0.13/0.14 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.14/0.16 % 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 0.16/0.38 % Computer : n012.cluster.edu 0.16/0.38 % Model : x86_64 x86_64 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.16/0.38 % Memory : 8042.1875MB 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64 0.16/0.38 % CPULimit : 1200 0.16/0.38 % WCLimit : 120 0.16/0.38 % DateTime : Tue Jul 13 13:55:31 EDT 2021 0.23/0.38 % CPUTime : 0.23/0.38 % Number of cores: 8 0.23/0.39 % Python version: Python 3.6.8 0.23/0.39 # Version: 2.6rc1-ho 0.23/0.40 # No SInE strategy applied 0.23/0.40 # Trying AutoSched0 for 59 seconds 0.24/0.50 # AutoSched0-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_S4d 0.24/0.50 # and selection function SelectCQIPrecWNTNp. 0.24/0.50 # 0.24/0.50 # Preprocessing time : 0.061 s 0.24/0.50 # Presaturation interreduction done 0.24/0.50 0.24/0.50 # Proof found! 0.24/0.50 # SZS status Theorem 0.24/0.50 # SZS output start CNFRefutation 0.24/0.50 thf(ex1, axiom, (ex1)=(^[X4:$i, X1:$i > $o]:?[X515:$i]:(in @ X515 @ (dsetconstr @ X4 @ (^[X2:$i]:X1 @ X2))&(dsetconstr @ X4 @ (^[X2:$i]:X1 @ X2))=(setadjoin @ X515 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ex1)). 0.24/0.50 thf(singleton, axiom, (singleton)=(^[X4:$i]:?[X2:$i]:(in @ X2 @ X4&(X4)=(setadjoin @ X2 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singleton)). 0.24/0.50 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:$i]:(in @ X3 @ X4&X6 @ X3 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', replAx)). 0.24/0.50 thf(exu, axiom, (exu)=(^[X1:$i > $o]:?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exu)). 0.24/0.50 thf(descrp, axiom, (descrp<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>X1 @ (descr @ (^[X2:$i]:X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', descrp)). 0.24/0.50 thf(exuE1, axiom, (exuE1<=>![X1:$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)). 0.24/0.50 thf(exuE3e, axiom, (exuE3e<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>?[X2:$i]:X1 @ X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuE3e)). 0.24/0.50 thf(nonemptyE1, axiom, (nonemptyE1<=>![X4:$i]:(nonempty @ X4=>?[X2:$i]:in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyE1)). 0.24/0.50 thf(nonempty, axiom, (nonempty)=(^[X2:$i]:(X2)!=(emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonempty)). 0.24/0.50 thf(nonemptyI, axiom, (nonemptyI<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyI)). 0.24/0.50 thf(nonemptyI1, axiom, (nonemptyI1<=>![X4:$i]:(?[X2:$i]:in @ X2 @ X4=>nonempty @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyI1)). 0.24/0.50 thf(exuE2, axiom, (exuE2<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuE2)). 0.24/0.50 thf(nonemptyImpWitness, axiom, (nonemptyImpWitness<=>![X4:$i]:(nonempty @ X4=>?[X2:$i]:(in @ X2 @ X4&$true))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyImpWitness)). 0.24/0.50 thf(exuI1, axiom, (exuI1<=>![X1:$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)). 0.24/0.50 thf(exuI3, axiom, (exuI3<=>![X1:$i > $o]:(?[X2:$i]:X1 @ X2=>(![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3)))=>exu @ (^[X2:$i]:X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuI3)). 0.24/0.50 thf(exuI2, axiom, (exuI2<=>![X1:$i > $o]:(?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2))=>exu @ (^[X2:$i]:X1 @ X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuI2)). 0.24/0.50 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)). 0.24/0.50 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:$i]:X17 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exu__Cong)). 0.24/0.50 thf(exuEu, axiom, (exuEu<=>![X1:$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)). 0.24/0.50 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:$i]:X17 @ X2)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', descr__Cong)). 0.24/0.50 thf(kpairiskpair, axiom, (kpairiskpair<=>![X2:$i, X3:$i]:iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', kpairiskpair)). 0.24/0.50 thf(iskpair, axiom, (iskpair)=(^[X4:$i]:?[X2:$i]:(in @ X2 @ (setunion @ X4)&?[X3:$i]:(in @ X3 @ (setunion @ X4)&(X4)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', iskpair)). 0.24/0.50 thf(kpairp, axiom, (kpairp<=>![X2:$i, X3:$i]:iskpair @ (kpair @ X2 @ X3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', kpairp)). 0.24/0.50 thf(cartprodmempair, axiom, (cartprodmempair<=>![X4:$i, X5:$i, X18:$i]:(in @ X18 @ (cartprod @ X4 @ X5)=>iskpair @ X18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodmempair)). 0.24/0.50 thf(singletonprop, axiom, (singletonprop<=>![X4:$i, X1:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(X1 @ X2=>(X1 @ X3=>(X2)=(X3)))))=>(?[X2:$i]:(in @ X2 @ X4&X1 @ X2)=>singleton @ (dsetconstr @ X4 @ (^[X2:$i]:X1 @ X2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletonprop)). 0.24/0.50 thf(ex1E1, axiom, (ex1E1<=>![X4:$i, X1:$i > $o]:(ex1 @ X4 @ (^[X2:$i]:X1 @ X2)=>?[X2:$i]:(in @ X2 @ X4&X1 @ X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ex1E1)). 0.24/0.50 thf(ex1I, axiom, (ex1I<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>(![X3:$i]:(in @ X3 @ X4=>(X1 @ X3=>(X3)=(X2)))=>ex1 @ X4 @ (^[X3:$i]:X1 @ X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ex1I)). 0.24/0.50 thf(ex1I2, axiom, (ex1I2<=>![X4:$i, X1:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(X1 @ X2=>(X1 @ X3=>(X2)=(X3)))))=>(?[X2:$i]:(in @ X2 @ X4&X1 @ X2)=>ex1 @ X4 @ (^[X2:$i]:X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ex1I2)). 0.24/0.50 thf(kfstsingleton, axiom, (kfstsingleton<=>![X18:$i]:(iskpair @ X18=>singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:in @ (setadjoin @ X2 @ emptyset) @ X18)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', kfstsingleton)). 0.24/0.50 thf(theprop, axiom, (theprop<=>![X21:$i]:(singleton @ X21=>in @ (setunion @ X21) @ X21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', theprop)). 0.24/0.50 thf(setukpairinjR1, conjecture, (setextAx=>(emptysetAx=>(setadjoinAx=>(powersetAx=>(setunionAx=>(omega0Ax=>(omegaSAx=>(((foundationAx=>(((dsetconstrI=>(dsetconstrEL=>(((((emptysetimpfalse=>(((((((nonemptyE1=>(((((setadjoinIR=>(setadjoinE=>(setadjoinOr=>(setoftrueEq=>(powersetI=>(((powersetE=>(setunionI=>((subPowSU=>(exuE2=>(nonemptyImpWitness=>(uniqinunit=>((eqinunit=>((upairsetE=>(upairsetIL=>((emptyE1=>((quantDeMorgan1=>((quantDeMorgan3=>((prop2setI=>(((((exuI3=>(exuI2=>(inCongP=>(in__Cong=>(((emptyset__Cong=>(setadjoin__Cong=>((((((((eqimpsubset2=>((subsetI2=>(emptysetsubset=>((subsetE2=>((notequalI1=>(((subsetTrans=>((setadjoinSub2=>(((((powersetE1=>((powersetsubset=>((sepSubset=>(binunionIL=>((binunionIR=>(binunionEcases=>(binunionE=>(binunionLsub=>((binintersectI=>((binintersectEL=>(binintersectLsub=>(((((binintersectRsub=>(binintersectSubset4=>(binintersectSubset1=>((setminusI=>(((setminusSubset2=>((setminusELneg=>((((setminusSubset1=>(symdiffE=>(symdiffI1=>(symdiffI2=>((((setukpairIL=>(((kpairp=>((singletoninpowerset=>((upairset2E=>((upairinpowunion=>(((ubforcartprodlem3=>(cartprodpairin=>(cartprodmempair1=>(cartprodmempair=>(setunionE2=>((((((((((kfstsingleton=>(((cartprodfstin=>(setukpairinjL2=>(setukpairinjL=>(setukpairinjR11=>(setukpairinjR12=>![X2:$i, X3:$i, X14:$i, X18:$i]:(((X3)=(X18)<=(X14)=(X18))<=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset))))))))<=kfstpairEq)<=theprop))<=setukpairinjL1)<=singletonsuniq)<=ex1I2)<=ex1I)<=ex1E1)<=singletonprop)<=setunionsingleton)<=setunionsingleton2)<=setunionsingleton1))))))<=ubforcartprodlem2)<=ubforcartprodlem1))<=upairsubunion))<=singletoninpowunion))<=singletonsubset))<=kpairiskpair)<=setukpairIR))<=secondinupair)<=symdiffIneg2)<=symdiffIneg1)))))<=setminusLsub)<=setminusIRneg)<=setminusILneg))<=setminusERneg))<=setminusER)<=setminusEL))<=bs114d))))<=disjointsetsI1)<=binintersectER)<=binintersectSubset3)<=binintersectSubset2)))<=binintersectSubset5))<=binunionRsub)))))<=upairset2IR)))<=sepInPowerset))<=inPowerset))<=powersetI1)<=subsetemptysetimpeq)<=setextsub)<=subset2powerset))<=setadjoinSub))<=subsetRefl)<=notequalI2))<=notsubsetI))<=subsetE)))<=eqimpsubset1))<=subsetI1)<=dsetconstr__Cong)<=descr__Cong)<=exuEu)<=omega__Cong)<=setunion__Cong)<=powerset__Cong)))<=exu__Cong)<=exuE3u)))))<=exuI1)<=notdallE)<=notdexE)<=prop2set2propI))<=quantDeMorgan4))<=quantDeMorgan2))<=vacuousDall))<=upairsetIR)))<=singletonsswitch))<=notinsingleton)))))<=setunionE)))<=emptyInPowerset)<=emptyinPowerset))))))<=emptyinunitempty)<=setadjoinIL)<=nonemptyI1)<=nonemptyI))<=setbeta)<=noeltsimpempty)<=emptyI)<=setext)<=exuE3e)<=notinemptyset))<=emptysetE)<=prop2setE)<=exuE1)<=dsetconstrER)))<=descrp)<=wellorderingAx))<=replAx)<=omegaIndAx)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairinjR1)). 0.24/0.50 thf(setextAx, axiom, (setextAx<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4<=>in @ X2 @ X5)=>(X4)=(X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setextAx)). 0.24/0.50 thf(emptysetAx, axiom, (emptysetAx<=>![X2:$i]:~(in @ X2 @ emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetAx)). 0.24/0.50 thf(setadjoinAx, axiom, (setadjoinAx<=>![X2:$i, X4:$i, X3:$i]:(in @ X3 @ (setadjoin @ X2 @ X4)<=>((X3)=(X2)|in @ X3 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinAx)). 0.24/0.50 thf(powersetAx, axiom, (powersetAx<=>![X4:$i, X5:$i]:(in @ X5 @ (powerset @ X4)<=>![X2:$i]:(in @ X2 @ X5=>in @ X2 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetAx)). 0.24/0.50 thf(setunionAx, axiom, (setunionAx<=>![X4:$i, X2:$i]:(in @ X2 @ (setunion @ X4)<=>?[X5:$i]:(in @ X2 @ X5&in @ X5 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionAx)). 0.24/0.50 thf(omega0Ax, axiom, (omega0Ax<=>in @ emptyset @ omega), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omega0Ax)). 0.24/0.50 thf(omegaSAx, axiom, (omegaSAx<=>![X2:$i]:(in @ X2 @ omega=>in @ (setadjoin @ X2 @ X2) @ omega)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omegaSAx)). 0.24/0.50 thf(omegaIndAx, axiom, (omegaIndAx<=>![X4:$i]:((in @ emptyset @ X4&![X2:$i]:((in @ X2 @ omega&in @ X2 @ X4)=>in @ (setadjoin @ X2 @ X2) @ X4))=>![X2:$i]:(in @ X2 @ omega=>in @ X2 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omegaIndAx)). 0.24/0.50 thf(foundationAx, axiom, (foundationAx<=>![X4:$i]:(?[X2:$i]:in @ X2 @ X4=>?[X5:$i]:(in @ X5 @ X4&~(?[X2:$i]:(in @ X2 @ X5&in @ X2 @ X4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', foundationAx)). 0.24/0.50 thf(wellorderingAx, axiom, (wellorderingAx<=>![X4:$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)). 0.24/0.50 thf(dsetconstrI, axiom, (dsetconstrI<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstrI)). 0.24/0.50 thf(dsetconstrEL, axiom, (dsetconstrEL<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))=>in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstrEL)). 0.24/0.50 thf(dsetconstrER, axiom, (dsetconstrER<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))=>X1 @ X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstrER)). 0.24/0.50 thf(prop2setE, axiom, (prop2setE<=>![X10:$o, X2:$i]:(in @ X2 @ (prop2set @ (X10))=>X10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prop2setE)). 0.24/0.50 thf(emptysetE, axiom, (emptysetE<=>![X2:$i]:(in @ X2 @ emptyset=>![X11:$o]:X11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetE)). 0.24/0.50 thf(emptysetimpfalse, axiom, (emptysetimpfalse<=>![X2:$i]:(in @ X2 @ emptyset=>~$true)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetimpfalse)). 0.24/0.50 thf(notinemptyset, axiom, (notinemptyset<=>![X2:$i]:~(in @ X2 @ emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notinemptyset)). 0.24/0.50 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)). 0.24/0.50 thf(emptyI, axiom, (emptyI<=>![X4:$i]:(![X2:$i]:~(in @ X2 @ X4)=>(X4)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyI)). 0.24/0.50 thf(noeltsimpempty, axiom, (noeltsimpempty<=>![X4:$i]:(![X2:$i]:~(in @ X2 @ X4)=>(X4)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', noeltsimpempty)). 0.24/0.50 thf(setbeta, axiom, (setbeta<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))<=>X1 @ X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setbeta)). 0.24/0.50 thf(setadjoinIL, axiom, (setadjoinIL<=>![X2:$i, X3:$i]:in @ X2 @ (setadjoin @ X2 @ X3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinIL)). 0.24/0.50 thf(emptyinunitempty, axiom, (emptyinunitempty<=>in @ emptyset @ (setadjoin @ emptyset @ emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyinunitempty)). 0.24/0.50 thf(setadjoinIR, axiom, (setadjoinIR<=>![X2:$i, X4:$i, X3:$i]:(in @ X3 @ X4=>in @ X3 @ (setadjoin @ X2 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinIR)). 0.24/0.50 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)). 0.24/0.50 thf(setadjoinOr, axiom, (setadjoinOr<=>![X2:$i, X4:$i, X3:$i]:(in @ X3 @ (setadjoin @ X2 @ X4)=>((X3)=(X2)|in @ X3 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinOr)). 0.24/0.50 thf(setoftrueEq, axiom, (setoftrueEq<=>![X4:$i]:(dsetconstr @ X4 @ (^[X2:$i]:$true))=(X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setoftrueEq)). 0.24/0.50 thf(powersetI, axiom, (powersetI<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X5=>in @ X2 @ X4)=>in @ X5 @ (powerset @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetI)). 0.24/0.50 thf(emptyinPowerset, axiom, (emptyinPowerset<=>![X4:$i]:in @ emptyset @ (powerset @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyinPowerset)). 0.24/0.50 thf(emptyInPowerset, axiom, (emptyInPowerset<=>![X4:$i]:in @ emptyset @ (powerset @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyInPowerset)). 0.24/0.50 thf(powersetE, axiom, (powersetE<=>![X4:$i, X5:$i, X2:$i]:(in @ X5 @ (powerset @ X4)=>(in @ X2 @ X5=>in @ X2 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetE)). 0.24/0.50 thf(setunionI, axiom, (setunionI<=>![X4:$i, X2:$i, X5:$i]:(in @ X2 @ X5=>(in @ X5 @ X4=>in @ X2 @ (setunion @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionI)). 0.24/0.50 thf(setunionE, axiom, (setunionE<=>![X4:$i, X2:$i]:(in @ X2 @ (setunion @ X4)=>![X13:$o]:(![X5:$i]:(in @ X2 @ X5=>(in @ X5 @ X4=>X13))=>X13))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionE)). 0.24/0.50 thf(subPowSU, axiom, (subPowSU<=>![X4:$i, X2:$i]:(in @ X2 @ X4=>in @ X2 @ (powerset @ (setunion @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subPowSU)). 0.24/0.50 thf(uniqinunit, axiom, (uniqinunit<=>![X2:$i, X3:$i]:(in @ X2 @ (setadjoin @ X3 @ emptyset)=>(X2)=(X3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', uniqinunit)). 0.24/0.50 thf(notinsingleton, axiom, (notinsingleton<=>![X2:$i, X3:$i]:((X2)!=(X3)=>~(in @ X3 @ (setadjoin @ X2 @ emptyset)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notinsingleton)). 0.24/0.50 thf(eqinunit, axiom, (eqinunit<=>![X2:$i, X3:$i]:((X2)=(X3)=>in @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqinunit)). 0.24/0.50 thf(singletonsswitch, axiom, (singletonsswitch<=>![X2:$i, X3:$i]:(in @ X2 @ (setadjoin @ X3 @ emptyset)=>in @ X3 @ (setadjoin @ X2 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletonsswitch)). 0.24/0.50 thf(upairsetE, axiom, (upairsetE<=>![X2:$i, X3:$i, X14:$i]:(in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=>((X14)=(X2)|(X14)=(X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsetE)). 0.24/0.50 thf(upairsetIL, axiom, (upairsetIL<=>![X2:$i, X3:$i]:in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsetIL)). 0.24/0.50 thf(upairsetIR, axiom, (upairsetIR<=>![X2:$i, X3:$i]:in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsetIR)). 0.24/0.50 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)). 0.24/0.50 thf(vacuousDall, axiom, (vacuousDall<=>![X1:$i > $o, X2:$i]:(in @ X2 @ emptyset=>X1 @ X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', vacuousDall)). 0.24/0.50 thf(quantDeMorgan1, axiom, (quantDeMorgan1<=>![X4:$i, X1:$i > $o]:(~(![X2:$i]:(in @ X2 @ X4=>X1 @ X2))=>?[X2:$i]:(in @ X2 @ X4&~(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan1)). 0.24/0.50 thf(quantDeMorgan2, axiom, (quantDeMorgan2<=>![X4:$i, X1:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>~(X1 @ X2))=>~(?[X2:$i]:(in @ X2 @ X4&X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan2)). 0.24/0.50 thf(quantDeMorgan3, axiom, (quantDeMorgan3<=>![X4:$i, X1:$i > $o]:(~(?[X2:$i]:(in @ X2 @ X4&X1 @ X2))=>![X2:$i]:(in @ X2 @ X4=>~(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan3)). 0.24/0.50 thf(quantDeMorgan4, axiom, (quantDeMorgan4<=>![X4:$i, X1:$i > $o]:(?[X2:$i]:(in @ X2 @ X4&~(X1 @ X2))=>~(![X2:$i]:(in @ X2 @ X4=>X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan4)). 0.24/0.50 thf(prop2setI, axiom, (prop2setI<=>![X15:$o]:(X15=>in @ emptyset @ (prop2set @ (X15)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prop2setI)). 0.24/0.50 thf(prop2set2propI, axiom, (prop2set2propI<=>![X16:$o]:(X16=>set2prop @ (prop2set @ (X16)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prop2set2propI)). 0.24/0.50 thf(notdexE, axiom, (notdexE<=>![X4:$i, X1:$i > $o]:(~(?[X2:$i]:(in @ X2 @ X4&X1 @ X2))=>![X2:$i]:(in @ X2 @ X4=>~(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notdexE)). 0.24/0.50 thf(notdallE, axiom, (notdallE<=>![X4:$i, X1:$i > $o]:(~(![X2:$i]:(in @ X2 @ X4=>X1 @ X2))=>?[X2:$i]:(in @ X2 @ X4&~(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notdallE)). 0.24/0.50 thf(inCongP, axiom, (inCongP<=>![X4:$i, X5:$i]:((X4)=(X5)=>![X2:$i, X3:$i]:((X2)=(X3)=>(in @ X2 @ X4=>in @ X3 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', inCongP)). 0.24/0.50 thf(in__Cong, axiom, (in__Cong<=>![X4:$i, X5:$i]:((X4)=(X5)=>![X2:$i, X3:$i]:((X2)=(X3)=>(in @ X2 @ X4<=>in @ X3 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', in__Cong)). 0.24/0.50 thf(emptyset__Cong, axiom, (emptyset__Cong<=>(emptyset)=(emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyset__Cong)). 0.24/0.50 thf(setadjoin__Cong, axiom, (setadjoin__Cong<=>![X2:$i, X3:$i]:((X2)=(X3)=>![X14:$i, X18:$i]:((X14)=(X18)=>(setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoin__Cong)). 0.24/0.50 thf(powerset__Cong, axiom, (powerset__Cong<=>![X4:$i, X5:$i]:((X4)=(X5)=>(powerset @ X4)=(powerset @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powerset__Cong)). 0.24/0.50 thf(setunion__Cong, axiom, (setunion__Cong<=>![X4:$i, X5:$i]:((X4)=(X5)=>(setunion @ X4)=(setunion @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunion__Cong)). 0.24/0.50 thf(omega__Cong, axiom, (omega__Cong<=>(omega)=(omega)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omega__Cong)). 0.24/0.50 thf(dsetconstr__Cong, axiom, (dsetconstr__Cong<=>![X4:$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:$i]:X17 @ X2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstr__Cong)). 0.24/0.50 thf(subsetI1, axiom, (subsetI1<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4=>in @ X2 @ X5)=>subset @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetI1)). 0.24/0.50 thf(eqimpsubset2, axiom, (eqimpsubset2<=>![X4:$i, X5:$i]:((X4)=(X5)=>subset @ X5 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqimpsubset2)). 0.24/0.50 thf(eqimpsubset1, axiom, (eqimpsubset1<=>![X4:$i, X5:$i]:((X4)=(X5)=>subset @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqimpsubset1)). 0.24/0.50 thf(subsetI2, axiom, (subsetI2<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4=>in @ X2 @ X5)=>subset @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetI2)). 0.24/0.50 thf(emptysetsubset, axiom, (emptysetsubset<=>![X4:$i]:subset @ emptyset @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetsubset)). 0.24/0.50 thf(subsetE, axiom, (subsetE<=>![X4:$i, X5:$i, X2:$i]:(subset @ X4 @ X5=>(in @ X2 @ X4=>in @ X2 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetE)). 0.24/0.50 thf(subsetE2, axiom, (subsetE2<=>![X4:$i, X5:$i, X2:$i]:(subset @ X4 @ X5=>(~(in @ X2 @ X5)=>~(in @ X2 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetE2)). 0.24/0.50 thf(notsubsetI, axiom, (notsubsetI<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X5)=>~(subset @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notsubsetI)). 0.24/0.50 thf(notequalI1, axiom, (notequalI1<=>![X4:$i, X5:$i]:(~(subset @ X4 @ X5)=>(X4)!=(X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notequalI1)). 0.24/0.50 thf(notequalI2, axiom, (notequalI2<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X5)=>(X4)!=(X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notequalI2)). 0.24/0.50 thf(subsetRefl, axiom, (subsetRefl<=>![X4:$i]:subset @ X4 @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetRefl)). 0.24/0.50 thf(subsetTrans, axiom, (subsetTrans<=>![X4:$i, X5:$i, X7:$i]:(subset @ X4 @ X5=>(subset @ X5 @ X7=>subset @ X4 @ X7))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetTrans)). 0.24/0.50 thf(setadjoinSub, axiom, (setadjoinSub<=>![X2:$i, X4:$i]:subset @ X4 @ (setadjoin @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinSub)). 0.24/0.50 thf(setadjoinSub2, axiom, (setadjoinSub2<=>![X4:$i, X2:$i, X5:$i]:(subset @ X4 @ X5=>subset @ X4 @ (setadjoin @ X2 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinSub2)). 0.24/0.50 thf(subset2powerset, axiom, (subset2powerset<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>in @ X4 @ (powerset @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subset2powerset)). 0.24/0.50 thf(setextsub, axiom, (setextsub<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>(subset @ X5 @ X4=>(X4)=(X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setextsub)). 0.24/0.50 thf(subsetemptysetimpeq, axiom, (subsetemptysetimpeq<=>![X4:$i]:(subset @ X4 @ emptyset=>(X4)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetemptysetimpeq)). 0.24/0.50 thf(powersetI1, axiom, (powersetI1<=>![X4:$i, X5:$i]:(subset @ X5 @ X4=>in @ X5 @ (powerset @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetI1)). 0.24/0.50 thf(powersetE1, axiom, (powersetE1<=>![X4:$i, X5:$i]:(in @ X5 @ (powerset @ X4)=>subset @ X5 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetE1)). 0.24/0.50 thf(inPowerset, axiom, (inPowerset<=>![X4:$i]:in @ X4 @ (powerset @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', inPowerset)). 0.24/0.50 thf(powersetsubset, axiom, (powersetsubset<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>subset @ (powerset @ X4) @ (powerset @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetsubset)). 0.24/0.50 thf(sepInPowerset, axiom, (sepInPowerset<=>![X4:$i, X1:$i > $o]:in @ (dsetconstr @ X4 @ (^[X2:$i]:X1 @ X2)) @ (powerset @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sepInPowerset)). 0.24/0.50 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)). 0.24/0.50 thf(binunionIL, axiom, (binunionIL<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>in @ X2 @ (binunion @ X4 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionIL)). 0.24/0.50 thf(upairset2IR, axiom, (upairset2IR<=>![X2:$i, X3:$i]:in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairset2IR)). 0.24/0.50 thf(binunionIR, axiom, (binunionIR<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X5=>in @ X2 @ (binunion @ X4 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionIR)). 0.24/0.50 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)). 0.24/0.50 thf(binunionE, axiom, (binunionE<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (binunion @ X4 @ X5)=>(in @ X2 @ X4|in @ X2 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionE)). 0.24/0.50 thf(binunionLsub, axiom, (binunionLsub<=>![X4:$i, X5:$i]:subset @ X4 @ (binunion @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionLsub)). 0.24/0.50 thf(binunionRsub, axiom, (binunionRsub<=>![X4:$i, X5:$i]:subset @ X5 @ (binunion @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionRsub)). 0.24/0.50 thf(binintersectI, axiom, (binintersectI<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X5=>in @ X2 @ (binintersect @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectI)). 0.24/0.50 thf(binintersectSubset5, axiom, (binintersectSubset5<=>![X4:$i, X5:$i, X7:$i]:(subset @ X7 @ X4=>(subset @ X7 @ X5=>subset @ X7 @ (binintersect @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset5)). 0.24/0.50 thf(binintersectEL, axiom, (binintersectEL<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (binintersect @ X4 @ X5)=>in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectEL)). 0.24/0.50 thf(binintersectLsub, axiom, (binintersectLsub<=>![X4:$i, X5:$i]:subset @ (binintersect @ X4 @ X5) @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectLsub)). 0.24/0.50 thf(binintersectSubset2, axiom, (binintersectSubset2<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>(binintersect @ X4 @ X5)=(X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset2)). 0.24/0.50 thf(binintersectSubset3, axiom, (binintersectSubset3<=>![X4:$i, X5:$i]:((binintersect @ X4 @ X5)=(X5)=>subset @ X5 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset3)). 0.24/0.50 thf(binintersectER, axiom, (binintersectER<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (binintersect @ X4 @ X5)=>in @ X2 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectER)). 0.24/0.50 thf(disjointsetsI1, axiom, (disjointsetsI1<=>![X4:$i, X5:$i]:(~(?[X2:$i]:(in @ X2 @ X4&in @ X2 @ X5))=>(binintersect @ X4 @ X5)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', disjointsetsI1)). 0.24/0.50 thf(binintersectRsub, axiom, (binintersectRsub<=>![X4:$i, X5:$i]:subset @ (binintersect @ X4 @ X5) @ X5), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectRsub)). 0.24/0.50 thf(binintersectSubset4, axiom, (binintersectSubset4<=>![X4:$i, X5:$i]:(subset @ X5 @ X4=>(binintersect @ X4 @ X5)=(X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset4)). 0.24/0.50 thf(binintersectSubset1, axiom, (binintersectSubset1<=>![X4:$i, X5:$i]:((binintersect @ X4 @ X5)=(X4)=>subset @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset1)). 0.24/0.50 thf(bs114d, axiom, (bs114d<=>![X4:$i, X5:$i, X7:$i]:(binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', bs114d)). 0.24/0.50 thf(setminusI, axiom, (setminusI<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X5)=>in @ X2 @ (setminus @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusI)). 0.24/0.50 thf(setminusEL, axiom, (setminusEL<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (setminus @ X4 @ X5)=>in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusEL)). 0.24/0.50 thf(setminusER, axiom, (setminusER<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (setminus @ X4 @ X5)=>~(in @ X2 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusER)). 0.24/0.50 thf(setminusSubset2, axiom, (setminusSubset2<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>(setminus @ X4 @ X5)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusSubset2)). 0.24/0.50 thf(setminusERneg, axiom, (setminusERneg<=>![X4:$i, X5:$i, X2:$i]:(~(in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4=>in @ X2 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusERneg)). 0.24/0.50 thf(setminusELneg, axiom, (setminusELneg<=>![X4:$i, X5:$i, X2:$i]:(~(in @ X2 @ (setminus @ X4 @ X5))=>(~(in @ X2 @ X5)=>~(in @ X2 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusELneg)). 0.24/0.50 thf(setminusILneg, axiom, (setminusILneg<=>![X4:$i, X5:$i, X2:$i]:(~(in @ X2 @ X4)=>~(in @ X2 @ (setminus @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusILneg)). 0.24/0.50 thf(setminusIRneg, axiom, (setminusIRneg<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X5=>~(in @ X2 @ (setminus @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusIRneg)). 0.24/0.50 thf(setminusLsub, axiom, (setminusLsub<=>![X4:$i, X5:$i]:subset @ (setminus @ X4 @ X5) @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusLsub)). 0.24/0.50 thf(setminusSubset1, axiom, (setminusSubset1<=>![X4:$i, X5:$i]:((setminus @ X4 @ X5)=(emptyset)=>subset @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusSubset1)). 0.24/0.50 thf(symdiffE, axiom, (symdiffE<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (symdiff @ X4 @ X5)=>![X20:$o]:((in @ X2 @ X4=>(~(in @ X2 @ X5)=>X20))=>((~(in @ X2 @ X4)=>(in @ X2 @ X5=>X20))=>X20)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', symdiffE)). 0.24/0.50 thf(symdiffI1, axiom, (symdiffI1<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X5)=>in @ X2 @ (symdiff @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', symdiffI1)). 0.24/0.50 thf(symdiffI2, axiom, (symdiffI2<=>![X4:$i, X5:$i, X2:$i]:(~(in @ X2 @ X4)=>(in @ X2 @ X5=>in @ X2 @ (symdiff @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', symdiffI2)). 0.24/0.50 thf(symdiffIneg1, axiom, (symdiffIneg1<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X5=>~(in @ X2 @ (symdiff @ X4 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', symdiffIneg1)). 0.24/0.50 thf(symdiffIneg2, axiom, (symdiffIneg2<=>![X4:$i, X5:$i, X2:$i]:(~(in @ X2 @ X4)=>(~(in @ X2 @ X5)=>~(in @ X2 @ (symdiff @ X4 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', symdiffIneg2)). 0.24/0.50 thf(secondinupair, axiom, (secondinupair<=>![X2:$i, X3:$i]:in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', secondinupair)). 0.24/0.50 thf(setukpairIL, axiom, (setukpairIL<=>![X2:$i, X3:$i]:in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairIL)). 0.24/0.50 thf(setukpairIR, axiom, (setukpairIR<=>![X2:$i, X3:$i]:in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairIR)). 0.24/0.50 thf(singletonsubset, axiom, (singletonsubset<=>![X4:$i, X2:$i]:(in @ X2 @ X4=>subset @ (setadjoin @ X2 @ emptyset) @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletonsubset)). 0.24/0.50 thf(singletoninpowerset, axiom, (singletoninpowerset<=>![X4:$i, X2:$i]:(in @ X2 @ X4=>in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletoninpowerset)). 0.24/0.50 thf(singletoninpowunion, axiom, (singletoninpowunion<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletoninpowunion)). 0.24/0.50 thf(upairset2E, axiom, (upairset2E<=>![X2:$i, X3:$i, X14:$i]:(in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=>((X14)=(X2)|(X14)=(X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairset2E)). 0.24/0.50 thf(upairsubunion, axiom, (upairsubunion<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsubunion)). 0.24/0.50 thf(upairinpowunion, axiom, (upairinpowunion<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairinpowunion)). 0.24/0.50 thf(ubforcartprodlem1, axiom, (ubforcartprodlem1<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ubforcartprodlem1)). 0.24/0.50 thf(ubforcartprodlem2, axiom, (ubforcartprodlem2<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ubforcartprodlem2)). 0.24/0.50 thf(ubforcartprodlem3, axiom, (ubforcartprodlem3<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ubforcartprodlem3)). 0.24/0.50 thf(cartprodpairin, axiom, (cartprodpairin<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodpairin)). 0.24/0.50 thf(cartprodmempair1, axiom, (cartprodmempair1<=>![X4:$i, X5:$i, X18:$i]:(in @ X18 @ (cartprod @ X4 @ X5)=>?[X2:$i]:(in @ X2 @ X4&?[X3:$i]:(in @ X3 @ X5&(X18)=(kpair @ X2 @ X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodmempair1)). 0.24/0.50 thf(setunionE2, axiom, (setunionE2<=>![X4:$i, X2:$i]:(in @ X2 @ (setunion @ X4)=>?[X21:$i]:(in @ X21 @ X4&in @ X2 @ X21))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionE2)). 0.24/0.50 thf(setunionsingleton1, axiom, (setunionsingleton1<=>![X4:$i]:subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionsingleton1)). 0.24/0.50 thf(setunionsingleton2, axiom, (setunionsingleton2<=>![X4:$i]:subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionsingleton2)). 0.24/0.50 thf(setunionsingleton, axiom, (setunionsingleton<=>![X2:$i]:(setunion @ (setadjoin @ X2 @ emptyset))=(X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionsingleton)). 0.24/0.50 thf(singletonsuniq, axiom, (singletonsuniq<=>![X2:$i, X3:$i]:((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset)=>(X2)=(X3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletonsuniq)). 0.24/0.50 thf(setukpairinjL1, axiom, (setukpairinjL1<=>![X2:$i, X3:$i, X14:$i]:(in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=>(X2)=(X14))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairinjL1)). 0.24/0.50 thf(kfstpairEq, axiom, (kfstpairEq<=>![X2:$i, X3:$i]:(kfst @ (kpair @ X2 @ X3))=(X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', kfstpairEq)). 0.24/0.50 thf(cartprodfstin, axiom, (cartprodfstin<=>![X4:$i, X5:$i, X18:$i]:(in @ X18 @ (cartprod @ X4 @ X5)=>in @ (kfst @ X18) @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodfstin)). 0.24/0.50 thf(setukpairinjL2, axiom, (setukpairinjL2<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset))=>(X2)=(X14))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairinjL2)). 0.24/0.50 thf(setukpairinjL, axiom, (setukpairinjL<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((kpair @ X2 @ X3)=(kpair @ X14 @ X18)=>(X2)=(X14))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairinjL)). 0.24/0.50 thf(setukpairinjR11, axiom, (setukpairinjR11<=>![X2:$i, X3:$i]:((X2)=(X3)=>(setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairinjR11)). 0.24/0.50 thf(setukpairinjR12, axiom, (setukpairinjR12<=>![X2:$i, X3:$i]:((X2)=(X3)=>(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairinjR12)). 0.24/0.50 thf(kpair, axiom, (kpair)=(^[X2:$i, X3:$i]:setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', kpair)). 0.24/0.50 thf(c_0_174, axiom, (ex1)=(^[X4:$i, X1:$i > $o]:?[X515:$i]:(in @ X515 @ (dsetconstr @ X4 @ (^[X2:$i]:X1 @ X2))&(dsetconstr @ X4 @ (^[X2:$i]:X1 @ X2))=(setadjoin @ X515 @ emptyset))), inference(apply_def,[status(thm)],[ex1, singleton])). 0.24/0.50 thf(c_0_175, axiom, (replAx)=(![X6:$i > $i > $o, X4:$i]:(![X2:$i]:(in @ X2 @ X4=>?[X479:$i]:(X6 @ X2 @ X479&![X481:$i]:(X6 @ X2 @ X481=>(X479)=(X481))))=>?[X5:$i]:![X2:$i]:(in @ X2 @ X5<=>?[X3:$i]:(in @ X3 @ X4&X6 @ X3 @ X2)))), inference(apply_def,[status(thm)],[replAx, exu])). 0.24/0.50 thf(c_0_176, axiom, (descrp)=(![X1:$i > $o]:(?[X482:$i]:(X1 @ X482&![X483:$i]:(X1 @ X483=>(X482)=(X483)))=>X1 @ (descr @ (^[X2:$i]:X1 @ X2)))), inference(apply_def,[status(thm)],[descrp, exu])). 0.24/0.50 thf(c_0_177, axiom, (exuE1)=(![X1:$i > $o]:(?[X484:$i]:(X1 @ X484&![X485:$i]:(X1 @ X485=>(X484)=(X485)))=>?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3))))), inference(apply_def,[status(thm)],[exuE1, exu])). 0.24/0.50 thf(c_0_178, axiom, (exuE3e)=(![X1:$i > $o]:(?[X486:$i]:(X1 @ X486&![X487:$i]:(X1 @ X487=>(X486)=(X487)))=>?[X2:$i]:X1 @ X2)), inference(apply_def,[status(thm)],[exuE3e, exu])). 0.24/0.50 thf(c_0_179, axiom, (nonemptyE1)=(![X4:$i]:((X4)!=(emptyset)=>?[X2:$i]:in @ X2 @ X4)), inference(apply_def,[status(thm)],[nonemptyE1, nonempty])). 0.24/0.50 thf(c_0_180, axiom, (nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>(dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))!=(emptyset)))), inference(apply_def,[status(thm)],[nonemptyI, nonempty])). 0.24/0.50 thf(c_0_181, axiom, (nonemptyI1)=(![X4:$i]:(?[X2:$i]:in @ X2 @ X4=>(X4)!=(emptyset))), inference(apply_def,[status(thm)],[nonemptyI1, nonempty])). 0.24/0.50 thf(c_0_182, axiom, (exuE2)=(![X1:$i > $o]:(?[X488:$i]:(X1 @ X488&![X489:$i]:(X1 @ X489=>(X488)=(X489)))=>?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2)))), inference(apply_def,[status(thm)],[exuE2, exu])). 0.24/0.50 thf(c_0_183, axiom, (nonemptyImpWitness)=(![X4:$i]:((X4)!=(emptyset)=>?[X2:$i]:(in @ X2 @ X4&$true))), inference(apply_def,[status(thm)],[nonemptyImpWitness, nonempty])). 0.24/0.50 thf(c_0_184, axiom, (exuI1)=(![X1:$i > $o]:(?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3)))=>?[X490:$i]:(X1 @ X490&![X491:$i]:(X1 @ X491=>(X490)=(X491))))), inference(apply_def,[status(thm)],[exuI1, exu])). 0.24/0.50 thf(c_0_185, axiom, (exuI3)=(![X1:$i > $o]:(?[X2:$i]:X1 @ X2=>(![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3)))=>?[X492:$i]:(X1 @ X492&![X493:$i]:(X1 @ X493=>(X492)=(X493)))))), inference(apply_def,[status(thm)],[exuI3, exu])). 0.24/0.50 thf(c_0_186, axiom, (exuI2)=(![X1:$i > $o]:(?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2))=>?[X494:$i]:(X1 @ X494&![X495:$i]:(X1 @ X495=>(X494)=(X495))))), inference(apply_def,[status(thm)],[exuI2, exu])). 0.24/0.50 thf(c_0_187, axiom, (exuE3u)=(![X1:$i > $o]:(?[X496:$i]:(X1 @ X496&![X497:$i]:(X1 @ X497=>(X496)=(X497)))=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))), inference(apply_def,[status(thm)],[exuE3u, exu])). 0.24/0.50 thf(c_0_188, axiom, (exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(?[X498:$i]:(X1 @ X498&![X499:$i]:(X1 @ X499=>(X498)=(X499)))<=>?[X500:$i]:(X17 @ X500&![X501:$i]:(X17 @ X501=>(X500)=(X501)))))), inference(apply_def,[status(thm)],[exu__Cong, exu])). 0.24/0.50 thf(c_0_189, axiom, (exuEu)=(![X1:$i > $o]:(?[X502:$i]:(X1 @ X502&![X503:$i]:(X1 @ X503=>(X502)=(X503)))=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))), inference(apply_def,[status(thm)],[exuEu, exu])). 0.24/0.50 thf(c_0_190, axiom, (descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(?[X504:$i]:(X1 @ X504&![X505:$i]:(X1 @ X505=>(X504)=(X505)))=>(?[X506:$i]:(X17 @ X506&![X507:$i]:(X17 @ X507=>(X506)=(X507)))=>(descr @ (^[X2:$i]:X1 @ X2))=(descr @ (^[X2:$i]:X17 @ X2)))))), inference(apply_def,[status(thm)],[descr__Cong, exu])). 0.24/0.50 thf(c_0_191, axiom, (kpairiskpair)=(![X2:$i, X3:$i]:?[X508:$i]:(in @ X508 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))&?[X509:$i]:(in @ X509 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))&(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X508 @ emptyset) @ (setadjoin @ (setadjoin @ X508 @ (setadjoin @ X509 @ emptyset)) @ emptyset))))), inference(apply_def,[status(thm)],[kpairiskpair, iskpair])). 0.24/0.50 thf(c_0_192, axiom, (kpairp)=(![X2:$i, X3:$i]:?[X510:$i]:(in @ X510 @ (setunion @ (kpair @ X2 @ X3))&?[X511:$i]:(in @ X511 @ (setunion @ (kpair @ X2 @ X3))&(kpair @ X2 @ X3)=(setadjoin @ (setadjoin @ X510 @ emptyset) @ (setadjoin @ (setadjoin @ X510 @ (setadjoin @ X511 @ emptyset)) @ emptyset))))), inference(apply_def,[status(thm)],[kpairp, iskpair])). 0.24/0.50 thf(c_0_193, axiom, (cartprodmempair)=(![X4:$i, X5:$i, X18:$i]:(in @ X18 @ (cartprod @ X4 @ X5)=>?[X512:$i]:(in @ X512 @ (setunion @ X18)&?[X513:$i]:(in @ X513 @ (setunion @ X18)&(X18)=(setadjoin @ (setadjoin @ X512 @ emptyset) @ (setadjoin @ (setadjoin @ X512 @ (setadjoin @ X513 @ emptyset)) @ emptyset)))))), inference(apply_def,[status(thm)],[cartprodmempair, iskpair])). 0.24/0.50 thf(c_0_194, axiom, (singletonprop)=(![X4:$i, X1:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(X1 @ X2=>(X1 @ X3=>(X2)=(X3)))))=>(?[X2:$i]:(in @ X2 @ X4&X1 @ X2)=>?[X514:$i]:(in @ X514 @ (dsetconstr @ X4 @ (^[X2:$i]:X1 @ X2))&(dsetconstr @ X4 @ (^[X2:$i]:X1 @ X2))=(setadjoin @ X514 @ emptyset))))), inference(apply_def,[status(thm)],[singletonprop, singleton])). 0.24/0.50 thf(c_0_195, axiom, (ex1E1)=(![X4:$i, X1:$i > $o]:(?[X516:$i]:(in @ X516 @ (dsetconstr @ X4 @ (^[X517:$i]:X1 @ X517))&(dsetconstr @ X4 @ (^[X518:$i]:X1 @ X518))=(setadjoin @ X516 @ emptyset))=>?[X2:$i]:(in @ X2 @ X4&X1 @ X2))), inference(apply_def,[status(thm)],[ex1E1, c_0_174])). 0.24/0.50 thf(c_0_196, axiom, (ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>(![X3:$i]:(in @ X3 @ X4=>(X1 @ X3=>(X3)=(X2)))=>?[X519:$i]:(in @ X519 @ (dsetconstr @ X4 @ (^[X520:$i]:X1 @ X520))&(dsetconstr @ X4 @ (^[X522:$i]:X1 @ X522))=(setadjoin @ X519 @ emptyset)))))), inference(apply_def,[status(thm)],[ex1I, c_0_174])). 0.24/0.50 thf(c_0_197, axiom, (ex1I2)=(![X4:$i, X1:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(X1 @ X2=>(X1 @ X3=>(X2)=(X3)))))=>(?[X2:$i]:(in @ X2 @ X4&X1 @ X2)=>?[X524:$i]:(in @ X524 @ (dsetconstr @ X4 @ (^[X525:$i]:X1 @ X525))&(dsetconstr @ X4 @ (^[X526:$i]:X1 @ X526))=(setadjoin @ X524 @ emptyset))))), inference(apply_def,[status(thm)],[ex1I2, c_0_174])). 0.24/0.50 thf(c_0_198, axiom, (kfstsingleton)=(![X18:$i]:(?[X527:$i]:(in @ X527 @ (setunion @ X18)&?[X528:$i]:(in @ X528 @ (setunion @ X18)&(X18)=(setadjoin @ (setadjoin @ X527 @ emptyset) @ (setadjoin @ (setadjoin @ X527 @ (setadjoin @ X528 @ emptyset)) @ emptyset))))=>?[X529:$i]:(in @ X529 @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:in @ (setadjoin @ X2 @ emptyset) @ X18))&(dsetconstr @ (setunion @ X18) @ (^[X2:$i]:in @ (setadjoin @ X2 @ emptyset) @ X18))=(setadjoin @ X529 @ emptyset)))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[kfstsingleton, iskpair]), singleton])). 0.24/0.50 thf(c_0_199, axiom, (theprop)=(![X21:$i]:(?[X530:$i]:(in @ X530 @ X21&(X21)=(setadjoin @ X530 @ emptyset))=>in @ (setunion @ X21) @ X21)), inference(apply_def,[status(thm)],[theprop, singleton])). 0.24/0.50 thf(c_0_200, plain, ![X3:$i, X1:$i > $o]:(epred1_2 @ X1 @ X3<=>X1 @ X3), introduced(definition)). 0.24/0.50 thf(c_0_201, plain, ![X2:$i, X18:$i]:(epred3_2 @ X18 @ X2<=>in @ (setadjoin @ X2 @ emptyset) @ X18), introduced(definition)). 0.24/0.50 thf(c_0_202, plain, ![X2:$i]:epred2_1 @ X2, inference(fof_simplification,[status(thm)],[introduced(definition)])). 0.24/0.50 thf(c_0_203, 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:$i]:(in @ X3 @ X9=>in @ X3 @ X8)|in @ X2 @ X9)))))), introduced(definition)). 0.24/0.50 thf(c_0_204, negated_conjecture, ~((![X4:$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:$i]:(in @ X2 @ X4=>?[X479:$i]:(X6 @ X2 @ X479&![X481:$i]:(X6 @ X2 @ X481=>(X479)=(X481))))=>?[X5:$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 > $o]:(?[X482:$i]:(X1 @ X482&![X483:$i]:(X1 @ X483=>(X482)=(X483)))=>X1 @ (descr @ (epred1_2 @ X1)))=>(![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>in @ X2 @ (dsetconstr @ X4 @ (epred1_2 @ X1))))=>(![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ (dsetconstr @ X4 @ (epred1_2 @ X1))=>in @ X2 @ X4)=>(![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ (dsetconstr @ X4 @ (epred1_2 @ X1))=>X1 @ X2)=>(![X1:$i > $o]:(?[X484:$i]:(X1 @ X484&![X485:$i]:(X1 @ X485=>(X484)=(X485)))=>?[X2:$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 > $o]:(?[X486:$i]:(X1 @ X486&![X487:$i]:(X1 @ X487=>(X486)=(X487)))=>?[X2:$i]:X1 @ X2)=>(![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4=>in @ X2 @ X5)=>(![X2:$i]:(in @ X2 @ X5=>in @ X2 @ X4)=>(X4)=(X5)))=>(![X4:$i]:(![X2:$i]:~in @ X2 @ X4=>(X4)=(emptyset))=>(![X4:$i]:(![X2:$i]:~in @ X2 @ X4=>(X4)=(emptyset))=>(![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (dsetconstr @ X4 @ (epred1_2 @ X1))<=>X1 @ X2))=>(![X4:$i]:((X4)!=(emptyset)=>?[X2:$i]:in @ X2 @ X4)=>(![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>(dsetconstr @ X4 @ (epred1_2 @ X1))!=(emptyset)))=>(![X4:$i]:(?[X2:$i]:in @ X2 @ X4=>(X4)!=(emptyset))=>(![X2:$i, X3:$i]:in @ X2 @ (setadjoin @ X2 @ X3)=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset)=>(![X2:$i, X4:$i, X3:$i]:(in @ X3 @ X4=>in @ X3 @ (setadjoin @ X2 @ X4))=>(![X2:$i, X4:$i, X3:$i]:(in @ X3 @ (setadjoin @ X2 @ X4)=>![X12:$o]:(((X3)=(X2)=>X12)=>((in @ X3 @ X4=>X12)=>X12)))=>(![X2:$i, X4:$i, X3:$i]:(in @ X3 @ (setadjoin @ X2 @ X4)=>((X3)=(X2)|in @ X3 @ X4))=>(![X4:$i]:(dsetconstr @ X4 @ epred2_1)=(X4)=>(![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X5=>in @ X2 @ X4)=>in @ X5 @ (powerset @ X4))=>(![X4:$i]:in @ emptyset @ (powerset @ X4)=>(![X4:$i]:in @ emptyset @ (powerset @ X4)=>(![X4:$i, X5:$i, X2:$i]:(in @ X5 @ (powerset @ X4)=>(in @ X2 @ X5=>in @ X2 @ X4))=>(![X4:$i, X2:$i, X5:$i]:(in @ X2 @ X5=>(in @ X5 @ X4=>in @ X2 @ (setunion @ X4)))=>(![X4:$i, X2:$i]:(in @ X2 @ (setunion @ X4)=>![X13:$o]:(![X5:$i]:(in @ X2 @ X5=>(in @ X5 @ X4=>X13))=>X13))=>(![X4:$i, X2:$i]:(in @ X2 @ X4=>in @ X2 @ (powerset @ (setunion @ X4)))=>(![X1:$i > $o]:(?[X488:$i]:(X1 @ X488&![X489:$i]:(X1 @ X489=>(X488)=(X489)))=>?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2)))=>(![X4:$i]:((X4)!=(emptyset)=>?[X2:$i]:in @ X2 @ X4)=>(![X2:$i, X3:$i]:(in @ X2 @ (setadjoin @ X3 @ emptyset)=>(X2)=(X3))=>(![X2:$i, X3:$i]:((X2)!=(X3)=>~in @ X3 @ (setadjoin @ X2 @ emptyset))=>(![X2:$i, X3:$i]:((X2)=(X3)=>in @ X2 @ (setadjoin @ X3 @ emptyset))=>(![X2:$i, X3:$i]:(in @ X2 @ (setadjoin @ X3 @ emptyset)=>in @ X3 @ (setadjoin @ X2 @ emptyset))=>(![X2:$i, X3:$i, X14:$i]:(in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=>((X14)=(X2)|(X14)=(X3)))=>(![X2:$i, X3:$i]:in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=>(![X2:$i, X3:$i]:in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=>(![X4:$i, X1:$i > $o]:(?[X2:$i]:(in @ X2 @ X4&X1 @ X2)=>(dsetconstr @ X4 @ (epred1_2 @ X1))!=(emptyset))=>(![X1:$i > $o, X2:$i]:(in @ X2 @ emptyset=>X1 @ X2)=>(![X4:$i, X1:$i > $o]:(~(![X2:$i]:(in @ X2 @ X4=>X1 @ X2))=>?[X2:$i]:(in @ X2 @ X4&~X1 @ X2))=>(![X4:$i, X1:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>~X1 @ X2)=>~(?[X2:$i]:(in @ X2 @ X4&X1 @ X2)))=>(![X4:$i, X1:$i > $o]:(~(?[X2:$i]:(in @ X2 @ X4&X1 @ X2))=>![X2:$i]:(in @ X2 @ X4=>~X1 @ X2))=>(![X4:$i, X1:$i > $o]:(?[X2:$i]:(in @ X2 @ X4&~X1 @ X2)=>~(![X2:$i]:(in @ X2 @ X4=>X1 @ X2)))=>(![X15:$o]:(X15=>((~X15|in @ emptyset @ (prop2set @ $true))&(X15|in @ emptyset @ (prop2set @ $false))))=>(![X16:$o]:(X16=>((~X16|set2prop @ (prop2set @ $true))&(X16|set2prop @ (prop2set @ $false))))=>(![X4:$i, X1:$i > $o]:(~(?[X2:$i]:(in @ X2 @ X4&X1 @ X2))=>![X2:$i]:(in @ X2 @ X4=>~X1 @ X2))=>(![X4:$i, X1:$i > $o]:(~(![X2:$i]:(in @ X2 @ X4=>X1 @ X2))=>?[X2:$i]:(in @ X2 @ X4&~X1 @ X2))=>(![X1:$i > $o]:(?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3)))=>?[X490:$i]:(X1 @ X490&![X491:$i]:(X1 @ X491=>(X490)=(X491))))=>(![X1:$i > $o]:(?[X2:$i]:X1 @ X2=>(![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3)))=>?[X492:$i]:(X1 @ X492&![X493:$i]:(X1 @ X493=>(X492)=(X493)))))=>(![X1:$i > $o]:(?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2))=>?[X494:$i]:(X1 @ X494&![X495:$i]:(X1 @ X495=>(X494)=(X495))))=>(![X4:$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 > $o]:(?[X496:$i]:(X1 @ X496&![X497:$i]:(X1 @ X497=>(X496)=(X497)))=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))=>(![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(?[X498:$i]:(X1 @ X498&![X499:$i]:(X1 @ X499=>(X498)=(X499)))<=>?[X500:$i]:(X17 @ X500&![X501:$i]:(X17 @ X501=>(X500)=(X501)))))=>((emptyset)=(emptyset)=>(![X2:$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 > $o]:(?[X502:$i]:(X1 @ X502&![X503:$i]:(X1 @ X503=>(X502)=(X503)))=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))=>(![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(?[X504:$i]:(X1 @ X504&![X505:$i]:(X1 @ X505=>(X504)=(X505)))=>(?[X506:$i]:(X17 @ X506&![X507:$i]:(X17 @ X507=>(X506)=(X507)))=>(descr @ (epred1_2 @ X1))=(descr @ (epred1_2 @ X17)))))=>(![X4:$i, X5:$i]:((X4)=(X5)=>![X1:$i > $o, X17:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))))=>(dsetconstr @ X4 @ (epred1_2 @ X1))=(dsetconstr @ X5 @ (epred1_2 @ X17))))=>(![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4=>in @ X2 @ X5)=>subset @ X4 @ X5)=>(![X4:$i, X5:$i]:((X4)=(X5)=>subset @ X5 @ X4)=>(![X4:$i, X5:$i]:((X4)=(X5)=>subset @ X4 @ X5)=>(![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4=>in @ X2 @ X5)=>subset @ X4 @ X5)=>(![X4:$i]:subset @ emptyset @ X4=>(![X4:$i, X5:$i, X2:$i]:(subset @ X4 @ X5=>(in @ X2 @ X4=>in @ X2 @ X5))=>(![X4:$i, X5:$i, X2:$i]:(subset @ X4 @ X5=>(~in @ X2 @ X5=>~in @ X2 @ X4))=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~in @ X2 @ X5=>~subset @ X4 @ X5))=>(![X4:$i, X5:$i]:(~subset @ X4 @ X5=>(X4)!=(X5))=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~in @ X2 @ X5=>(X4)!=(X5)))=>(![X4:$i]:subset @ X4 @ X4=>(![X4:$i, X5:$i, X7:$i]:(subset @ X4 @ X5=>(subset @ X5 @ X7=>subset @ X4 @ X7))=>(![X2:$i, X4:$i]:subset @ X4 @ (setadjoin @ X2 @ X4)=>(![X4:$i, X2:$i, X5:$i]:(subset @ X4 @ X5=>subset @ X4 @ (setadjoin @ X2 @ X5))=>(![X4:$i, X5:$i]:(subset @ X4 @ X5=>in @ X4 @ (powerset @ X5))=>(![X4:$i, X5:$i]:(subset @ X4 @ X5=>(subset @ X5 @ X4=>(X4)=(X5)))=>(![X4:$i]:(subset @ X4 @ emptyset=>(X4)=(emptyset))=>(![X4:$i, X5:$i]:(subset @ X5 @ X4=>in @ X5 @ (powerset @ X4))=>(![X4:$i, X5:$i]:(in @ X5 @ (powerset @ X4)=>subset @ X5 @ X4)=>(![X4:$i]:in @ X4 @ (powerset @ X4)=>(![X4:$i, X5:$i]:(subset @ X4 @ X5=>subset @ (powerset @ X4) @ (powerset @ X5))=>(![X4:$i, X1:$i > $o]:in @ (dsetconstr @ X4 @ (epred1_2 @ X1)) @ (powerset @ X4)=>(![X4:$i, X1:$i > $o]:subset @ (dsetconstr @ X4 @ (epred1_2 @ X1)) @ X4=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>in @ X2 @ (binunion @ X4 @ X5))=>(![X2:$i, X3:$i]:in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X5=>in @ X2 @ (binunion @ X4 @ X5))=>(![X4:$i, X5:$i, X2:$i, X19:$o]:(in @ X2 @ (binunion @ X4 @ X5)=>((in @ X2 @ X4=>X19)=>((in @ X2 @ X5=>X19)=>X19)))=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (binunion @ X4 @ X5)=>(in @ X2 @ X4|in @ X2 @ X5))=>(![X4:$i, X5:$i]:subset @ X4 @ (binunion @ X4 @ X5)=>(![X4:$i, X5:$i]:subset @ X5 @ (binunion @ X4 @ X5)=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X5=>in @ X2 @ (binintersect @ X4 @ X5)))=>(![X4:$i, X5:$i, X7:$i]:(subset @ X7 @ X4=>(subset @ X7 @ X5=>subset @ X7 @ (binintersect @ X4 @ X5)))=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (binintersect @ X4 @ X5)=>in @ X2 @ X4)=>(![X4:$i, X5:$i]:subset @ (binintersect @ X4 @ X5) @ X4=>(![X4:$i, X5:$i]:(subset @ X4 @ X5=>(binintersect @ X4 @ X5)=(X4))=>(![X4:$i, X5:$i]:((binintersect @ X4 @ X5)=(X5)=>subset @ X5 @ X4)=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (binintersect @ X4 @ X5)=>in @ X2 @ X5)=>(![X4:$i, X5:$i]:(~(?[X2:$i]:(in @ X2 @ X4&in @ X2 @ X5))=>(binintersect @ X4 @ X5)=(emptyset))=>(![X4:$i, X5:$i]:subset @ (binintersect @ X4 @ X5) @ X5=>(![X4:$i, X5:$i]:(subset @ X5 @ X4=>(binintersect @ X4 @ X5)=(X5))=>(![X4:$i, X5:$i]:((binintersect @ X4 @ X5)=(X4)=>subset @ X4 @ X5)=>(![X4:$i, X5:$i, X7:$i]:(binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~in @ X2 @ X5=>in @ X2 @ (setminus @ X4 @ X5)))=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (setminus @ X4 @ X5)=>in @ X2 @ X4)=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (setminus @ X4 @ X5)=>~in @ X2 @ X5)=>(![X4:$i, X5:$i]:(subset @ X4 @ X5=>(setminus @ X4 @ X5)=(emptyset))=>(![X4:$i, X5:$i, X2:$i]:(~in @ X2 @ (setminus @ X4 @ X5)=>(in @ X2 @ X4=>in @ X2 @ X5))=>(![X4:$i, X5:$i, X2:$i]:(~in @ X2 @ (setminus @ X4 @ X5)=>(~in @ X2 @ X5=>~in @ X2 @ X4))=>(![X4:$i, X5:$i, X2:$i]:(~in @ X2 @ X4=>~in @ X2 @ (setminus @ X4 @ X5))=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X5=>~in @ X2 @ (setminus @ X4 @ X5))=>(![X4:$i, X5:$i]:subset @ (setminus @ X4 @ X5) @ X4=>(![X4:$i, X5:$i]:((setminus @ X4 @ X5)=(emptyset)=>subset @ X4 @ X5)=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (symdiff @ X4 @ X5)=>![X20:$o]:((in @ X2 @ X4=>(~in @ X2 @ X5=>X20))=>((~in @ X2 @ X4=>(in @ X2 @ X5=>X20))=>X20)))=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~in @ X2 @ X5=>in @ X2 @ (symdiff @ X4 @ X5)))=>(![X4:$i, X5:$i, X2:$i]:(~in @ X2 @ X4=>(in @ X2 @ X5=>in @ X2 @ (symdiff @ X4 @ X5)))=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X5=>~in @ X2 @ (symdiff @ X4 @ X5)))=>(![X4:$i, X5:$i, X2:$i]:(~in @ X2 @ X4=>(~in @ X2 @ X5=>~in @ X2 @ (symdiff @ X4 @ X5)))=>(![X2:$i, X3:$i]:in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=>(![X2:$i, X3:$i]:in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>(![X2:$i, X3:$i]:in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>(![X2:$i, X3:$i]:?[X508:$i]:(in @ X508 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))&?[X509:$i]:(in @ X509 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))&(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X508 @ emptyset) @ (setadjoin @ (setadjoin @ X508 @ (setadjoin @ X509 @ emptyset)) @ emptyset))))=>(![X2:$i, X3:$i]:?[X510:$i]:(in @ X510 @ (setunion @ (kpair @ X2 @ X3))&?[X511:$i]:(in @ X511 @ (setunion @ (kpair @ X2 @ X3))&(kpair @ X2 @ X3)=(setadjoin @ (setadjoin @ X510 @ emptyset) @ (setadjoin @ (setadjoin @ X510 @ (setadjoin @ X511 @ emptyset)) @ emptyset))))=>(![X4:$i, X2:$i]:(in @ X2 @ X4=>subset @ (setadjoin @ X2 @ emptyset) @ X4)=>(![X4:$i, X2:$i]:(in @ X2 @ X4=>in @ (setadjoin @ X2 @ emptyset) 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X5)))))=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5)))))=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5)))=>(![X4:$i, X5:$i, X18:$i]:(in @ X18 @ (cartprod @ X4 @ X5)=>?[X2:$i]:(in @ X2 @ X4&?[X3:$i]:(in @ X3 @ X5&(X18)=(kpair @ X2 @ X3))))=>(![X4:$i, X5:$i, X18:$i]:(in @ X18 @ (cartprod @ X4 @ X5)=>?[X512:$i]:(in @ X512 @ (setunion @ X18)&?[X513:$i]:(in @ X513 @ (setunion @ X18)&(X18)=(setadjoin @ (setadjoin @ X512 @ emptyset) @ (setadjoin @ (setadjoin @ X512 @ (setadjoin @ X513 @ emptyset)) @ emptyset)))))=>(![X4:$i, X2:$i]:(in @ X2 @ (setunion @ X4)=>?[X21:$i]:(in @ X21 @ X4&in @ X2 @ X21))=>(![X4:$i]:subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4=>(![X4:$i]:subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))=>(![X2:$i]:(setunion @ (setadjoin @ X2 @ emptyset))=(X2)=>(![X4:$i, X1:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in 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X3:$i, X14:$i]:(in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=>(X2)=(X14))=>(![X18:$i]:(?[X527:$i]:(in @ X527 @ (setunion @ X18)&?[X528:$i]:(in @ X528 @ (setunion @ X18)&(X18)=(setadjoin @ (setadjoin @ X527 @ emptyset) @ (setadjoin @ (setadjoin @ X527 @ (setadjoin @ X528 @ emptyset)) @ emptyset))))=>?[X529:$i]:(in @ X529 @ (dsetconstr @ (setunion @ X18) @ (epred3_2 @ X18))&(dsetconstr @ (setunion @ X18) @ (epred3_2 @ X18))=(setadjoin @ X529 @ emptyset)))=>(![X21:$i]:(?[X530:$i]:(in @ X530 @ X21&(X21)=(setadjoin @ X530 @ emptyset))=>in @ (setunion @ X21) @ X21)=>(![X2:$i, X3:$i]:(kfst @ (kpair @ X2 @ X3))=(X2)=>(![X4:$i, X5:$i, X18:$i]:(in @ X18 @ (cartprod @ X4 @ X5)=>in @ (kfst @ X18) @ X4)=>(![X2:$i, X3:$i, X14:$i, X18:$i]:((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) 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setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_175]), foundationAx]), wellorderingAx]), c_0_176]), dsetconstrI]), dsetconstrEL]), dsetconstrER]), c_0_177]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_178]), setext]), emptyI]), noeltsimpempty]), setbeta]), c_0_179]), c_0_180]), c_0_181]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), setoftrueEq]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_182]), c_0_183]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), emptyE1]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_184]), c_0_185]), c_0_186]), inCongP]), in__Cong]), c_0_187]), c_0_188]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_189]), c_0_190]), dsetconstr__Cong]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), sepInPowerset]), sepSubset]), binunionIL]), upairset2IR]), binunionIR]), binunionEcases]), binunionE]), binunionLsub]), binunionRsub]), binintersectI]), binintersectSubset5]), binintersectEL]), binintersectLsub]), binintersectSubset2]), binintersectSubset3]), binintersectER]), disjointsetsI1]), binintersectRsub]), binintersectSubset4]), binintersectSubset1]), bs114d]), setminusI]), setminusEL]), setminusER]), setminusSubset2]), setminusERneg]), setminusELneg]), setminusILneg]), setminusIRneg]), setminusLsub]), setminusSubset1]), symdiffE]), symdiffI1]), symdiffI2]), symdiffIneg1]), symdiffIneg2]), secondinupair]), setukpairIL]), setukpairIR]), c_0_191]), c_0_192]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1]), c_0_193]), setunionE2]), setunionsingleton1]), setunionsingleton2]), setunionsingleton]), c_0_194]), c_0_195]), c_0_196]), c_0_197]), singletonsuniq]), setukpairinjL1]), c_0_198]), c_0_199]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), c_0_200]), c_0_200]), c_0_200]), c_0_200]), c_0_200]), c_0_200]), c_0_200]), c_0_200]), c_0_200]), c_0_200]), c_0_200]), c_0_200]), c_0_200]), c_0_200]), c_0_200]), c_0_200]), c_0_200]), c_0_201]), c_0_201]), c_0_200]), c_0_200]), c_0_202]), c_0_200]), c_0_200])])]), c_0_203])). 0.24/0.50 thf(c_0_205, negated_conjecture, ![X533:$i, X534:$i, X536:$i, X537:$i, X538:$i, X539:$i, X540:$i, X541:$i, X542:$i, X543:$i, X544:$i, X546:$i, X547:$i, X549:$i, X550:$i, X551:$i, X552:$i, X553:$i, X555:$i, X556:$i > $i > $o, X557:$i, X559:$i, X562:$i, X564:$i, X565:$i, X566:$i, X567:$i, X569:$i, X570:$i > $o, X571:$i, X573:$i, X574:$i > $o, X575:$i, X576:$i, X577:$i > $o, X578:$i, X579:$i, X580:$i > $o, X581:$i, X582:$i > $o, X583:$i, X586:$i, X587:$o, X588:$i, X589:$i, X590:$o, X591:$i, X592:$i, X593:$i > $o, X594:$i, X597:$i, X598:$i, X601:$i, X603:$i, X605:$i, X606:$i > $o, X607:$i, X608:$i, X610:$i, X611:$i > $o, X612:$i, X613:$i, X614:$i, X615:$i, X616:$i, X617:$i, X618:$i, X619:$i, X620:$i, X621:$i, X622:$i, X623:$o, X624:$i, X625:$i, X626:$i, X627:$i, X628:$i, X629:$i, X631:$i, X632:$i, X633:$i, X634:$i, X635:$i, X636:$i, X637:$i, X638:$i, X639:$i, X640:$i, X641:$o, X643:$i, X644:$i, X645:$i > $o, X646:$i, X649:$i, X650:$i, X651:$i, X653:$i, X654:$i, X655:$i, X656:$i, X657:$i, X658:$i, X659:$i, X660:$i, X661:$i, X662:$i, X663:$i, X664:$i, X665:$i, X666:$i, X667:$i, X668:$i, X669:$i > $o, X670:$i, X671:$i > $o, X672:$i, X673:$i, X674:$i > $o, X675:$i, X677:$i, X678:$i > $o, X680:$i, X681:$i, X682:$i > $o, X684:$i, X685:$i, X686:$i > $o, X687:$i, X689:$o, X690:$o, X691:$i, X692:$i > $o, X694:$i, X695:$i, X696:$i > $o, X697:$i, X699:$i > $o, X700:$i, X703:$i, X704:$i > $o, X705:$i, X709:$i, X710:$i > $o, X711:$i, X714:$i, X715:$i, X716:$i, X717:$i, X718:$i, X719:$i, X720:$i, X721:$i, X722:$i, X723:$i > $o, X724:$i, X726:$i, X727:$i, X728:$i > $o, X729:$i > $o, X732:$i, X735:$i, X736:$i, X739:$i, X740:$i, X741:$i, X742:$i, X743:$i, X744:$i, X745:$i, X746:$i, X747:$i, X748:$i > $o, X749:$i, X751:$i, X752:$i, X753:$i > $o, X754:$i > $o, X757:$i, X759:$i, X761:$i, X762:$i, X763:$i > $o, X764:$i > $o, X767:$i, X768:$i, X770:$i, X771:$i, X772:$i, X773:$i, X774:$i, X775:$i, X777:$i, X778:$i, X779:$i, X780:$i, X781:$i, X782:$i, X783:$i, X784:$i, X785:$i, X786:$i, X787:$i, X788:$i, X789:$i, X790:$i, X791:$i, X792:$i, X793:$i, X794:$i, X795:$i, X796:$i, X797:$i, X798:$i, X799:$i, X800:$i, X801:$i, X802:$i, X803:$i, X804:$i, X805:$i, X806:$i, X807:$i, X808:$i, X809:$i, X810:$i, X811:$i, X812:$i, X813:$i, X814:$i > $o, X815:$i, X816:$i > $o, X817:$i, X818:$i, X819:$i, X820:$i, X821:$i, X822:$i, X823:$i, X824:$i, X825:$i, X826:$i, X827:$i, X828:$o, X829:$i, X830:$i, X831:$i, X832:$i, X833:$i, X834:$i, X835:$i, X836:$i, X837:$i, X838:$i, X839:$i, X840:$i, X841:$i, X842:$i, X843:$i, X844:$i, X845:$i, X846:$i, X847:$i, X848:$i, X849:$i, X850:$i, X851:$i, X852:$i, X853:$i, X854:$i, X855:$i, X857:$i, X858:$i, X859:$i, X860:$i, X861:$i, X862:$i, X863:$i, X864:$i, X865:$i, X866:$i, X867:$i, X868:$i, X869:$i, X870:$i, X871:$i, X872:$i, X873:$i, X874:$i, X875:$i, X876:$i, X877:$i, X878:$i, X879:$i, X880:$i, X881:$i, X882:$i, X883:$i, X884:$i, X885:$i, X886:$i, X887:$i, X888:$i, X889:$i, X890:$i, X891:$i, X892:$i, X893:$i, X894:$i, X895:$i, X896:$o, X897:$i, X898:$i, X899:$i, X900:$i, X901:$i, X902:$i, X903:$i, X904:$i, X905:$i, X906:$i, X907:$i, X908:$i, X909:$i, X910:$i, X911:$i, X912:$i, X913:$i, X914:$i, X915:$i, X916:$i, X919:$i, X920:$i, X923:$i, X924:$i, X925:$i, X926:$i, X927:$i, X928:$i, X929:$i, X930:$i, X931:$i, X932:$i, X933:$i, X934:$i, X935:$i, X936:$i, X937:$i, X938:$i, X939:$i, X940:$i, X941:$i, X942:$i, X943:$i, X944:$i, X945:$i, X946:$i, X947:$i, X948:$i, X949:$i, X950:$i, X951:$i, X952:$i, X953:$i, X954:$i, X955:$i, X956:$i, X957:$i, X958:$i, X959:$i, X962:$i, X963:$i, X964:$i, X967:$i, X968:$i, X970:$i, X971:$i, X972:$i, X973:$i, X974:$i > $o, X977:$i, X979:$i, X980:$i > $o, X981:$i, X983:$i, X984:$i > $o, X985:$i, X988:$i, X989:$i > $o, X992:$i, X994:$i, X995:$i, X996:$i, X997:$i, X998:$i, X999:$i, X1000:$i, X1001:$i, X1003:$i, X1004:$i, X1005:$i, X1006:$i, X1007:$i, X1008:$i, X1009:$i, X1010:$i, X1011:$i, X1012:$i, X1013:$i, X1014:$i, X1015:$i, X1016:$i, X1017:$i, X1018:$i, X1019:$i, X1020:$i, X1021:$i]:(((~in @ (esk1_2 @ X533 @ X534) @ X533|~in @ (esk1_2 @ X533 @ X534) @ X534|(X533)=(X534))&(in @ (esk1_2 @ X533 @ X534) @ X533|in @ (esk1_2 @ X533 @ X534) @ X534|(X533)=(X534)))&(~in @ X536 @ emptyset&(((~in @ X539 @ (setadjoin @ X537 @ X538)|((X539)=(X537)|in @ X539 @ X538))&(((X539)!=(X537)|in @ X539 @ (setadjoin @ X537 @ X538))&(~in @ X539 @ X538|in @ X539 @ (setadjoin @ X537 @ X538))))&(((~in @ X541 @ (powerset @ X540)|(~in @ X542 @ X541|in @ X542 @ X540))&((in @ (esk2_2 @ X543 @ X544) @ X544|in @ X544 @ (powerset @ X543))&(~in @ (esk2_2 @ X543 @ X544) @ X543|in @ X544 @ (powerset @ X543))))&((((in @ X547 @ (esk3_2 @ X546 @ X547)|~in @ X547 @ (setunion @ X546))&(in @ (esk3_2 @ X546 @ X547) @ X546|~in @ X547 @ (setunion @ X546)))&(~in @ X550 @ X551|~in @ X551 @ X549|in @ X550 @ (setunion @ X549)))&(in @ emptyset @ omega&((~in @ X552 @ omega|in @ (setadjoin @ X552 @ X552) @ omega)&((((in @ (esk4_1 @ X553) @ omega|~in @ emptyset @ X553|(~in @ X555 @ omega|in @ X555 @ X553))&(in @ (esk4_1 @ X553) @ X553|~in @ emptyset @ X553|(~in @ X555 @ omega|in @ X555 @ X553)))&(~in @ (setadjoin @ (esk4_1 @ X553) @ (esk4_1 @ X553)) @ X553|~in @ emptyset @ X553|(~in @ X555 @ omega|in @ X555 @ X553)))&(((((in @ (esk8_3 @ X556 @ X557 @ X562) @ X557|~in @ X562 @ (esk7_2 @ X556 @ X557)|in @ (esk5_2 @ X556 @ X557) @ X557)&(X556 @ (esk8_3 @ X556 @ X557 @ X562) @ X562|~in @ X562 @ (esk7_2 @ X556 @ X557)|in @ (esk5_2 @ X556 @ X557) @ X557))&(~in @ X565 @ X557|~X556 @ X565 @ X564|in @ X564 @ (esk7_2 @ X556 @ X557)|in @ (esk5_2 @ X556 @ X557) @ X557))&((((in @ (esk8_3 @ X556 @ X557 @ X562) @ X557|~in @ X562 @ (esk7_2 @ X556 @ X557)|(X556 @ (esk5_2 @ X556 @ X557) @ (esk6_3 @ X556 @ X557 @ X559)|~X556 @ (esk5_2 @ X556 @ X557) @ X559))&(X556 @ (esk8_3 @ X556 @ X557 @ X562) @ X562|~in @ X562 @ (esk7_2 @ X556 @ X557)|(X556 @ (esk5_2 @ X556 @ X557) @ (esk6_3 @ X556 @ X557 @ X559)|~X556 @ (esk5_2 @ X556 @ X557) @ X559)))&(~in @ X565 @ X557|~X556 @ X565 @ X564|in @ X564 @ (esk7_2 @ X556 @ X557)|(X556 @ (esk5_2 @ X556 @ X557) @ (esk6_3 @ X556 @ X557 @ X559)|~X556 @ (esk5_2 @ X556 @ X557) @ X559)))&(((in @ (esk8_3 @ X556 @ X557 @ X562) @ X557|~in @ X562 @ (esk7_2 @ X556 @ X557)|((X559)!=(esk6_3 @ X556 @ X557 @ X559)|~X556 @ (esk5_2 @ X556 @ X557) @ X559))&(X556 @ (esk8_3 @ X556 @ X557 @ X562) @ X562|~in @ X562 @ (esk7_2 @ X556 @ X557)|((X559)!=(esk6_3 @ X556 @ X557 @ X559)|~X556 @ (esk5_2 @ X556 @ X557) @ X559)))&(~in @ X565 @ X557|~X556 @ X565 @ X564|in @ X564 @ (esk7_2 @ X556 @ X557)|((X559)!=(esk6_3 @ X556 @ X557 @ X559)|~X556 @ (esk5_2 @ X556 @ X557) @ X559)))))&(((in @ (esk9_1 @ X566) @ X566|~in @ X567 @ X566)&(~in @ X569 @ (esk9_1 @ X566)|~in @ X569 @ X566|~in @ X567 @ X566))&(epred4_0&(((X570 @ (esk10_2 @ X570 @ X571)|~X570 @ X571|X570 @ (descr @ (epred1_2 @ X570)))&((X571)!=(esk10_2 @ X570 @ X571)|~X570 @ X571|X570 @ (descr @ (epred1_2 @ X570))))&((~in @ X575 @ X573|(~X574 @ X575|in @ X575 @ (dsetconstr @ X573 @ (epred1_2 @ X574))))&((~in @ X578 @ (dsetconstr @ X576 @ (epred1_2 @ X577))|in @ X578 @ X576)&((~in @ X581 @ (dsetconstr @ X579 @ (epred1_2 @ X580))|X580 @ X581)&((((X582 @ (esk12_1 @ X582)|(X582 @ (esk11_2 @ X582 @ X583)|~X582 @ X583))&(~X582 @ X586|(esk12_1 @ X582)=(X586)|(X582 @ (esk11_2 @ X582 @ X583)|~X582 @ X583)))&((X582 @ (esk12_1 @ X582)|((X583)!=(esk11_2 @ X582 @ X583)|~X582 @ X583))&(~X582 @ X586|(esk12_1 @ X582)=(X586)|((X583)!=(esk11_2 @ X582 @ X583)|~X582 @ X583))))&((((~X587|X587|X587)&(~in @ X588 @ (prop2set @ $false)|X587|X587))&((~X587|~in @ X588 @ (prop2set @ $true)|X587)&(~in @ X588 @ (prop2set @ $false)|~in @ X588 @ (prop2set @ $true)|X587)))&((~in @ X589 @ emptyset|X590)&(~in @ X591 @ emptyset&(~in @ X592 @ emptyset&(((X593 @ (esk13_2 @ X593 @ X594)|~X593 @ X594|X593 @ (esk14_1 @ X593))&((X594)!=(esk13_2 @ X593 @ X594)|~X593 @ X594|X593 @ (esk14_1 @ X593)))&((((in @ (esk16_2 @ X597 @ X598) @ X598|(X597)=(X598)|in @ (esk15_2 @ X597 @ X598) @ X597)&(~in @ (esk16_2 @ X597 @ X598) @ X597|(X597)=(X598)|in @ (esk15_2 @ X597 @ X598) @ X597))&((in @ (esk16_2 @ X597 @ X598) @ X598|(X597)=(X598)|~in @ (esk15_2 @ X597 @ X598) @ X598)&(~in @ (esk16_2 @ X597 @ X598) @ X597|(X597)=(X598)|~in @ (esk15_2 @ X597 @ X598) @ X598)))&((in @ (esk17_1 @ X601) @ X601|(X601)=(emptyset))&((in @ (esk18_1 @ X603) @ X603|(X603)=(emptyset))&(((~in @ X607 @ (dsetconstr @ X605 @ (epred1_2 @ X606))|X606 @ X607|~in @ X607 @ X605)&(~X606 @ X607|in @ X607 @ (dsetconstr @ X605 @ (epred1_2 @ X606))|~in @ X607 @ X605))&(((X608)=(emptyset)|in @ (esk19_1 @ X608) @ X608)&((~in @ X612 @ X610|(~X611 @ X612|(dsetconstr @ X610 @ (epred1_2 @ X611))!=(emptyset)))&((~in @ X614 @ X613|(X613)!=(emptyset))&(in @ X615 @ (setadjoin @ X615 @ X616)&(in @ emptyset @ (setadjoin @ emptyset @ emptyset)&((~in @ X619 @ X618|in @ X619 @ (setadjoin @ X617 @ X618))&((((in @ X622 @ X621|X623|(X622)=(X620)|~in @ X622 @ (setadjoin @ X620 @ X621))&(~X623|X623|(X622)=(X620)|~in @ X622 @ (setadjoin @ X620 @ X621)))&((in @ X622 @ X621|X623|~X623|~in @ X622 @ (setadjoin @ X620 @ X621))&(~X623|X623|~X623|~in @ X622 @ (setadjoin @ X620 @ X621))))&((~in @ X626 @ (setadjoin @ X624 @ X625)|((X626)=(X624)|in @ X626 @ X625))&((dsetconstr @ X627 @ epred2_1)=(X627)&(((in @ (esk20_2 @ X628 @ X629) @ X629|in @ X629 @ (powerset @ X628))&(~in @ (esk20_2 @ X628 @ X629) @ X628|in @ X629 @ (powerset @ X628)))&(in @ emptyset @ (powerset @ X631)&(in @ emptyset @ (powerset @ X632)&((~in @ X634 @ (powerset @ X633)|(~in @ X635 @ X634|in @ X635 @ X633))&((~in @ X637 @ X638|(~in @ X638 @ X636|in @ X637 @ (setunion @ X636)))&(((in @ X640 @ (esk21_3 @ X639 @ X640 @ X641)|X641|~in @ X640 @ (setunion @ X639))&((in @ (esk21_3 @ X639 @ X640 @ X641) @ X639|X641|~in @ X640 @ (setunion @ X639))&(~X641|X641|~in @ X640 @ (setunion @ X639))))&((~in @ X644 @ X643|in @ X644 @ (powerset @ (setunion @ X643)))&((((~X645 @ X649|(X649)=(esk23_1 @ X645)|(X645 @ (esk22_2 @ X645 @ X646)|~X645 @ X646))&((X650)!=(esk23_1 @ X645)|X645 @ X650|(X645 @ (esk22_2 @ X645 @ X646)|~X645 @ X646)))&((~X645 @ X649|(X649)=(esk23_1 @ X645)|((X646)!=(esk22_2 @ X645 @ X646)|~X645 @ X646))&((X650)!=(esk23_1 @ X645)|X645 @ X650|((X646)!=(esk22_2 @ X645 @ X646)|~X645 @ X646))))&(((X651)=(emptyset)|in @ (esk24_1 @ X651) @ X651)&((~in @ X653 @ (setadjoin @ X654 @ emptyset)|(X653)=(X654))&(((X655)=(X656)|~in @ X656 @ (setadjoin @ X655 @ emptyset))&(((X657)!=(X658)|in @ X657 @ (setadjoin @ X658 @ emptyset))&((~in @ X659 @ (setadjoin @ X660 @ emptyset)|in @ X660 @ (setadjoin @ X659 @ emptyset))&((~in @ X663 @ (setadjoin @ X661 @ (setadjoin @ X662 @ emptyset))|((X663)=(X661)|(X663)=(X662)))&(in @ X664 @ (setadjoin @ X664 @ (setadjoin @ X665 @ emptyset))&(in @ X667 @ (setadjoin @ X666 @ (setadjoin @ X667 @ emptyset))&((~in @ X670 @ X668|~X669 @ X670|(dsetconstr @ X668 @ (epred1_2 @ X669))!=(emptyset))&((~in @ X672 @ emptyset|X671 @ X672)&(((in @ (esk25_2 @ X673 @ X674) @ X673|(~in @ X675 @ X673|X674 @ X675))&(~X674 @ (esk25_2 @ X673 @ X674)|(~in @ X675 @ X673|X674 @ X675)))&(((in @ (esk26_2 @ X677 @ X678) @ X677|(~in @ X680 @ X677|~X678 @ X680))&(X678 @ (esk26_2 @ X677 @ X678)|(~in @ X680 @ X677|~X678 @ X680)))&(((in @ (esk27_2 @ X681 @ X682) @ X681|(~in @ X684 @ X681|~X682 @ X684))&(X682 @ (esk27_2 @ X681 @ X682)|(~in @ X684 @ X681|~X682 @ X684)))&(((in @ (esk28_2 @ X685 @ X686) @ X685|(~in @ X687 @ X685|X686 @ X687))&(~X686 @ (esk28_2 @ X685 @ X686)|(~in @ X687 @ X685|X686 @ X687)))&(((~X689|in @ emptyset @ (prop2set @ $true)|~X689)&(X689|in @ emptyset @ (prop2set @ $false)|~X689))&(((~X690|set2prop @ (prop2set @ $true)|~X690)&(X690|set2prop @ (prop2set @ $false)|~X690))&(((in @ (esk29_2 @ X691 @ X692) @ X691|(~in @ X694 @ X691|~X692 @ X694))&(X692 @ (esk29_2 @ X691 @ X692)|(~in @ X694 @ X691|~X692 @ X694)))&(((in @ (esk30_2 @ X695 @ X696) @ X695|(~in @ X697 @ X695|X696 @ X697))&(~X696 @ (esk30_2 @ X695 @ X696)|(~in @ X697 @ X695|X696 @ X697)))&((((X699 @ (esk32_1 @ X699)|(X699 @ (esk31_2 @ X699 @ X700)|~X699 @ X700))&(~X699 @ X703|(esk32_1 @ X699)=(X703)|(X699 @ (esk31_2 @ X699 @ X700)|~X699 @ X700)))&((X699 @ (esk32_1 @ X699)|((X700)!=(esk31_2 @ X699 @ X700)|~X699 @ X700))&(~X699 @ X703|(esk32_1 @ X699)=(X703)|((X700)!=(esk31_2 @ X699 @ X700)|~X699 @ X700))))&((((X704 @ (esk35_1 @ X704)|X704 @ (esk33_1 @ X704)|~X704 @ X705)&(~X704 @ X709|(esk35_1 @ X704)=(X709)|X704 @ (esk33_1 @ X704)|~X704 @ X705))&(((X704 @ (esk35_1 @ X704)|X704 @ (esk34_1 @ X704)|~X704 @ X705)&(~X704 @ X709|(esk35_1 @ X704)=(X709)|X704 @ (esk34_1 @ X704)|~X704 @ X705))&((X704 @ (esk35_1 @ X704)|(esk33_1 @ X704)!=(esk34_1 @ X704)|~X704 @ X705)&(~X704 @ X709|(esk35_1 @ X704)=(X709)|(esk33_1 @ X704)!=(esk34_1 @ X704)|~X704 @ X705))))&((((X710 @ (esk37_1 @ X710)|(~X710 @ (esk36_2 @ X710 @ X711)|(esk36_2 @ X710 @ X711)!=(X711)))&(~X710 @ X714|(esk37_1 @ X710)=(X714)|(~X710 @ (esk36_2 @ X710 @ X711)|(esk36_2 @ X710 @ X711)!=(X711))))&((X710 @ (esk37_1 @ X710)|(X710 @ (esk36_2 @ X710 @ X711)|(esk36_2 @ X710 @ X711)=(X711)))&(~X710 @ X714|(esk37_1 @ X710)=(X714)|(X710 @ (esk36_2 @ X710 @ X711)|(esk36_2 @ X710 @ X711)=(X711)))))&(((X715)!=(X716)|((X717)!=(X718)|(~in @ X717 @ X715|in @ X718 @ X716)))&(((~in @ X721 @ 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X895 @ (symdiff @ X893 @ X894))&((in @ X895 @ X894|X896|~X896|~in @ X895 @ (symdiff @ X893 @ X894))&(~X896|X896|~X896|~in @ X895 @ (symdiff @ X893 @ X894))))))&((~in @ X899 @ X897|(in @ X899 @ X898|in @ X899 @ (symdiff @ X897 @ X898)))&((in @ X902 @ X900|(~in @ X902 @ X901|in @ X902 @ (symdiff @ X900 @ X901)))&((~in @ X905 @ X903|(~in @ X905 @ X904|~in @ X905 @ (symdiff @ X903 @ X904)))&((in @ X908 @ X906|(in @ X908 @ X907|~in @ X908 @ (symdiff @ X906 @ X907)))&(in @ X910 @ (setadjoin @ X909 @ (setadjoin @ X910 @ emptyset))&(in @ X911 @ (setunion @ (setadjoin @ (setadjoin @ X911 @ emptyset) @ (setadjoin @ (setadjoin @ X911 @ (setadjoin @ X912 @ emptyset)) @ emptyset)))&(in @ X914 @ (setunion @ (setadjoin @ (setadjoin @ X913 @ emptyset) @ (setadjoin @ (setadjoin @ X913 @ (setadjoin @ X914 @ emptyset)) @ emptyset)))&((in @ (esk55_2 @ X915 @ X916) @ (setunion @ (setadjoin @ (setadjoin @ X915 @ emptyset) @ (setadjoin @ (setadjoin @ X915 @ (setadjoin @ X916 @ emptyset)) @ emptyset)))&(in @ (esk56_2 @ X915 @ X916) @ (setunion @ (setadjoin @ (setadjoin @ X915 @ emptyset) @ (setadjoin @ (setadjoin @ X915 @ (setadjoin @ X916 @ emptyset)) @ emptyset)))&(setadjoin @ (setadjoin @ X915 @ emptyset) @ (setadjoin @ (setadjoin @ X915 @ (setadjoin @ X916 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ (esk55_2 @ X915 @ X916) @ emptyset) @ (setadjoin @ (setadjoin @ (esk55_2 @ X915 @ X916) @ (setadjoin @ (esk56_2 @ X915 @ X916) @ emptyset)) @ emptyset))))&((in @ (esk57_2 @ X919 @ X920) @ (setunion @ (kpair @ X919 @ X920))&(in @ (esk58_2 @ X919 @ X920) @ (setunion @ (kpair @ X919 @ X920))&(kpair @ X919 @ X920)=(setadjoin @ (setadjoin @ (esk57_2 @ X919 @ X920) @ emptyset) @ (setadjoin @ (setadjoin @ (esk57_2 @ X919 @ X920) @ (setadjoin @ (esk58_2 @ X919 @ X920) @ emptyset)) @ emptyset))))&((~in @ X924 @ X923|subset @ (setadjoin @ X924 @ emptyset) @ X923)&((~in @ X926 @ X925|in @ (setadjoin @ X926 @ emptyset) @ (powerset @ X925))&((~in @ X929 @ X927|in @ (setadjoin @ X929 @ emptyset) @ (powerset @ (binunion @ X927 @ X928)))&((~in @ X932 @ (setadjoin @ X930 @ (setadjoin @ X931 @ emptyset))|((X932)=(X930)|(X932)=(X931)))&((~in @ X935 @ X933|(~in @ X936 @ X934|subset @ (setadjoin @ X935 @ (setadjoin @ X936 @ emptyset)) @ (binunion @ X933 @ X934)))&((~in @ X939 @ X937|(~in @ X940 @ X938|in @ (setadjoin @ X939 @ (setadjoin @ X940 @ emptyset)) @ (powerset @ (binunion @ X937 @ X938))))&((~in @ X943 @ X941|(~in @ X944 @ X942|subset @ (setadjoin @ (setadjoin @ X943 @ emptyset) @ (setadjoin @ (setadjoin @ X943 @ (setadjoin @ X944 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X941 @ X942))))&((~in @ X947 @ X945|(~in @ X948 @ X946|in @ (setadjoin @ (setadjoin @ X947 @ emptyset) @ (setadjoin @ (setadjoin @ X947 @ (setadjoin @ X948 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X945 @ X946)))))&((~in @ X951 @ X949|(~in @ X952 @ X950|in @ (kpair @ X951 @ X952) @ (powerset @ (powerset @ (binunion @ X949 @ X950)))))&((~in @ X955 @ X953|(~in @ X956 @ X954|in @ (kpair @ X955 @ X956) @ (cartprod @ X953 @ X954)))&(((in @ (esk59_3 @ X957 @ X958 @ X959) @ X957|~in @ X959 @ (cartprod @ X957 @ X958))&((in @ (esk60_3 @ X957 @ X958 @ X959) @ X958|~in @ X959 @ (cartprod @ X957 @ X958))&((X959)=(kpair @ (esk59_3 @ X957 @ X958 @ X959) @ (esk60_3 @ X957 @ X958 @ X959))|~in @ X959 @ (cartprod @ X957 @ X958))))&(((in @ (esk61_3 @ X962 @ X963 @ X964) @ (setunion @ X964)|~in @ X964 @ (cartprod @ X962 @ X963))&((in @ (esk62_3 @ X962 @ X963 @ X964) @ (setunion @ X964)|~in @ X964 @ (cartprod @ X962 @ X963))&((X964)=(setadjoin @ (setadjoin @ (esk61_3 @ X962 @ X963 @ X964) @ emptyset) @ (setadjoin @ (setadjoin @ (esk61_3 @ X962 @ X963 @ X964) @ (setadjoin @ (esk62_3 @ X962 @ X963 @ X964) @ emptyset)) @ emptyset))|~in @ X964 @ (cartprod @ X962 @ X963))))&(((in @ (esk63_2 @ X967 @ X968) @ X967|~in @ X968 @ (setunion @ X967))&(in @ X968 @ (esk63_2 @ X967 @ X968)|~in @ X968 @ (setunion @ X967)))&(subset @ (setunion @ (setadjoin @ X970 @ emptyset)) @ X970&(subset @ X971 @ (setunion @ (setadjoin @ X971 @ emptyset))&((setunion @ (setadjoin @ X972 @ emptyset))=(X972)&((((in @ (esk66_2 @ X973 @ X974) @ (dsetconstr @ X973 @ (epred1_2 @ X974))|(~in @ X977 @ X973|~X974 @ X977)|in @ (esk64_2 @ X973 @ X974) @ X973)&((dsetconstr @ X973 @ (epred1_2 @ X974))=(setadjoin @ (esk66_2 @ X973 @ X974) @ emptyset)|(~in @ X977 @ X973|~X974 @ X977)|in @ (esk64_2 @ X973 @ X974) @ X973))&(((in @ (esk66_2 @ X973 @ X974) @ (dsetconstr @ X973 @ (epred1_2 @ X974))|(~in @ X977 @ X973|~X974 @ X977)|in @ (esk65_2 @ X973 @ X974) @ X973)&((dsetconstr @ X973 @ (epred1_2 @ X974))=(setadjoin @ (esk66_2 @ X973 @ X974) @ emptyset)|(~in @ X977 @ X973|~X974 @ X977)|in @ (esk65_2 @ X973 @ X974) @ X973))&(((in @ (esk66_2 @ X973 @ X974) @ (dsetconstr @ X973 @ (epred1_2 @ X974))|(~in @ X977 @ X973|~X974 @ X977)|X974 @ (esk64_2 @ X973 @ X974))&((dsetconstr @ X973 @ (epred1_2 @ X974))=(setadjoin @ (esk66_2 @ X973 @ X974) @ emptyset)|(~in @ X977 @ X973|~X974 @ X977)|X974 @ (esk64_2 @ X973 @ X974)))&(((in @ (esk66_2 @ X973 @ X974) @ (dsetconstr @ X973 @ (epred1_2 @ X974))|(~in @ X977 @ X973|~X974 @ X977)|X974 @ (esk65_2 @ X973 @ X974))&((dsetconstr @ X973 @ (epred1_2 @ X974))=(setadjoin @ (esk66_2 @ X973 @ X974) @ emptyset)|(~in @ X977 @ X973|~X974 @ X977)|X974 @ (esk65_2 @ X973 @ X974)))&((in @ (esk66_2 @ X973 @ X974) @ (dsetconstr @ X973 @ (epred1_2 @ X974))|(~in @ X977 @ X973|~X974 @ X977)|(esk64_2 @ X973 @ X974)!=(esk65_2 @ X973 @ X974))&((dsetconstr @ X973 @ (epred1_2 @ X974))=(setadjoin @ (esk66_2 @ X973 @ X974) @ emptyset)|(~in @ X977 @ X973|~X974 @ X977)|(esk64_2 @ X973 @ X974)!=(esk65_2 @ X973 @ X974)))))))&(((in @ (esk67_2 @ X979 @ X980) @ X979|(~in @ X981 @ (dsetconstr @ X979 @ (epred1_2 @ X980))|(dsetconstr @ X979 @ (epred1_2 @ X980))!=(setadjoin @ X981 @ emptyset)))&(X980 @ (esk67_2 @ X979 @ X980)|(~in @ X981 @ (dsetconstr @ X979 @ (epred1_2 @ X980))|(dsetconstr @ X979 @ (epred1_2 @ X980))!=(setadjoin @ X981 @ emptyset))))&((((in @ (esk69_3 @ X983 @ X984 @ X985) @ (dsetconstr @ X983 @ (epred1_2 @ X984))|in @ (esk68_3 @ X983 @ X984 @ X985) @ X983|~X984 @ X985|~in @ X985 @ X983)&((dsetconstr @ X983 @ (epred1_2 @ X984))=(setadjoin @ (esk69_3 @ X983 @ X984 @ X985) @ emptyset)|in @ (esk68_3 @ X983 @ X984 @ X985) @ X983|~X984 @ X985|~in @ X985 @ X983))&(((in @ (esk69_3 @ X983 @ X984 @ X985) @ (dsetconstr @ X983 @ (epred1_2 @ X984))|X984 @ (esk68_3 @ X983 @ X984 @ X985)|~X984 @ X985|~in @ X985 @ X983)&((dsetconstr @ X983 @ (epred1_2 @ X984))=(setadjoin @ (esk69_3 @ X983 @ X984 @ X985) @ emptyset)|X984 @ (esk68_3 @ X983 @ X984 @ X985)|~X984 @ X985|~in @ X985 @ X983))&((in @ (esk69_3 @ X983 @ X984 @ X985) @ (dsetconstr @ X983 @ (epred1_2 @ X984))|(esk68_3 @ X983 @ X984 @ X985)!=(X985)|~X984 @ X985|~in @ X985 @ X983)&((dsetconstr @ X983 @ (epred1_2 @ X984))=(setadjoin @ (esk69_3 @ X983 @ X984 @ X985) @ emptyset)|(esk68_3 @ X983 @ X984 @ X985)!=(X985)|~X984 @ X985|~in @ X985 @ X983))))&((((in @ (esk72_2 @ X988 @ X989) @ (dsetconstr @ X988 @ (epred1_2 @ X989))|(~in @ X992 @ X988|~X989 @ X992)|in @ (esk70_2 @ X988 @ X989) @ X988)&((dsetconstr @ X988 @ (epred1_2 @ X989))=(setadjoin @ (esk72_2 @ X988 @ X989) @ emptyset)|(~in @ X992 @ X988|~X989 @ X992)|in @ (esk70_2 @ X988 @ X989) @ X988))&(((in @ (esk72_2 @ X988 @ X989) @ (dsetconstr @ X988 @ (epred1_2 @ X989))|(~in @ X992 @ X988|~X989 @ X992)|in @ (esk71_2 @ X988 @ X989) @ X988)&((dsetconstr @ X988 @ (epred1_2 @ X989))=(setadjoin @ (esk72_2 @ X988 @ X989) @ emptyset)|(~in @ X992 @ X988|~X989 @ X992)|in @ (esk71_2 @ X988 @ X989) @ X988))&(((in @ (esk72_2 @ X988 @ X989) @ (dsetconstr @ X988 @ (epred1_2 @ X989))|(~in @ X992 @ X988|~X989 @ X992)|X989 @ (esk70_2 @ X988 @ X989))&((dsetconstr @ X988 @ (epred1_2 @ X989))=(setadjoin @ (esk72_2 @ X988 @ X989) @ emptyset)|(~in @ X992 @ X988|~X989 @ X992)|X989 @ (esk70_2 @ X988 @ X989)))&(((in @ (esk72_2 @ X988 @ X989) @ (dsetconstr @ X988 @ (epred1_2 @ X989))|(~in @ X992 @ X988|~X989 @ X992)|X989 @ (esk71_2 @ X988 @ X989))&((dsetconstr @ X988 @ (epred1_2 @ X989))=(setadjoin @ (esk72_2 @ X988 @ X989) @ emptyset)|(~in @ X992 @ X988|~X989 @ X992)|X989 @ (esk71_2 @ X988 @ X989)))&((in @ (esk72_2 @ X988 @ X989) @ (dsetconstr @ X988 @ (epred1_2 @ X989))|(~in @ X992 @ X988|~X989 @ X992)|(esk70_2 @ X988 @ X989)!=(esk71_2 @ X988 @ X989))&((dsetconstr @ X988 @ (epred1_2 @ X989))=(setadjoin @ (esk72_2 @ X988 @ X989) @ emptyset)|(~in @ X992 @ X988|~X989 @ X992)|(esk70_2 @ X988 @ X989)!=(esk71_2 @ X988 @ X989)))))))&(((setadjoin @ X994 @ emptyset)!=(setadjoin @ X995 @ emptyset)|(X994)=(X995))&((~in @ (setadjoin @ X998 @ emptyset) @ (setadjoin @ (setadjoin @ X996 @ emptyset) @ (setadjoin @ (setadjoin @ X996 @ (setadjoin @ X997 @ emptyset)) @ emptyset))|(X996)=(X998))&(((in @ (esk73_1 @ X999) @ (dsetconstr @ (setunion @ X999) @ (epred3_2 @ X999))|(~in @ X1000 @ (setunion @ X999)|(~in @ X1001 @ (setunion @ X999)|(X999)!=(setadjoin @ (setadjoin @ X1000 @ emptyset) @ (setadjoin @ (setadjoin @ X1000 @ (setadjoin @ X1001 @ emptyset)) @ emptyset)))))&((dsetconstr @ (setunion @ X999) @ (epred3_2 @ X999))=(setadjoin @ (esk73_1 @ X999) @ emptyset)|(~in @ X1000 @ (setunion @ X999)|(~in @ X1001 @ (setunion @ X999)|(X999)!=(setadjoin @ (setadjoin @ X1000 @ emptyset) @ (setadjoin @ (setadjoin @ X1000 @ (setadjoin @ X1001 @ emptyset)) @ emptyset))))))&((~in @ X1004 @ X1003|(X1003)!=(setadjoin @ X1004 @ emptyset)|in @ (setunion @ X1003) @ X1003)&((kfst @ (kpair @ X1005 @ X1006))=(X1005)&((~in @ X1009 @ (cartprod @ X1007 @ X1008)|in @ (kfst @ X1009) @ X1007)&(((setadjoin @ (setadjoin @ X1010 @ emptyset) @ (setadjoin @ (setadjoin @ X1010 @ (setadjoin @ X1011 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1012 @ emptyset) @ (setadjoin @ (setadjoin @ X1012 @ (setadjoin @ X1013 @ emptyset)) @ emptyset))|(X1010)=(X1012))&(((kpair @ X1014 @ X1015)!=(kpair @ X1016 @ X1017)|(X1014)=(X1016))&(((X1018)!=(X1019)|(setadjoin @ X1018 @ (setadjoin @ X1019 @ emptyset))=(setadjoin @ X1018 @ emptyset))&(((X1020)!=(X1021)|(setadjoin @ (setadjoin @ X1020 @ emptyset) @ (setadjoin @ (setadjoin @ X1020 @ (setadjoin @ X1021 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X1020 @ emptyset) @ emptyset))&((setadjoin @ (setadjoin @ esk74_0 @ emptyset) @ (setadjoin @ (setadjoin @ esk74_0 @ (setadjoin @ esk75_0 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ esk76_0 @ emptyset) @ (setadjoin @ (setadjoin @ esk76_0 @ (setadjoin @ esk77_0 @ emptyset)) @ emptyset))&((esk76_0)=(esk77_0)&(esk75_0)!=(esk77_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_204])])])])])])). 0.24/0.50 thf(c_0_206, plain, ![X2:$i, X3:$i]:(kpair @ X2 @ X3)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)), inference(fof_simplification,[status(thm)],[kpair])). 0.24/0.50 thf(c_0_207, negated_conjecture, (setadjoin @ (setadjoin @ esk74_0 @ emptyset) @ (setadjoin @ (setadjoin @ esk74_0 @ (setadjoin @ esk75_0 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ esk76_0 @ emptyset) @ (setadjoin @ (setadjoin @ esk76_0 @ (setadjoin @ esk77_0 @ emptyset)) @ emptyset)), inference(split_conjunct,[status(thm)],[c_0_205])). 0.24/0.50 thf(c_0_208, negated_conjecture, (esk76_0)=(esk77_0), inference(split_conjunct,[status(thm)],[c_0_205])). 0.24/0.50 thf(c_0_209, negated_conjecture, ![X2:$i, X3:$i]:((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset)|(X2)!=(X3)), inference(split_conjunct,[status(thm)],[c_0_205])). 0.24/0.50 thf(c_0_210, plain, ![X531:$i, X532:$i]:(kpair @ X531 @ X532)=(setadjoin @ (setadjoin @ X531 @ emptyset) @ (setadjoin @ (setadjoin @ X531 @ (setadjoin @ X532 @ emptyset)) @ emptyset)), inference(variable_rename,[status(thm)],[c_0_206])). 0.24/0.50 thf(c_0_211, negated_conjecture, (setadjoin @ (setadjoin @ esk74_0 @ emptyset) @ (setadjoin @ (setadjoin @ esk74_0 @ (setadjoin @ esk75_0 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ esk76_0 @ emptyset) @ (setadjoin @ (setadjoin @ esk76_0 @ (setadjoin @ esk76_0 @ emptyset)) @ emptyset)), inference(rw,[status(thm)],[c_0_207, c_0_208])). 0.24/0.50 thf(c_0_212, negated_conjecture, ![X2:$i]:(setadjoin @ X2 @ (setadjoin @ X2 @ emptyset))=(setadjoin @ X2 @ emptyset), inference(er,[status(thm)],[c_0_209])). 0.24/0.50 thf(c_0_213, negated_conjecture, ![X3:$i, X2:$i]:in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset)) @ emptyset))), inference(split_conjunct,[status(thm)],[c_0_205])). 0.24/0.50 thf(c_0_214, plain, ![X2:$i, X3:$i]:(kpair @ X2 @ X3)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)), inference(split_conjunct,[status(thm)],[c_0_210])). 0.24/0.50 thf(c_0_215, negated_conjecture, (setadjoin @ (setadjoin @ esk74_0 @ emptyset) @ (setadjoin @ (setadjoin @ esk74_0 @ (setadjoin @ esk75_0 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ esk76_0 @ emptyset) @ emptyset), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_211, c_0_212]), c_0_212])). 0.24/0.50 thf(c_0_216, negated_conjecture, ![X3:$i, X2:$i]:in @ X2 @ (setunion @ (kpair @ X3 @ X2)), inference(rw,[status(thm)],[c_0_213, c_0_214])). 0.24/0.50 thf(c_0_217, negated_conjecture, (kpair @ esk74_0 @ esk75_0)=(setadjoin @ (setadjoin @ esk76_0 @ emptyset) @ emptyset), inference(rw,[status(thm)],[c_0_215, c_0_214])). 0.24/0.50 thf(c_0_218, negated_conjecture, ![X2:$i]:(setunion @ (setadjoin @ X2 @ emptyset))=(X2), inference(split_conjunct,[status(thm)],[c_0_205])). 0.24/0.50 thf(c_0_219, negated_conjecture, (esk75_0)!=(esk77_0), inference(split_conjunct,[status(thm)],[c_0_205])). 0.24/0.50 thf(c_0_220, negated_conjecture, ![X3:$i, X2:$i]:((X2)=(X3)|~in @ X3 @ (setadjoin @ X2 @ emptyset)), inference(split_conjunct,[status(thm)],[c_0_205])). 0.24/0.50 thf(c_0_221, negated_conjecture, in @ esk75_0 @ (setadjoin @ esk76_0 @ emptyset), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_216, c_0_217]), c_0_218])). 0.24/0.50 thf(c_0_222, negated_conjecture, (esk75_0)!=(esk76_0), inference(rw,[status(thm)],[c_0_219, c_0_208])). 0.24/0.50 thf(c_0_223, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_220, c_0_221]), c_0_222]), ['proof']). 0.24/0.50 # SZS output end CNFRefutation 0.24/0.50 # Proof object total steps : 224 0.24/0.50 # Proof object clause steps : 16 0.24/0.50 # Proof object formula steps : 208 0.24/0.50 # Proof object conjectures : 18 0.24/0.50 # Proof object clause conjectures : 15 0.24/0.50 # Proof object formula conjectures : 3 0.24/0.50 # Proof object initial clauses used : 8 0.24/0.50 # Proof object initial formulas used : 174 0.24/0.50 # Proof object generating inferences : 2 0.24/0.50 # Proof object simplifying inferences : 9 0.24/0.50 # Training examples: 0 positive, 0 negative 0.24/0.50 # Parsed axioms : 371 0.24/0.50 # Removed by relevancy pruning/SinE : 0 0.24/0.50 # Initial clauses : 533 0.24/0.50 # Removed in clause preprocessing : 224 0.24/0.50 # Initial clauses in saturation : 309 0.24/0.50 # Processed clauses : 491 0.24/0.50 # ...of these trivial : 6 0.24/0.50 # ...subsumed : 50 0.24/0.50 # ...remaining for further processing : 435 0.24/0.50 # Other redundant clauses eliminated : 30 0.24/0.50 # Clauses deleted for lack of memory : 0 0.24/0.50 # Backward-subsumed : 0 0.24/0.50 # Backward-rewritten : 9 0.24/0.50 # Generated clauses : 706 0.24/0.50 # ...of the previous two non-trivial : 262 0.24/0.50 # Contextual simplify-reflections : 0 0.24/0.50 # Paramodulations : 299 0.24/0.50 # Factorizations : 0 0.24/0.50 # NegExts : 0 0.24/0.50 # Equation resolutions : 30 0.24/0.50 # Propositional unsat checks : 0 0.24/0.50 # Propositional check models : 0 0.24/0.50 # Propositional check unsatisfiable : 0 0.24/0.50 # Propositional clauses : 0 0.24/0.50 # Propositional clauses after purity: 0 0.24/0.50 # Propositional unsat core size : 0 0.24/0.50 # Propositional preprocessing time : 0.000 0.24/0.50 # Propositional encoding time : 0.000 0.24/0.50 # Propositional solver time : 0.000 0.24/0.50 # Success case prop preproc time : 0.000 0.24/0.50 # Success case prop encoding time : 0.000 0.24/0.50 # Success case prop solver time : 0.000 0.24/0.50 # Current number of processed clauses : 141 0.24/0.50 # Positive orientable unit clauses : 73 0.24/0.50 # Positive unorientable unit clauses: 0 0.24/0.50 # Negative unit clauses : 34 0.24/0.50 # Non-unit-clauses : 34 0.24/0.50 # Current number of unprocessed clauses: 335 0.24/0.50 # ...number of literals in the above : 943 0.24/0.50 # Current number of archived formulas : 0 0.24/0.50 # Current number of archived clauses : 276 0.24/0.50 # Clause-clause subsumption calls (NU) : 12385 0.24/0.50 # Rec. Clause-clause subsumption calls : 4829 0.24/0.50 # Non-unit clause-clause subsumptions : 25 0.24/0.50 # Unit Clause-clause subsumption calls : 190 0.24/0.50 # Rewrite failures with RHS unbound : 0 0.24/0.50 # BW rewrite match attempts : 171 0.24/0.50 # BW rewrite match successes : 9 0.24/0.50 # Condensation attempts : 0 0.24/0.50 # Condensation successes : 0 0.24/0.50 # Termbank termtop insertions : 51038 0.24/0.50 0.24/0.50 # ------------------------------------------------- 0.24/0.50 # User time : 0.107 s 0.24/0.50 # System time : 0.009 s 0.24/0.50 # Total time : 0.116 s 0.24/0.50 # Maximum resident set size: 2032 pages 0.24/0.50 EOF