0.06/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.13 % Command : eprover-ho %s --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --free-numbers -auto-schedule -p --cpu-limit=%d --neg-ext=all --pos-ext=all --ext-sup-max-depth=2 --schedule-kind=CASC 0.12/0.33 % Computer : n011.cluster.edu 0.12/0.33 % Model : x86_64 x86_64 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 % Memory : 8042.1875MB 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.33 % CPULimit : 1200 0.12/0.33 % WCLimit : 120 0.12/0.33 % DateTime : Thu Jul 15 06:05:54 EDT 2021 0.12/0.34 % CPUTime : 0.12/0.34 % Number of cores: 8 0.12/0.34 % Python version: Python 3.6.8 0.18/0.34 # Version: 2.6rc1-ho 0.18/0.35 # No SInE strategy applied 0.18/0.35 # Trying AutoSched0 for 59 seconds 1.20/1.39 # AutoSched0-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_S4d 1.20/1.39 # and selection function SelectCQIPrecWNTNp. 1.20/1.39 # 1.20/1.39 # Preprocessing time : 0.053 s 1.20/1.39 # Presaturation interreduction done 1.20/1.39 1.20/1.39 # Proof found! 1.20/1.39 # SZS status Theorem 1.20/1.39 # SZS output start CNFRefutation 1.20/1.39 thf(replAx, axiom, (replAx<=>![X6:$i > $i > $o, X4:$i]:(![X2:$i]:(in @ X2 @ X4=>exu @ (^[X3:$i]:X6 @ X2 @ X3))=>?[X5:$i]:![X2:$i]:(in @ X2 @ X5<=>?[X3:$i]:(in @ X3 @ X4&X6 @ X3 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', replAx)). 1.20/1.39 thf(exu, axiom, (exu)=(^[X1:$i > $o]:?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exu)). 1.20/1.39 thf(descrp, axiom, (descrp<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>X1 @ (descr @ (^[X2:$i]:X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', descrp)). 1.20/1.39 thf(exuE1, axiom, (exuE1<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuE1)). 1.20/1.39 thf(exuE3e, axiom, (exuE3e<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>?[X2:$i]:X1 @ X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuE3e)). 1.20/1.39 thf(nonemptyE1, axiom, (nonemptyE1<=>![X4:$i]:(nonempty @ X4=>?[X2:$i]:in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyE1)). 1.20/1.39 thf(nonempty, axiom, (nonempty)=(^[X2:$i]:(X2)!=(emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonempty)). 1.20/1.39 thf(nonemptyI, axiom, (nonemptyI<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyI)). 1.20/1.39 thf(nonemptyI1, axiom, (nonemptyI1<=>![X4:$i]:(?[X2:$i]:in @ X2 @ X4=>nonempty @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyI1)). 1.20/1.39 thf(exuE2, axiom, (exuE2<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuE2)). 1.20/1.39 thf(nonemptyImpWitness, axiom, (nonemptyImpWitness<=>![X4:$i]:(nonempty @ X4=>?[X2:$i]:(in @ X2 @ X4&$true))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyImpWitness)). 1.20/1.39 thf(exuI1, axiom, (exuI1<=>![X1:$i > $o]:(?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3)))=>exu @ (^[X2:$i]:X1 @ X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuI1)). 1.20/1.39 thf(exuI3, axiom, (exuI3<=>![X1:$i > $o]:(?[X2:$i]:X1 @ X2=>(![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3)))=>exu @ (^[X2:$i]:X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuI3)). 1.20/1.39 thf(exuI2, axiom, (exuI2<=>![X1:$i > $o]:(?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2))=>exu @ (^[X2:$i]:X1 @ X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuI2)). 1.20/1.39 thf(exuE3u, axiom, (exuE3u<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuE3u)). 1.20/1.39 thf(exu__Cong, axiom, (exu__Cong<=>![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(exu @ (^[X2:$i]:X1 @ X2)<=>exu @ (^[X2:$i]:X17 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exu__Cong)). 1.20/1.39 thf(exuEu, axiom, (exuEu<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuEu)). 1.20/1.39 thf(descr__Cong, axiom, (descr__Cong<=>![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(exu @ (^[X2:$i]:X1 @ X2)=>(exu @ (^[X2:$i]:X17 @ X2)=>(descr @ (^[X2:$i]:X1 @ X2))=(descr @ (^[X2:$i]:X17 @ X2)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', descr__Cong)). 1.20/1.39 thf(kpairiskpair, axiom, (kpairiskpair<=>![X2:$i, X3:$i]:iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', kpairiskpair)). 1.20/1.39 thf(iskpair, axiom, (iskpair)=(^[X4:$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)). 1.20/1.39 thf(kpairp, axiom, (kpairp<=>![X2:$i, X3:$i]:iskpair @ (kpair @ X2 @ X3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', kpairp)). 1.20/1.39 thf(cartprodmempair, axiom, (cartprodmempair<=>![X4:$i, X5:$i, X18:$i]:(in @ X18 @ (cartprod @ X4 @ X5)=>iskpair @ X18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodmempair)). 1.20/1.39 thf(singletonprop, axiom, (singletonprop<=>![X4:$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:$i]:X1 @ X2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletonprop)). 1.20/1.39 thf(singleton, axiom, (singleton)=(^[X4:$i]:?[X2:$i]:(in @ X2 @ X4&(X4)=(setadjoin @ X2 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singleton)). 1.20/1.39 thf(ex1, axiom, (ex1)=(^[X4:$i, X1:$i > $o]:?[X478:$i]:(in @ X478 @ (dsetconstr @ X4 @ (^[X2:$i]:X1 @ X2))&(dsetconstr @ X4 @ (^[X2:$i]:X1 @ X2))=(setadjoin @ X478 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ex1)). 1.20/1.39 thf(ex1E1, conjecture, (setextAx=>(emptysetAx=>(((((((((((((dsetconstrER=>(((emptysetE=>((notinemptyset=>((setext=>(emptyI=>(noeltsimpempty=>(setbeta=>((((setadjoinIL=>(emptyinunitempty=>(setadjoinIR=>(setadjoinE=>((setoftrueEq=>(powersetI=>(emptyinPowerset=>((((setunionE=>(subPowSU=>(exuE2=>(((notinsingleton=>((singletonsswitch=>(((upairsetIR=>(emptyE1=>((quantDeMorgan1=>((quantDeMorgan3=>((((notdexE=>(((exuI3=>(exuI2=>((((exu__Cong=>((((setunion__Cong=>(((descr__Cong=>(((eqimpsubset2=>(eqimpsubset1=>((emptysetsubset=>(subsetE=>((notsubsetI=>((notequalI2=>((subsetTrans=>((setadjoinSub2=>(subset2powerset=>(((((((sepInPowerset=>(((upairset2IR=>(binunionIR=>(binunionEcases=>(binunionE=>(binunionLsub=>(binunionRsub=>((binintersectSubset5=>((binintersectLsub=>(binintersectSubset2=>(binintersectSubset3=>(binintersectER=>((((binintersectSubset1=>((setminusI=>(setminusEL=>(setminusER=>((setminusERneg=>(setminusELneg=>(((setminusLsub=>(setminusSubset1=>(symdiffE=>((symdiffI2=>(symdiffIneg1=>(symdiffIneg2=>(secondinupair=>(((kpairiskpair=>((singletonsubset=>((((((ubforcartprodlem1=>(((cartprodpairin=>((cartprodmempair=>((setunionsingleton1=>(setunionsingleton2=>((singletonprop=>![X4:$i, X1:$i > $o]:(?[X2:$i]:(X1 @ X2&in @ X2 @ X4)<=ex1 @ X4 @ (^[X2:$i]:X1 @ X2)))<=setunionsingleton)))<=setunionE2))<=cartprodmempair1))<=ubforcartprodlem3)<=ubforcartprodlem2))<=upairinpowunion)<=upairsubunion)<=upairset2E)<=singletoninpowunion)<=singletoninpowerset))<=kpairp))<=setukpairIR)<=setukpairIL)))))<=symdiffI1))))<=setminusIRneg)<=setminusILneg)))<=setminusSubset2))))<=bs114d))<=binintersectSubset4)<=binintersectRsub)<=disjointsetsI1)))))<=binintersectEL))<=binintersectI)))))))<=binunionIL)<=sepSubset))<=powersetsubset)<=inPowerset)<=powersetE1)<=powersetI1)<=subsetemptysetimpeq)<=setextsub)))<=setadjoinSub))<=subsetRefl))<=notequalI1))<=subsetE2)))<=subsetI2)))<=subsetI1)<=dsetconstr__Cong))<=exuEu)<=omega__Cong))<=powerset__Cong)<=setadjoin__Cong)<=emptyset__Cong))<=exuE3u)<=in__Cong)<=inCongP)))<=exuI1)<=notdallE))<=prop2set2propI)<=prop2setI)<=quantDeMorgan4))<=quantDeMorgan2))<=vacuousDall)))<=upairsetIL)<=upairsetE))<=eqinunit))<=uniqinunit)<=nonemptyImpWitness))))<=setunionI)<=powersetE)<=emptyInPowerset))))<=setadjoinOr)))))<=nonemptyI1)<=nonemptyI)<=nonemptyE1)))))<=exuE3e))<=emptysetimpfalse))<=prop2setE)<=exuE1))<=dsetconstrEL)<=dsetconstrI)<=descrp)<=wellorderingAx)<=foundationAx)<=replAx)<=omegaIndAx)<=omegaSAx)<=omega0Ax)<=setunionAx)<=powersetAx)<=setadjoinAx))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ex1E1)). 1.20/1.39 thf(setextAx, axiom, (setextAx<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4<=>in @ X2 @ X5)=>(X4)=(X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setextAx)). 1.20/1.39 thf(emptysetAx, axiom, (emptysetAx<=>![X2:$i]:~(in @ X2 @ emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetAx)). 1.20/1.39 thf(setadjoinAx, axiom, (setadjoinAx<=>![X2:$i, X4:$i, X3:$i]:(in @ X3 @ (setadjoin @ X2 @ X4)<=>((X3)=(X2)|in @ X3 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinAx)). 1.20/1.39 thf(powersetAx, axiom, (powersetAx<=>![X4:$i, X5:$i]:(in @ X5 @ (powerset @ X4)<=>![X2:$i]:(in @ X2 @ X5=>in @ X2 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetAx)). 1.20/1.39 thf(setunionAx, axiom, (setunionAx<=>![X4:$i, X2:$i]:(in @ X2 @ (setunion @ X4)<=>?[X5:$i]:(in @ X2 @ X5&in @ X5 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionAx)). 1.20/1.39 thf(omega0Ax, axiom, (omega0Ax<=>in @ emptyset @ omega), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omega0Ax)). 1.20/1.39 thf(omegaSAx, axiom, (omegaSAx<=>![X2:$i]:(in @ X2 @ omega=>in @ (setadjoin @ X2 @ X2) @ omega)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omegaSAx)). 1.20/1.39 thf(omegaIndAx, axiom, (omegaIndAx<=>![X4:$i]:((in @ emptyset @ X4&![X2:$i]:((in @ X2 @ omega&in @ X2 @ X4)=>in @ (setadjoin @ X2 @ X2) @ X4))=>![X2:$i]:(in @ X2 @ omega=>in @ X2 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omegaIndAx)). 1.20/1.39 thf(foundationAx, axiom, (foundationAx<=>![X4:$i]:(?[X2:$i]:in @ X2 @ X4=>?[X5:$i]:(in @ X5 @ X4&~(?[X2:$i]:(in @ X2 @ X5&in @ X2 @ X4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', foundationAx)). 1.20/1.39 thf(wellorderingAx, axiom, (wellorderingAx<=>![X4:$i]:?[X5:$i]:(((![X7:$i]:(in @ X7 @ X5=>![X2:$i]:(in @ X2 @ X7=>in @ X2 @ X4))&![X2:$i, X3:$i]:((in @ X2 @ X4&in @ X3 @ X4)=>(![X7:$i]:(in @ X7 @ X5=>(in @ X2 @ X7<=>in @ X3 @ X7))=>(X2)=(X3))))&![X7:$i, X8:$i]:((in @ X7 @ X5&in @ X8 @ X5)=>(![X2:$i]:(in @ X2 @ X7=>in @ X2 @ X8)|![X2:$i]:(in @ X2 @ X8=>in @ X2 @ X7))))&![X7:$i]:((![X2:$i]:(in @ X2 @ X7=>in @ X2 @ X4)&?[X2:$i]:in @ X2 @ X7)=>?[X8:$i, X2:$i]:(((in @ X8 @ X5&in @ X2 @ X7)&~(?[X3:$i]:(in @ X3 @ X8&in @ X3 @ X7)))&![X9:$i]:(in @ X9 @ X5=>(![X3:$i]:(in @ X3 @ X9=>in @ X3 @ X8)|in @ X2 @ X9)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', wellorderingAx)). 1.20/1.39 thf(dsetconstrI, axiom, (dsetconstrI<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstrI)). 1.20/1.39 thf(dsetconstrEL, axiom, (dsetconstrEL<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))=>in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstrEL)). 1.20/1.39 thf(dsetconstrER, axiom, (dsetconstrER<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))=>X1 @ X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstrER)). 1.20/1.39 thf(prop2setE, axiom, (prop2setE<=>![X10:$o, X2:$i]:(in @ X2 @ (prop2set @ (X10))=>X10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prop2setE)). 1.20/1.39 thf(emptysetE, axiom, (emptysetE<=>![X2:$i]:(in @ X2 @ emptyset=>![X11:$o]:X11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetE)). 1.20/1.39 thf(emptysetimpfalse, axiom, (emptysetimpfalse<=>![X2:$i]:(in @ X2 @ emptyset=>~$true)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetimpfalse)). 1.20/1.39 thf(notinemptyset, axiom, (notinemptyset<=>![X2:$i]:~(in @ X2 @ emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notinemptyset)). 1.20/1.39 thf(setext, axiom, (setext<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4=>in @ X2 @ X5)=>(![X2:$i]:(in @ X2 @ X5=>in @ X2 @ X4)=>(X4)=(X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setext)). 1.20/1.39 thf(emptyI, axiom, (emptyI<=>![X4:$i]:(![X2:$i]:~(in @ X2 @ X4)=>(X4)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyI)). 1.20/1.39 thf(noeltsimpempty, axiom, (noeltsimpempty<=>![X4:$i]:(![X2:$i]:~(in @ X2 @ X4)=>(X4)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', noeltsimpempty)). 1.20/1.39 thf(setbeta, axiom, (setbeta<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))<=>X1 @ X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setbeta)). 1.20/1.39 thf(setadjoinIL, axiom, (setadjoinIL<=>![X2:$i, X3:$i]:in @ X2 @ (setadjoin @ X2 @ X3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinIL)). 1.20/1.39 thf(emptyinunitempty, axiom, (emptyinunitempty<=>in @ emptyset @ (setadjoin @ emptyset @ emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyinunitempty)). 1.20/1.39 thf(setadjoinIR, axiom, (setadjoinIR<=>![X2:$i, X4:$i, X3:$i]:(in @ X3 @ X4=>in @ X3 @ (setadjoin @ X2 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinIR)). 1.20/1.39 thf(setadjoinE, axiom, (setadjoinE<=>![X2:$i, X4:$i, X3:$i]:(in @ X3 @ (setadjoin @ X2 @ X4)=>![X12:$o]:(((X3)=(X2)=>X12)=>((in @ X3 @ X4=>X12)=>X12)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinE)). 1.20/1.39 thf(setadjoinOr, axiom, (setadjoinOr<=>![X2:$i, X4:$i, X3:$i]:(in @ X3 @ (setadjoin @ X2 @ X4)=>((X3)=(X2)|in @ X3 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinOr)). 1.20/1.39 thf(setoftrueEq, axiom, (setoftrueEq<=>![X4:$i]:(dsetconstr @ X4 @ (^[X2:$i]:$true))=(X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setoftrueEq)). 1.20/1.39 thf(powersetI, axiom, (powersetI<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X5=>in @ X2 @ X4)=>in @ X5 @ (powerset @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetI)). 1.20/1.39 thf(emptyinPowerset, axiom, (emptyinPowerset<=>![X4:$i]:in @ emptyset @ (powerset @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyinPowerset)). 1.20/1.39 thf(emptyInPowerset, axiom, (emptyInPowerset<=>![X4:$i]:in @ emptyset @ (powerset @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyInPowerset)). 1.20/1.39 thf(powersetE, axiom, (powersetE<=>![X4:$i, X5:$i, X2:$i]:(in @ X5 @ (powerset @ X4)=>(in @ X2 @ X5=>in @ X2 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetE)). 1.20/1.39 thf(setunionI, axiom, (setunionI<=>![X4:$i, X2:$i, X5:$i]:(in @ X2 @ X5=>(in @ X5 @ X4=>in @ X2 @ (setunion @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionI)). 1.20/1.39 thf(setunionE, axiom, (setunionE<=>![X4:$i, X2:$i]:(in @ X2 @ (setunion @ X4)=>![X13:$o]:(![X5:$i]:(in @ X2 @ X5=>(in @ X5 @ X4=>X13))=>X13))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionE)). 1.20/1.39 thf(subPowSU, axiom, (subPowSU<=>![X4:$i, X2:$i]:(in @ X2 @ X4=>in @ X2 @ (powerset @ (setunion @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subPowSU)). 1.20/1.39 thf(uniqinunit, axiom, (uniqinunit<=>![X2:$i, X3:$i]:(in @ X2 @ (setadjoin @ X3 @ emptyset)=>(X2)=(X3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', uniqinunit)). 1.20/1.39 thf(notinsingleton, axiom, (notinsingleton<=>![X2:$i, X3:$i]:((X2)!=(X3)=>~(in @ X3 @ (setadjoin @ X2 @ emptyset)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notinsingleton)). 1.20/1.39 thf(eqinunit, axiom, (eqinunit<=>![X2:$i, X3:$i]:((X2)=(X3)=>in @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqinunit)). 1.20/1.39 thf(singletonsswitch, axiom, (singletonsswitch<=>![X2:$i, X3:$i]:(in @ X2 @ (setadjoin @ X3 @ emptyset)=>in @ X3 @ (setadjoin @ X2 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletonsswitch)). 1.20/1.39 thf(upairsetE, axiom, (upairsetE<=>![X2:$i, X3:$i, X14:$i]:(in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=>((X14)=(X2)|(X14)=(X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsetE)). 1.20/1.39 thf(upairsetIL, axiom, (upairsetIL<=>![X2:$i, X3:$i]:in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsetIL)). 1.20/1.39 thf(upairsetIR, axiom, (upairsetIR<=>![X2:$i, X3:$i]:in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsetIR)). 1.20/1.39 thf(emptyE1, axiom, (emptyE1<=>![X4:$i, X1:$i > $o]:(?[X2:$i]:(in @ X2 @ X4&X1 @ X2)=>((dsetconstr @ X4 @ (^[X2:$i]:X1 @ X2))=(emptyset)=>~$true))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyE1)). 1.20/1.39 thf(vacuousDall, axiom, (vacuousDall<=>![X1:$i > $o, X2:$i]:(in @ X2 @ emptyset=>X1 @ X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', vacuousDall)). 1.20/1.39 thf(quantDeMorgan1, axiom, (quantDeMorgan1<=>![X4:$i, X1:$i > $o]:(~(![X2:$i]:(in @ X2 @ X4=>X1 @ X2))=>?[X2:$i]:(in @ X2 @ X4&~(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan1)). 1.20/1.39 thf(quantDeMorgan2, axiom, (quantDeMorgan2<=>![X4:$i, X1:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>~(X1 @ X2))=>~(?[X2:$i]:(in @ X2 @ X4&X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan2)). 1.20/1.39 thf(quantDeMorgan3, axiom, (quantDeMorgan3<=>![X4:$i, X1:$i > $o]:(~(?[X2:$i]:(in @ X2 @ X4&X1 @ X2))=>![X2:$i]:(in @ X2 @ X4=>~(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan3)). 1.20/1.39 thf(quantDeMorgan4, axiom, (quantDeMorgan4<=>![X4:$i, X1:$i > $o]:(?[X2:$i]:(in @ X2 @ X4&~(X1 @ X2))=>~(![X2:$i]:(in @ X2 @ X4=>X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan4)). 1.20/1.39 thf(prop2setI, axiom, (prop2setI<=>![X15:$o]:(X15=>in @ emptyset @ (prop2set @ (X15)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prop2setI)). 1.20/1.39 thf(prop2set2propI, axiom, (prop2set2propI<=>![X16:$o]:(X16=>set2prop @ (prop2set @ (X16)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prop2set2propI)). 1.20/1.39 thf(notdexE, axiom, (notdexE<=>![X4:$i, X1:$i > $o]:(~(?[X2:$i]:(in @ X2 @ X4&X1 @ X2))=>![X2:$i]:(in @ X2 @ X4=>~(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notdexE)). 1.20/1.39 thf(notdallE, axiom, (notdallE<=>![X4:$i, X1:$i > $o]:(~(![X2:$i]:(in @ X2 @ X4=>X1 @ X2))=>?[X2:$i]:(in @ X2 @ X4&~(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notdallE)). 1.20/1.39 thf(inCongP, axiom, (inCongP<=>![X4:$i, X5:$i]:((X4)=(X5)=>![X2:$i, X3:$i]:((X2)=(X3)=>(in @ X2 @ X4=>in @ X3 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', inCongP)). 1.20/1.39 thf(in__Cong, axiom, (in__Cong<=>![X4:$i, X5:$i]:((X4)=(X5)=>![X2:$i, X3:$i]:((X2)=(X3)=>(in @ X2 @ X4<=>in @ X3 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', in__Cong)). 1.20/1.39 thf(emptyset__Cong, axiom, (emptyset__Cong<=>(emptyset)=(emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyset__Cong)). 1.20/1.39 thf(setadjoin__Cong, axiom, (setadjoin__Cong<=>![X2:$i, X3:$i]:((X2)=(X3)=>![X14:$i, X18:$i]:((X14)=(X18)=>(setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoin__Cong)). 1.20/1.39 thf(powerset__Cong, axiom, (powerset__Cong<=>![X4:$i, X5:$i]:((X4)=(X5)=>(powerset @ X4)=(powerset @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powerset__Cong)). 1.20/1.39 thf(setunion__Cong, axiom, (setunion__Cong<=>![X4:$i, X5:$i]:((X4)=(X5)=>(setunion @ X4)=(setunion @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunion__Cong)). 1.20/1.39 thf(omega__Cong, axiom, (omega__Cong<=>(omega)=(omega)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omega__Cong)). 1.20/1.39 thf(dsetconstr__Cong, axiom, (dsetconstr__Cong<=>![X4:$i, X5:$i]:((X4)=(X5)=>![X1:$i > $o, X17:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))))=>(dsetconstr @ X4 @ (^[X2:$i]:X1 @ X2))=(dsetconstr @ X5 @ (^[X2:$i]:X17 @ X2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstr__Cong)). 1.20/1.39 thf(subsetI1, axiom, (subsetI1<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4=>in @ X2 @ X5)=>subset @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetI1)). 1.20/1.39 thf(eqimpsubset2, axiom, (eqimpsubset2<=>![X4:$i, X5:$i]:((X4)=(X5)=>subset @ X5 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqimpsubset2)). 1.20/1.39 thf(eqimpsubset1, axiom, (eqimpsubset1<=>![X4:$i, X5:$i]:((X4)=(X5)=>subset @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqimpsubset1)). 1.20/1.39 thf(subsetI2, axiom, (subsetI2<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4=>in @ X2 @ X5)=>subset @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetI2)). 1.20/1.39 thf(emptysetsubset, axiom, (emptysetsubset<=>![X4:$i]:subset @ emptyset @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetsubset)). 1.20/1.39 thf(subsetE, axiom, (subsetE<=>![X4:$i, X5:$i, X2:$i]:(subset @ X4 @ X5=>(in @ X2 @ X4=>in @ X2 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetE)). 1.20/1.39 thf(subsetE2, axiom, (subsetE2<=>![X4:$i, X5:$i, X2:$i]:(subset @ X4 @ X5=>(~(in @ X2 @ X5)=>~(in @ X2 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetE2)). 1.20/1.39 thf(notsubsetI, axiom, (notsubsetI<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X5)=>~(subset @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notsubsetI)). 1.20/1.39 thf(notequalI1, axiom, (notequalI1<=>![X4:$i, X5:$i]:(~(subset @ X4 @ X5)=>(X4)!=(X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notequalI1)). 1.20/1.39 thf(notequalI2, axiom, (notequalI2<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X5)=>(X4)!=(X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notequalI2)). 1.20/1.39 thf(subsetRefl, axiom, (subsetRefl<=>![X4:$i]:subset @ X4 @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetRefl)). 1.20/1.39 thf(subsetTrans, axiom, (subsetTrans<=>![X4:$i, X5:$i, X7:$i]:(subset @ X4 @ X5=>(subset @ X5 @ X7=>subset @ X4 @ X7))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetTrans)). 1.20/1.39 thf(setadjoinSub, axiom, (setadjoinSub<=>![X2:$i, X4:$i]:subset @ X4 @ (setadjoin @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinSub)). 1.20/1.39 thf(setadjoinSub2, axiom, (setadjoinSub2<=>![X4:$i, X2:$i, X5:$i]:(subset @ X4 @ X5=>subset @ X4 @ (setadjoin @ X2 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinSub2)). 1.20/1.39 thf(subset2powerset, axiom, (subset2powerset<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>in @ X4 @ (powerset @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subset2powerset)). 1.20/1.39 thf(setextsub, axiom, (setextsub<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>(subset @ X5 @ X4=>(X4)=(X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setextsub)). 1.20/1.39 thf(subsetemptysetimpeq, axiom, (subsetemptysetimpeq<=>![X4:$i]:(subset @ X4 @ emptyset=>(X4)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetemptysetimpeq)). 1.20/1.39 thf(powersetI1, axiom, (powersetI1<=>![X4:$i, X5:$i]:(subset @ X5 @ X4=>in @ X5 @ (powerset @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetI1)). 1.20/1.39 thf(powersetE1, axiom, (powersetE1<=>![X4:$i, X5:$i]:(in @ X5 @ (powerset @ X4)=>subset @ X5 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetE1)). 1.20/1.39 thf(inPowerset, axiom, (inPowerset<=>![X4:$i]:in @ X4 @ (powerset @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', inPowerset)). 1.20/1.39 thf(powersetsubset, axiom, (powersetsubset<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>subset @ (powerset @ X4) @ (powerset @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetsubset)). 1.20/1.39 thf(sepInPowerset, axiom, (sepInPowerset<=>![X4:$i, X1:$i > $o]:in @ (dsetconstr @ X4 @ (^[X2:$i]:X1 @ X2)) @ (powerset @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sepInPowerset)). 1.20/1.39 thf(sepSubset, axiom, (sepSubset<=>![X4:$i, X1:$i > $o]:subset @ (dsetconstr @ X4 @ (^[X2:$i]:X1 @ X2)) @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sepSubset)). 1.20/1.39 thf(binunionIL, axiom, (binunionIL<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>in @ X2 @ (binunion @ X4 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionIL)). 1.20/1.39 thf(upairset2IR, axiom, (upairset2IR<=>![X2:$i, X3:$i]:in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairset2IR)). 1.20/1.39 thf(binunionIR, axiom, (binunionIR<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X5=>in @ X2 @ (binunion @ X4 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionIR)). 1.20/1.39 thf(binunionEcases, axiom, (binunionEcases<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(in @ X2 @ (binunion @ X4 @ X5)=>((in @ X2 @ X4=>X19)=>((in @ X2 @ X5=>X19)=>X19)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionEcases)). 1.20/1.39 thf(binunionE, axiom, (binunionE<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (binunion @ X4 @ X5)=>(in @ X2 @ X4|in @ X2 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionE)). 1.20/1.39 thf(binunionLsub, axiom, (binunionLsub<=>![X4:$i, X5:$i]:subset @ X4 @ (binunion @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionLsub)). 1.20/1.39 thf(binunionRsub, axiom, (binunionRsub<=>![X4:$i, X5:$i]:subset @ X5 @ (binunion @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionRsub)). 1.20/1.39 thf(binintersectI, axiom, (binintersectI<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X5=>in @ X2 @ (binintersect @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectI)). 1.20/1.39 thf(binintersectSubset5, axiom, (binintersectSubset5<=>![X4:$i, X5:$i, X7:$i]:(subset @ X7 @ X4=>(subset @ X7 @ X5=>subset @ X7 @ (binintersect @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset5)). 1.20/1.39 thf(binintersectEL, axiom, (binintersectEL<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (binintersect @ X4 @ X5)=>in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectEL)). 1.20/1.39 thf(binintersectLsub, axiom, (binintersectLsub<=>![X4:$i, X5:$i]:subset @ (binintersect @ X4 @ X5) @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectLsub)). 1.20/1.39 thf(binintersectSubset2, axiom, (binintersectSubset2<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>(binintersect @ X4 @ X5)=(X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset2)). 1.20/1.39 thf(binintersectSubset3, axiom, (binintersectSubset3<=>![X4:$i, X5:$i]:((binintersect @ X4 @ X5)=(X5)=>subset @ X5 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset3)). 1.20/1.39 thf(binintersectER, axiom, (binintersectER<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (binintersect @ X4 @ X5)=>in @ X2 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectER)). 1.20/1.39 thf(disjointsetsI1, axiom, (disjointsetsI1<=>![X4:$i, X5:$i]:(~(?[X2:$i]:(in @ X2 @ X4&in @ X2 @ X5))=>(binintersect @ X4 @ X5)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', disjointsetsI1)). 1.20/1.39 thf(binintersectRsub, axiom, (binintersectRsub<=>![X4:$i, X5:$i]:subset @ (binintersect @ X4 @ X5) @ X5), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectRsub)). 1.20/1.39 thf(binintersectSubset4, axiom, (binintersectSubset4<=>![X4:$i, X5:$i]:(subset @ X5 @ X4=>(binintersect @ X4 @ X5)=(X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset4)). 1.20/1.39 thf(binintersectSubset1, axiom, (binintersectSubset1<=>![X4:$i, X5:$i]:((binintersect @ X4 @ X5)=(X4)=>subset @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset1)). 1.20/1.39 thf(bs114d, axiom, (bs114d<=>![X4:$i, X5:$i, X7:$i]:(binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', bs114d)). 1.20/1.39 thf(setminusI, axiom, (setminusI<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X5)=>in @ X2 @ (setminus @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusI)). 1.20/1.39 thf(setminusEL, axiom, (setminusEL<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (setminus @ X4 @ X5)=>in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusEL)). 1.20/1.39 thf(setminusER, axiom, (setminusER<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (setminus @ X4 @ X5)=>~(in @ X2 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusER)). 1.20/1.39 thf(setminusSubset2, axiom, (setminusSubset2<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>(setminus @ X4 @ X5)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusSubset2)). 1.20/1.39 thf(setminusERneg, axiom, (setminusERneg<=>![X4:$i, X5:$i, X2:$i]:(~(in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4=>in @ X2 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusERneg)). 1.20/1.39 thf(setminusELneg, axiom, (setminusELneg<=>![X4:$i, X5:$i, X2:$i]:(~(in @ X2 @ (setminus @ X4 @ X5))=>(~(in @ X2 @ X5)=>~(in @ X2 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusELneg)). 1.20/1.39 thf(setminusILneg, axiom, (setminusILneg<=>![X4:$i, X5:$i, X2:$i]:(~(in @ X2 @ X4)=>~(in @ X2 @ (setminus @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusILneg)). 1.20/1.39 thf(setminusIRneg, axiom, (setminusIRneg<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X5=>~(in @ X2 @ (setminus @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusIRneg)). 1.20/1.39 thf(setminusLsub, axiom, (setminusLsub<=>![X4:$i, X5:$i]:subset @ (setminus @ X4 @ X5) @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusLsub)). 1.20/1.39 thf(setminusSubset1, axiom, (setminusSubset1<=>![X4:$i, X5:$i]:((setminus @ X4 @ X5)=(emptyset)=>subset @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusSubset1)). 1.20/1.39 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)). 1.20/1.39 thf(symdiffI1, axiom, (symdiffI1<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X5)=>in @ X2 @ (symdiff @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', symdiffI1)). 1.20/1.39 thf(symdiffI2, axiom, (symdiffI2<=>![X4:$i, X5:$i, X2:$i]:(~(in @ X2 @ X4)=>(in @ X2 @ X5=>in @ X2 @ (symdiff @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', symdiffI2)). 1.20/1.39 thf(symdiffIneg1, axiom, (symdiffIneg1<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X5=>~(in @ X2 @ (symdiff @ X4 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', symdiffIneg1)). 1.20/1.39 thf(symdiffIneg2, axiom, (symdiffIneg2<=>![X4:$i, X5:$i, X2:$i]:(~(in @ X2 @ X4)=>(~(in @ X2 @ X5)=>~(in @ X2 @ (symdiff @ X4 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', symdiffIneg2)). 1.20/1.39 thf(secondinupair, axiom, (secondinupair<=>![X2:$i, X3:$i]:in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', secondinupair)). 1.20/1.39 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)). 1.20/1.39 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)). 1.20/1.39 thf(singletonsubset, axiom, (singletonsubset<=>![X4:$i, X2:$i]:(in @ X2 @ X4=>subset @ (setadjoin @ X2 @ emptyset) @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletonsubset)). 1.20/1.39 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)). 1.20/1.39 thf(singletoninpowunion, axiom, (singletoninpowunion<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletoninpowunion)). 1.20/1.39 thf(upairset2E, axiom, (upairset2E<=>![X2:$i, X3:$i, X14:$i]:(in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=>((X14)=(X2)|(X14)=(X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairset2E)). 1.20/1.39 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)). 1.20/1.39 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)). 1.20/1.39 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)). 1.20/1.39 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)). 1.20/1.39 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)). 1.20/1.39 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)). 1.20/1.39 thf(cartprodmempair1, axiom, (cartprodmempair1<=>![X4:$i, X5:$i, X18:$i]:(in @ X18 @ (cartprod @ X4 @ X5)=>?[X2:$i]:(in @ X2 @ X4&?[X3:$i]:(in @ X3 @ X5&(X18)=(kpair @ X2 @ X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodmempair1)). 1.20/1.39 thf(setunionE2, axiom, (setunionE2<=>![X4:$i, X2:$i]:(in @ X2 @ (setunion @ X4)=>?[X21:$i]:(in @ X21 @ X4&in @ X2 @ X21))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionE2)). 1.20/1.39 thf(setunionsingleton1, axiom, (setunionsingleton1<=>![X4:$i]:subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionsingleton1)). 1.20/1.39 thf(setunionsingleton2, axiom, (setunionsingleton2<=>![X4:$i]:subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionsingleton2)). 1.20/1.39 thf(setunionsingleton, axiom, (setunionsingleton<=>![X2:$i]:(setunion @ (setadjoin @ X2 @ emptyset))=(X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionsingleton)). 1.20/1.39 thf(c_0_160, axiom, (replAx)=(![X6:$i > $i > $o, X4:$i]:(![X2:$i]:(in @ X2 @ X4=>?[X442:$i]:(X6 @ X2 @ X442&![X444:$i]:(X6 @ X2 @ X444=>(X442)=(X444))))=>?[X5:$i]:![X2:$i]:(in @ X2 @ X5<=>?[X3:$i]:(in @ X3 @ X4&X6 @ X3 @ X2)))), inference(apply_def,[status(thm)],[replAx, exu])). 1.20/1.39 thf(c_0_161, axiom, (descrp)=(![X1:$i > $o]:(?[X445:$i]:(X1 @ X445&![X446:$i]:(X1 @ X446=>(X445)=(X446)))=>X1 @ (descr @ (^[X2:$i]:X1 @ X2)))), inference(apply_def,[status(thm)],[descrp, exu])). 1.20/1.39 thf(c_0_162, axiom, (exuE1)=(![X1:$i > $o]:(?[X447:$i]:(X1 @ X447&![X448:$i]:(X1 @ X448=>(X447)=(X448)))=>?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3))))), inference(apply_def,[status(thm)],[exuE1, exu])). 1.20/1.39 thf(c_0_163, axiom, (exuE3e)=(![X1:$i > $o]:(?[X449:$i]:(X1 @ X449&![X450:$i]:(X1 @ X450=>(X449)=(X450)))=>?[X2:$i]:X1 @ X2)), inference(apply_def,[status(thm)],[exuE3e, exu])). 1.20/1.39 thf(c_0_164, axiom, (nonemptyE1)=(![X4:$i]:((X4)!=(emptyset)=>?[X2:$i]:in @ X2 @ X4)), inference(apply_def,[status(thm)],[nonemptyE1, nonempty])). 1.20/1.39 thf(c_0_165, axiom, (nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>(dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))!=(emptyset)))), inference(apply_def,[status(thm)],[nonemptyI, nonempty])). 1.20/1.39 thf(c_0_166, axiom, (nonemptyI1)=(![X4:$i]:(?[X2:$i]:in @ X2 @ X4=>(X4)!=(emptyset))), inference(apply_def,[status(thm)],[nonemptyI1, nonempty])). 1.20/1.39 thf(c_0_167, axiom, (exuE2)=(![X1:$i > $o]:(?[X451:$i]:(X1 @ X451&![X452:$i]:(X1 @ X452=>(X451)=(X452)))=>?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2)))), inference(apply_def,[status(thm)],[exuE2, exu])). 1.20/1.39 thf(c_0_168, axiom, (nonemptyImpWitness)=(![X4:$i]:((X4)!=(emptyset)=>?[X2:$i]:(in @ X2 @ X4&$true))), inference(apply_def,[status(thm)],[nonemptyImpWitness, nonempty])). 1.20/1.39 thf(c_0_169, axiom, (exuI1)=(![X1:$i > $o]:(?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3)))=>?[X453:$i]:(X1 @ X453&![X454:$i]:(X1 @ X454=>(X453)=(X454))))), inference(apply_def,[status(thm)],[exuI1, exu])). 1.20/1.39 thf(c_0_170, axiom, (exuI3)=(![X1:$i > $o]:(?[X2:$i]:X1 @ X2=>(![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3)))=>?[X455:$i]:(X1 @ X455&![X456:$i]:(X1 @ X456=>(X455)=(X456)))))), inference(apply_def,[status(thm)],[exuI3, exu])). 1.20/1.39 thf(c_0_171, axiom, (exuI2)=(![X1:$i > $o]:(?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2))=>?[X457:$i]:(X1 @ X457&![X458:$i]:(X1 @ X458=>(X457)=(X458))))), inference(apply_def,[status(thm)],[exuI2, exu])). 1.20/1.39 thf(c_0_172, axiom, (exuE3u)=(![X1:$i > $o]:(?[X459:$i]:(X1 @ X459&![X460:$i]:(X1 @ X460=>(X459)=(X460)))=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))), inference(apply_def,[status(thm)],[exuE3u, exu])). 1.20/1.39 thf(c_0_173, axiom, (exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(?[X461:$i]:(X1 @ X461&![X462:$i]:(X1 @ X462=>(X461)=(X462)))<=>?[X463:$i]:(X17 @ X463&![X464:$i]:(X17 @ X464=>(X463)=(X464)))))), inference(apply_def,[status(thm)],[exu__Cong, exu])). 1.20/1.39 thf(c_0_174, axiom, (exuEu)=(![X1:$i > $o]:(?[X465:$i]:(X1 @ X465&![X466:$i]:(X1 @ X466=>(X465)=(X466)))=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))), inference(apply_def,[status(thm)],[exuEu, exu])). 1.20/1.39 thf(c_0_175, axiom, (descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(?[X467:$i]:(X1 @ X467&![X468:$i]:(X1 @ X468=>(X467)=(X468)))=>(?[X469:$i]:(X17 @ X469&![X470:$i]:(X17 @ X470=>(X469)=(X470)))=>(descr @ (^[X2:$i]:X1 @ X2))=(descr @ (^[X2:$i]:X17 @ X2)))))), inference(apply_def,[status(thm)],[descr__Cong, exu])). 1.20/1.39 thf(c_0_176, axiom, (kpairiskpair)=(![X2:$i, X3:$i]:?[X471:$i]:(in @ X471 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))&?[X472:$i]:(in @ X472 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))&(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X471 @ emptyset) @ (setadjoin @ (setadjoin @ X471 @ (setadjoin @ X472 @ emptyset)) @ emptyset))))), inference(apply_def,[status(thm)],[kpairiskpair, iskpair])). 1.20/1.39 thf(c_0_177, axiom, (kpairp)=(![X2:$i, X3:$i]:?[X473:$i]:(in @ X473 @ (setunion @ (kpair @ X2 @ X3))&?[X474:$i]:(in @ X474 @ (setunion @ (kpair @ X2 @ X3))&(kpair @ X2 @ X3)=(setadjoin @ (setadjoin @ X473 @ emptyset) @ (setadjoin @ (setadjoin @ X473 @ (setadjoin @ X474 @ emptyset)) @ emptyset))))), inference(apply_def,[status(thm)],[kpairp, iskpair])). 1.20/1.39 thf(c_0_178, axiom, (cartprodmempair)=(![X4:$i, X5:$i, X18:$i]:(in @ X18 @ (cartprod @ X4 @ X5)=>?[X475:$i]:(in @ X475 @ (setunion @ X18)&?[X476:$i]:(in @ X476 @ (setunion @ X18)&(X18)=(setadjoin @ (setadjoin @ X475 @ emptyset) @ (setadjoin @ (setadjoin @ X475 @ (setadjoin @ X476 @ emptyset)) @ emptyset)))))), inference(apply_def,[status(thm)],[cartprodmempair, iskpair])). 1.20/1.39 thf(c_0_179, 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)=>?[X477:$i]:(in @ X477 @ (dsetconstr @ X4 @ (^[X2:$i]:X1 @ X2))&(dsetconstr @ X4 @ (^[X2:$i]:X1 @ X2))=(setadjoin @ X477 @ emptyset))))), inference(apply_def,[status(thm)],[singletonprop, singleton])). 1.20/1.39 thf(c_0_180, axiom, (ex1)=(^[X4:$i, X1:$i > $o]:?[X478:$i]:(in @ X478 @ (dsetconstr @ X4 @ (^[X2:$i]:X1 @ X2))&(dsetconstr @ X4 @ (^[X2:$i]:X1 @ X2))=(setadjoin @ X478 @ emptyset))), inference(apply_def,[status(thm)],[ex1, singleton])). 1.20/1.39 thf(c_0_181, plain, ![X3:$i, X1:$i > $o]:(epred1_2 @ X1 @ X3<=>X1 @ X3), introduced(definition)). 1.20/1.39 thf(c_0_182, plain, ![X2:$i]:epred2_1 @ X2, inference(fof_simplification,[status(thm)],[introduced(definition)])). 1.20/1.39 thf(c_0_183, plain, (epred3_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:$i]:(in @ X3 @ X9=>in @ X3 @ X8)|in @ X2 @ X9)))))), introduced(definition)). 1.20/1.39 thf(c_0_184, negated_conjecture, ~((![X4:$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:$i]:(in @ X2 @ X4=>?[X442:$i]:(X6 @ X2 @ X442&![X444:$i]:(X6 @ X2 @ X444=>(X442)=(X444))))=>?[X5:$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))))=>(epred3_0=>(![X1:$i > $o]:(?[X445:$i]:(X1 @ X445&![X446:$i]:(X1 @ X446=>(X445)=(X446)))=>X1 @ (descr @ (epred1_2 @ X1)))=>(![X4:$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 > $o]:(?[X447:$i]:(X1 @ X447&![X448:$i]:(X1 @ X448=>(X447)=(X448)))=>?[X2:$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 > $o]:(?[X449:$i]:(X1 @ X449&![X450:$i]:(X1 @ X450=>(X449)=(X450)))=>?[X2:$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 > $o]:(?[X451:$i]:(X1 @ X451&![X452:$i]:(X1 @ X452=>(X451)=(X452)))=>?[X2:$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:$i]:(X1 @ X3=>(X2)=(X3)))=>?[X453:$i]:(X1 @ X453&![X454:$i]:(X1 @ X454=>(X453)=(X454))))=>(![X1:$i > $o]:(?[X2:$i]:X1 @ X2=>(![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3)))=>?[X455:$i]:(X1 @ X455&![X456:$i]:(X1 @ X456=>(X455)=(X456)))))=>(![X1:$i > $o]:(?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2))=>?[X457:$i]:(X1 @ X457&![X458:$i]:(X1 @ X458=>(X457)=(X458))))=>(![X4:$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 > $o]:(?[X459:$i]:(X1 @ X459&![X460:$i]:(X1 @ X460=>(X459)=(X460)))=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))=>(![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(?[X461:$i]:(X1 @ X461&![X462:$i]:(X1 @ X462=>(X461)=(X462)))<=>?[X463:$i]:(X17 @ X463&![X464:$i]:(X17 @ X464=>(X463)=(X464)))))=>((emptyset)=(emptyset)=>(![X2:$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 > $o]:(?[X465:$i]:(X1 @ X465&![X466:$i]:(X1 @ X466=>(X465)=(X466)))=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))=>(![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(?[X467:$i]:(X1 @ X467&![X468:$i]:(X1 @ X468=>(X467)=(X468)))=>(?[X469:$i]:(X17 @ X469&![X470:$i]:(X17 @ X470=>(X469)=(X470)))=>(descr @ (epred1_2 @ X1))=(descr @ (epred1_2 @ X17)))))=>(![X4:$i, X5:$i]:((X4)=(X5)=>![X1:$i > $o, 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X4 @ X5=>subset @ X4 @ (setadjoin @ X2 @ X5))=>(![X4:$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:$i]:((binintersect @ X4 @ X5)=(X4)=>subset @ X4 @ 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(setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))&(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X471 @ emptyset) @ (setadjoin @ (setadjoin @ X471 @ (setadjoin @ X472 @ emptyset)) @ emptyset))))=>(![X2:$i, X3:$i]:?[X473:$i]:(in @ X473 @ (setunion @ (kpair @ X2 @ X3))&?[X474:$i]:(in @ X474 @ (setunion @ (kpair @ X2 @ X3))&(kpair @ X2 @ X3)=(setadjoin @ (setadjoin @ X473 @ emptyset) @ (setadjoin @ (setadjoin @ X473 @ (setadjoin @ X474 @ emptyset)) @ emptyset))))=>(![X4:$i, X2:$i]:(in @ X2 @ X4=>subset @ (setadjoin @ X2 @ emptyset) @ X4)=>(![X4:$i, X2:$i]:(in @ X2 @ X4=>in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))=>(![X2:$i, X3:$i, X14:$i]:(in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=>((X14)=(X2)|(X14)=(X3)))=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5)))=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5))))=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5))))=>(![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5)))))=>(![X4:$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:$i]:(in @ X18 @ (cartprod @ X4 @ X5)=>?[X475:$i]:(in @ X475 @ (setunion @ X18)&?[X476:$i]:(in @ X476 @ (setunion @ X18)&(X18)=(setadjoin @ (setadjoin @ X475 @ emptyset) @ (setadjoin @ (setadjoin @ X475 @ (setadjoin @ X476 @ emptyset)) @ emptyset)))))=>(![X4:$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:$i]:(in @ X3 @ X4=>(X1 @ X2=>(X1 @ X3=>(X2)=(X3)))))=>(?[X2:$i]:(in @ X2 @ X4&X1 @ X2)=>?[X477:$i]:(in @ X477 @ (dsetconstr @ X4 @ (epred1_2 @ X1))&(dsetconstr @ X4 @ (epred1_2 @ X1))=(setadjoin @ X477 @ emptyset))))=>![X4:$i, X1:$i > $o]:(?[X479:$i]:(in @ X479 @ (dsetconstr @ X4 @ (epred1_2 @ X1))&(dsetconstr @ X4 @ (epred1_2 @ X1))=(setadjoin @ X479 @ emptyset))=>?[X2:$i]:(X1 @ X2&in @ X2 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def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setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_160]), foundationAx]), wellorderingAx]), c_0_161]), dsetconstrI]), dsetconstrEL]), dsetconstrER]), c_0_162]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_163]), setext]), emptyI]), noeltsimpempty]), setbeta]), c_0_164]), c_0_165]), c_0_166]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), setoftrueEq]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_167]), c_0_168]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), emptyE1]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_169]), c_0_170]), c_0_171]), inCongP]), in__Cong]), c_0_172]), c_0_173]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_174]), c_0_175]), 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_176]), c_0_177]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1]), c_0_178]), setunionE2]), setunionsingleton1]), setunionsingleton2]), setunionsingleton]), c_0_179]), c_0_180]), c_0_181]), c_0_181]), c_0_181]), c_0_181]), c_0_181]), c_0_181]), c_0_181]), c_0_181]), c_0_181]), c_0_181]), c_0_181]), c_0_181]), c_0_181]), c_0_181]), c_0_181]), c_0_182]), c_0_181]), c_0_181])])]), c_0_183])). 1.20/1.40 thf(c_0_185, negated_conjecture, ![X484:$i, X485:$i, X487:$i, X488:$i, X489:$i, X490:$i, X491:$i, X492:$i, X493:$i, X494:$i, X495:$i, X497:$i, X498:$i, X500:$i, X501:$i, X502:$i, X503:$i, X504:$i, X506:$i, X507:$i > $i > $o, X508:$i, X510:$i, X513:$i, X515:$i, X516:$i, X517:$i, X518:$i, X520:$i, X521:$i > $o, X522:$i, X524:$i, X525:$i > $o, X526:$i, X527:$i, X528:$i > $o, X529:$i, X530:$i, X531:$i > $o, X532:$i, X533:$i > $o, X534:$i, X537:$i, X538:$o, X539:$i, X540:$i, X541:$o, X542:$i, X543:$i, X544:$i > $o, X545:$i, X548:$i, X549:$i, X552:$i, X554:$i, X556:$i, X557:$i > $o, X558:$i, X559:$i, X561:$i, X562:$i > $o, X563:$i, X564:$i, X565:$i, X566:$i, X567:$i, X568:$i, X569:$i, X570:$i, X571:$i, X572:$i, X573:$i, X574:$o, X575:$i, X576:$i, X577:$i, X578:$i, X579:$i, X580:$i, X582:$i, X583:$i, X584:$i, X585:$i, X586:$i, X587:$i, X588:$i, X589:$i, X590:$i, X591:$i, X592:$o, X594:$i, X595:$i, X596:$i > $o, X597:$i, X600:$i, X601:$i, X602:$i, X604:$i, X605:$i, X606:$i, X607:$i, X608:$i, X609:$i, X610:$i, X611:$i, X612:$i, X613:$i, X614:$i, X615:$i, X616:$i, X617:$i, X618:$i, X619:$i, X620:$i > $o, X621:$i, X622:$i > $o, X623:$i, X624:$i, X625:$i > $o, X626:$i, X628:$i, X629:$i > $o, X631:$i, X632:$i, X633:$i > $o, X635:$i, X636:$i, X637:$i > $o, X638:$i, X640:$o, X641:$o, X642:$i, X643:$i > $o, X645:$i, X646:$i, X647:$i > $o, X648:$i, X650:$i > $o, X651:$i, X654:$i, X655:$i > $o, X656:$i, X660:$i, X661:$i > $o, X662:$i, X665:$i, X666:$i, X667:$i, X668:$i, X669:$i, X670:$i, X671:$i, X672:$i, X673:$i, X674:$i > $o, X675:$i, X677:$i, X678:$i, X679:$i > $o, X680:$i > $o, X683:$i, X686:$i, X687:$i, X690:$i, X691:$i, X692:$i, X693:$i, X694:$i, X695:$i, X696:$i, X697:$i, X698:$i, X699:$i > $o, X700:$i, X702:$i, X703:$i, X704:$i > $o, X705:$i > $o, X708:$i, X710:$i, X712:$i, X713:$i, X714:$i > $o, X715:$i > $o, X718:$i, X719:$i, X721:$i, X722:$i, X723:$i, X724:$i, X725:$i, X726:$i, X728:$i, X729:$i, X730:$i, X731:$i, X732:$i, X733:$i, X734:$i, X735:$i, X736:$i, X737:$i, X738:$i, X739:$i, X740:$i, X741:$i, X742:$i, X743:$i, X744:$i, X745:$i, X746:$i, X747:$i, X748:$i, X749:$i, X750:$i, X751:$i, X752:$i, X753:$i, X754:$i, X755:$i, X756:$i, X757:$i, X758:$i, X759:$i, X760:$i, X761:$i, X762:$i, X763:$i, X764:$i, X765:$i > $o, X766:$i, X767:$i > $o, X768:$i, X769:$i, X770:$i, X771:$i, X772:$i, X773:$i, X774:$i, X775:$i, X776:$i, X777:$i, X778:$i, X779:$o, X780:$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, X808:$i, X809:$i, X810:$i, X811:$i, X812:$i, X813:$i, X814:$i, X815:$i, X816:$i, X817:$i, X818:$i, X819:$i, X820:$i, X821:$i, X822:$i, X823:$i, X824:$i, X825:$i, X826:$i, X827:$i, X828:$i, X829:$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:$i, X847:$o, X848:$i, X849:$i, X850:$i, X851:$i, X852:$i, X853:$i, X854:$i, X855:$i, X856:$i, X857:$i, X858:$i, X859:$i, X860:$i, X861:$i, X862:$i, X863:$i, X864:$i, X865:$i, X866:$i, X867:$i, X870:$i, X871:$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:$i, X897:$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:$i, X913:$i, X914:$i, X915:$i, X918:$i, X919:$i, X921:$i, X922:$i, X923:$i, X924:$i, X925:$i > $o, X928:$i, X933:$i]:(((~in @ (esk1_2 @ X484 @ X485) @ X484|~in @ (esk1_2 @ X484 @ X485) @ X485|(X484)=(X485))&(in @ (esk1_2 @ X484 @ X485) @ X484|in @ (esk1_2 @ X484 @ X485) @ X485|(X484)=(X485)))&(~in @ X487 @ emptyset&(((~in @ X490 @ (setadjoin @ X488 @ X489)|((X490)=(X488)|in @ X490 @ X489))&(((X490)!=(X488)|in @ X490 @ (setadjoin @ X488 @ X489))&(~in @ X490 @ X489|in @ X490 @ (setadjoin @ X488 @ X489))))&(((~in @ X492 @ (powerset @ X491)|(~in @ X493 @ X492|in @ X493 @ X491))&((in @ (esk2_2 @ X494 @ X495) @ X495|in @ X495 @ (powerset @ X494))&(~in @ (esk2_2 @ X494 @ X495) @ X494|in @ X495 @ (powerset @ X494))))&((((in @ X498 @ (esk3_2 @ X497 @ X498)|~in @ X498 @ (setunion @ X497))&(in @ (esk3_2 @ X497 @ X498) @ X497|~in @ X498 @ (setunion @ X497)))&(~in @ X501 @ X502|~in @ X502 @ X500|in @ X501 @ (setunion @ X500)))&(in @ emptyset @ omega&((~in @ X503 @ omega|in @ (setadjoin @ X503 @ X503) @ omega)&((((in @ (esk4_1 @ X504) @ omega|~in @ emptyset @ X504|(~in @ X506 @ omega|in @ X506 @ X504))&(in @ (esk4_1 @ X504) @ X504|~in @ emptyset @ X504|(~in @ X506 @ omega|in @ X506 @ X504)))&(~in @ (setadjoin @ (esk4_1 @ X504) @ (esk4_1 @ X504)) @ X504|~in @ emptyset @ X504|(~in @ X506 @ omega|in @ X506 @ X504)))&(((((in @ (esk8_3 @ X507 @ X508 @ X513) @ X508|~in @ X513 @ (esk7_2 @ X507 @ X508)|in @ (esk5_2 @ X507 @ X508) @ X508)&(X507 @ (esk8_3 @ X507 @ X508 @ X513) @ X513|~in @ X513 @ (esk7_2 @ X507 @ X508)|in @ (esk5_2 @ X507 @ X508) @ X508))&(~in @ X516 @ X508|~X507 @ X516 @ X515|in @ X515 @ (esk7_2 @ X507 @ X508)|in @ (esk5_2 @ X507 @ X508) @ X508))&((((in @ (esk8_3 @ X507 @ X508 @ X513) @ X508|~in @ X513 @ (esk7_2 @ X507 @ X508)|(X507 @ (esk5_2 @ X507 @ X508) @ (esk6_3 @ X507 @ X508 @ X510)|~X507 @ (esk5_2 @ X507 @ X508) @ X510))&(X507 @ (esk8_3 @ X507 @ X508 @ X513) @ X513|~in @ X513 @ (esk7_2 @ X507 @ X508)|(X507 @ (esk5_2 @ X507 @ X508) @ (esk6_3 @ X507 @ X508 @ X510)|~X507 @ (esk5_2 @ X507 @ X508) @ X510)))&(~in @ X516 @ X508|~X507 @ X516 @ X515|in @ X515 @ (esk7_2 @ X507 @ X508)|(X507 @ (esk5_2 @ X507 @ X508) @ (esk6_3 @ X507 @ X508 @ X510)|~X507 @ (esk5_2 @ X507 @ X508) @ X510)))&(((in @ (esk8_3 @ X507 @ X508 @ X513) @ X508|~in @ X513 @ (esk7_2 @ X507 @ X508)|((X510)!=(esk6_3 @ X507 @ X508 @ X510)|~X507 @ (esk5_2 @ X507 @ X508) @ X510))&(X507 @ (esk8_3 @ X507 @ X508 @ X513) @ X513|~in @ X513 @ (esk7_2 @ X507 @ X508)|((X510)!=(esk6_3 @ X507 @ X508 @ X510)|~X507 @ (esk5_2 @ X507 @ X508) @ X510)))&(~in @ X516 @ X508|~X507 @ X516 @ X515|in @ X515 @ (esk7_2 @ X507 @ X508)|((X510)!=(esk6_3 @ X507 @ X508 @ X510)|~X507 @ (esk5_2 @ X507 @ X508) @ X510)))))&(((in @ (esk9_1 @ X517) @ X517|~in @ X518 @ X517)&(~in @ X520 @ (esk9_1 @ X517)|~in @ X520 @ X517|~in @ X518 @ X517))&(epred3_0&(((X521 @ (esk10_2 @ X521 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X708)|~X704 @ X708)|(X704 @ (esk46_2 @ X704 @ X705)|X705 @ (esk47_2 @ X704 @ X705))))&((X705 @ (esk49_3 @ X704 @ X705 @ X710)|~X705 @ X710|(descr @ (epred1_2 @ X704))=(descr @ (epred1_2 @ X705))|((X708)!=(esk48_3 @ X704 @ X705 @ X708)|~X704 @ X708)|(X704 @ (esk46_2 @ X704 @ X705)|X705 @ (esk47_2 @ X704 @ X705)))&((X710)!=(esk49_3 @ X704 @ X705 @ X710)|~X705 @ X710|(descr @ (epred1_2 @ X704))=(descr @ (epred1_2 @ X705))|((X708)!=(esk48_3 @ X704 @ X705 @ X708)|~X704 @ X708)|(X704 @ (esk46_2 @ X704 @ X705)|X705 @ (esk47_2 @ X704 @ X705)))))))&(((in @ (esk50_4 @ X712 @ X713 @ X714 @ X715) @ X712|(dsetconstr @ X712 @ (epred1_2 @ X714))=(dsetconstr @ X713 @ (epred1_2 @ X715))|(X712)!=(X713))&((in @ (esk51_4 @ X712 @ X713 @ X714 @ X715) @ X713|(dsetconstr @ X712 @ (epred1_2 @ X714))=(dsetconstr @ X713 @ (epred1_2 @ X715))|(X712)!=(X713))&(((esk50_4 @ X712 @ X713 @ X714 @ X715)=(esk51_4 @ X712 @ X713 @ X714 @ X715)|(dsetconstr @ X712 @ (epred1_2 @ X714))=(dsetconstr @ X713 @ (epred1_2 @ X715))|(X712)!=(X713))&((~X714 @ (esk50_4 @ X712 @ X713 @ X714 @ X715)|~X715 @ (esk51_4 @ X712 @ X713 @ X714 @ X715)|(dsetconstr @ X712 @ (epred1_2 @ X714))=(dsetconstr @ X713 @ (epred1_2 @ X715))|(X712)!=(X713))&(X714 @ (esk50_4 @ X712 @ X713 @ X714 @ X715)|X715 @ (esk51_4 @ X712 @ X713 @ X714 @ X715)|(dsetconstr @ X712 @ (epred1_2 @ X714))=(dsetconstr @ X713 @ (epred1_2 @ X715))|(X712)!=(X713))))))&(((in @ (esk52_2 @ X718 @ X719) @ X718|subset @ X718 @ X719)&(~in @ (esk52_2 @ X718 @ X719) @ X719|subset @ X718 @ X719))&(((X721)!=(X722)|subset @ X722 @ X721)&(((X723)!=(X724)|subset @ X723 @ X724)&(((in @ (esk53_2 @ X725 @ X726) @ X725|subset @ X725 @ X726)&(~in @ (esk53_2 @ X725 @ X726) @ X726|subset @ X725 @ X726))&(subset @ emptyset @ X728&((~subset @ X729 @ X730|(~in @ X731 @ X729|in @ X731 @ X730))&((~subset @ X732 @ X733|(in @ X734 @ X733|~in @ X734 @ X732))&((~in @ X737 @ X735|(in @ X737 @ X736|~subset @ X735 @ X736))&((subset @ X738 @ X739|(X738)!=(X739))&((~in @ X742 @ X740|(in @ X742 @ X741|(X740)!=(X741)))&(subset @ X743 @ X743&((~subset @ X744 @ X745|(~subset @ X745 @ X746|subset @ X744 @ X746))&(subset @ X748 @ (setadjoin @ X747 @ X748)&((~subset @ X749 @ X751|subset @ X749 @ (setadjoin @ X750 @ X751))&((~subset @ X752 @ X753|in @ X752 @ (powerset @ X753))&((~subset @ X754 @ X755|(~subset @ X755 @ X754|(X754)=(X755)))&((~subset @ X756 @ emptyset|(X756)=(emptyset))&((~subset @ X758 @ X757|in @ X758 @ (powerset @ X757))&((~in @ X760 @ (powerset @ X759)|subset @ X760 @ X759)&(in @ X761 @ (powerset @ X761)&((~subset @ X762 @ X763|subset @ (powerset @ X762) @ (powerset @ X763))&(in @ (dsetconstr @ X764 @ (epred1_2 @ X765)) @ (powerset @ X764)&(subset @ (dsetconstr @ X766 @ (epred1_2 @ X767)) @ X766&((~in @ X770 @ X768|in @ X770 @ (binunion @ X768 @ X769))&(in @ X772 @ (setadjoin @ X771 @ (setadjoin @ X772 @ emptyset))&((~in @ X775 @ X774|in @ X775 @ (binunion @ X773 @ X774))&((((in @ X778 @ X777|X779|in @ X778 @ X776|~in @ X778 @ (binunion @ X776 @ X777))&(~X779|X779|in @ X778 @ X776|~in @ X778 @ (binunion @ X776 @ X777)))&((in @ X778 @ X777|X779|~X779|~in @ X778 @ (binunion @ X776 @ X777))&(~X779|X779|~X779|~in @ X778 @ (binunion @ X776 @ X777))))&((~in @ X782 @ (binunion @ X780 @ X781)|(in @ X782 @ X780|in @ X782 @ X781))&(subset @ X783 @ (binunion @ X783 @ X784)&(subset @ X786 @ (binunion @ X785 @ X786)&((~in @ X789 @ X787|(~in @ X789 @ X788|in @ X789 @ (binintersect @ X787 @ X788)))&((~subset @ X792 @ X790|(~subset @ X792 @ X791|subset @ X792 @ (binintersect @ X790 @ X791)))&((~in @ X795 @ (binintersect @ X793 @ X794)|in @ X795 @ X793)&(subset @ (binintersect @ X796 @ X797) @ X796&((~subset @ X798 @ X799|(binintersect @ X798 @ X799)=(X798))&(((binintersect @ X800 @ X801)!=(X801)|subset @ X801 @ X800)&((~in @ X804 @ (binintersect @ X802 @ X803)|in @ X804 @ X803)&(((in @ (esk54_2 @ X805 @ X806) @ X805|(binintersect @ X805 @ X806)=(emptyset))&(in @ (esk54_2 @ X805 @ X806) @ X806|(binintersect @ X805 @ X806)=(emptyset)))&(subset @ (binintersect @ X808 @ X809) @ X809&((~subset @ X811 @ X810|(binintersect @ X810 @ X811)=(X811))&(((binintersect @ X812 @ X813)!=(X812)|subset @ X812 @ X813)&((binintersect @ X814 @ (binunion @ X815 @ X816))=(binunion @ (binintersect @ X814 @ X815) @ (binintersect @ X814 @ X816))&((~in @ X819 @ X817|(in @ X819 @ X818|in @ X819 @ (setminus @ X817 @ X818)))&((~in @ X822 @ (setminus @ X820 @ X821)|in @ X822 @ X820)&((~in @ X825 @ (setminus @ X823 @ X824)|~in @ X825 @ X824)&((~subset @ X826 @ X827|(setminus @ X826 @ X827)=(emptyset))&((in @ X830 @ (setminus @ X828 @ X829)|(~in @ X830 @ X828|in @ X830 @ X829))&((in @ X833 @ (setminus @ X831 @ X832)|(in @ X833 @ X832|~in @ X833 @ X831))&((in @ X836 @ X834|~in @ X836 @ (setminus @ X834 @ X835))&((~in @ X839 @ X838|~in @ X839 @ (setminus @ X837 @ X838))&(subset @ (setminus @ X840 @ X841) @ X840&(((setminus @ X842 @ X843)!=(emptyset)|subset @ X842 @ X843)&((((~in @ X846 @ X844|X847|in @ X846 @ X844|~in @ X846 @ (symdiff @ X844 @ X845))&((in @ X846 @ X845|X847|in @ X846 @ X844|~in @ X846 @ (symdiff @ X844 @ X845))&(~X847|X847|in @ X846 @ X844|~in @ X846 @ (symdiff @ X844 @ X845))))&(((~in @ X846 @ X844|X847|~in @ X846 @ X845|~in @ X846 @ (symdiff @ X844 @ X845))&((in @ X846 @ X845|X847|~in @ X846 @ X845|~in @ X846 @ (symdiff @ X844 @ X845))&(~X847|X847|~in @ X846 @ X845|~in @ X846 @ (symdiff @ X844 @ X845))))&((~in @ X846 @ X844|X847|~X847|~in @ X846 @ (symdiff @ X844 @ X845))&((in @ X846 @ X845|X847|~X847|~in @ X846 @ (symdiff @ X844 @ X845))&(~X847|X847|~X847|~in @ X846 @ (symdiff @ X844 @ X845))))))&((~in @ X850 @ X848|(in @ X850 @ X849|in @ X850 @ (symdiff @ X848 @ X849)))&((in @ X853 @ X851|(~in @ X853 @ X852|in @ X853 @ (symdiff @ X851 @ X852)))&((~in @ X856 @ X854|(~in @ X856 @ X855|~in @ X856 @ (symdiff @ X854 @ X855)))&((in @ X859 @ X857|(in @ X859 @ X858|~in @ X859 @ (symdiff @ X857 @ X858)))&(in @ X861 @ (setadjoin @ X860 @ (setadjoin @ X861 @ emptyset))&(in @ X862 @ (setunion @ (setadjoin @ (setadjoin @ X862 @ emptyset) @ (setadjoin @ (setadjoin @ X862 @ (setadjoin @ X863 @ emptyset)) @ emptyset)))&(in @ X865 @ (setunion @ (setadjoin @ (setadjoin @ X864 @ emptyset) @ (setadjoin @ (setadjoin @ X864 @ (setadjoin @ X865 @ emptyset)) @ emptyset)))&((in @ (esk55_2 @ X866 @ X867) @ (setunion @ (setadjoin @ (setadjoin @ X866 @ emptyset) @ (setadjoin @ (setadjoin @ X866 @ (setadjoin @ X867 @ emptyset)) @ emptyset)))&(in @ (esk56_2 @ X866 @ X867) @ (setunion @ (setadjoin @ (setadjoin @ X866 @ emptyset) @ (setadjoin @ (setadjoin @ X866 @ (setadjoin @ X867 @ emptyset)) @ emptyset)))&(setadjoin @ (setadjoin @ X866 @ emptyset) @ (setadjoin @ (setadjoin @ X866 @ (setadjoin @ X867 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ (esk55_2 @ X866 @ X867) @ emptyset) @ (setadjoin @ (setadjoin @ (esk55_2 @ X866 @ X867) @ (setadjoin @ (esk56_2 @ X866 @ X867) @ emptyset)) @ emptyset))))&((in @ (esk57_2 @ X870 @ X871) @ (setunion @ (kpair @ X870 @ X871))&(in @ (esk58_2 @ X870 @ X871) @ (setunion @ (kpair @ X870 @ X871))&(kpair @ X870 @ X871)=(setadjoin @ (setadjoin @ (esk57_2 @ X870 @ X871) @ emptyset) @ (setadjoin @ (setadjoin @ (esk57_2 @ X870 @ X871) @ (setadjoin @ (esk58_2 @ X870 @ X871) @ emptyset)) @ emptyset))))&((~in @ X875 @ X874|subset @ (setadjoin @ X875 @ emptyset) @ X874)&((~in @ X877 @ X876|in @ (setadjoin @ X877 @ emptyset) @ (powerset @ X876))&((~in @ X880 @ X878|in @ (setadjoin @ X880 @ emptyset) @ (powerset @ (binunion @ X878 @ X879)))&((~in @ X883 @ (setadjoin @ X881 @ (setadjoin @ X882 @ emptyset))|((X883)=(X881)|(X883)=(X882)))&((~in @ X886 @ X884|(~in @ X887 @ X885|subset @ (setadjoin @ X886 @ (setadjoin @ X887 @ emptyset)) @ (binunion @ X884 @ X885)))&((~in @ X890 @ X888|(~in @ X891 @ X889|in @ (setadjoin @ X890 @ (setadjoin @ X891 @ emptyset)) @ (powerset @ (binunion @ X888 @ X889))))&((~in @ X894 @ X892|(~in @ X895 @ X893|subset @ (setadjoin @ (setadjoin @ X894 @ emptyset) @ (setadjoin @ (setadjoin @ X894 @ (setadjoin @ X895 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X892 @ X893))))&((~in @ X898 @ X896|(~in @ X899 @ X897|in @ (setadjoin @ (setadjoin @ X898 @ emptyset) @ (setadjoin @ (setadjoin @ X898 @ (setadjoin @ X899 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X896 @ X897)))))&((~in @ X902 @ X900|(~in @ X903 @ X901|in @ (kpair @ X902 @ X903) @ (powerset @ (powerset @ (binunion @ X900 @ X901)))))&((~in @ X906 @ X904|(~in @ X907 @ X905|in @ (kpair @ X906 @ X907) @ (cartprod @ X904 @ X905)))&(((in @ (esk59_3 @ X908 @ X909 @ X910) @ X908|~in @ X910 @ (cartprod @ X908 @ X909))&((in @ (esk60_3 @ X908 @ X909 @ X910) @ X909|~in @ X910 @ (cartprod @ X908 @ X909))&((X910)=(kpair @ (esk59_3 @ X908 @ X909 @ X910) @ (esk60_3 @ X908 @ X909 @ X910))|~in @ X910 @ (cartprod @ X908 @ X909))))&(((in @ (esk61_3 @ X913 @ X914 @ X915) @ (setunion @ X915)|~in @ X915 @ (cartprod @ X913 @ X914))&((in @ (esk62_3 @ X913 @ X914 @ X915) @ (setunion @ X915)|~in @ X915 @ (cartprod @ X913 @ X914))&((X915)=(setadjoin @ (setadjoin @ (esk61_3 @ X913 @ X914 @ X915) @ emptyset) @ (setadjoin @ (setadjoin @ (esk61_3 @ X913 @ X914 @ X915) @ (setadjoin @ (esk62_3 @ X913 @ X914 @ X915) @ emptyset)) @ emptyset))|~in @ X915 @ (cartprod @ X913 @ X914))))&(((in @ (esk63_2 @ X918 @ X919) @ X918|~in @ X919 @ (setunion @ X918))&(in @ X919 @ (esk63_2 @ X918 @ X919)|~in @ X919 @ (setunion @ X918)))&(subset @ (setunion @ (setadjoin @ X921 @ emptyset)) @ X921&(subset @ X922 @ (setunion @ (setadjoin @ X922 @ emptyset))&((setunion @ (setadjoin @ X923 @ emptyset))=(X923)&((((in @ (esk66_2 @ X924 @ X925) @ (dsetconstr @ X924 @ (epred1_2 @ X925))|(~in @ X928 @ X924|~X925 @ X928)|in @ (esk64_2 @ X924 @ X925) @ X924)&((dsetconstr @ X924 @ (epred1_2 @ X925))=(setadjoin @ (esk66_2 @ X924 @ X925) @ emptyset)|(~in @ X928 @ X924|~X925 @ X928)|in @ (esk64_2 @ X924 @ X925) @ X924))&(((in @ (esk66_2 @ X924 @ X925) @ (dsetconstr @ X924 @ (epred1_2 @ X925))|(~in @ X928 @ X924|~X925 @ X928)|in @ (esk65_2 @ X924 @ X925) @ X924)&((dsetconstr @ X924 @ (epred1_2 @ X925))=(setadjoin @ (esk66_2 @ X924 @ X925) @ emptyset)|(~in @ X928 @ X924|~X925 @ X928)|in @ (esk65_2 @ X924 @ X925) @ X924))&(((in @ (esk66_2 @ X924 @ X925) @ (dsetconstr @ X924 @ (epred1_2 @ X925))|(~in @ X928 @ X924|~X925 @ X928)|X925 @ (esk64_2 @ X924 @ X925))&((dsetconstr @ X924 @ (epred1_2 @ X925))=(setadjoin @ (esk66_2 @ X924 @ X925) @ emptyset)|(~in @ X928 @ X924|~X925 @ X928)|X925 @ (esk64_2 @ X924 @ X925)))&(((in @ (esk66_2 @ X924 @ X925) @ (dsetconstr @ X924 @ (epred1_2 @ X925))|(~in @ X928 @ X924|~X925 @ X928)|X925 @ (esk65_2 @ X924 @ X925))&((dsetconstr @ X924 @ (epred1_2 @ X925))=(setadjoin @ (esk66_2 @ X924 @ X925) @ emptyset)|(~in @ X928 @ X924|~X925 @ X928)|X925 @ (esk65_2 @ X924 @ X925)))&((in @ (esk66_2 @ X924 @ X925) @ (dsetconstr @ X924 @ (epred1_2 @ X925))|(~in @ X928 @ X924|~X925 @ X928)|(esk64_2 @ X924 @ X925)!=(esk65_2 @ X924 @ X925))&((dsetconstr @ X924 @ (epred1_2 @ X925))=(setadjoin @ (esk66_2 @ X924 @ X925) @ emptyset)|(~in @ X928 @ X924|~X925 @ X928)|(esk64_2 @ X924 @ X925)!=(esk65_2 @ X924 @ X925)))))))&((in @ esk68_0 @ (dsetconstr @ esk67_0 @ (epred1_2 @ epred4_0))&(dsetconstr @ esk67_0 @ (epred1_2 @ epred4_0))=(setadjoin @ esk68_0 @ emptyset))&(~epred4_0 @ X933|~in @ X933 @ esk67_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_184])])])])])])). 1.20/1.40 thf(c_0_186, negated_conjecture, ![X1:$i > $o, X2:$i]:subset @ (dsetconstr @ X2 @ (epred1_2 @ X1)) @ X2, inference(split_conjunct,[status(thm)],[c_0_185])). 1.20/1.40 thf(c_0_187, negated_conjecture, (dsetconstr @ esk67_0 @ (epred1_2 @ epred4_0))=(setadjoin @ esk68_0 @ emptyset), inference(split_conjunct,[status(thm)],[c_0_185])). 1.20/1.40 thf(c_0_188, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(in @ X2 @ X4|~in @ X2 @ (binintersect @ X3 @ X4)), inference(split_conjunct,[status(thm)],[c_0_185])). 1.20/1.40 thf(c_0_189, negated_conjecture, ![X2:$i]:(in @ (esk17_1 @ X2) @ X2|(X2)=(emptyset)), inference(split_conjunct,[status(thm)],[c_0_185])). 1.20/1.40 thf(c_0_190, negated_conjecture, ![X2:$i, X3:$i]:((binintersect @ X2 @ X3)=(X2)|~subset @ X2 @ X3), inference(split_conjunct,[status(thm)],[c_0_185])). 1.20/1.40 thf(c_0_191, negated_conjecture, subset @ (setadjoin @ esk68_0 @ emptyset) @ esk67_0, inference(spm,[status(thm)],[c_0_186, c_0_187])). 1.20/1.40 thf(c_0_192, negated_conjecture, ![X2:$i, X3:$i]:((binintersect @ X2 @ X3)=(emptyset)|in @ (esk17_1 @ (binintersect @ X2 @ X3)) @ X3), inference(spm,[status(thm)],[c_0_188, c_0_189])). 1.20/1.40 thf(c_0_193, negated_conjecture, (binintersect @ (setadjoin @ esk68_0 @ emptyset) @ esk67_0)=(setadjoin @ esk68_0 @ emptyset), inference(spm,[status(thm)],[c_0_190, c_0_191])). 1.20/1.40 thf(c_0_194, negated_conjecture, ![X3:$i, X2:$i]:((X2)=(X3)|~in @ X3 @ (setadjoin @ X2 @ emptyset)), inference(split_conjunct,[status(thm)],[c_0_185])). 1.20/1.40 thf(c_0_195, negated_conjecture, ((setadjoin @ esk68_0 @ emptyset)=(emptyset)|in @ (esk17_1 @ (setadjoin @ esk68_0 @ emptyset)) @ esk67_0), inference(spm,[status(thm)],[c_0_192, c_0_193])). 1.20/1.40 thf(c_0_196, negated_conjecture, ![X2:$i]:((esk17_1 @ (setadjoin @ X2 @ emptyset))=(X2)|(setadjoin @ X2 @ emptyset)=(emptyset)), inference(spm,[status(thm)],[c_0_194, c_0_189])). 1.20/1.40 thf(c_0_197, negated_conjecture, ![X3:$i, X2:$i, X1:$i > $o]:(X1 @ X2|~in @ X2 @ (dsetconstr @ X3 @ (epred1_2 @ X1))), inference(split_conjunct,[status(thm)],[c_0_185])). 1.20/1.40 thf(c_0_198, negated_conjecture, ![X2:$i, X3:$i]:in @ X2 @ (setadjoin @ X2 @ X3), inference(split_conjunct,[status(thm)],[c_0_185])). 1.20/1.40 thf(c_0_199, negated_conjecture, ((setadjoin @ esk68_0 @ emptyset)=(emptyset)|in @ esk68_0 @ esk67_0), inference(spm,[status(thm)],[c_0_195, c_0_196])). 1.20/1.40 thf(c_0_200, negated_conjecture, ![X2:$i]:~in @ X2 @ emptyset, inference(split_conjunct,[status(thm)],[c_0_185])). 1.20/1.40 thf(c_0_201, negated_conjecture, ![X2:$i]:(epred4_0 @ X2|~in @ X2 @ (setadjoin @ esk68_0 @ emptyset)), inference(spm,[status(thm)],[c_0_197, c_0_187])). 1.20/1.40 thf(c_0_202, negated_conjecture, ![X2:$i]:(~epred4_0 @ X2|~in @ X2 @ esk67_0), inference(split_conjunct,[status(thm)],[c_0_185])). 1.20/1.40 thf(c_0_203, negated_conjecture, in @ esk68_0 @ esk67_0, inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_198, c_0_199]), c_0_200])). 1.20/1.40 thf(c_0_204, negated_conjecture, epred4_0 @ esk68_0, inference(spm,[status(thm)],[c_0_201, c_0_198])). 1.20/1.40 thf(c_0_205, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_202, c_0_203]), c_0_204])]), ['proof']). 1.20/1.40 # SZS output end CNFRefutation 1.20/1.40 # Proof object total steps : 206 1.20/1.40 # Proof object clause steps : 20 1.20/1.40 # Proof object formula steps : 186 1.20/1.40 # Proof object conjectures : 23 1.20/1.40 # Proof object clause conjectures : 20 1.20/1.40 # Proof object formula conjectures : 3 1.20/1.40 # Proof object initial clauses used : 10 1.20/1.40 # Proof object initial formulas used : 160 1.20/1.40 # Proof object generating inferences : 10 1.20/1.40 # Proof object simplifying inferences : 3 1.20/1.40 # Training examples: 0 positive, 0 negative 1.20/1.40 # Parsed axioms : 340 1.20/1.40 # Removed by relevancy pruning/SinE : 0 1.20/1.40 # Initial clauses : 484 1.20/1.40 # Removed in clause preprocessing : 206 1.20/1.40 # Initial clauses in saturation : 278 1.20/1.40 # Processed clauses : 4910 1.20/1.40 # ...of these trivial : 40 1.20/1.40 # ...subsumed : 2963 1.20/1.40 # ...remaining for further processing : 1907 1.20/1.40 # Other redundant clauses eliminated : 3518 1.20/1.40 # Clauses deleted for lack of memory : 0 1.20/1.40 # Backward-subsumed : 17 1.20/1.40 # Backward-rewritten : 48 1.20/1.40 # Generated clauses : 59208 1.20/1.40 # ...of the previous two non-trivial : 42310 1.20/1.40 # Contextual simplify-reflections : 0 1.20/1.40 # Paramodulations : 42429 1.20/1.40 # Factorizations : 2 1.20/1.40 # NegExts : 19 1.20/1.40 # Equation resolutions : 3518 1.20/1.40 # Propositional unsat checks : 0 1.20/1.40 # Propositional check models : 0 1.20/1.40 # Propositional check unsatisfiable : 0 1.20/1.40 # Propositional clauses : 0 1.20/1.40 # Propositional clauses after purity: 0 1.20/1.40 # Propositional unsat core size : 0 1.20/1.40 # Propositional preprocessing time : 0.000 1.20/1.40 # Propositional encoding time : 0.000 1.20/1.40 # Propositional solver time : 0.000 1.20/1.40 # Success case prop preproc time : 0.000 1.20/1.40 # Success case prop encoding time : 0.000 1.20/1.40 # Success case prop solver time : 0.000 1.20/1.40 # Current number of processed clauses : 1590 1.20/1.40 # Positive orientable unit clauses : 515 1.20/1.40 # Positive unorientable unit clauses: 0 1.20/1.40 # Negative unit clauses : 505 1.20/1.40 # Non-unit-clauses : 570 1.20/1.40 # Current number of unprocessed clauses: 37710 1.20/1.40 # ...number of literals in the above : 119422 1.20/1.40 # Current number of archived formulas : 0 1.20/1.40 # Current number of archived clauses : 304 1.20/1.40 # Clause-clause subsumption calls (NU) : 36831 1.20/1.40 # Rec. Clause-clause subsumption calls : 22102 1.20/1.40 # Non-unit clause-clause subsumptions : 477 1.20/1.40 # Unit Clause-clause subsumption calls : 65479 1.20/1.40 # Rewrite failures with RHS unbound : 0 1.20/1.40 # BW rewrite match attempts : 755 1.20/1.40 # BW rewrite match successes : 42 1.20/1.40 # Condensation attempts : 0 1.20/1.40 # Condensation successes : 0 1.20/1.40 # Termbank termtop insertions : 1041112 1.20/1.40 1.20/1.40 # ------------------------------------------------- 1.20/1.40 # User time : 1.030 s 1.20/1.40 # System time : 0.031 s 1.20/1.40 # Total time : 1.061 s 1.20/1.40 # Maximum resident set size: 1996 pages 1.20/1.40 EOF