 @ X377) @ X377|~in @ X377 @ (esk7_2 @ X371 @ X372)|(X371 @ (esk5_2 @ X371 @ X372) @ (esk6_3 @ X371 @ X372 @ X374)|~X371 @ (esk5_2 @ X371 @ X372) @ X374)))&(~in @ X380 @ X372|~X371 @ X380 @ X379|in @ X379 @ (esk7_2 @ X371 @ X372)|(X371 @ (esk5_2 @ X371 @ X372) @ (esk6_3 @ X371 @ X372 @ X374)|~X371 @ (esk5_2 @ X371 @ X372) @ X374)))&(((in @ (esk8_3 @ X371 @ X372 @ X377) @ X372|~in @ X377 @ (esk7_2 @ X371 @ X372)|((X374)!=(esk6_3 @ X371 @ X372 @ X374)|~X371 @ (esk5_2 @ X371 @ X372) @ X374))&(X371 @ (esk8_3 @ X371 @ X372 @ X377) @ X377|~in @ X377 @ (esk7_2 @ X371 @ X372)|((X374)!=(esk6_3 @ X371 @ X372 @ X374)|~X371 @ (esk5_2 @ X371 @ X372) @ X374)))&(~in @ X380 @ X372|~X371 @ X380 @ X379|in @ X379 @ (esk7_2 @ X371 @ X372)|((X374)!=(esk6_3 @ X371 @ X372 @ X374)|~X371 @ (esk5_2 @ X371 @ X372) @ X374)))))&(((in @ (esk9_1 @ X381) @ X381|~in @ X382 @ X381)&(~in @ X384 @ (esk9_1 @ X381)|~in @ X384 @ X381|~in @ X382 @ X381))&(epred4_0&(((X385 @ (esk10_2 @ X385 @ X386)|~X385 @ X386|X385 @ (descr @ (epred2_2 @ X385)))&((X386)!=(esk10_2 @ X385 @ X386)|~X385 @ X386|X385 @ (descr @ (epred2_2 @ X385))))&((~in @ X390 @ X388|(~X389 @ X390|in @ X390 @ (dsetconstr @ X388 @ (epred2_2 @ X389))))&((~in @ X393 @ (dsetconstr @ X391 @ (epred2_2 @ X392))|in @ X393 @ X391)&((~in @ X396 @ (dsetconstr @ X394 @ (epred2_2 @ X395))|X395 @ X396)&((((X397 @ (esk12_1 @ X397)|(X397 @ (esk11_2 @ X397 @ X398)|~X397 @ X398))&(~X397 @ X401|(esk12_1 @ X397)=(X401)|(X397 @ (esk11_2 @ X397 @ X398)|~X397 @ X398)))&((X397 @ (esk12_1 @ X397)|((X398)!=(esk11_2 @ X397 @ X398)|~X397 @ X398))&(~X397 @ X401|(esk12_1 @ X397)=(X401)|((X398)!=(esk11_2 @ X397 @ X398)|~X397 @ X398))))&((((~X402|X402|X402)&(~in @ X403 @ (prop2set @ $false)|X402|X402))&((~X402|~in @ X403 @ (prop2set @ $true)|X402)&(~in @ X403 @ (prop2set @ $false)|~in @ X403 @ (prop2set @ $true)|X402)))&((~in @ X404 @ emptyset|X405)&(~in @ X406 @ emptyset&(~in @ X407 @ emptyset&(((X408 @ (esk13_2 @ X408 @ X409)|~X408 @ X409|X408 @ (esk14_1 @ X408))&((X409)!=(esk13_2 @ X408 @ X409)|~X408 @ X409|X408 @ (esk14_1 @ X408)))&((((in @ (esk16_2 @ X412 @ X413) @ X413|(X412)=(X413)|in @ (esk15_2 @ X412 @ X413) @ X412)&(~in @ (esk16_2 @ X412 @ X413) @ X412|(X412)=(X413)|in @ (esk15_2 @ X412 @ X413) @ X412))&((in @ (esk16_2 @ X412 @ X413) @ X413|(X412)=(X413)|~in @ (esk15_2 @ X412 @ X413) @ X413)&(~in @ (esk16_2 @ X412 @ X413) @ X412|(X412)=(X413)|~in @ (esk15_2 @ X412 @ X413) @ X413)))&((in @ (esk17_1 @ X416) @ X416|(X416)=(emptyset))&((in @ (esk18_1 @ X418) @ X418|(X418)=(emptyset))&(((~in @ X422 @ (dsetconstr @ X420 @ (epred2_2 @ X421))|X421 @ X422|~in @ X422 @ X420)&(~X421 @ X422|in @ X422 @ (dsetconstr @ X420 @ (epred2_2 @ X421))|~in @ X422 @ X420))&(((X423)=(emptyset)|in @ (esk19_1 @ X423) @ X423)&((~in @ X427 @ X425|(~X426 @ X427|(dsetconstr @ X425 @ (epred2_2 @ X426))!=(emptyset)))&((~in @ X429 @ X428|(X428)!=(emptyset))&(in @ X430 @ (setadjoin @ X430 @ X431)&(in @ emptyset @ (setadjoin @ emptyset @ emptyset)&((~in @ X434 @ X433|in @ X434 @ (setadjoin @ X432 @ X433))&((((in @ X437 @ X436|X438|(X437)=(X435)|~in @ X437 @ (setadjoin @ X435 @ X436))&(~X438|X438|(X437)=(X435)|~in @ X437 @ (setadjoin @ X435 @ X436)))&((in @ X437 @ X436|X438|~X438|~in @ X437 @ (setadjoin @ X435 @ X436))&(~X438|X438|~X438|~in @ X437 @ (setadjoin @ X435 @ X436))))&((~in @ X441 @ (setadjoin @ X439 @ X440)|((X441)=(X439)|in @ X441 @ X440))&((dsetconstr @ X442 @ epred3_1)=(X442)&(((in @ (esk20_2 @ X443 @ X444) @ X444|in @ X444 @ (powerset @ X443))&(~in @ (esk20_2 @ X443 @ X444) @ X443|in @ X444 @ (powerset @ X443)))&(in @ emptyset @ (powerset @ X446)&(in @ emptyset @ (powerset @ X447)&((~in @ X449 @ (powerset @ X448)|(~in @ X450 @ X449|in @ X450 @ X448))&((~in @ X452 @ X453|(~in @ X453 @ X451|in @ X452 @ (setunion @ X451)))&(((in @ X455 @ (esk21_3 @ X454 @ X455 @ X456)|X456|~in @ X455 @ (setunion @ X454))&((in @ (esk21_3 @ X454 @ X455 @ X456) @ X454|X456|~in @ X455 @ (setunion @ X454))&(~X456|X456|~in @ X455 @ (setunion @ X454))))&((~in @ X459 @ X458|in @ X459 @ (powerset @ (setunion @ X458)))&((((~X460 @ X464|(X464)=(esk23_1 @ X460)|(X460 @ (esk22_2 @ X460 @ X461)|~X460 @ X461))&((X465)!=(esk23_1 @ X460)|X460 @ X465|(X460 @ (esk22_2 @ X460 @ X461)|~X460 @ X461)))&((~X460 @ X464|(X464)=(esk23_1 @ X460)|((X461)!=(esk22_2 @ X460 @ X461)|~X460 @ X461))&((X465)!=(esk23_1 @ X460)|X460 @ X465|((X461)!=(esk22_2 @ X460 @ X461)|~X460 @ X461))))&(((X466)=(emptyset)|in @ (esk24_1 @ X466) @ X466)&((~in @ X468 @ (setadjoin @ X469 @ emptyset)|(X468)=(X469))&(((X470)=(X471)|~in @ X471 @ (setadjoin @ X470 @ emptyset))&(((X472)!=(X473)|in @ X472 @ (setadjoin @ X473 @ emptyset))&((~in @ X474 @ (setadjoin @ X475 @ emptyset)|in @ X475 @ (setadjoin @ X474 @ emptyset))&((~in @ X478 @ (setadjoin @ X476 @ (setadjoin @ X477 @ emptyset))|((X478)=(X476)|(X478)=(X477)))&(in @ X479 @ (setadjoin @ X479 @ (setadjoin @ X480 @ emptyset))&(in @ X482 @ (setadjoin @ X481 @ (setadjoin @ X482 @ emptyset))&((~in @ X485 @ X483|~X484 @ X485|(dsetconstr @ X483 @ (epred2_2 @ X484))!=(emptyset))&((~in @ X487 @ emptyset|X486 @ X487)&(((in @ (esk25_2 @ X488 @ X489) @ X488|(~in @ X490 @ X488|X489 @ X490))&(~X489 @ (esk25_2 @ X488 @ X489)|(~in @ X490 @ X488|X489 @ X490)))&(((in @ (esk26_2 @ X492 @ X493) @ X492|(~in @ X495 @ X492|~X493 @ X495))&(X493 @ (esk26_2 @ X492 @ X493)|(~in @ X495 @ X492|~X493 @ X495)))&(((in @ (esk27_2 @ X496 @ X497) @ X496|(~in @ X499 @ X496|~X497 @ X499))&(X497 @ (esk27_2 @ X496 @ X497)|(~in @ X499 @ X496|~X497 @ X499)))&(((in @ (esk28_2 @ X500 @ X501) @ X500|(~in @ X502 @ X500|X501 @ X502))&(~X501 @ (esk28_2 @ X500 @ X501)|(~in @ X502 @ X500|X501 @ X502)))&(((~X504|in @ emptyset @ (prop2set @ $true)|~X504)&(X504|in @ emptyset @ (prop2set @ $false)|~X504))&(((~X505|set2prop @ (prop2set @ $true)|~X505)&(X505|set2prop @ (prop2set @ $false)|~X505))&(((in @ (esk29_2 @ X506 @ X507) @ X506|(~in @ X509 @ X506|~X507 @ X509))&(X507 @ (esk29_2 @ X506 @ X507)|(~in @ X509 @ X506|~X507 @ X509)))&(((in @ (esk30_2 @ X510 @ X511) @ X510|(~in @ X512 @ X510|X511 @ X512))&(~X511 @ (esk30_2 @ X510 @ X511)|(~in @ X512 @ X510|X511 @ X512)))&((((X514 @ (esk32_1 @ X514)|(X514 @ (esk31_2 @ X514 @ X515)|~X514 @ X515))&(~X514 @ X518|(esk32_1 @ X514)=(X518)|(X514 @ (esk31_2 @ X514 @ X515)|~X514 @ X515)))&((X514 @ (esk32_1 @ X514)|((X515)!=(esk31_2 @ X514 @ X515)|~X514 @ X515))&(~X514 @ X518|(esk32_1 @ X514)=(X518)|((X515)!=(esk31_2 @ X514 @ X515)|~X514 @ X515))))&((((X519 @ (esk35_1 @ X519)|X519 @ (esk33_1 @ X519)|~X519 @ X520)&(~X519 @ X524|(esk35_1 @ X519)=(X524)|X519 @ (esk33_1 @ X519)|~X519 @ X520))&(((X519 @ (esk35_1 @ X519)|X519 @ (esk34_1 @ X519)|~X519 @ X520)&(~X519 @ X524|(esk35_1 @ X519)=(X524)|X519 @ (esk34_1 @ X519)|~X519 @ X520))&((X519 @ (esk35_1 @ X519)|(esk33_1 @ X519)!=(esk34_1 @ X519)|~X519 @ X520)&(~X519 @ X524|(esk35_1 @ X519)=(X524)|(esk33_1 @ X519)!=(esk34_1 @ X519)|~X519 @ X520))))&((((X525 @ (esk37_1 @ X525)|(~X525 @ (esk36_2 @ X525 @ X526)|(esk36_2 @ X525 @ X526)!=(X526)))&(~X525 @ X529|(esk37_1 @ X525)=(X529)|(~X525 @ (esk36_2 @ X525 @ X526)|(esk36_2 @ X525 @ X526)!=(X526))))&((X525 @ (esk37_1 @ X525)|(X525 @ (esk36_2 @ X525 @ X526)|(esk36_2 @ X525 @ X526)=(X526)))&(~X525 @ X529|(esk37_1 @ X525)=(X529)|(X525 @ (esk36_2 @ X525 @ X526)|(esk36_2 @ X525 @ X526)=(X526)))))&(((X530)!=(X531)|((X532)!=(X533)|(~in @ X532 @ X530|in @ X533 @ X531)))&(((~in @ X536 @ X534|in @ X537 @ X535|(X536)!=(X537)|(X534)!=(X535))&(~in @ X537 @ X535|in @ X536 @ X534|(X536)!=(X537)|(X534)!=(X535)))&(((X538 @ (esk38_2 @ X538 @ X539)|~X538 @ X539|(~X538 @ X541|(~X538 @ X542|(X541)=(X542))))&((X539)!=(esk38_2 @ X538 @ X539)|~X538 @ X539|(~X538 @ X541|(~X538 @ X542|(X541)=(X542)))))&((((((X544 @ (esk42_2 @ X543 @ X544)|(X543 @ (esk41_3 @ X543 @ X544 @ X547)|~X543 @ X547)|(esk39_2 @ X543 @ X544)=(esk40_2 @ X543 @ X544))&(~X544 @ X550|(esk42_2 @ X543 @ X544)=(X550)|(X543 @ (esk41_3 @ X543 @ X544 @ X547)|~X543 @ X547)|(esk39_2 @ X543 @ X544)=(esk40_2 @ X543 @ X544)))&((X544 @ (esk42_2 @ X543 @ X544)|((X547)!=(esk41_3 @ X543 @ X544 @ X547)|~X543 @ X547)|(esk39_2 @ X543 @ X544)=(esk40_2 @ X543 @ X544))&(~X544 @ X550|(esk42_2 @ X543 @ X544)=(X550)|((X547)!=(esk41_3 @ X543 @ X544 @ X547)|~X543 @ X547)|(esk39_2 @ X543 @ X544)=(esk40_2 @ X543 @ X544))))&(((X543 @ (esk44_2 @ X543 @ X544)|(X544 @ (esk43_3 @ X543 @ X544 @ X551)|~X544 @ X551)|(esk39_2 @ X543 @ X544)=(esk40_2 @ X543 @ X544))&(~X543 @ X554|(esk44_2 @ X543 @ X544)=(X554)|(X544 @ (esk43_3 @ X543 @ X544 @ X551)|~X544 @ X551)|(esk39_2 @ X543 @ X544)=(esk40_2 @ X543 @ X544)))&((X543 @ (esk44_2 @ X543 @ X544)|((X551)!=(esk43_3 @ X543 @ X544 @ X551)|~X544 @ X551)|(esk39_2 @ X543 @ X544)=(esk40_2 @ X543 @ X544))&(~X543 @ X554|(esk44_2 @ X543 @ X544)=(X554)|((X551)!=(esk43_3 @ X543 @ X544 @ X551)|~X544 @ X551)|(esk39_2 @ X543 @ X544)=(esk40_2 @ X543 @ X544)))))&(((((X544 @ (esk42_2 @ X543 @ X544)|(X543 @ (esk41_3 @ X543 @ X544 @ X547)|~X543 @ X547)|(~X543 @ (esk39_2 @ X543 @ X544)|~X544 @ (esk40_2 @ X543 @ X544)))&(~X544 @ X550|(esk42_2 @ X543 @ X544)=(X550)|(X543 @ (esk41_3 @ X543 @ X544 @ X547)|~X543 @ X547)|(~X543 @ (esk39_2 @ X543 @ X544)|~X544 @ (esk40_2 @ X543 @ X544))))&((X544 @ (esk42_2 @ X543 @ X544)|((X547)!=(esk41_3 @ X543 @ X544 @ X547)|~X543 @ X547)|(~X543 @ (esk39_2 @ X543 @ X544)|~X544 @ (esk40_2 @ X543 @ X544)))&(~X544 @ X550|(esk42_2 @ X543 @ X544)=(X550)|((X547)!=(esk41_3 @ X543 @ X544 @ X547)|~X543 @ X547)|(~X543 @ (esk39_2 @ X543 @ X544)|~X544 @ (esk40_2 @ X543 @ X544)))))&(((X543 @ (esk44_2 @ X543 @ X544)|(X544 @ (esk43_3 @ X543 @ X544 @ X551)|~X544 @ X551)|(~X543 @ (esk39_2 @ X543 @ X544)|~X544 @ (esk40_2 @ X543 @ X544)))&(~X543 @ X554|(esk44_2 @ X543 @ X544)=(X554)|(X544 @ (esk43_3 @ X543 @ X544 @ X551)|~X544 @ X551)|(~X543 @ (esk39_2 @ X543 @ X544)|~X544 @ (esk40_2 @ X543 @ X544))))&((X543 @ (esk44_2 @ X543 @ X544)|((X551)!=(esk43_3 @ X543 @ X544 @ X551)|~X544 @ X551)|(~X543 @ (esk39_2 @ X543 @ X544)|~X544 @ (esk40_2 @ X543 @ X544)))&(~X543 @ X554|(esk44_2 @ X543 @ X544)=(X554)|((X551)!=(esk43_3 @ X543 @ X544 @ X551)|~X544 @ X551)|(~X543 @ (esk39_2 @ X543 @ X544)|~X544 @ (esk40_2 @ X543 @ X544))))))&((((X544 @ (esk42_2 @ X543 @ X544)|(X543 @ (esk41_3 @ X543 @ X544 @ X547)|~X543 @ X547)|(X543 @ (esk39_2 @ X543 @ X544)|X544 @ (esk40_2 @ X543 @ X544)))&(~X544 @ X550|(esk42_2 @ X543 @ X544)=(X550)|(X543 @ (esk41_3 @ X543 @ X544 @ X547)|~X543 @ X547)|(X543 @ (esk39_2 @ X543 @ X544)|X544 @ (esk40_2 @ X543 @ X544))))&((X544 @ (esk42_2 @ X543 @ X544)|((X547)!=(esk41_3 @ X543 @ X544 @ X547)|~X543 @ X547)|(X543 @ (esk39_2 @ X543 @ X544)|X544 @ (esk40_2 @ X543 @ X544)))&(~X544 @ X550|(esk42_2 @ X543 @ X544)=(X550)|((X547)!=(esk41_3 @ X543 @ X544 @ X547)|~X543 @ X547)|(X543 @ (esk39_2 @ X543 @ X544)|X544 @ (esk40_2 @ X543 @ X544)))))&(((X543 @ (esk44_2 @ X543 @ X544)|(X544 @ (esk43_3 @ X543 @ X544 @ X551)|~X544 @ X551)|(X543 @ (esk39_2 @ X543 @ X544)|X544 @ (esk40_2 @ X543 @ X544)))&(~X543 @ X554|(esk44_2 @ X543 @ X544)=(X554)|(X544 @ (esk43_3 @ X543 @ X544 @ X551)|~X544 @ X551)|(X543 @ (esk39_2 @ X543 @ X544)|X544 @ (esk40_2 @ X543 @ X544))))&((X543 @ (esk44_2 @ X543 @ X544)|((X551)!=(esk43_3 @ X543 @ X544 @ X551)|~X544 @ X551)|(X543 @ (esk39_2 @ X543 @ X544)|X544 @ (esk40_2 @ X543 @ X544)))&(~X543 @ X554|(esk44_2 @ X543 @ X544)=(X554)|((X551)!=(esk43_3 @ X543 @ X544 @ X551)|~X544 @ X551)|(X543 @ (esk39_2 @ X543 @ X544)|X544 @ (esk40_2 @ X543 @ X544))))))))&((emptyset)=(emptyset)&(((X555)!=(X556)|((X557)!=(X558)|(setadjoin @ X555 @ X557)=(setadjoin @ X556 @ X558)))&(((X559)!=(X560)|(powerset @ X559)=(powerset @ X560))&(((X561)!=(X562)|(setunion @ X561)=(setunion @ X562))&((omega)=(omega)&(((X563 @ (esk45_2 @ X563 @ X564)|~X563 @ X564|(~X563 @ X566|(~X563 @ X567|(X566)=(X567))))&((X564)!=(esk45_2 @ X563 @ X564)|~X563 @ X564|(~X563 @ X566|(~X563 @ X567|(X566)=(X567)))))&(((((X569 @ (esk49_3 @ X568 @ X569 @ X574)|~X569 @ X574|(descr @ (epred2_2 @ X568))=(descr @ (epred2_2 @ X569))|(X568 @ (esk48_3 @ X568 @ X569 @ X572)|~X568 @ X572)|(esk46_2 @ X568 @ X569)=(esk47_2 @ X568 @ X569))&((X574)!=(esk49_3 @ X568 @ X569 @ X574)|~X569 @ X574|(descr @ (epred2_2 @ X568))=(descr @ (epred2_2 @ X569))|(X568 @ (esk48_3 @ X568 @ X569 @ X572)|~X568 @ X572)|(esk46_2 @ X568 @ X569)=(esk47_2 @ X568 @ X569)))&((X569 @ (esk49_3 @ X568 @ X569 @ X574)|~X569 @ X574|(descr @ (epred2_2 @ X568))=(descr @ (epred2_2 @ X569))|((X572)!=(esk48_3 @ X568 @ X569 @ X572)|~X568 @ X572)|(esk46_2 @ X568 @ X569)=(esk47_2 @ X568 @ X569))&((X574)!=(esk49_3 @ X568 @ X569 @ X574)|~X569 @ X574|(descr @ (epred2_2 @ X568))=(descr @ (epred2_2 @ X569))|((X572)!=(esk48_3 @ X568 @ X569 @ X572)|~X568 @ X572)|(esk46_2 @ X568 @ X569)=(esk47_2 @ X568 @ X569))))&((((X569 @ (esk49_3 @ X568 @ X569 @ X574)|~X569 @ X574|(descr @ (epred2_2 @ X568))=(descr @ (epred2_2 @ X569))|(X568 @ (esk48_3 @ X568 @ X569 @ X572)|~X568 @ X572)|(~X568 @ (esk46_2 @ X568 @ X569)|~X569 @ (esk47_2 @ X568 @ X569)))&((X574)!=(esk49_3 @ X568 @ X569 @ X574)|~X569 @ X574|(descr @ (epred2_2 @ X568))=(descr @ (epred2_2 @ X569))|(X568 @ (esk48_3 @ X568 @ X569 @ X572)|~X568 @ X572)|(~X568 @ (esk46_2 @ X568 @ X569)|~X569 @ (esk47_2 @ X568 @ X569))))&((X569 @ (esk49_3 @ X568 @ X569 @ X574)|~X569 @ X574|(descr @ (epred2_2 @ X568))=(descr @ (epred2_2 @ X569))|((X572)!=(esk48_3 @ X568 @ X569 @ X572)|~X568 @ X572)|(~X568 @ (esk46_2 @ X568 @ X569)|~X569 @ (esk47_2 @ X568 @ X569)))&((X574)!=(esk49_3 @ X568 @ X569 @ X574)|~X569 @ X574|(descr @ (epred2_2 @ X568))=(descr @ (epred2_2 @ X569))|((X572)!=(esk48_3 @ X568 @ X569 @ X572)|~X568 @ X572)|(~X568 @ (esk46_2 @ X568 @ X569)|~X569 @ (esk47_2 @ X568 @ X569)))))&(((X569 @ (esk49_3 @ X568 @ X569 @ X574)|~X569 @ X574|(descr @ (epred2_2 @ X568))=(descr @ (epred2_2 @ X569))|(X568 @ (esk48_3 @ X568 @ X569 @ X572)|~X568 @ X572)|(X568 @ (esk46_2 @ X568 @ X569)|X569 @ (esk47_2 @ X568 @ X569)))&((X574)!=(esk49_3 @ X568 @ X569 @ X574)|~X569 @ X574|(descr @ (epred2_2 @ X568))=(descr @ (epred2_2 @ X569))|(X568 @ (esk48_3 @ X568 @ X569 @ X572)|~X568 @ X572)|(X568 @ (esk46_2 @ X568 @ X569)|X569 @ (esk47_2 @ X568 @ X569))))&((X569 @ (esk49_3 @ X568 @ X569 @ X574)|~X569 @ X574|(descr @ (epred2_2 @ X568))=(descr @ (epred2_2 @ X569))|((X572)!=(esk48_3 @ X568 @ X569 @ X572)|~X568 @ X572)|(X568 @ (esk46_2 @ X568 @ X569)|X569 @ (esk47_2 @ X568 @ X569)))&((X574)!=(esk49_3 @ X568 @ X569 @ X574)|~X569 @ X574|(descr @ (epred2_2 @ X568))=(descr @ (epred2_2 @ X569))|((X572)!=(esk48_3 @ X568 @ X569 @ X572)|~X568 @ X572)|(X568 @ (esk46_2 @ X568 @ X569)|X569 @ (esk47_2 @ X568 @ X569)))))))&(((in @ (esk50_4 @ X576 @ X577 @ X578 @ X579) @ X576|(dsetconstr @ X576 @ (epred2_2 @ X578))=(dsetconstr @ X577 @ (epred2_2 @ X579))|(X576)!=(X577))&((in @ (esk51_4 @ X576 @ X577 @ X578 @ X579) @ X577|(dsetconstr @ X576 @ (epred2_2 @ X578))=(dsetconstr @ X577 @ (epred2_2 @ X579))|(X576)!=(X577))&(((esk50_4 @ X576 @ X577 @ X578 @ X579)=(esk51_4 @ X576 @ X577 @ X578 @ X579)|(dsetconstr @ X576 @ (epred2_2 @ X578))=(dsetconstr @ X577 @ (epred2_2 @ X579))|(X576)!=(X577))&((~X578 @ (esk50_4 @ X576 @ X577 @ X578 @ X579)|~X579 @ (esk51_4 @ X576 @ X577 @ X578 @ X579)|(dsetconstr @ X576 @ (epred2_2 @ X578))=(dsetconstr @ X577 @ (epred2_2 @ X579))|(X576)!=(X577))&(X578 @ (esk50_4 @ X576 @ X577 @ X578 @ X579)|X579 @ (esk51_4 @ X576 @ X577 @ X578 @ X579)|(dsetconstr @ X576 @ (epred2_2 @ X578))=(dsetconstr @ X577 @ (epred2_2 @ X579))|(X576)!=(X577))))))&(((in @ (esk52_2 @ X582 @ X583) @ X582|subset @ X582 @ X583)&(~in @ (esk52_2 @ X582 @ X583) @ X583|subset @ X582 @ X583))&(((X585)!=(X586)|subset @ X586 @ X585)&(((X587)!=(X588)|subset @ X587 @ X588)&(((in @ (esk53_2 @ X589 @ X590) @ X589|subset @ X589 @ X590)&(~in @ (esk53_2 @ X589 @ X590) @ X590|subset @ X589 @ X590))&(subset @ emptyset @ X592&((~subset @ X593 @ X594|(~in @ X595 @ X593|in @ X595 @ X594))&((~subset @ X596 @ X597|(in @ X598 @ X597|~in @ X598 @ X596))&((~in @ X601 @ X599|(in @ X601 @ X600|~subset @ X599 @ X600))&((subset @ X602 @ X603|(X602)!=(X603))&((~in @ X606 @ X604|(in @ X606 @ X605|(X604)!=(X605)))&(subset @ X607 @ X607&((~subset @ X608 @ X609|(~subset @ X609 @ X610|subset @ X608 @ X610))&(subset @ X612 @ (setadjoin @ X611 @ X612)&((~subset @ X613 @ X615|subset @ X613 @ (setadjoin @ X614 @ X615))&((~subset @ X616 @ X617|in @ X616 @ (powerset @ X617))&((~subset @ X618 @ X619|(~subset @ X619 @ X618|(X618)=(X619)))&((~subset @ X620 @ emptyset|(X620)=(emptyset))&((~subset @ X622 @ X621|in @ X622 @ (powerset @ X621))&((~in @ X624 @ (powerset @ X623)|subset @ X624 @ X623)&(in @ X625 @ (powerset @ X625)&((~subset @ X626 @ X627|subset @ (powerset @ X626) @ (powerset @ X627))&(in @ (dsetconstr @ X628 @ (epred2_2 @ X629)) @ (powerset @ X628)&(subset @ (dsetconstr @ X630 @ (epred2_2 @ X631)) @ X630&((~in @ X634 @ X632|in @ X634 @ (binunion @ X632 @ X633))&(in @ X636 @ (setadjoin @ X635 @ (setadjoin @ X636 @ emptyset))&((~in @ X639 @ X638|in @ X639 @ (binunion @ X637 @ X638))&((((in @ X642 @ X641|X643|in @ X642 @ X640|~in @ X642 @ (binunion @ X640 @ X641))&(~X643|X643|in @ X642 @ X640|~in @ X642 @ (binunion @ X640 @ X641)))&((in @ X642 @ X641|X643|~X643|~in @ X642 @ (binunion @ X640 @ X641))&(~X643|X643|~X643|~in @ X642 @ (binunion @ X640 @ X641))))&((~in @ X646 @ (binunion @ X644 @ X645)|(in @ X646 @ X644|in @ X646 @ X645))&(subset @ X647 @ (binunion @ X647 @ X648)&(subset @ X650 @ (binunion @ X649 @ X650)&((~in @ X653 @ X651|(~in @ X653 @ X652|in @ X653 @ (binintersect @ X651 @ X652)))&((~subset @ X656 @ X654|(~subset @ X656 @ X655|subset @ X656 @ (binintersect @ X654 @ X655)))&((~in @ X659 @ (binintersect @ X657 @ X658)|in @ X659 @ X657)&(subset @ (binintersect @ X660 @ X661) @ X660&((~subset @ X662 @ X663|(binintersect @ X662 @ X663)=(X662))&((binintersect @ esk54_0 @ esk55_0)=(esk55_0)&~subset @ 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_132])])])])])])). 0.17/0.39 thf(c_0_134, negated_conjecture, ![X3:$i, X2:$i]:subset @ (binintersect @ X2 @ X3) @ X2, inference(split_conjunct,[status(thm)],[c_0_133])). 0.17/0.39 thf(c_0_135, negated_conjecture, (binintersect @ esk54_0 @ esk55_0)=(esk55_0), inference(split_conjunct,[status(thm)],[c_0_133])). 0.17/0.39 thf(c_0_136, negated_conjecture, ~subset @ esk55_0 @ esk54_0, inference(split_conjunct,[status(thm)],[c_0_133])). 0.17/0.39 thf(c_0_137, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_134, c_0_135]), c_0_136]), ['proof']). 0.17/0.39 # SZS output end CNFRefutation 0.17/0.39 # Proof object total steps : 138 0.17/0.39 # Proof object clause steps : 4 0.17/0.39 # Proof object formula steps : 134 0.17/0.39 # Proof object conjectures : 7 0.17/0.39 # Proof object clause conjectures : 4 0.17/0.39 # Proof object formula conjectures : 3 0.17/0.39 # Proof object initial clauses used : 3 0.17/0.39 # Proof object initial formulas used : 113 0.17/0.39 # Proof object generating inferences : 1 0.17/0.39 # Proof object simplifying inferences : 1 0.17/0.39 # Training examples: 0 positive, 0 negative 0.17/0.39 # Parsed axioms : 241 0.17/0.39 # Removed by relevancy pruning/SinE : 0 0.17/0.39 # Initial clauses : 362 0.17/0.39 # Removed in clause preprocessing : 147 0.17/0.39 # Initial clauses in saturation : 215 0.17/0.39 # Processed clauses : 50 0.17/0.39 # ...of these trivial : 1 0.17/0.39 # ...subsumed : 7 0.17/0.39 # ...remaining for further processing : 42 0.17/0.39 # Other redundant clauses eliminated : 9 0.17/0.39 # Clauses deleted for lack of memory : 0 0.17/0.39 # Backward-subsumed : 0 0.17/0.39 # Backward-rewritten : 1 0.17/0.39 # Generated clauses : 64 0.17/0.39 # ...of the previous two non-trivial : 42 0.17/0.39 # Contextual simplify-reflections : 0 0.17/0.39 # Paramodulations : 47 0.17/0.39 # Factorizations : 0 0.17/0.39 # NegExts : 0 0.17/0.39 # Equation resolutions : 9 0.17/0.39 # Propositional unsat checks : 0 0.17/0.39 # Propositional check models : 0 0.17/0.39 # Propositional check unsatisfiable : 0 0.17/0.39 # Propositional clauses : 0 0.17/0.39 # Propositional clauses after purity: 0 0.17/0.39 # Propositional unsat core size : 0 0.17/0.39 # Propositional preprocessing time : 0.000 0.17/0.39 # Propositional encoding time : 0.000 0.17/0.39 # Propositional solver time : 0.000 0.17/0.39 # Success case prop preproc time : 0.000 0.17/0.39 # Success case prop encoding time : 0.000 0.17/0.39 # Success case prop solver time : 0.000 0.17/0.39 # Current number of processed clauses : 38 0.17/0.39 # Positive orientable unit clauses : 16 0.17/0.39 # Positive unorientable unit clauses: 0 0.17/0.39 # Negative unit clauses : 3 0.17/0.39 # Non-unit-clauses : 19 0.17/0.39 # Current number of unprocessed clauses: 206 0.17/0.39 # ...number of literals in the above : 689 0.17/0.39 # Current number of archived formulas : 0 0.17/0.39 # Current number of archived clauses : 1 0.17/0.39 # Clause-clause subsumption calls (NU) : 38 0.17/0.39 # Rec. Clause-clause subsumption calls : 36 0.17/0.39 # Non-unit clause-clause subsumptions : 2 0.17/0.39 # Unit Clause-clause subsumption calls : 1 0.17/0.39 # Rewrite failures with RHS unbound : 0 0.17/0.39 # BW rewrite match attempts : 5 0.17/0.39 # BW rewrite match successes : 1 0.17/0.39 # Condensation attempts : 0 0.17/0.39 # Condensation successes : 0 0.17/0.39 # Termbank termtop insertions : 26991 0.17/0.39 0.17/0.39 # ------------------------------------------------- 0.17/0.39 # User time : 0.057 s 0.17/0.39 # System time : 0.005 s 0.17/0.39 # Total time : 0.062 s 0.17/0.39 # Maximum resident set size: 1896 pages 0.17/0.39 EOF