0.12/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.17 % 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 0.17/0.38 % Computer : n013.cluster.edu 0.17/0.38 % Model : x86_64 x86_64 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.17/0.38 % Memory : 8042.1875MB 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64 0.17/0.38 % CPULimit : 1200 0.17/0.38 % WCLimit : 120 0.17/0.38 % DateTime : Tue Jul 13 12:46:18 EDT 2021 0.17/0.38 % CPUTime : 0.17/0.38 % Number of cores: 8 0.17/0.38 % Python version: Python 3.6.8 0.17/0.38 # Version: 2.6rc1-ho 0.17/0.40 # No SInE strategy applied 0.17/0.40 # Trying AutoSched0 for 59 seconds 1.33/1.49 # AutoSched0-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S2g 1.33/1.49 # and selection function SelectCQArNpEqFirst. 1.33/1.49 # 1.33/1.49 # Preprocessing time : 0.187 s 1.33/1.49 # Presaturation interreduction done 1.33/1.49 1.33/1.49 # Proof found! 1.33/1.49 # SZS status Theorem 1.33/1.49 # SZS output start CNFRefutation 1.33/1.49 thf(wellorderedByIn, axiom, (wellorderedByIn)=(^[X4:$i]:(((![X1193:$i]:(in @ X1193 @ X4=>![X1194:$i]:(in @ X1194 @ X4=>![X1195:$i]:(in @ X1195 @ X4=>((in @ X1193 @ X1194&in @ X1194 @ X1195)=>in @ X1193 @ X1195))))&![X1196:$i]:(in @ X1196 @ X4=>![X1197:$i]:(in @ X1197 @ X4=>(((X1196)=(X1197)|in @ X1196 @ X1197)|in @ X1197 @ X1196))))&![X1198:$i]:(in @ X1198 @ X4=>~(in @ X1198 @ X1198)))&![X21:$i]:(in @ X21 @ (powerset @ X4)=>((X21)!=(emptyset)=>?[X2:$i]:(in @ X2 @ X21&![X48:$i]:(in @ X48 @ X21=>((X2)=(X48)|in @ X2 @ X48))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', wellorderedByIn)). 1.33/1.49 thf(nonempty, axiom, (nonempty)=(^[X2:$i]:(X2)!=(emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonempty)). 1.33/1.49 thf(stricttotalorderedByIn, axiom, (stricttotalorderedByIn)=(^[X4:$i]:((![X2:$i]:(in @ X2 @ X4=>![X21:$i]:(in @ X21 @ X4=>![X48:$i]:(in @ X48 @ X4=>((in @ X2 @ X21&in @ X21 @ X48)=>in @ X2 @ X48))))&![X21:$i]:(in @ X21 @ X4=>![X48:$i]:(in @ X48 @ X4=>(((X21)=(X48)|in @ X21 @ X48)|in @ X48 @ X21))))&![X21:$i]:(in @ X21 @ X4=>~(in @ X21 @ X21)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', stricttotalorderedByIn)). 1.33/1.49 thf(ordinal, axiom, (ordinal)=(^[X2:$i]:(![X1199:$i]:(in @ X1199 @ X2=>subset @ X1199 @ X2)&(((![X1200:$i]:(in @ X1200 @ X2=>![X1201:$i]:(in @ X1201 @ X2=>![X1202:$i]:(in @ X1202 @ X2=>((in @ X1200 @ X1201&in @ X1201 @ X1202)=>in @ X1200 @ X1202))))&![X1203:$i]:(in @ X1203 @ X2=>![X1204:$i]:(in @ X1204 @ X2=>(((X1203)=(X1204)|in @ X1203 @ X1204)|in @ X1204 @ X1203))))&![X1205:$i]:(in @ X1205 @ X2=>~(in @ X1205 @ X1205)))&![X1206:$i]:(in @ X1206 @ (powerset @ X2)=>((X1206)!=(emptyset)=>?[X1207:$i]:(in @ X1207 @ X1206&![X1208:$i]:(in @ X1208 @ X1206=>((X1207)=(X1208)|in @ X1207 @ X1208)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ordinal)). 1.33/1.49 thf(transitiveset, axiom, (transitiveset)=(^[X4:$i]:![X21:$i]:(in @ X21 @ X4=>subset @ X21 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', transitiveset)). 1.33/1.49 thf(replAx, axiom, (replAx<=>![X6:$i > $i > $o, X4:$i]:(![X2:$i]:(in @ X2 @ X4=>exu @ (^[X3:$i]:X6 @ X2 @ X3))=>?[X5:$i]:![X2:$i]:(in @ X2 @ X5<=>?[X3:$i]:(in @ X3 @ X4&X6 @ X3 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', replAx)). 1.33/1.49 thf(exu, axiom, (exu)=(^[X1:$i > $o]:?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exu)). 1.33/1.49 thf(descrp, axiom, (descrp<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>X1 @ (descr @ (^[X2:$i]:X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', descrp)). 1.33/1.49 thf(exuE1, axiom, (exuE1<=>![X1:$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)). 1.33/1.49 thf(exuE3e, axiom, (exuE3e<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>?[X2:$i]:X1 @ X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuE3e)). 1.33/1.49 thf(nonemptyE1, axiom, (nonemptyE1<=>![X4:$i]:(nonempty @ X4=>?[X2:$i]:in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyE1)). 1.33/1.49 thf(nonemptyI, axiom, (nonemptyI<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyI)). 1.33/1.49 thf(nonemptyI1, axiom, (nonemptyI1<=>![X4:$i]:(?[X2:$i]:in @ X2 @ X4=>nonempty @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyI1)). 1.33/1.49 thf(exuE2, axiom, (exuE2<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuE2)). 1.33/1.49 thf(nonemptyImpWitness, axiom, (nonemptyImpWitness<=>![X4:$i]:(nonempty @ X4=>?[X2:$i]:(in @ X2 @ X4&$true))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyImpWitness)). 1.33/1.49 thf(exuI1, axiom, (exuI1<=>![X1:$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)). 1.33/1.49 thf(exuI3, axiom, (exuI3<=>![X1:$i > $o]:(?[X2:$i]:X1 @ X2=>(![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3)))=>exu @ (^[X2:$i]:X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuI3)). 1.33/1.49 thf(exuI2, axiom, (exuI2<=>![X1:$i > $o]:(?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2))=>exu @ (^[X2:$i]:X1 @ X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuI2)). 1.33/1.49 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)). 1.33/1.49 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:$i]:X17 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exu__Cong)). 1.33/1.49 thf(exuEu, axiom, (exuEu<=>![X1:$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)). 1.33/1.49 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:$i]:X17 @ X2)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', descr__Cong)). 1.33/1.49 thf(image1Ex1, axiom, (image1Ex1<=>![X4:$i, X58:$i > $i]:exu @ (^[X5:$i]:![X2:$i]:(in @ X2 @ X5<=>?[X3:$i]:(in @ X3 @ X4&(X2)=(X58 @ X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', image1Ex1)). 1.33/1.49 thf(foundation2, axiom, (foundation2<=>![X4:$i]:(nonempty @ X4=>?[X21:$i]:(in @ X21 @ X4&(binintersect @ X21 @ X4)=(emptyset)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', foundation2)). 1.33/1.49 thf(transitivesetOp1, axiom, (transitivesetOp1<=>![X21:$i]:(transitiveset @ X21=>![X4:$i]:(in @ X4 @ X21=>subset @ X4 @ X21))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', transitivesetOp1)). 1.33/1.49 thf(binintTransitive, axiom, (binintTransitive<=>![X21:$i]:(transitiveset @ X21=>![X48:$i]:(transitiveset @ X48=>transitiveset @ (binintersect @ X21 @ X48)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintTransitive)). 1.33/1.49 thf(transitivesetOp2, axiom, (transitivesetOp2<=>![X21:$i]:(transitiveset @ X21=>![X4:$i, X2:$i]:(in @ X4 @ X21=>(in @ X2 @ X4=>in @ X2 @ X21)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', transitivesetOp2)). 1.33/1.49 thf(setunionTransitive, axiom, (setunionTransitive<=>![X21:$i]:(![X2:$i]:(in @ X2 @ X21=>transitiveset @ X2)=>transitiveset @ (setunion @ X21))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionTransitive)). 1.33/1.49 thf(ordinalMinLem1, axiom, (ordinalMinLem1<=>![X21:$i]:(ordinal @ X21=>![X48:$i]:(ordinal @ X48=>transitiveset @ (binintersect @ X21 @ X48)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ordinalMinLem1)). 1.33/1.49 thf(ordinalTransSet, conjecture, (setextAx=>(emptysetAx=>(setadjoinAx=>(powersetAx=>((omega0Ax=>((((foundationAx=>((descrp=>(dsetconstrI=>(dsetconstrEL=>((exuE1=>(prop2setE=>((((exuE3e=>(((noeltsimpempty=>((nonemptyE1=>((((emptyinunitempty=>(setadjoinIR=>(setadjoinE=>((setoftrueEq=>((emptyinPowerset=>((((((((uniqinunit=>(notinsingleton=>(((upairsetE=>(((emptyE1=>((quantDeMorgan1=>(((((((((exuI3=>(exuI2=>(inCongP=>((exuE3u=>((((powerset__Cong=>(setunion__Cong=>((((dsetconstr__Cong=>((eqimpsubset2=>(eqimpsubset1=>(subsetI2=>(emptysetsubset=>(((notsubsetI=>((notequalI2=>((subsetTrans=>((setadjoinSub2=>(((subsetemptysetimpeq=>((powersetE1=>((((((upairset2IR=>(binunionIR=>(((binunionLsub=>((binintersectI=>((binintersectEL=>((((binintersectER=>((((binintersectSubset1=>((setminusI=>(setminusEL=>(setminusER=>(setminusSubset2=>(((((setminusLsub=>(setminusSubset1=>((symdiffI1=>(symdiffI2=>((symdiffIneg2=>((setukpairIL=>(((((singletoninpowerset=>((upairset2E=>(upairsubunion=>((ubforcartprodlem1=>(ubforcartprodlem2=>(ubforcartprodlem3=>(cartprodpairin=>((cartprodmempair=>((((setunionsingleton=>(singletonprop=>((ex1I=>(ex1I2=>(singletonsuniq=>(setukpairinjL1=>(kfstsingleton=>(theprop=>(kfstpairEq=>((setukpairinjL2=>((((setukpairinjR1=>((setukpairinjR2=>(setukpairinjR=>(ksndsingleton=>(ksndpairEq=>(kpairsurjEq=>(cartprodsndin=>((cartprodpairmemER=>(cartprodmempaircEq=>(cartprodfstpairEq=>(((dpsetconstrI=>(dpsetconstrSub=>(setOfPairsIsBReln=>(dpsetconstrERa=>(dpsetconstrEL1=>(dpsetconstrEL2=>(dpsetconstrER=>(funcImageSingleton=>((app=>(infuncsetfunc=>((funcinfuncset=>((lamp=>(lam2p=>((brelnall2=>((((((funcGraphProp4=>(subbreln=>(((((((eta1=>((beta2=>(eta2=>(iffalseProp1=>(iffalseProp2=>(((ifSingleton=>(ifp=>((((iftrueorfalse=>(binintersectT_lem=>(((((setextT=>(((powersetTE1=>(complementTI1=>(((binintersectTERcontra=>((((((((((complementTnotintersectT=>((complementSubsetComplementIntersect=>(((((binunionTIRcontra=>(inIntersectImpInUnion=>((inIntersectImpInIntersectUnions=>(((inComplementUnionImpInComplement1=>(((demorgan2a1=>((demorgan2a2=>((demorgan1b=>((demorgan2a=>(demorgan2b2=>(demorgan2b=>(demorgan2=>(woz13rule0=>(woz13rule1=>((woz13rule3=>(((woz1_2=>(woz1_3=>(woz1_4=>(((breln1SetBreln1=>(choice2fnsingleton=>(((subbreln1=>(eqbreln1=>(breln1invprop=>((breln1invE=>((((((breln1unionIL=>(breln1unionIR=>(breln1unionI=>((breln1unionEcases=>((woz2Ex=>(((woz2B=>(image1Ex=>((((image1I=>((injFuncSetFuncIn=>(injFuncSetFuncInj=>(surjFuncSetFuncIn=>(((surjCantorThm=>(((notinself2=>((omegaSclos=>(((transitivesetOp1=>((transitivesetOp2=>(setunionTransitive=>(![X21:$i]:(![X2:$i, X4:$i]:((in @ X2 @ X21<=in @ X2 @ X4)<=in @ X4 @ X21)<=ordinal @ X21)<=ordinalMinLem1)))<=binintTransitive))<=peanoSinj)<=peano0notS))<=omegaSp))<=notinself)<=foundation2))<=leftInvIsSurj)<=surjFuncSetFuncSurj))))<=injFuncInInjFuncSet))<=image1E)<=image1Equiv)<=image1Ex1)))<=woz2A)<=woz2W))<=breln1unionCommutes))<=breln1unionE))))<=breln1unionprop)<=breln1compEex)<=breln1compE)<=breln1compI)<=breln1compprop))<=breln1invI))))<=breln1all1)<=setOfPairsIsBReln1)))<=breln1all2)<=woz1_5))))<=woz1_1)<=woz13rule4))<=woz13rule2)))))))<=demorgan1))<=demorgan1a))<=complementUnionInPowersetComplement))<=binunionTEcontra)<=binunionTE))<=inComplementUnionImpNotIn1)<=intersectInPowersetIntersectUnions))<=inIntersectImpInUnion2)))<=binunionTILcontra)<=complementTcontraSubset)<=contraSubsetComplement)<=complementInPowersetComplementIntersect))<=complementImpComplementIntersect))<=doubleComplementEq)<=doubleComplementSub2)<=doubleComplementSub1)<=doubleComplementE1)<=doubleComplementI1)<=contrasubsetT3)<=contrasubsetT2)<=contrasubsetT1)<=contrasubsetT))<=binintersectTELcontra)<=complementTE1)))<=powersetTI1)<=subsetTI))<=complementT_lem)<=setminusT_lem)<=powersetT_lem)<=binunionT_lem)))<=iffalse)<=iftrue)<=theeq)))<=iftrueProp2)<=iftrueProp1)))))<=lam2lamEq))<=beta1)<=ap2apEq2)<=ap2apEq1)<=funcext2)<=funcext)<=eqbreln)))<=funcextLem)<=funcGraphProp2)<=funcGraphProp3)<=funcGraphProp1)<=ex1E2))<=brelnall1)))<=lamProp))<=ap2p)))<=apProp)))))))))<=cartprodpairsurjEq)<=cartprodsndpairEq))))<=cartprodpairmemEL)))))))<=upairequniteq))<=setukpairinjR12)<=setukpairinjR11)<=setukpairinjL))<=cartprodfstin))))))))<=ex1E1)))<=setunionsingleton2)<=setunionsingleton1)<=setunionE2))<=cartprodmempair1)))))<=upairinpowunion)))<=singletoninpowunion))<=singletonsubset)<=kpairp)<=kpairiskpair)<=setukpairIR))<=secondinupair))<=symdiffIneg1)))<=symdiffE)))<=setminusIRneg)<=setminusILneg)<=setminusELneg)<=setminusERneg)))))<=bs114d))<=binintersectSubset4)<=binintersectRsub)<=disjointsetsI1))<=binintersectSubset3)<=binintersectSubset2)<=binintersectLsub))<=binintersectSubset5))<=binunionRsub))<=binunionE)<=binunionEcases)))<=binunionIL)<=sepSubset)<=sepInPowerset)<=powersetsubset)<=inPowerset))<=powersetI1))<=setextsub)<=subset2powerset))<=setadjoinSub))<=subsetRefl))<=notequalI1))<=subsetE2)<=subsetE)))))<=subsetI1))<=descr__Cong)<=exuEu)<=omega__Cong)))<=setadjoin__Cong)<=emptyset__Cong)<=exu__Cong))<=in__Cong))))<=exuI1)<=notdallE)<=notdexE)<=prop2set2propI)<=prop2setI)<=quantDeMorgan4)<=quantDeMorgan3)<=quantDeMorgan2))<=vacuousDall))<=upairsetIR)<=upairsetIL))<=singletonsswitch)<=eqinunit)))<=nonemptyImpWitness)<=exuE2)<=subPowSU)<=setunionE)<=setunionI)<=powersetE)<=emptyInPowerset))<=powersetI))<=setadjoinOr))))<=setadjoinIL)<=nonemptyI1)<=nonemptyI))<=setbeta))<=emptyI)<=setext))<=notinemptyset)<=emptysetimpfalse)<=emptysetE)))<=dsetconstrER))))<=wellorderingAx))<=replAx)<=omegaIndAx)<=omegaSAx))<=setunionAx))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ordinalTransSet)). 1.33/1.50 thf(setextAx, axiom, (setextAx<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4<=>in @ X2 @ X5)=>(X4)=(X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setextAx)). 1.33/1.50 thf(emptysetAx, axiom, (emptysetAx<=>![X2:$i]:~(in @ X2 @ emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetAx)). 1.33/1.50 thf(setadjoinAx, axiom, (setadjoinAx<=>![X2:$i, X4:$i, X3:$i]:(in @ X3 @ (setadjoin @ X2 @ X4)<=>((X3)=(X2)|in @ X3 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinAx)). 1.33/1.50 thf(powersetAx, axiom, (powersetAx<=>![X4:$i, X5:$i]:(in @ X5 @ (powerset @ X4)<=>![X2:$i]:(in @ X2 @ X5=>in @ X2 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetAx)). 1.33/1.50 thf(setunionAx, axiom, (setunionAx<=>![X4:$i, X2:$i]:(in @ X2 @ (setunion @ X4)<=>?[X5:$i]:(in @ X2 @ X5&in @ X5 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionAx)). 1.33/1.50 thf(omega0Ax, axiom, (omega0Ax<=>in @ emptyset @ omega), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omega0Ax)). 1.33/1.50 thf(omegaSAx, axiom, (omegaSAx<=>![X2:$i]:(in @ X2 @ omega=>in @ (setadjoin @ X2 @ X2) @ omega)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omegaSAx)). 1.33/1.50 thf(omegaIndAx, axiom, (omegaIndAx<=>![X4:$i]:((in @ emptyset @ X4&![X2:$i]:((in @ X2 @ omega&in @ X2 @ X4)=>in @ (setadjoin @ X2 @ X2) @ X4))=>![X2:$i]:(in @ X2 @ omega=>in @ X2 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omegaIndAx)). 1.33/1.50 thf(foundationAx, axiom, (foundationAx<=>![X4:$i]:(?[X2:$i]:in @ X2 @ X4=>?[X5:$i]:(in @ X5 @ X4&~(?[X2:$i]:(in @ X2 @ X5&in @ X2 @ X4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', foundationAx)). 1.33/1.50 thf(wellorderingAx, axiom, (wellorderingAx<=>![X4:$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)). 1.33/1.50 thf(dsetconstrI, axiom, (dsetconstrI<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstrI)). 1.33/1.50 thf(dsetconstrEL, axiom, (dsetconstrEL<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))=>in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstrEL)). 1.33/1.50 thf(dsetconstrER, axiom, (dsetconstrER<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))=>X1 @ X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstrER)). 1.33/1.50 thf(prop2setE, axiom, (prop2setE<=>![X10:$o, X2:$i]:(in @ X2 @ (prop2set @ (X10))=>X10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prop2setE)). 1.33/1.50 thf(emptysetE, axiom, (emptysetE<=>![X2:$i]:(in @ X2 @ emptyset=>![X11:$o]:X11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetE)). 1.33/1.50 thf(emptysetimpfalse, axiom, (emptysetimpfalse<=>![X2:$i]:(in @ X2 @ emptyset=>~$true)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetimpfalse)). 1.33/1.50 thf(notinemptyset, axiom, (notinemptyset<=>![X2:$i]:~(in @ X2 @ emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notinemptyset)). 1.33/1.50 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)). 1.33/1.50 thf(emptyI, axiom, (emptyI<=>![X4:$i]:(![X2:$i]:~(in @ X2 @ X4)=>(X4)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyI)). 1.33/1.50 thf(noeltsimpempty, axiom, (noeltsimpempty<=>![X4:$i]:(![X2:$i]:~(in @ X2 @ X4)=>(X4)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', noeltsimpempty)). 1.33/1.50 thf(setbeta, axiom, (setbeta<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))<=>X1 @ X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setbeta)). 1.33/1.50 thf(setadjoinIL, axiom, (setadjoinIL<=>![X2:$i, X3:$i]:in @ X2 @ (setadjoin @ X2 @ X3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinIL)). 1.33/1.50 thf(emptyinunitempty, axiom, (emptyinunitempty<=>in @ emptyset @ (setadjoin @ emptyset @ emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyinunitempty)). 1.33/1.50 thf(setadjoinIR, axiom, (setadjoinIR<=>![X2:$i, X4:$i, X3:$i]:(in @ X3 @ X4=>in @ X3 @ (setadjoin @ X2 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinIR)). 1.33/1.50 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)). 1.33/1.50 thf(setadjoinOr, axiom, (setadjoinOr<=>![X2:$i, X4:$i, X3:$i]:(in @ X3 @ (setadjoin @ X2 @ X4)=>((X3)=(X2)|in @ X3 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinOr)). 1.33/1.50 thf(setoftrueEq, axiom, (setoftrueEq<=>![X4:$i]:(dsetconstr @ X4 @ (^[X2:$i]:$true))=(X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setoftrueEq)). 1.33/1.50 thf(powersetI, axiom, (powersetI<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X5=>in @ X2 @ X4)=>in @ X5 @ (powerset @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetI)). 1.33/1.50 thf(emptyinPowerset, axiom, (emptyinPowerset<=>![X4:$i]:in @ emptyset @ (powerset @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyinPowerset)). 1.33/1.50 thf(emptyInPowerset, axiom, (emptyInPowerset<=>![X4:$i]:in @ emptyset @ (powerset @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyInPowerset)). 1.33/1.50 thf(powersetE, axiom, (powersetE<=>![X4:$i, X5:$i, X2:$i]:(in @ X5 @ (powerset @ X4)=>(in @ X2 @ X5=>in @ X2 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetE)). 1.33/1.50 thf(setunionI, axiom, (setunionI<=>![X4:$i, X2:$i, X5:$i]:(in @ X2 @ X5=>(in @ X5 @ X4=>in @ X2 @ (setunion @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionI)). 1.33/1.50 thf(setunionE, axiom, (setunionE<=>![X4:$i, X2:$i]:(in @ X2 @ (setunion @ X4)=>![X13:$o]:(![X5:$i]:(in @ X2 @ X5=>(in @ X5 @ X4=>X13))=>X13))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionE)). 1.33/1.50 thf(subPowSU, axiom, (subPowSU<=>![X4:$i, X2:$i]:(in @ X2 @ X4=>in @ X2 @ (powerset @ (setunion @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subPowSU)). 1.33/1.50 thf(uniqinunit, axiom, (uniqinunit<=>![X2:$i, X3:$i]:(in @ X2 @ (setadjoin @ X3 @ emptyset)=>(X2)=(X3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', uniqinunit)). 1.33/1.50 thf(notinsingleton, axiom, (notinsingleton<=>![X2:$i, X3:$i]:((X2)!=(X3)=>~(in @ X3 @ (setadjoin @ X2 @ emptyset)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notinsingleton)). 1.33/1.50 thf(eqinunit, axiom, (eqinunit<=>![X2:$i, X3:$i]:((X2)=(X3)=>in @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqinunit)). 1.33/1.50 thf(singletonsswitch, axiom, (singletonsswitch<=>![X2:$i, X3:$i]:(in @ X2 @ (setadjoin @ X3 @ emptyset)=>in @ X3 @ (setadjoin @ X2 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletonsswitch)). 1.33/1.50 thf(upairsetE, axiom, (upairsetE<=>![X2:$i, X3:$i, X14:$i]:(in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=>((X14)=(X2)|(X14)=(X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsetE)). 1.33/1.50 thf(upairsetIL, axiom, (upairsetIL<=>![X2:$i, X3:$i]:in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsetIL)). 1.33/1.50 thf(upairsetIR, axiom, (upairsetIR<=>![X2:$i, X3:$i]:in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsetIR)). 1.33/1.50 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)). 1.33/1.50 thf(vacuousDall, axiom, (vacuousDall<=>![X1:$i > $o, X2:$i]:(in @ X2 @ emptyset=>X1 @ X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', vacuousDall)). 1.33/1.50 thf(quantDeMorgan1, axiom, (quantDeMorgan1<=>![X4:$i, X1:$i > $o]:(~(![X2:$i]:(in @ X2 @ X4=>X1 @ X2))=>?[X2:$i]:(in @ X2 @ X4&~(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan1)). 1.33/1.50 thf(quantDeMorgan2, axiom, (quantDeMorgan2<=>![X4:$i, X1:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>~(X1 @ X2))=>~(?[X2:$i]:(in @ X2 @ X4&X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan2)). 1.33/1.50 thf(quantDeMorgan3, axiom, (quantDeMorgan3<=>![X4:$i, X1:$i > $o]:(~(?[X2:$i]:(in @ X2 @ X4&X1 @ X2))=>![X2:$i]:(in @ X2 @ X4=>~(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan3)). 1.33/1.50 thf(quantDeMorgan4, axiom, (quantDeMorgan4<=>![X4:$i, X1:$i > $o]:(?[X2:$i]:(in @ X2 @ X4&~(X1 @ X2))=>~(![X2:$i]:(in @ X2 @ X4=>X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan4)). 1.33/1.50 thf(prop2setI, axiom, (prop2setI<=>![X15:$o]:(X15=>in @ emptyset @ (prop2set @ (X15)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prop2setI)). 1.33/1.50 thf(prop2set2propI, axiom, (prop2set2propI<=>![X16:$o]:(X16=>set2prop @ (prop2set @ (X16)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prop2set2propI)). 1.33/1.50 thf(notdexE, axiom, (notdexE<=>![X4:$i, X1:$i > $o]:(~(?[X2:$i]:(in @ X2 @ X4&X1 @ X2))=>![X2:$i]:(in @ X2 @ X4=>~(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notdexE)). 1.33/1.50 thf(notdallE, axiom, (notdallE<=>![X4:$i, X1:$i > $o]:(~(![X2:$i]:(in @ X2 @ X4=>X1 @ X2))=>?[X2:$i]:(in @ X2 @ X4&~(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notdallE)). 1.33/1.50 thf(inCongP, axiom, (inCongP<=>![X4:$i, X5:$i]:((X4)=(X5)=>![X2:$i, X3:$i]:((X2)=(X3)=>(in @ X2 @ X4=>in @ X3 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', inCongP)). 1.33/1.50 thf(in__Cong, axiom, (in__Cong<=>![X4:$i, X5:$i]:((X4)=(X5)=>![X2:$i, X3:$i]:((X2)=(X3)=>(in @ X2 @ X4<=>in @ X3 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', in__Cong)). 1.33/1.50 thf(emptyset__Cong, axiom, (emptyset__Cong<=>(emptyset)=(emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyset__Cong)). 1.33/1.50 thf(setadjoin__Cong, axiom, (setadjoin__Cong<=>![X2:$i, X3:$i]:((X2)=(X3)=>![X14:$i, X18:$i]:((X14)=(X18)=>(setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoin__Cong)). 1.33/1.50 thf(powerset__Cong, axiom, (powerset__Cong<=>![X4:$i, X5:$i]:((X4)=(X5)=>(powerset @ X4)=(powerset @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powerset__Cong)). 1.33/1.50 thf(setunion__Cong, axiom, (setunion__Cong<=>![X4:$i, X5:$i]:((X4)=(X5)=>(setunion @ X4)=(setunion @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunion__Cong)). 1.33/1.50 thf(omega__Cong, axiom, (omega__Cong<=>(omega)=(omega)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omega__Cong)). 1.33/1.50 thf(dsetconstr__Cong, axiom, (dsetconstr__Cong<=>![X4:$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:$i]:X17 @ X2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstr__Cong)). 1.33/1.50 thf(subsetI1, axiom, (subsetI1<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4=>in @ X2 @ X5)=>subset @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetI1)). 1.33/1.50 thf(eqimpsubset2, axiom, (eqimpsubset2<=>![X4:$i, X5:$i]:((X4)=(X5)=>subset @ X5 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqimpsubset2)). 1.33/1.50 thf(eqimpsubset1, axiom, (eqimpsubset1<=>![X4:$i, X5:$i]:((X4)=(X5)=>subset @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqimpsubset1)). 1.33/1.50 thf(subsetI2, axiom, (subsetI2<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4=>in @ X2 @ X5)=>subset @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetI2)). 1.33/1.50 thf(emptysetsubset, axiom, (emptysetsubset<=>![X4:$i]:subset @ emptyset @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetsubset)). 1.33/1.50 thf(subsetE, axiom, (subsetE<=>![X4:$i, X5:$i, X2:$i]:(subset @ X4 @ X5=>(in @ X2 @ X4=>in @ X2 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetE)). 1.33/1.50 thf(subsetE2, axiom, (subsetE2<=>![X4:$i, X5:$i, X2:$i]:(subset @ X4 @ X5=>(~(in @ X2 @ X5)=>~(in @ X2 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetE2)). 1.33/1.50 thf(notsubsetI, axiom, (notsubsetI<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X5)=>~(subset @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notsubsetI)). 1.33/1.50 thf(notequalI1, axiom, (notequalI1<=>![X4:$i, X5:$i]:(~(subset @ X4 @ X5)=>(X4)!=(X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notequalI1)). 1.33/1.50 thf(notequalI2, axiom, (notequalI2<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X5)=>(X4)!=(X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notequalI2)). 1.33/1.50 thf(subsetRefl, axiom, (subsetRefl<=>![X4:$i]:subset @ X4 @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetRefl)). 1.33/1.50 thf(subsetTrans, axiom, (subsetTrans<=>![X4:$i, X5:$i, X7:$i]:(subset @ X4 @ X5=>(subset @ X5 @ X7=>subset @ X4 @ X7))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetTrans)). 1.33/1.50 thf(setadjoinSub, axiom, (setadjoinSub<=>![X2:$i, X4:$i]:subset @ X4 @ (setadjoin @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinSub)). 1.33/1.50 thf(setadjoinSub2, axiom, (setadjoinSub2<=>![X4:$i, X2:$i, X5:$i]:(subset @ X4 @ X5=>subset @ X4 @ (setadjoin @ X2 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinSub2)). 1.33/1.50 thf(subset2powerset, axiom, (subset2powerset<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>in @ X4 @ (powerset @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subset2powerset)). 1.33/1.50 thf(setextsub, axiom, (setextsub<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>(subset @ X5 @ X4=>(X4)=(X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setextsub)). 1.33/1.50 thf(subsetemptysetimpeq, axiom, (subsetemptysetimpeq<=>![X4:$i]:(subset @ X4 @ emptyset=>(X4)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetemptysetimpeq)). 1.33/1.50 thf(powersetI1, axiom, (powersetI1<=>![X4:$i, X5:$i]:(subset @ X5 @ X4=>in @ X5 @ (powerset @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetI1)). 1.33/1.50 thf(powersetE1, axiom, (powersetE1<=>![X4:$i, X5:$i]:(in @ X5 @ (powerset @ X4)=>subset @ X5 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetE1)). 1.33/1.50 thf(inPowerset, axiom, (inPowerset<=>![X4:$i]:in @ X4 @ (powerset @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', inPowerset)). 1.33/1.50 thf(powersetsubset, axiom, (powersetsubset<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>subset @ (powerset @ X4) @ (powerset @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetsubset)). 1.33/1.50 thf(sepInPowerset, axiom, (sepInPowerset<=>![X4:$i, X1:$i > $o]:in @ (dsetconstr @ X4 @ (^[X2:$i]:X1 @ X2)) @ (powerset @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sepInPowerset)). 1.33/1.50 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)). 1.33/1.50 thf(binunionIL, axiom, (binunionIL<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>in @ X2 @ (binunion @ X4 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionIL)). 1.33/1.50 thf(upairset2IR, axiom, (upairset2IR<=>![X2:$i, X3:$i]:in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairset2IR)). 1.33/1.50 thf(binunionIR, axiom, (binunionIR<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X5=>in @ X2 @ (binunion @ X4 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionIR)). 1.33/1.50 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)). 1.33/1.50 thf(binunionE, axiom, (binunionE<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (binunion @ X4 @ X5)=>(in @ X2 @ X4|in @ X2 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionE)). 1.33/1.50 thf(binunionLsub, axiom, (binunionLsub<=>![X4:$i, X5:$i]:subset @ X4 @ (binunion @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionLsub)). 1.33/1.50 thf(binunionRsub, axiom, (binunionRsub<=>![X4:$i, X5:$i]:subset @ X5 @ (binunion @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionRsub)). 1.33/1.50 thf(binintersectI, axiom, (binintersectI<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X5=>in @ X2 @ (binintersect @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectI)). 1.33/1.50 thf(binintersectSubset5, axiom, (binintersectSubset5<=>![X4:$i, X5:$i, X7:$i]:(subset @ X7 @ X4=>(subset @ X7 @ X5=>subset @ X7 @ (binintersect @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset5)). 1.33/1.50 thf(binintersectEL, axiom, (binintersectEL<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (binintersect @ X4 @ X5)=>in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectEL)). 1.33/1.50 thf(binintersectLsub, axiom, (binintersectLsub<=>![X4:$i, X5:$i]:subset @ (binintersect @ X4 @ X5) @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectLsub)). 1.33/1.50 thf(binintersectSubset2, axiom, (binintersectSubset2<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>(binintersect @ X4 @ X5)=(X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset2)). 1.33/1.50 thf(binintersectSubset3, axiom, (binintersectSubset3<=>![X4:$i, X5:$i]:((binintersect @ X4 @ X5)=(X5)=>subset @ X5 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset3)). 1.33/1.50 thf(binintersectER, axiom, (binintersectER<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (binintersect @ X4 @ X5)=>in @ X2 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectER)). 1.33/1.50 thf(disjointsetsI1, axiom, (disjointsetsI1<=>![X4:$i, X5:$i]:(~(?[X2:$i]:(in @ X2 @ X4&in @ X2 @ X5))=>(binintersect @ X4 @ X5)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', disjointsetsI1)). 1.33/1.50 thf(binintersectRsub, axiom, (binintersectRsub<=>![X4:$i, X5:$i]:subset @ (binintersect @ X4 @ X5) @ X5), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectRsub)). 1.33/1.50 thf(binintersectSubset4, axiom, (binintersectSubset4<=>![X4:$i, X5:$i]:(subset @ X5 @ X4=>(binintersect @ X4 @ X5)=(X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset4)). 1.33/1.50 thf(binintersectSubset1, axiom, (binintersectSubset1<=>![X4:$i, X5:$i]:((binintersect @ X4 @ X5)=(X4)=>subset @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset1)). 1.33/1.50 thf(bs114d, axiom, (bs114d<=>![X4:$i, X5:$i, X7:$i]:(binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', bs114d)). 1.33/1.50 thf(setminusI, axiom, (setminusI<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X5)=>in @ X2 @ (setminus @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusI)). 1.33/1.50 thf(setminusEL, axiom, (setminusEL<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (setminus @ X4 @ X5)=>in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusEL)). 1.33/1.50 thf(setminusER, axiom, (setminusER<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (setminus @ X4 @ X5)=>~(in @ X2 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusER)). 1.33/1.50 thf(setminusSubset2, axiom, (setminusSubset2<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>(setminus @ X4 @ X5)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusSubset2)). 1.33/1.50 thf(setminusERneg, axiom, (setminusERneg<=>![X4:$i, X5:$i, X2:$i]:(~(in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4=>in @ X2 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusERneg)). 1.33/1.50 thf(setminusELneg, axiom, (setminusELneg<=>![X4:$i, X5:$i, X2:$i]:(~(in @ X2 @ (setminus @ X4 @ X5))=>(~(in @ X2 @ X5)=>~(in @ X2 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusELneg)). 1.33/1.50 thf(setminusILneg, axiom, (setminusILneg<=>![X4:$i, X5:$i, X2:$i]:(~(in @ X2 @ X4)=>~(in @ X2 @ (setminus @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusILneg)). 1.33/1.50 thf(setminusIRneg, axiom, (setminusIRneg<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X5=>~(in @ X2 @ (setminus @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusIRneg)). 1.33/1.50 thf(setminusLsub, axiom, (setminusLsub<=>![X4:$i, X5:$i]:subset @ (setminus @ X4 @ X5) @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusLsub)). 1.33/1.50 thf(setminusSubset1, axiom, (setminusSubset1<=>![X4:$i, X5:$i]:((setminus @ X4 @ X5)=(emptyset)=>subset @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusSubset1)). 1.33/1.50 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)). 1.33/1.50 thf(symdiffI1, axiom, (symdiffI1<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X5)=>in @ X2 @ (symdiff @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', symdiffI1)). 1.33/1.50 thf(symdiffI2, axiom, (symdiffI2<=>![X4:$i, X5:$i, X2:$i]:(~(in @ X2 @ X4)=>(in @ X2 @ X5=>in @ X2 @ (symdiff @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', symdiffI2)). 1.33/1.50 thf(symdiffIneg1, axiom, (symdiffIneg1<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X5=>~(in @ X2 @ (symdiff @ X4 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', symdiffIneg1)). 1.33/1.50 thf(symdiffIneg2, axiom, (symdiffIneg2<=>![X4:$i, X5:$i, X2:$i]:(~(in @ X2 @ X4)=>(~(in @ X2 @ X5)=>~(in @ X2 @ (symdiff @ X4 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', symdiffIneg2)). 1.33/1.50 thf(secondinupair, axiom, (secondinupair<=>![X2:$i, X3:$i]:in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', secondinupair)). 1.33/1.50 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)). 1.33/1.50 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)). 1.33/1.50 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)). 1.33/1.50 thf(kpairp, axiom, (kpairp<=>![X2:$i, X3:$i]:iskpair @ (kpair @ X2 @ X3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', kpairp)). 1.33/1.50 thf(singletonsubset, axiom, (singletonsubset<=>![X4:$i, X2:$i]:(in @ X2 @ X4=>subset @ (setadjoin @ X2 @ emptyset) @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletonsubset)). 1.33/1.50 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)). 1.33/1.50 thf(singletoninpowunion, axiom, (singletoninpowunion<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletoninpowunion)). 1.33/1.50 thf(upairset2E, axiom, (upairset2E<=>![X2:$i, X3:$i, X14:$i]:(in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=>((X14)=(X2)|(X14)=(X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairset2E)). 1.33/1.50 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)). 1.33/1.50 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)). 1.33/1.50 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)). 1.33/1.50 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)). 1.33/1.50 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)). 1.33/1.50 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)). 1.33/1.50 thf(cartprodmempair1, axiom, (cartprodmempair1<=>![X4:$i, X5:$i, X18:$i]:(in @ X18 @ (cartprod @ X4 @ X5)=>?[X2:$i]:(in @ X2 @ X4&?[X3:$i]:(in @ X3 @ X5&(X18)=(kpair @ X2 @ X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodmempair1)). 1.33/1.50 thf(cartprodmempair, axiom, (cartprodmempair<=>![X4:$i, X5:$i, X18:$i]:(in @ X18 @ (cartprod @ X4 @ X5)=>iskpair @ X18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodmempair)). 1.33/1.50 thf(setunionE2, axiom, (setunionE2<=>![X4:$i, X2:$i]:(in @ X2 @ (setunion @ X4)=>?[X21:$i]:(in @ X21 @ X4&in @ X2 @ X21))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionE2)). 1.33/1.50 thf(setunionsingleton1, axiom, (setunionsingleton1<=>![X4:$i]:subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionsingleton1)). 1.33/1.50 thf(setunionsingleton2, axiom, (setunionsingleton2<=>![X4:$i]:subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionsingleton2)). 1.33/1.50 thf(setunionsingleton, axiom, (setunionsingleton<=>![X2:$i]:(setunion @ (setadjoin @ X2 @ emptyset))=(X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionsingleton)). 1.33/1.50 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:$i]:X1 @ X2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletonprop)). 1.33/1.50 thf(ex1E1, axiom, (ex1E1<=>![X4:$i, X1:$i > $o]:(ex1 @ X4 @ (^[X2:$i]:X1 @ X2)=>?[X2:$i]:(in @ X2 @ X4&X1 @ X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ex1E1)). 1.33/1.50 thf(ex1I, axiom, (ex1I<=>![X4:$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)). 1.33/1.50 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:$i]:X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ex1I2)). 1.33/1.50 thf(singletonsuniq, axiom, (singletonsuniq<=>![X2:$i, X3:$i]:((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset)=>(X2)=(X3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletonsuniq)). 1.33/1.50 thf(setukpairinjL1, axiom, (setukpairinjL1<=>![X2:$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)). 1.33/1.50 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)). 1.33/1.50 thf(theprop, axiom, (theprop<=>![X21:$i]:(singleton @ X21=>in @ (setunion @ X21) @ X21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', theprop)). 1.33/1.50 thf(kfstpairEq, axiom, (kfstpairEq<=>![X2:$i, X3:$i]:(kfst @ (kpair @ X2 @ X3))=(X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', kfstpairEq)). 1.33/1.50 thf(cartprodfstin, axiom, (cartprodfstin<=>![X4:$i, X5:$i, X18:$i]:(in @ X18 @ (cartprod @ X4 @ X5)=>in @ (kfst @ X18) @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodfstin)). 1.33/1.50 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)). 1.33/1.50 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)). 1.33/1.50 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)). 1.33/1.50 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)). 1.33/1.50 thf(setukpairinjR1, axiom, (setukpairinjR1<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset))=>((X14)=(X18)=>(X3)=(X18)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairinjR1)). 1.33/1.50 thf(upairequniteq, axiom, (upairequniteq<=>![X2:$i, X3:$i, X14:$i]:((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset)=>(X2)=(X3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairequniteq)). 1.33/1.50 thf(setukpairinjR2, axiom, (setukpairinjR2<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset))=>(X3)=(X18))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairinjR2)). 1.33/1.50 thf(setukpairinjR, axiom, (setukpairinjR<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((kpair @ X2 @ X3)=(kpair @ X14 @ X18)=>(X3)=(X18))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairinjR)). 1.33/1.50 thf(ksndsingleton, axiom, (ksndsingleton<=>![X18:$i]:(iskpair @ X18=>singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(X18)=(kpair @ (kfst @ X18) @ X2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ksndsingleton)). 1.33/1.50 thf(ksndpairEq, axiom, (ksndpairEq<=>![X2:$i, X3:$i]:(ksnd @ (kpair @ X2 @ X3))=(X3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ksndpairEq)). 1.33/1.50 thf(kpairsurjEq, axiom, (kpairsurjEq<=>![X18:$i]:(iskpair @ X18=>(kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', kpairsurjEq)). 1.33/1.50 thf(cartprodsndin, axiom, (cartprodsndin<=>![X4:$i, X5:$i, X18:$i]:(in @ X18 @ (cartprod @ X4 @ X5)=>in @ (ksnd @ X18) @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodsndin)). 1.33/1.50 thf(cartprodpairmemEL, axiom, (cartprodpairmemEL<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5)=>in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodpairmemEL)). 1.33/1.50 thf(cartprodpairmemER, axiom, (cartprodpairmemER<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5)=>in @ X3 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodpairmemER)). 1.33/1.50 thf(cartprodmempaircEq, axiom, (cartprodmempaircEq<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(kpair @ X2 @ X3)=(kpair @ X2 @ X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodmempaircEq)). 1.33/1.50 thf(cartprodfstpairEq, axiom, (cartprodfstpairEq<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodfstpairEq)). 1.33/1.50 thf(cartprodsndpairEq, axiom, (cartprodsndpairEq<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodsndpairEq)). 1.33/1.50 thf(cartprodpairsurjEq, axiom, (cartprodpairsurjEq<=>![X4:$i, X5:$i, X18:$i]:(in @ X18 @ (cartprod @ X4 @ X5)=>(kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodpairsurjEq)). 1.33/1.50 thf(dpsetconstrI, axiom, (dpsetconstrI<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(X22 @ X2 @ X3=>in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:X22 @ X14 @ X18)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dpsetconstrI)). 1.33/1.50 thf(dpsetconstrSub, axiom, (dpsetconstrSub<=>![X4:$i, X5:$i, X23:$i > $i > $o]:subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:X23 @ X2 @ X3)) @ (cartprod @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dpsetconstrSub)). 1.33/1.50 thf(setOfPairsIsBReln, axiom, (setOfPairsIsBReln<=>![X4:$i, X5:$i, X24:$i > $i > $o]:breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:X24 @ X2 @ X3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setOfPairsIsBReln)). 1.33/1.50 thf(dpsetconstrERa, axiom, (dpsetconstrERa<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:X25 @ X14 @ X18))=>X25 @ X2 @ X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dpsetconstrERa)). 1.33/1.50 thf(dpsetconstrEL1, axiom, (dpsetconstrEL1<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:X26 @ X14 @ X18))=>in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dpsetconstrEL1)). 1.33/1.50 thf(dpsetconstrEL2, axiom, (dpsetconstrEL2<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:X27 @ X14 @ X18))=>in @ X3 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dpsetconstrEL2)). 1.33/1.50 thf(dpsetconstrER, axiom, (dpsetconstrER<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:X28 @ X14 @ X18))=>X28 @ X2 @ X3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dpsetconstrER)). 1.33/1.50 thf(funcImageSingleton, axiom, (funcImageSingleton<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>![X2:$i]:(in @ X2 @ X4=>singleton @ (dsetconstr @ X5 @ (^[X3:$i]:in @ (kpair @ X2 @ X3) @ X29))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', funcImageSingleton)). 1.33/1.50 thf(apProp, axiom, (apProp<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>![X2:$i]:(in @ X2 @ X4=>in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:in @ (kpair @ X2 @ X3) @ X29))) @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', apProp)). 1.33/1.50 thf(app, axiom, (app<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>![X2:$i]:(in @ X2 @ X4=>in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', app)). 1.33/1.50 thf(infuncsetfunc, axiom, (infuncsetfunc<=>![X4:$i, X5:$i, X29:$i]:(in @ X29 @ (funcSet @ X4 @ X5)=>func @ X4 @ X5 @ X29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', infuncsetfunc)). 1.33/1.50 thf(ap2p, axiom, (ap2p<=>![X4:$i, X5:$i, X29:$i]:(in @ X29 @ (funcSet @ X4 @ X5)=>![X2:$i]:(in @ X2 @ X4=>in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ap2p)). 1.33/1.50 thf(funcinfuncset, axiom, (funcinfuncset<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>in @ X29 @ (funcSet @ X4 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', funcinfuncset)). 1.33/1.50 thf(lamProp, axiom, (lamProp<=>![X4:$i, X5:$i, X30:$i > $i]:(![X2:$i]:(in @ X2 @ X4=>in @ (X30 @ X2) @ X5)=>func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(X30 @ X2)=(X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', lamProp)). 1.33/1.50 thf(lamp, axiom, (lamp<=>![X4:$i, X5:$i, X31:$i > $i]:(![X2:$i]:(in @ X2 @ X4=>in @ (X31 @ X2) @ X5)=>func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:X31 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', lamp)). 1.33/1.50 thf(lam2p, axiom, (lam2p<=>![X4:$i, X5:$i, X32:$i > $i]:(![X2:$i]:(in @ X2 @ X4=>in @ (X32 @ X2) @ X5)=>in @ (lam @ X4 @ X5 @ (^[X2:$i]:X32 @ X2)) @ (funcSet @ X4 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', lam2p)). 1.33/1.50 thf(brelnall1, axiom, (brelnall1<=>![X4:$i, X5:$i, X33:$i]:(breln @ X4 @ X5 @ X33=>![X1:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ X33=>X1 @ (kpair @ X2 @ X3))))=>![X2:$i]:(in @ X2 @ X33=>X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', brelnall1)). 1.33/1.50 thf(brelnall2, axiom, (brelnall2<=>![X4:$i, X5:$i, X33:$i]:(breln @ X4 @ X5 @ X33=>![X1:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ X33=>X1 @ (kpair @ X2 @ X3))))=>![X2:$i]:(in @ X2 @ X33=>X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', brelnall2)). 1.33/1.50 thf(ex1E2, axiom, (ex1E2<=>![X4:$i, X1:$i > $o]:(ex1 @ X4 @ (^[X2:$i]:X1 @ X2)=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ex1E2)). 1.33/1.50 thf(funcGraphProp1, axiom, (funcGraphProp1<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>![X2:$i]:(in @ X2 @ X4=>in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', funcGraphProp1)). 1.33/1.50 thf(funcGraphProp3, axiom, (funcGraphProp3<=>![X4:$i, X5:$i, X29:$i]:(in @ X29 @ (funcSet @ X4 @ X5)=>![X2:$i]:(in @ X2 @ X4=>in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', funcGraphProp3)). 1.33/1.50 thf(funcGraphProp2, axiom, (funcGraphProp2<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ X29=>(ap @ X4 @ X5 @ X29 @ X2)=(X3)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', funcGraphProp2)). 1.33/1.50 thf(funcextLem, axiom, (funcextLem<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>![X34:$i]:(func @ X4 @ X5 @ X34=>(![X2:$i]:(in @ X2 @ X4=>(ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ X34=>in @ (kpair @ X2 @ X3) @ X29))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', funcextLem)). 1.33/1.50 thf(funcGraphProp4, axiom, (funcGraphProp4<=>![X4:$i, X5:$i, X29:$i]:(in @ X29 @ (funcSet @ X4 @ X5)=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ X29=>(ap @ X4 @ X5 @ X29 @ X2)=(X3)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', funcGraphProp4)). 1.33/1.50 thf(subbreln, axiom, (subbreln<=>![X4:$i, X5:$i, X33:$i]:(breln @ X4 @ X5 @ X33=>![X35:$i]:(breln @ X4 @ X5 @ X35=>(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ X33=>in @ (kpair @ X2 @ X3) @ X35)))=>subset @ X33 @ X35)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subbreln)). 1.33/1.50 thf(eqbreln, axiom, (eqbreln<=>![X4:$i, X5:$i, X33:$i]:(breln @ X4 @ X5 @ X33=>![X35:$i]:(breln @ X4 @ X5 @ X35=>(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ X33=>in @ (kpair @ X2 @ X3) @ X35)))=>(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ X35=>in @ (kpair @ X2 @ X3) @ X33)))=>(X33)=(X35)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqbreln)). 1.33/1.50 thf(funcext, axiom, (funcext<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>![X34:$i]:(func @ X4 @ X5 @ X34=>(![X2:$i]:(in @ X2 @ X4=>(ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))=>(X29)=(X34))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', funcext)). 1.33/1.50 thf(funcext2, axiom, (funcext2<=>![X4:$i, X5:$i, X29:$i]:(in @ X29 @ (funcSet @ X4 @ X5)=>![X34:$i]:(in @ X34 @ (funcSet @ X4 @ X5)=>(![X2:$i]:(in @ X2 @ X4=>(ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))=>(X29)=(X34))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', funcext2)). 1.33/1.50 thf(ap2apEq1, axiom, (ap2apEq1<=>![X4:$i, X5:$i, X29:$i]:(in @ X29 @ (funcSet @ X4 @ X5)=>![X2:$i]:(in @ X2 @ X4=>(ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ap2apEq1)). 1.33/1.50 thf(ap2apEq2, axiom, (ap2apEq2<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>![X2:$i]:(in @ X2 @ X4=>(ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ap2apEq2)). 1.33/1.50 thf(beta1, axiom, (beta1<=>![X4:$i, X5:$i, X36:$i > $i]:(![X2:$i]:(in @ X2 @ X4=>in @ (X36 @ X2) @ X5)=>![X2:$i]:(in @ X2 @ X4=>(ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:X36 @ X3)) @ X2)=(X36 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', beta1)). 1.33/1.50 thf(eta1, axiom, (eta1<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>(lam @ X4 @ X5 @ (^[X2:$i]:ap @ X4 @ X5 @ X29 @ X2))=(X29))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eta1)). 1.33/1.50 thf(lam2lamEq, axiom, (lam2lamEq<=>![X4:$i, X5:$i, X37:$i > $i]:(![X2:$i]:(in @ X2 @ X4=>in @ (X37 @ X2) @ X5)=>(lam @ X4 @ X5 @ (^[X2:$i]:X37 @ X2))=(lam @ X4 @ X5 @ (^[X2:$i]:X37 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', lam2lamEq)). 1.33/1.50 thf(beta2, axiom, (beta2<=>![X4:$i, X5:$i, X38:$i > $i]:(![X2:$i]:(in @ X2 @ X4=>in @ (X38 @ X2) @ X5)=>![X2:$i]:(in @ X2 @ X4=>(ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:X38 @ X3)) @ X2)=(X38 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', beta2)). 1.33/1.50 thf(eta2, axiom, (eta2<=>![X4:$i, X5:$i, X29:$i]:(in @ X29 @ (funcSet @ X4 @ X5)=>(lam @ X4 @ X5 @ (^[X2:$i]:ap @ X4 @ X5 @ X29 @ X2))=(X29))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eta2)). 1.33/1.50 thf(iffalseProp1, axiom, (iffalseProp1<=>![X4:$i, X39:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(~(X39)=>in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((X39&(X14)=(X2))|(~(X39)&(X14)=(X3))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', iffalseProp1)). 1.33/1.50 thf(iffalseProp2, axiom, (iffalseProp2<=>![X4:$i, X40:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(~(X40)=>(dsetconstr @ X4 @ (^[X14:$i]:((X40&(X14)=(X2))|(~(X40)&(X14)=(X3)))))=(setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', iffalseProp2)). 1.33/1.50 thf(iftrueProp1, axiom, (iftrueProp1<=>![X4:$i, X41:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(X41=>in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((X41&(X14)=(X2))|(~(X41)&(X14)=(X3))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', iftrueProp1)). 1.33/1.50 thf(iftrueProp2, axiom, (iftrueProp2<=>![X4:$i, X42:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(X42=>(dsetconstr @ X4 @ (^[X14:$i]:((X42&(X14)=(X2))|(~(X42)&(X14)=(X3)))))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', iftrueProp2)). 1.33/1.50 thf(ifSingleton, axiom, (ifSingleton<=>![X4:$i, X43:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((X43&(X14)=(X2))|(~(X43)&(X14)=(X3)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ifSingleton)). 1.33/1.50 thf(ifp, axiom, (ifp<=>![X4:$i, X44:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>in @ (if @ X4 @ (X44) @ X2 @ X3) @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ifp)). 1.33/1.50 thf(theeq, axiom, (theeq<=>![X21:$i]:(singleton @ X21=>![X2:$i]:(in @ X2 @ X21=>(setunion @ X21)=(X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', theeq)). 1.33/1.50 thf(iftrue, axiom, (iftrue<=>![X4:$i, X45:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(X45=>(if @ X4 @ (X45) @ X2 @ X3)=(X2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', iftrue)). 1.33/1.50 thf(iffalse, axiom, (iffalse<=>![X4:$i, X46:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(~(X46)=>(if @ X4 @ (X46) @ X2 @ X3)=(X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', iffalse)). 1.33/1.50 thf(iftrueorfalse, axiom, (iftrueorfalse<=>![X4:$i, X47:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>in @ (if @ X4 @ (X47) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', iftrueorfalse)). 1.33/1.50 thf(binintersectT_lem, axiom, (binintersectT_lem<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>in @ (binintersect @ X21 @ X48) @ (powerset @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectT_lem)). 1.33/1.50 thf(binunionT_lem, axiom, (binunionT_lem<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>in @ (binunion @ X21 @ X48) @ (powerset @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionT_lem)). 1.33/1.50 thf(powersetT_lem, axiom, (powersetT_lem<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetT_lem)). 1.33/1.50 thf(setminusT_lem, axiom, (setminusT_lem<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>in @ (setminus @ X21 @ X48) @ (powerset @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusT_lem)). 1.33/1.50 thf(complementT_lem, axiom, (complementT_lem<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>in @ (setminus @ X4 @ X21) @ (powerset @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', complementT_lem)). 1.33/1.50 thf(setextT, axiom, (setextT<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>(![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X21=>in @ X2 @ X48))=>(![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X48=>in @ X2 @ X21))=>(X21)=(X48)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setextT)). 1.33/1.50 thf(subsetTI, axiom, (subsetTI<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>(![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X21=>in @ X2 @ X48))=>subset @ X21 @ X48)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetTI)). 1.33/1.50 thf(powersetTI1, axiom, (powersetTI1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>(![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X21=>in @ X2 @ X48))=>in @ X21 @ (powerset @ X48))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetTI1)). 1.33/1.50 thf(powersetTE1, axiom, (powersetTE1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X21 @ (powerset @ X48)=>(in @ X2 @ X21=>in @ X2 @ X48)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetTE1)). 1.33/1.50 thf(complementTI1, axiom, (complementTI1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X21=>~(in @ X2 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', complementTI1)). 1.33/1.50 thf(complementTE1, axiom, (complementTE1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ (setminus @ X4 @ X21))=>in @ X2 @ X21)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', complementTE1)). 1.33/1.50 thf(binintersectTELcontra, axiom, (binintersectTELcontra<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X21)=>~(in @ X2 @ (binintersect @ X21 @ X48))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectTELcontra)). 1.33/1.50 thf(binintersectTERcontra, axiom, (binintersectTERcontra<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X48)=>~(in @ X2 @ (binintersect @ X21 @ X48))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectTERcontra)). 1.33/1.50 thf(contrasubsetT, axiom, (contrasubsetT<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(subset @ X21 @ (setminus @ X4 @ X48)=>(in @ X2 @ X48=>~(in @ X2 @ X21))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', contrasubsetT)). 1.33/1.50 thf(contrasubsetT1, axiom, (contrasubsetT1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(subset @ X21 @ X48=>(~(in @ X2 @ X48)=>~(in @ X2 @ X21))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', contrasubsetT1)). 1.33/1.50 thf(contrasubsetT2, axiom, (contrasubsetT2<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>(subset @ X21 @ X48=>subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', contrasubsetT2)). 1.33/1.50 thf(contrasubsetT3, axiom, (contrasubsetT3<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)=>subset @ X21 @ X48)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', contrasubsetT3)). 1.33/1.50 thf(doubleComplementI1, axiom, (doubleComplementI1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X21=>in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', doubleComplementI1)). 1.33/1.50 thf(doubleComplementE1, axiom, (doubleComplementE1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))=>in @ X2 @ X21)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', doubleComplementE1)). 1.33/1.50 thf(doubleComplementSub1, axiom, (doubleComplementSub1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', doubleComplementSub1)). 1.33/1.50 thf(doubleComplementSub2, axiom, (doubleComplementSub2<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', doubleComplementSub2)). 1.33/1.50 thf(doubleComplementEq, axiom, (doubleComplementEq<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>(X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', doubleComplementEq)). 1.33/1.50 thf(complementTnotintersectT, axiom, (complementTnotintersectT<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (setminus @ X4 @ X21)=>~(in @ X2 @ (binintersect @ X21 @ X48))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', complementTnotintersectT)). 1.33/1.50 thf(complementImpComplementIntersect, axiom, (complementImpComplementIntersect<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (setminus @ X4 @ X21)=>in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', complementImpComplementIntersect)). 1.33/1.50 thf(complementSubsetComplementIntersect, axiom, (complementSubsetComplementIntersect<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', complementSubsetComplementIntersect)). 1.33/1.50 thf(complementInPowersetComplementIntersect, axiom, (complementInPowersetComplementIntersect<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', complementInPowersetComplementIntersect)). 1.33/1.50 thf(contraSubsetComplement, axiom, (contraSubsetComplement<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>(subset @ X21 @ (setminus @ X4 @ X48)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X48=>in @ X2 @ (setminus @ X4 @ X21))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', contraSubsetComplement)). 1.33/1.50 thf(complementTcontraSubset, axiom, (complementTcontraSubset<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>(subset @ X21 @ (setminus @ X4 @ X48)=>subset @ X48 @ (setminus @ X4 @ X21))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', complementTcontraSubset)). 1.33/1.50 thf(binunionTILcontra, axiom, (binunionTILcontra<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ (binunion @ X21 @ X48))=>~(in @ X2 @ X21)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionTILcontra)). 1.33/1.50 thf(binunionTIRcontra, axiom, (binunionTIRcontra<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ (binunion @ X21 @ X48))=>~(in @ X2 @ X48)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionTIRcontra)). 1.33/1.50 thf(inIntersectImpInUnion, axiom, (inIntersectImpInUnion<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X49:$i]:(in @ X49 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (binintersect @ X21 @ X48)=>in @ X2 @ (binunion @ X21 @ X49))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', inIntersectImpInUnion)). 1.33/1.50 thf(inIntersectImpInUnion2, axiom, (inIntersectImpInUnion2<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X49:$i]:(in @ X49 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (binintersect @ X21 @ X48)=>in @ X2 @ (binunion @ X48 @ X49))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', inIntersectImpInUnion2)). 1.33/1.50 thf(inIntersectImpInIntersectUnions, axiom, (inIntersectImpInIntersectUnions<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X49:$i]:(in @ X49 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (binintersect @ X21 @ X48)=>in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', inIntersectImpInIntersectUnions)). 1.33/1.50 thf(intersectInPowersetIntersectUnions, axiom, (intersectInPowersetIntersectUnions<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X49:$i]:(in @ X49 @ (powerset @ X4)=>in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', intersectInPowersetIntersectUnions)). 1.33/1.50 thf(inComplementUnionImpNotIn1, axiom, (inComplementUnionImpNotIn1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))=>~(in @ X2 @ X21)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', inComplementUnionImpNotIn1)). 1.33/1.50 thf(inComplementUnionImpInComplement1, axiom, (inComplementUnionImpInComplement1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))=>in @ X2 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', inComplementUnionImpInComplement1)). 1.33/1.50 thf(binunionTE, axiom, (binunionTE<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X50:$o, X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (binunion @ X21 @ X48)=>((in @ X2 @ X21=>X50)=>((in @ X2 @ X48=>X50)=>X50))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionTE)). 1.33/1.50 thf(binunionTEcontra, axiom, (binunionTEcontra<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X21)=>(~(in @ X2 @ X48)=>~(in @ X2 @ (binunion @ X21 @ X48)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionTEcontra)). 1.33/1.50 thf(demorgan2a1, axiom, (demorgan2a1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))=>in @ X2 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', demorgan2a1)). 1.33/1.50 thf(complementUnionInPowersetComplement, axiom, (complementUnionInPowersetComplement<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', complementUnionInPowersetComplement)). 1.33/1.50 thf(demorgan2a2, axiom, (demorgan2a2<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))=>in @ X2 @ (setminus @ X4 @ X48)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', demorgan2a2)). 1.33/1.50 thf(demorgan1a, axiom, (demorgan1a<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))=>in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', demorgan1a)). 1.33/1.50 thf(demorgan1b, axiom, (demorgan1b<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))=>in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', demorgan1b)). 1.33/1.50 thf(demorgan1, axiom, (demorgan1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>(setminus @ X4 @ (binintersect @ X21 @ X48))=(binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', demorgan1)). 1.33/1.50 thf(demorgan2a, axiom, (demorgan2a<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))=>in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', demorgan2a)). 1.33/1.50 thf(demorgan2b2, axiom, (demorgan2b2<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (setminus @ X4 @ X21)=>(in @ X2 @ (setminus @ X4 @ X48)=>in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', demorgan2b2)). 1.33/1.50 thf(demorgan2b, axiom, (demorgan2b<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))=>in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', demorgan2b)). 1.33/1.50 thf(demorgan2, axiom, (demorgan2<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>(setminus @ X4 @ (binunion @ X21 @ X48))=(binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', demorgan2)). 1.33/1.50 thf(woz13rule0, axiom, (woz13rule0<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ (binintersect @ X21 @ X48)=>in @ X2 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', woz13rule0)). 1.33/1.50 thf(woz13rule1, axiom, (woz13rule1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X49:$i]:(in @ X49 @ (powerset @ X4)=>(subset @ X21 @ X49=>subset @ (binintersect @ X21 @ X48) @ X49))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', woz13rule1)). 1.33/1.50 thf(woz13rule2, axiom, (woz13rule2<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X49:$i]:(in @ X49 @ (powerset @ X4)=>(subset @ X48 @ X49=>subset @ (binintersect @ X21 @ X48) @ X49))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', woz13rule2)). 1.33/1.50 thf(woz13rule3, axiom, (woz13rule3<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X49:$i]:(in @ X49 @ (powerset @ X4)=>(subset @ X21 @ X48=>(subset @ X21 @ X49=>subset @ X21 @ (binintersect @ X48 @ X49))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', woz13rule3)). 1.33/1.50 thf(woz13rule4, axiom, (woz13rule4<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X49:$i]:(in @ X49 @ (powerset @ X4)=>![X51:$i]:(in @ X51 @ (powerset @ X4)=>(subset @ X21 @ X49=>(subset @ X48 @ X51=>subset @ (binintersect @ X21 @ X48) @ (binintersect @ X49 @ X51)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', woz13rule4)). 1.33/1.50 thf(woz1_1, axiom, (woz1_1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', woz1_1)). 1.33/1.50 thf(woz1_2, axiom, (woz1_2<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X49:$i]:(in @ X49 @ (powerset @ X4)=>![X51:$i]:(in @ X51 @ (powerset @ X4)=>(setminus @ X4 @ (binintersect @ (binunion @ X21 @ X48) @ (binunion @ X49 @ X51)))=(binunion @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)) @ (binintersect @ (setminus @ X4 @ X49) @ (setminus @ X4 @ X51)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', woz1_2)). 1.33/1.50 thf(woz1_3, axiom, (woz1_3<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X49:$i]:(in @ X49 @ (powerset @ X4)=>in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', woz1_3)). 1.33/1.50 thf(woz1_4, axiom, (woz1_4<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>(subset @ X21 @ (setminus @ X4 @ X48)=>subset @ X48 @ (setminus @ X4 @ X21))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', woz1_4)). 1.33/1.50 thf(woz1_5, axiom, (woz1_5<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', woz1_5)). 1.33/1.50 thf(breln1all2, axiom, (breln1all2<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X1:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(in @ (kpair @ X2 @ X3) @ X33=>X1 @ (kpair @ X2 @ X3))))=>![X2:$i]:(in @ X2 @ X33=>X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln1all2)). 1.33/1.50 thf(breln1SetBreln1, axiom, (breln1SetBreln1<=>![X4:$i, X33:$i]:(in @ X33 @ (breln1Set @ X4)=>breln1 @ X4 @ X33)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln1SetBreln1)). 1.33/1.50 thf(choice2fnsingleton, axiom, (choice2fnsingleton<=>![X4:$i, X5:$i, X52:$i > $i > $o]:(![X2:$i]:(in @ X2 @ X4=>?[X3:$i]:(in @ X3 @ X5&X52 @ X2 @ X3))=>![X33:$i]:(in @ X33 @ (breln1Set @ X5)=>(reflwellordering @ X5 @ X33=>![X2:$i]:(in @ X2 @ X4=>singleton @ (dsetconstr @ X5 @ (^[X3:$i]:(X52 @ X2 @ X3&![X14:$i]:(in @ X14 @ X5=>(X52 @ X2 @ X14=>in @ (kpair @ X3 @ X14) @ X33)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', choice2fnsingleton)). 1.33/1.50 thf(setOfPairsIsBReln1, axiom, (setOfPairsIsBReln1<=>![X4:$i, X53:$i > $i > $o]:breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:X53 @ X2 @ X3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setOfPairsIsBReln1)). 1.33/1.50 thf(breln1all1, axiom, (breln1all1<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X1:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(in @ (kpair @ X2 @ X3) @ X33=>X1 @ (kpair @ X2 @ X3))))=>![X2:$i]:(in @ X2 @ X33=>X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln1all1)). 1.33/1.50 thf(subbreln1, axiom, (subbreln1<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X35:$i]:(breln1 @ X4 @ X35=>(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(in @ (kpair @ X2 @ X3) @ X33=>in @ (kpair @ X2 @ X3) @ X35)))=>subset @ X33 @ X35)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subbreln1)). 1.33/1.50 thf(eqbreln1, axiom, (eqbreln1<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X35:$i]:(breln1 @ X4 @ X35=>(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(in @ (kpair @ X2 @ X3) @ X33=>in @ (kpair @ X2 @ X3) @ X35)))=>(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(in @ (kpair @ X2 @ X3) @ X35=>in @ (kpair @ X2 @ X3) @ X33)))=>(X33)=(X35)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqbreln1)). 1.33/1.50 thf(breln1invprop, axiom, (breln1invprop<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>breln1 @ X4 @ (breln1invset @ X4 @ X33))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln1invprop)). 1.33/1.50 thf(breln1invI, axiom, (breln1invI<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(in @ (kpair @ X2 @ X3) @ X33=>in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln1invI)). 1.33/1.50 thf(breln1invE, axiom, (breln1invE<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33)=>in @ (kpair @ X2 @ X3) @ X33))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln1invE)). 1.33/1.50 thf(breln1compprop, axiom, (breln1compprop<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X35:$i]:(breln1 @ X4 @ X35=>breln1 @ X4 @ (breln1compset @ X4 @ X33 @ X35)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln1compprop)). 1.33/1.50 thf(breln1compI, axiom, (breln1compI<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X35:$i]:(breln1 @ X4 @ X35=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>![X14:$i]:(in @ X14 @ X4=>(in @ (kpair @ X2 @ X14) @ X33=>(in @ (kpair @ X14 @ X3) @ X35=>in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln1compI)). 1.33/1.50 thf(breln1compE, axiom, (breln1compE<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X35:$i]:(breln1 @ X4 @ X35=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35)=>?[X14:$i]:((in @ X14 @ X4&in @ (kpair @ X2 @ X14) @ X33)&in @ (kpair @ X14 @ X3) @ X35))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln1compE)). 1.33/1.50 thf(breln1compEex, axiom, (breln1compEex<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X35:$i]:(breln1 @ X4 @ X35=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35)=>![X54:$o]:(![X14:$i]:(in @ X14 @ X4=>(in @ (kpair @ X2 @ X14) @ X33=>(in @ (kpair @ X14 @ X3) @ X35=>X54)))=>X54))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln1compEex)). 1.33/1.50 thf(breln1unionprop, axiom, (breln1unionprop<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X35:$i]:(breln1 @ X4 @ X35=>breln1 @ X4 @ (binunion @ X33 @ X35)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln1unionprop)). 1.33/1.50 thf(breln1unionIL, axiom, (breln1unionIL<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X35:$i]:(breln1 @ X4 @ X35=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(in @ (kpair @ X2 @ X3) @ X33=>in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln1unionIL)). 1.33/1.50 thf(breln1unionIR, axiom, (breln1unionIR<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X35:$i]:(breln1 @ X4 @ X35=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(in @ (kpair @ X2 @ X3) @ X35=>in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln1unionIR)). 1.33/1.50 thf(breln1unionI, axiom, (breln1unionI<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X35:$i]:(breln1 @ X4 @ X35=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>((in @ (kpair @ X2 @ X3) @ X33|in @ (kpair @ X2 @ X3) @ X35)=>in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln1unionI)). 1.33/1.50 thf(breln1unionE, axiom, (breln1unionE<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X35:$i]:(breln1 @ X4 @ X35=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)=>(in @ (kpair @ X2 @ X3) @ X33|in @ (kpair @ X2 @ X3) @ X35))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln1unionE)). 1.33/1.50 thf(breln1unionEcases, axiom, (breln1unionEcases<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X35:$i]:(breln1 @ X4 @ X35=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)=>![X55:$o]:((in @ (kpair @ X2 @ X3) @ X33=>X55)=>((in @ (kpair @ X2 @ X3) @ X35=>X55)=>X55)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln1unionEcases)). 1.33/1.50 thf(breln1unionCommutes, axiom, (breln1unionCommutes<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X35:$i]:(breln1 @ X4 @ X35=>(binunion @ X33 @ X35)=(binunion @ X35 @ X33)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln1unionCommutes)). 1.33/1.50 thf(woz2Ex, axiom, (woz2Ex<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>(X33)=(breln1invset @ X4 @ (breln1invset @ X4 @ X33)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', woz2Ex)). 1.33/1.50 thf(woz2W, axiom, (woz2W<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X35:$i]:(breln1 @ X4 @ X35=>(breln1invset @ X4 @ (breln1compset @ X4 @ X33 @ X35))=(breln1compset @ X4 @ (breln1invset @ X4 @ X35) @ (breln1invset @ X4 @ X33))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', woz2W)). 1.33/1.50 thf(woz2A, axiom, (woz2A<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X35:$i]:(breln1 @ X4 @ X35=>![X56:$i]:(breln1 @ X4 @ X56=>(breln1compset @ X4 @ (binunion @ X33 @ X35) @ X56)=(binunion @ (breln1compset @ X4 @ X33 @ X56) @ (breln1compset @ X4 @ X35 @ X56)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', woz2A)). 1.33/1.50 thf(woz2B, axiom, (woz2B<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X35:$i]:(breln1 @ X4 @ X35=>![X56:$i]:(breln1 @ X4 @ X56=>(breln1compset @ X4 @ (binunion @ X33 @ X35) @ X56)=(binunion @ (breln1invset @ X4 @ (breln1compset @ X4 @ (breln1invset @ X4 @ X56) @ (breln1invset @ X4 @ X35))) @ (breln1invset @ X4 @ (breln1compset @ X4 @ (breln1invset @ X4 @ X56) @ (breln1invset @ X4 @ X33)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', woz2B)). 1.33/1.50 thf(image1Ex, axiom, (image1Ex<=>![X4:$i, X57:$i > $i]:?[X5:$i]:![X2:$i]:(in @ X2 @ X5<=>?[X3:$i]:(in @ X3 @ X4&(X2)=(X57 @ X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', image1Ex)). 1.33/1.50 thf(image1Equiv, axiom, (image1Equiv<=>![X4:$i, X59:$i > $i, X2:$i]:(in @ X2 @ (image1 @ X4 @ (^[X3:$i]:X59 @ X3))<=>?[X3:$i]:(in @ X3 @ X4&(X2)=(X59 @ X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', image1Equiv)). 1.33/1.50 thf(image1E, axiom, (image1E<=>![X4:$i, X60:$i > $i, X2:$i]:(in @ X2 @ (image1 @ X4 @ (^[X3:$i]:X60 @ X3))=>?[X3:$i]:(in @ X3 @ X4&(X2)=(X60 @ X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', image1E)). 1.33/1.50 thf(image1I, axiom, (image1I<=>![X4:$i, X61:$i > $i, X2:$i]:(?[X3:$i]:(in @ X3 @ X4&(X2)=(X61 @ X3))=>in @ X2 @ (image1 @ X4 @ (^[X3:$i]:X61 @ X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', image1I)). 1.33/1.50 thf(injFuncInInjFuncSet, axiom, (injFuncInInjFuncSet<=>![X4:$i, X5:$i, X29:$i]:(in @ X29 @ (funcSet @ X4 @ X5)=>(injective @ X4 @ X5 @ X29=>in @ X29 @ (injFuncSet @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', injFuncInInjFuncSet)). 1.33/1.50 thf(injFuncSetFuncIn, axiom, (injFuncSetFuncIn<=>![X4:$i, X5:$i, X29:$i]:(in @ X29 @ (injFuncSet @ X4 @ X5)=>in @ X29 @ (funcSet @ X4 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', injFuncSetFuncIn)). 1.33/1.50 thf(injFuncSetFuncInj, axiom, (injFuncSetFuncInj<=>![X2:$i, X3:$i, X29:$i]:(in @ X29 @ (injFuncSet @ X2 @ X3)=>injective @ X2 @ X3 @ X29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', injFuncSetFuncInj)). 1.33/1.50 thf(surjFuncSetFuncIn, axiom, (surjFuncSetFuncIn<=>![X4:$i, X5:$i, X29:$i]:(in @ X29 @ (surjFuncSet @ X4 @ X5)=>in @ X29 @ (funcSet @ X4 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', surjFuncSetFuncIn)). 1.33/1.50 thf(surjFuncSetFuncSurj, axiom, (surjFuncSetFuncSurj<=>![X2:$i, X3:$i, X29:$i]:(in @ X29 @ (surjFuncSet @ X2 @ X3)=>surjective @ X2 @ X3 @ X29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', surjFuncSetFuncSurj)). 1.33/1.50 thf(leftInvIsSurj, axiom, (leftInvIsSurj<=>![X4:$i, X5:$i, X62:$i > $i]:(![X2:$i]:(in @ X2 @ X4=>in @ (X62 @ X2) @ X5)=>![X34:$i]:(in @ X34 @ (funcSet @ X5 @ X4)=>(![X2:$i]:(in @ X2 @ X4=>(ap @ X5 @ X4 @ X34 @ (X62 @ X2))=(X2))=>surjective @ X5 @ X4 @ X34)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', leftInvIsSurj)). 1.33/1.50 thf(surjCantorThm, axiom, (surjCantorThm<=>![X4:$i, X29:$i]:(in @ X29 @ (funcSet @ X4 @ (powerset @ X4))=>~(surjective @ X4 @ (powerset @ X4) @ X29))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', surjCantorThm)). 1.33/1.50 thf(notinself, axiom, (notinself<=>![X4:$i]:~(in @ X4 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notinself)). 1.33/1.50 thf(notinself2, axiom, (notinself2<=>![X4:$i, X5:$i]:(in @ X4 @ X5=>~(in @ X5 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notinself2)). 1.33/1.50 thf(omegaSp, axiom, (omegaSp<=>![X2:$i]:(in @ X2 @ omega=>in @ (omegaS @ X2) @ omega)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omegaSp)). 1.33/1.50 thf(omegaSclos, axiom, (omegaSclos<=>![X2:$i]:(in @ X2 @ omega=>in @ (setadjoin @ X2 @ X2) @ omega)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omegaSclos)). 1.33/1.50 thf(peano0notS, axiom, (peano0notS<=>![X2:$i]:(in @ X2 @ omega=>(omegaS @ X2)!=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', peano0notS)). 1.33/1.50 thf(peanoSinj, axiom, (peanoSinj<=>![X2:$i]:(in @ X2 @ omega=>![X3:$i]:(in @ X3 @ omega=>((omegaS @ X2)=(omegaS @ X3)=>(X2)=(X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', peanoSinj)). 1.33/1.50 thf(c_0_340, axiom, (wellorderedByIn)=(^[X4:$i]:(((![X1193:$i]:(in @ X1193 @ X4=>![X1194:$i]:(in @ X1194 @ X4=>![X1195:$i]:(in @ X1195 @ X4=>((in @ X1193 @ X1194&in @ X1194 @ X1195)=>in @ X1193 @ X1195))))&![X1196:$i]:(in @ X1196 @ X4=>![X1197:$i]:(in @ X1197 @ X4=>(((X1196)=(X1197)|in @ X1196 @ X1197)|in @ X1197 @ X1196))))&![X1198:$i]:(in @ X1198 @ X4=>~(in @ X1198 @ X1198)))&![X21:$i]:(in @ X21 @ (powerset @ X4)=>((X21)!=(emptyset)=>?[X2:$i]:(in @ X2 @ X21&![X48:$i]:(in @ X48 @ X21=>((X2)=(X48)|in @ X2 @ X48))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[wellorderedByIn, nonempty]), stricttotalorderedByIn])). 1.33/1.50 thf(c_0_341, axiom, (ordinal)=(^[X2:$i]:(![X1199:$i]:(in @ X1199 @ X2=>subset @ X1199 @ X2)&(((![X1200:$i]:(in @ X1200 @ X2=>![X1201:$i]:(in @ X1201 @ X2=>![X1202:$i]:(in @ X1202 @ X2=>((in @ X1200 @ X1201&in @ X1201 @ X1202)=>in @ X1200 @ X1202))))&![X1203:$i]:(in @ X1203 @ X2=>![X1204:$i]:(in @ X1204 @ X2=>(((X1203)=(X1204)|in @ X1203 @ X1204)|in @ X1204 @ X1203))))&![X1205:$i]:(in @ X1205 @ X2=>~(in @ X1205 @ X1205)))&![X1206:$i]:(in @ X1206 @ (powerset @ X2)=>((X1206)!=(emptyset)=>?[X1207:$i]:(in @ X1207 @ X1206&![X1208:$i]:(in @ X1208 @ X1206=>((X1207)=(X1208)|in @ X1207 @ X1208)))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[ordinal, transitiveset]), c_0_340])). 1.33/1.50 thf(c_0_342, plain, ![X21:$i]:(epred13_1 @ X21<=>(![X1230:$i]:(in @ X1230 @ X21=>subset @ X1230 @ X21)&(((![X1231:$i]:(in @ X1231 @ X21=>![X1232:$i]:(in @ X1232 @ X21=>![X1233:$i]:(in @ X1233 @ X21=>((in @ X1231 @ X1232&in @ X1232 @ X1233)=>in @ X1231 @ X1233))))&![X1234:$i]:(in @ X1234 @ X21=>![X1235:$i]:(in @ X1235 @ X21=>((X1234)=(X1235)|in @ X1234 @ X1235|in @ X1235 @ X1234))))&![X1236:$i]:(in @ X1236 @ X21=>~in @ X1236 @ X1236))&![X1237:$i]:(in @ X1237 @ (powerset @ X21)=>((X1237)!=(emptyset)=>?[X1238:$i]:(in @ X1238 @ X1237&![X1239:$i]:(in @ X1239 @ X1237=>((X1238)=(X1239)|in @ X1238 @ X1239)))))))), introduced(definition)). 1.33/1.50 thf(c_0_343, axiom, (replAx)=(![X6:$i > $i > $o, X4:$i]:(![X2:$i]:(in @ X2 @ X4=>?[X1148:$i]:(X6 @ X2 @ X1148&![X1150:$i]:(X6 @ X2 @ X1150=>(X1148)=(X1150))))=>?[X5:$i]:![X2:$i]:(in @ X2 @ X5<=>?[X3:$i]:(in @ X3 @ X4&X6 @ X3 @ X2)))), inference(apply_def,[status(thm)],[replAx, exu])). 1.33/1.50 thf(c_0_344, axiom, (descrp)=(![X1:$i > $o]:(?[X1151:$i]:(X1 @ X1151&![X1152:$i]:(X1 @ X1152=>(X1151)=(X1152)))=>X1 @ (descr @ (^[X2:$i]:X1 @ X2)))), inference(apply_def,[status(thm)],[descrp, exu])). 1.33/1.50 thf(c_0_345, axiom, (exuE1)=(![X1:$i > $o]:(?[X1153:$i]:(X1 @ X1153&![X1154:$i]:(X1 @ X1154=>(X1153)=(X1154)))=>?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3))))), inference(apply_def,[status(thm)],[exuE1, exu])). 1.33/1.50 thf(c_0_346, axiom, (exuE3e)=(![X1:$i > $o]:(?[X1155:$i]:(X1 @ X1155&![X1156:$i]:(X1 @ X1156=>(X1155)=(X1156)))=>?[X2:$i]:X1 @ X2)), inference(apply_def,[status(thm)],[exuE3e, exu])). 1.33/1.50 thf(c_0_347, axiom, (nonemptyE1)=(![X4:$i]:((X4)!=(emptyset)=>?[X2:$i]:in @ X2 @ X4)), inference(apply_def,[status(thm)],[nonemptyE1, nonempty])). 1.33/1.50 thf(c_0_348, axiom, (nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>(dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))!=(emptyset)))), inference(apply_def,[status(thm)],[nonemptyI, nonempty])). 1.33/1.50 thf(c_0_349, axiom, (nonemptyI1)=(![X4:$i]:(?[X2:$i]:in @ X2 @ X4=>(X4)!=(emptyset))), inference(apply_def,[status(thm)],[nonemptyI1, nonempty])). 1.33/1.50 thf(c_0_350, axiom, (exuE2)=(![X1:$i > $o]:(?[X1157:$i]:(X1 @ X1157&![X1158:$i]:(X1 @ X1158=>(X1157)=(X1158)))=>?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2)))), inference(apply_def,[status(thm)],[exuE2, exu])). 1.33/1.50 thf(c_0_351, axiom, (nonemptyImpWitness)=(![X4:$i]:((X4)!=(emptyset)=>?[X2:$i]:(in @ X2 @ X4&$true))), inference(apply_def,[status(thm)],[nonemptyImpWitness, nonempty])). 1.33/1.50 thf(c_0_352, axiom, (exuI1)=(![X1:$i > $o]:(?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3)))=>?[X1159:$i]:(X1 @ X1159&![X1160:$i]:(X1 @ X1160=>(X1159)=(X1160))))), inference(apply_def,[status(thm)],[exuI1, exu])). 1.33/1.50 thf(c_0_353, axiom, (exuI3)=(![X1:$i > $o]:(?[X2:$i]:X1 @ X2=>(![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3)))=>?[X1161:$i]:(X1 @ X1161&![X1162:$i]:(X1 @ X1162=>(X1161)=(X1162)))))), inference(apply_def,[status(thm)],[exuI3, exu])). 1.33/1.50 thf(c_0_354, axiom, (exuI2)=(![X1:$i > $o]:(?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2))=>?[X1163:$i]:(X1 @ X1163&![X1164:$i]:(X1 @ X1164=>(X1163)=(X1164))))), inference(apply_def,[status(thm)],[exuI2, exu])). 1.33/1.50 thf(c_0_355, axiom, (exuE3u)=(![X1:$i > $o]:(?[X1165:$i]:(X1 @ X1165&![X1166:$i]:(X1 @ X1166=>(X1165)=(X1166)))=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))), inference(apply_def,[status(thm)],[exuE3u, exu])). 1.33/1.50 thf(c_0_356, axiom, (exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(?[X1167:$i]:(X1 @ X1167&![X1168:$i]:(X1 @ X1168=>(X1167)=(X1168)))<=>?[X1169:$i]:(X17 @ X1169&![X1170:$i]:(X17 @ X1170=>(X1169)=(X1170)))))), inference(apply_def,[status(thm)],[exu__Cong, exu])). 1.33/1.50 thf(c_0_357, axiom, (exuEu)=(![X1:$i > $o]:(?[X1171:$i]:(X1 @ X1171&![X1172:$i]:(X1 @ X1172=>(X1171)=(X1172)))=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))), inference(apply_def,[status(thm)],[exuEu, exu])). 1.33/1.50 thf(c_0_358, axiom, (descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(?[X1173:$i]:(X1 @ X1173&![X1174:$i]:(X1 @ X1174=>(X1173)=(X1174)))=>(?[X1175:$i]:(X17 @ X1175&![X1176:$i]:(X17 @ X1176=>(X1175)=(X1176)))=>(descr @ (^[X2:$i]:X1 @ X2))=(descr @ (^[X2:$i]:X17 @ X2)))))), inference(apply_def,[status(thm)],[descr__Cong, exu])). 1.33/1.50 thf(c_0_359, axiom, (image1Ex1)=(![X4:$i, X58:$i > $i]:?[X1177:$i]:(![X1182:$i]:(in @ X1182 @ X1177<=>?[X1183:$i]:(in @ X1183 @ X4&(X1182)=(X58 @ X1183)))&![X1180:$i]:(![X1184:$i]:(in @ X1184 @ X1180<=>?[X1185:$i]:(in @ X1185 @ X4&(X1184)=(X58 @ X1185)))=>(X1177)=(X1180)))), inference(apply_def,[status(thm)],[image1Ex1, exu])). 1.33/1.50 thf(c_0_360, axiom, (foundation2)=(![X4:$i]:((X4)!=(emptyset)=>?[X21:$i]:(in @ X21 @ X4&(binintersect @ X21 @ X4)=(emptyset)))), inference(apply_def,[status(thm)],[foundation2, nonempty])). 1.33/1.50 thf(c_0_361, axiom, (transitivesetOp1)=(![X21:$i]:(![X1186:$i]:(in @ X1186 @ X21=>subset @ X1186 @ X21)=>![X4:$i]:(in @ X4 @ X21=>subset @ X4 @ X21))), inference(apply_def,[status(thm)],[transitivesetOp1, transitiveset])). 1.33/1.50 thf(c_0_362, axiom, (binintTransitive)=(![X21:$i]:(![X1187:$i]:(in @ X1187 @ X21=>subset @ X1187 @ X21)=>![X48:$i]:(![X1188:$i]:(in @ X1188 @ X48=>subset @ X1188 @ X48)=>![X1189:$i]:(in @ X1189 @ (binintersect @ X21 @ X48)=>subset @ X1189 @ (binintersect @ X21 @ X48))))), inference(apply_def,[status(thm)],[binintTransitive, transitiveset])). 1.33/1.50 thf(c_0_363, axiom, (transitivesetOp2)=(![X21:$i]:(![X1190:$i]:(in @ X1190 @ X21=>subset @ X1190 @ X21)=>![X4:$i, X2:$i]:(in @ X4 @ X21=>(in @ X2 @ X4=>in @ X2 @ X21)))), inference(apply_def,[status(thm)],[transitivesetOp2, transitiveset])). 1.33/1.50 thf(c_0_364, axiom, (setunionTransitive)=(![X21:$i]:(![X2:$i]:(in @ X2 @ X21=>![X1191:$i]:(in @ X1191 @ X2=>subset @ X1191 @ X2))=>![X1192:$i]:(in @ X1192 @ (setunion @ X21)=>subset @ X1192 @ (setunion @ X21)))), inference(apply_def,[status(thm)],[setunionTransitive, transitiveset])). 1.33/1.50 thf(c_0_365, axiom, (ordinalMinLem1)=(![X21:$i]:((![X1209:$i]:(in @ X1209 @ X21=>subset @ X1209 @ X21)&(((![X1210:$i]:(in @ X1210 @ X21=>![X1211:$i]:(in @ X1211 @ X21=>![X1212:$i]:(in @ X1212 @ X21=>((in @ X1210 @ X1211&in @ X1211 @ X1212)=>in @ X1210 @ X1212))))&![X1213:$i]:(in @ X1213 @ X21=>![X1214:$i]:(in @ X1214 @ X21=>(((X1213)=(X1214)|in @ X1213 @ X1214)|in @ X1214 @ X1213))))&![X1215:$i]:(in @ X1215 @ X21=>~(in @ X1215 @ X1215)))&![X1216:$i]:(in @ X1216 @ (powerset @ X21)=>((X1216)!=(emptyset)=>?[X1217:$i]:(in @ X1217 @ X1216&![X1218:$i]:(in @ X1218 @ X1216=>((X1217)=(X1218)|in @ X1217 @ X1218)))))))=>![X48:$i]:((![X1219:$i]:(in @ X1219 @ X48=>subset @ X1219 @ X48)&(((![X1220:$i]:(in @ X1220 @ X48=>![X1221:$i]:(in @ X1221 @ X48=>![X1222:$i]:(in @ X1222 @ X48=>((in @ X1220 @ X1221&in @ X1221 @ X1222)=>in @ X1220 @ X1222))))&![X1223:$i]:(in @ X1223 @ X48=>![X1224:$i]:(in @ X1224 @ X48=>(((X1223)=(X1224)|in @ X1223 @ X1224)|in @ X1224 @ X1223))))&![X1225:$i]:(in @ X1225 @ X48=>~(in @ X1225 @ X1225)))&![X1226:$i]:(in @ X1226 @ (powerset @ X48)=>((X1226)!=(emptyset)=>?[X1227:$i]:(in @ X1227 @ X1226&![X1228:$i]:(in @ X1228 @ X1226=>((X1227)=(X1228)|in @ X1227 @ X1228)))))))=>![X1229:$i]:(in @ X1229 @ (binintersect @ X21 @ X48)=>subset @ X1229 @ (binintersect @ X21 @ X48))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[ordinalMinLem1, transitiveset]), c_0_341])). 1.33/1.50 thf(c_0_366, plain, ![X2:$i, X1:$i > $o]:(epred1_2 @ X1 @ X2<=>X1 @ X2), introduced(definition)). 1.33/1.50 thf(c_0_367, plain, ![X3:$i, X29:$i, X2:$i]:(epred6_3 @ X2 @ X29 @ X3<=>in @ (kpair @ X2 @ X3) @ X29), introduced(definition)). 1.33/1.50 thf(c_0_368, plain, ![X3:$i, X2:$i, X30:$i > $i]:(epred9_3 @ X30 @ X2 @ X3<=>(X30 @ X2)=(X3)), introduced(definition)). 1.33/1.50 thf(c_0_369, plain, ![X2:$i, X31:$i > $i]:(esk1_2 @ X31 @ X2)=(X31 @ X2), introduced(definition)). 1.33/1.50 thf(c_0_370, plain, ![X14:$i, X2:$i, X39:$o, X3:$i]:(epred7_4 @ X3 @ X39 @ X2 @ X14<=>((X39&(X14)=(X2))|(~X39&(X14)=(X3)))), inference(fof_simplification,[status(thm)],[introduced(definition)])). 1.33/1.50 thf(c_0_371, plain, ![X18:$i, X14:$i, X22:$i > $i > $o]:(epred5_3 @ X22 @ X14 @ X18<=>X22 @ X14 @ X18), introduced(definition)). 1.33/1.50 thf(c_0_372, plain, ![X3:$i, X52:$i > $i > $o, X33:$i, X5:$i, X2:$i]:(epred8_5 @ X2 @ X5 @ X33 @ X52 @ X3<=>(X52 @ X2 @ X3&![X14:$i]:(in @ X14 @ X5=>(X52 @ X2 @ X14=>in @ (kpair @ X3 @ X14) @ X33)))), introduced(definition)). 1.33/1.50 thf(c_0_373, plain, ![X2:$i, X18:$i]:(epred4_2 @ X18 @ X2<=>(X18)=(kpair @ (kfst @ X18) @ X2)), introduced(definition)). 1.33/1.50 thf(c_0_374, plain, ![X2:$i, X18:$i]:(epred3_2 @ X18 @ X2<=>in @ (setadjoin @ X2 @ emptyset) @ X18), introduced(definition)). 1.33/1.50 thf(c_0_375, plain, ![X2:$i]:epred2_1 @ X2, inference(fof_simplification,[status(thm)],[introduced(definition)])). 1.33/1.50 thf(c_0_376, plain, (epred10_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:$i]:(in @ X3 @ X9=>in @ X3 @ X8)|in @ X2 @ X9)))))), introduced(definition)). 1.33/1.50 thf(c_0_377, plain, ![X21:$i]:(epred11_1 @ X21<=>(![X1210:$i]:(in @ X1210 @ X21=>![X1211:$i]:(in @ X1211 @ X21=>![X1212:$i]:(in @ X1212 @ X21=>((in @ X1210 @ X1211&in @ X1211 @ X1212)=>in @ X1210 @ X1212))))&![X1213:$i]:(in @ X1213 @ X21=>![X1214:$i]:(in @ X1214 @ X21=>((X1213)=(X1214)|in @ X1213 @ X1214|in @ X1214 @ X1213))))), introduced(definition)). 1.33/1.50 thf(c_0_378, plain, ![X48:$i]:(epred12_1 @ X48<=>(![X1220:$i]:(in @ X1220 @ X48=>![X1221:$i]:(in @ X1221 @ X48=>![X1222:$i]:(in @ X1222 @ X48=>((in @ X1220 @ X1221&in @ X1221 @ X1222)=>in @ X1220 @ X1222))))&![X1223:$i]:(in @ X1223 @ X48=>![X1224:$i]:(in @ X1224 @ X48=>((X1223)=(X1224)|in @ X1223 @ X1224|in @ X1224 @ X1223))))), introduced(definition)). 1.33/1.50 thf(c_0_379, plain, ![X21:$i]:(epred13_1 @ X21=>(![X1230:$i]:(in @ X1230 @ X21=>subset @ X1230 @ X21)&(((![X1231:$i]:(in @ X1231 @ X21=>![X1232:$i]:(in @ X1232 @ X21=>![X1233:$i]:(in @ X1233 @ X21=>((in @ X1231 @ X1232&in @ X1232 @ X1233)=>in @ X1231 @ X1233))))&![X1234:$i]:(in @ X1234 @ X21=>![X1235:$i]:(in @ X1235 @ X21=>((X1234)=(X1235)|in @ X1234 @ X1235|in @ X1235 @ X1234))))&![X1236:$i]:(in @ X1236 @ X21=>~in @ X1236 @ X1236))&![X1237:$i]:(in @ X1237 @ (powerset @ X21)=>((X1237)!=(emptyset)=>?[X1238:$i]:(in @ X1238 @ X1237&![X1239:$i]:(in @ X1239 @ X1237=>((X1238)=(X1239)|in @ X1238 @ X1239)))))))), inference(split_equiv,[status(thm)],[c_0_342])). 1.33/1.50 thf(c_0_380, 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:$i]:(in @ X2 @ X4=>?[X1148:$i]:(X6 @ X2 @ X1148&![X1150:$i]:(X6 @ X2 @ X1150=>(X1148)=(X1150))))=>?[X5:$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))))=>(epred10_0=>(![X1:$i > $o]:(?[X1151:$i]:(X1 @ X1151&![X1152:$i]:(X1 @ X1152=>(X1151)=(X1152)))=>X1 @ (descr @ (epred1_2 @ X1)))=>(![X4:$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 > $o]:(?[X1153:$i]:(X1 @ X1153&![X1154:$i]:(X1 @ X1154=>(X1153)=(X1154)))=>?[X2:$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 > $o]:(?[X1155:$i]:(X1 @ X1155&![X1156:$i]:(X1 @ X1156=>(X1155)=(X1156)))=>?[X2:$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 > $o]:(?[X1157:$i]:(X1 @ X1157&![X1158:$i]:(X1 @ X1158=>(X1157)=(X1158)))=>?[X2:$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:$i]:(X1 @ X3=>(X2)=(X3)))=>?[X1159:$i]:(X1 @ X1159&![X1160:$i]:(X1 @ X1160=>(X1159)=(X1160))))=>(![X1:$i > $o]:(?[X2:$i]:X1 @ X2=>(![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3)))=>?[X1161:$i]:(X1 @ X1161&![X1162:$i]:(X1 @ X1162=>(X1161)=(X1162)))))=>(![X1:$i > $o]:(?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2))=>?[X1163:$i]:(X1 @ X1163&![X1164:$i]:(X1 @ X1164=>(X1163)=(X1164))))=>(![X4:$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 > $o]:(?[X1165:$i]:(X1 @ X1165&![X1166:$i]:(X1 @ X1166=>(X1165)=(X1166)))=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))=>(![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(?[X1167:$i]:(X1 @ X1167&![X1168:$i]:(X1 @ X1168=>(X1167)=(X1168)))<=>?[X1169:$i]:(X17 @ X1169&![X1170:$i]:(X17 @ X1170=>(X1169)=(X1170)))))=>((emptyset)=(emptyset)=>(![X2:$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 > $o]:(?[X1171:$i]:(X1 @ X1171&![X1172:$i]:(X1 @ X1172=>(X1171)=(X1172)))=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))=>(![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(?[X1173:$i]:(X1 @ X1173&![X1174:$i]:(X1 @ X1174=>(X1173)=(X1174)))=>(?[X1175:$i]:(X17 @ X1175&![X1176:$i]:(X17 @ X1176=>(X1175)=(X1176)))=>(descr @ (epred1_2 @ X1))=(descr @ (epred1_2 @ X17)))))=>(![X4:$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 @ 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setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_343]), foundationAx]), wellorderingAx]), c_0_344]), dsetconstrI]), dsetconstrEL]), dsetconstrER]), c_0_345]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_346]), setext]), emptyI]), noeltsimpempty]), setbeta]), c_0_347]), c_0_348]), c_0_349]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), setoftrueEq]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_350]), c_0_351]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), emptyE1]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_352]), c_0_353]), c_0_354]), inCongP]), in__Cong]), c_0_355]), c_0_356]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_357]), c_0_358]), dsetconstr__Cong]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), sepInPowerset]), sepSubset]), binunionIL]), upairset2IR]), binunionIR]), binunionEcases]), binunionE]), binunionLsub]), binunionRsub]), binintersectI]), binintersectSubset5]), binintersectEL]), binintersectLsub]), binintersectSubset2]), binintersectSubset3]), binintersectER]), disjointsetsI1]), binintersectRsub]), binintersectSubset4]), binintersectSubset1]), bs114d]), setminusI]), setminusEL]), setminusER]), setminusSubset2]), setminusERneg]), setminusELneg]), setminusILneg]), setminusIRneg]), setminusLsub]), setminusSubset1]), symdiffE]), symdiffI1]), symdiffI2]), symdiffIneg1]), symdiffIneg2]), secondinupair]), setukpairIL]), setukpairIR]), kpairiskpair]), kpairp]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1]), cartprodmempair]), setunionE2]), setunionsingleton1]), setunionsingleton2]), setunionsingleton]), singletonprop]), ex1E1]), ex1I]), ex1I2]), singletonsuniq]), setukpairinjL1]), kfstsingleton]), theprop]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), ksndsingleton]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), dpsetconstrI]), dpsetconstrSub]), setOfPairsIsBReln]), dpsetconstrERa]), dpsetconstrEL1]), dpsetconstrEL2]), dpsetconstrER]), funcImageSingleton]), apProp]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), lamProp]), lamp]), lam2p]), brelnall1]), brelnall2]), ex1E2]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), subbreln]), eqbreln]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), beta1]), eta1]), lam2lamEq]), beta2]), eta2]), iffalseProp1]), iffalseProp2]), iftrueProp1]), iftrueProp2]), ifSingleton]), ifp]), theeq]), iftrue]), iffalse]), iftrueorfalse]), binintersectT_lem]), binunionT_lem]), powersetT_lem]), setminusT_lem]), complementT_lem]), setextT]), subsetTI]), powersetTI1]), powersetTE1]), complementTI1]), complementTE1]), binintersectTELcontra]), binintersectTERcontra]), contrasubsetT]), contrasubsetT1]), contrasubsetT2]), contrasubsetT3]), doubleComplementI1]), doubleComplementE1]), doubleComplementSub1]), doubleComplementSub2]), doubleComplementEq]), complementTnotintersectT]), complementImpComplementIntersect]), complementSubsetComplementIntersect]), complementInPowersetComplementIntersect]), contraSubsetComplement]), complementTcontraSubset]), binunionTILcontra]), binunionTIRcontra]), inIntersectImpInUnion]), inIntersectImpInUnion2]), inIntersectImpInIntersectUnions]), intersectInPowersetIntersectUnions]), inComplementUnionImpNotIn1]), inComplementUnionImpInComplement1]), binunionTE]), binunionTEcontra]), demorgan2a1]), complementUnionInPowersetComplement]), demorgan2a2]), demorgan1a]), demorgan1b]), demorgan1]), demorgan2a]), demorgan2b2]), demorgan2b]), demorgan2]), woz13rule0]), woz13rule1]), woz13rule2]), woz13rule3]), woz13rule4]), woz1_1]), woz1_2]), woz1_3]), woz1_4]), woz1_5]), breln1all2]), breln1SetBreln1]), choice2fnsingleton]), setOfPairsIsBReln1]), breln1all1]), subbreln1]), eqbreln1]), breln1invprop]), breln1invI]), breln1invE]), breln1compprop]), breln1compI]), breln1compE]), breln1compEex]), breln1unionprop]), breln1unionIL]), breln1unionIR]), breln1unionI]), breln1unionE]), breln1unionEcases]), breln1unionCommutes]), woz2Ex]), woz2W]), woz2A]), woz2B]), image1Ex]), c_0_359]), image1Equiv]), image1E]), image1I]), injFuncInInjFuncSet]), injFuncSetFuncIn]), injFuncSetFuncInj]), surjFuncSetFuncIn]), surjFuncSetFuncSurj]), leftInvIsSurj]), surjCantorThm]), c_0_360]), notinself]), notinself2]), omegaSp]), omegaSclos]), peano0notS]), peanoSinj]), c_0_361]), c_0_362]), c_0_363]), c_0_364]), c_0_341]), c_0_365]), c_0_366]), c_0_366]), c_0_366]), c_0_366]), c_0_366]), c_0_366]), c_0_366]), c_0_366]), c_0_367]), c_0_368]), c_0_366]), c_0_369]), c_0_369]), c_0_369]), c_0_370]), c_0_370]), c_0_371]), c_0_369]), c_0_369]), c_0_369]), c_0_372]), c_0_370]), c_0_370]), c_0_370]), c_0_369]), c_0_369]), c_0_369]), c_0_369]), c_0_369]), c_0_367]), c_0_371]), c_0_371]), c_0_371]), c_0_371]), c_0_371]), c_0_371]), c_0_371]), c_0_373]), c_0_374]), c_0_366]), c_0_366]), c_0_366]), c_0_366]), c_0_366]), c_0_366]), c_0_375]), c_0_366]), c_0_366]), c_0_366])])]), c_0_376]), c_0_377]), c_0_378]), c_0_342])). 1.33/1.50 thf(c_0_381, plain, ![X2445:$i, X2446:$i, X2447:$i, X2448:$i, X2449:$i, X2450:$i, X2451:$i, X2452:$i, X2453:$i, X2455:$i]:((~in @ X2446 @ X2445|subset @ X2446 @ X2445|~epred13_1 @ X2445)&((((~in @ X2447 @ X2445|(~in @ X2448 @ X2445|(~in @ X2449 @ X2445|(~in @ X2447 @ X2448|~in @ X2448 @ X2449|in @ X2447 @ X2449)))|~epred13_1 @ X2445)&(~in @ X2450 @ X2445|(~in @ X2451 @ X2445|((X2450)=(X2451)|in @ X2450 @ X2451|in @ X2451 @ X2450))|~epred13_1 @ X2445))&(~in @ X2452 @ X2445|~in @ X2452 @ X2452|~epred13_1 @ X2445))&((in @ (esk145_2 @ X2445 @ X2453) @ X2453|(X2453)=(emptyset)|~in @ X2453 @ (powerset @ X2445)|~epred13_1 @ X2445)&(~in @ X2455 @ X2453|((esk145_2 @ X2445 @ X2453)=(X2455)|in @ (esk145_2 @ X2445 @ X2453) @ X2455)|(X2453)=(emptyset)|~in @ X2453 @ (powerset @ X2445)|~epred13_1 @ X2445)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_379])])])])])). 1.33/1.50 thf(c_0_382, negated_conjecture, ![X1240:$i, X1241:$i, X1243:$i, X1244:$i, X1245:$i, X1246:$i, X1247:$i, X1248:$i, X1249:$i, X1250:$i, X1251:$i, X1253:$i, X1254:$i, X1256:$i, X1257:$i, X1258:$i, X1259:$i, X1260:$i, X1262:$i, X1263:$i > $i > $o, X1264:$i, X1266:$i, X1269:$i, X1271:$i, X1272:$i, X1273:$i, X1274:$i, X1276:$i, X1277:$i > $o, X1278:$i, X1280:$i, X1281:$i > $o, X1282:$i, X1283:$i, X1284:$i > $o, X1285:$i, X1286:$i, X1287:$i > $o, X1288:$i, X1289:$i > $o, X1290:$i, X1293:$i, X1294:$o, X1295:$i, X1296:$i, X1297:$o, X1298:$i, X1299:$i, X1300:$i > $o, X1301:$i, X1304:$i, X1305:$i, X1308:$i, X1310:$i, X1312:$i, X1313:$i > $o, X1314:$i, X1315:$i, X1317:$i, X1318:$i > $o, X1319:$i, X1320:$i, X1321:$i, X1322:$i, X1323:$i, X1324:$i, X1325:$i, X1326:$i, X1327:$i, X1328:$i, X1329:$i, X1330:$o, X1331:$i, X1332:$i, X1333:$i, X1334:$i, X1335:$i, X1336:$i, X1338:$i, X1339:$i, X1340:$i, X1341:$i, X1342:$i, X1343:$i, X1344:$i, X1345:$i, X1346:$i, X1347:$i, X1348:$o, X1350:$i, X1351:$i, X1352:$i > $o, X1353:$i, X1356:$i, X1357:$i, X1358:$i, X1360:$i, X1361:$i, X1362:$i, X1363:$i, X1364:$i, X1365:$i, X1366:$i, X1367:$i, X1368:$i, X1369:$i, X1370:$i, X1371:$i, X1372:$i, X1373:$i, X1374:$i, X1375:$i, X1376:$i > $o, X1377:$i, X1378:$i > $o, X1379:$i, X1380:$i, X1381:$i > $o, X1382:$i, X1384:$i, X1385:$i > $o, X1387:$i, X1388:$i, X1389:$i > $o, X1391:$i, X1392:$i, X1393:$i > $o, X1394:$i, X1396:$o, X1397:$o, X1398:$i, X1399:$i > $o, X1401:$i, X1402:$i, X1403:$i > $o, X1404:$i, X1406:$i > $o, X1407:$i, X1410:$i, X1411:$i > $o, X1412:$i, X1416:$i, X1417:$i > $o, X1418:$i, X1421:$i, X1422:$i, X1423:$i, X1424:$i, X1425:$i, X1426:$i, X1427:$i, X1428:$i, X1429:$i, X1430:$i > $o, X1431:$i, X1433:$i, X1434:$i, X1435:$i > $o, X1436:$i > $o, X1439:$i, X1442:$i, X1443:$i, X1446:$i, X1447:$i, X1448:$i, X1449:$i, X1450:$i, X1451:$i, X1452:$i, X1453:$i, X1454:$i, X1455:$i > $o, X1456:$i, X1458:$i, X1459:$i, X1460:$i > $o, X1461:$i > $o, X1464:$i, X1466:$i, X1468:$i, X1469:$i, X1470:$i > $o, X1471:$i > $o, X1474:$i, X1475:$i, X1477:$i, X1478:$i, X1479:$i, X1480:$i, X1481:$i, X1482:$i, X1484:$i, X1485:$i, X1486:$i, X1487:$i, X1488:$i, X1489:$i, X1490:$i, X1491:$i, X1492:$i, X1493:$i, X1494:$i, X1495:$i, X1496:$i, X1497:$i, X1498:$i, X1499:$i, X1500:$i, X1501:$i, X1502:$i, X1503:$i, X1504:$i, X1505:$i, X1506:$i, X1507:$i, X1508:$i, X1509:$i, X1510:$i, X1511:$i, X1512:$i, X1513:$i, X1514:$i, X1515:$i, X1516:$i, X1517:$i, X1518:$i, X1519:$i, X1520:$i, X1521:$i > $o, X1522:$i, X1523:$i > $o, X1524:$i, X1525:$i, X1526:$i, X1527:$i, X1528:$i, X1529:$i, X1530:$i, X1531:$i, X1532:$i, X1533:$i, X1534:$i, X1535:$o, X1536:$i, X1537:$i, X1538:$i, X1539:$i, X1540:$i, X1541:$i, X1542:$i, X1543:$i, X1544:$i, X1545:$i, X1546:$i, X1547:$i, X1548:$i, X1549:$i, X1550:$i, X1551:$i, X1552:$i, X1553:$i, X1554:$i, X1555:$i, X1556:$i, X1557:$i, X1558:$i, X1559:$i, X1560:$i, X1561:$i, X1562:$i, X1564:$i, X1565:$i, X1566:$i, X1567:$i, X1568:$i, X1569:$i, X1570:$i, X1571:$i, X1572:$i, X1573:$i, X1574:$i, X1575:$i, X1576:$i, X1577:$i, X1578:$i, X1579:$i, X1580:$i, X1581:$i, X1582:$i, X1583:$i, X1584:$i, X1585:$i, X1586:$i, X1587:$i, X1588:$i, X1589:$i, X1590:$i, X1591:$i, X1592:$i, X1593:$i, X1594:$i, X1595:$i, X1596:$i, X1597:$i, X1598:$i, X1599:$i, X1600:$i, X1601:$i, X1602:$i, X1603:$o, X1604:$i, X1605:$i, X1606:$i, X1607:$i, X1608:$i, X1609:$i, X1610:$i, X1611:$i, X1612:$i, X1613:$i, X1614:$i, X1615:$i, X1616:$i, X1617:$i, X1618:$i, X1619:$i, X1620:$i, X1621:$i, X1622:$i, X1623:$i, X1624:$i, X1625:$i, X1626:$i, X1627:$i, X1628:$i, X1629:$i, X1630:$i, X1631:$i, X1632:$i, X1633:$i, X1634:$i, X1635:$i, X1636:$i, X1637:$i, X1638:$i, X1639:$i, X1640:$i, X1641:$i, X1642:$i, X1643:$i, X1644:$i, X1645:$i, X1646:$i, X1647:$i, X1648:$i, X1649:$i, X1650:$i, X1651:$i, X1652:$i, X1653:$i, X1654:$i, X1655:$i, X1656:$i, X1657:$i, X1658:$i, X1659:$i, X1660:$i, X1661:$i, X1662:$i, X1665:$i, X1666:$i, X1667:$i, X1668:$i, X1669:$i, X1671:$i, X1672:$i, X1673:$i, X1674:$i, X1675:$i > $o, X1678:$i, X1679:$i, X1680:$i > $o, X1682:$i, X1683:$i > $o, X1684:$i, X1686:$i, X1687:$i > $o, X1690:$i, X1691:$i, X1692:$i, X1693:$i, X1694:$i, X1695:$i, X1696:$i, X1697:$i, X1698:$i, X1699:$i, X1700:$i, X1701:$i, X1702:$i, X1703:$i, X1704:$i, X1705:$i, X1706:$i, X1707:$i, X1708:$i, X1709:$i, X1710:$i, X1711:$i, X1712:$i, X1713:$i, X1714:$i, X1715:$i, X1716:$i, X1717:$i, X1718:$i, X1719:$i, X1720:$i, X1721:$i, X1722:$i, X1723:$i, X1724:$i, X1725:$i, X1726:$i, X1727:$i, X1728:$i, X1729:$i, X1730:$i, X1731:$i, X1732:$i, X1733:$i, X1734:$i, X1735:$i, X1736:$i, X1737:$i, X1738:$i, X1739:$i, X1740:$i, X1741:$i, X1742:$i, X1743:$i, X1744:$i, X1745:$i, X1746:$i, X1747:$i, X1748:$i, X1749:$i, X1750:$i, X1751:$i, X1752:$i, X1753:$i, X1754:$i, X1755:$i, X1756:$i, X1757:$i, X1758:$i, X1759:$i, X1760:$i, X1761:$i, X1762:$i > $i > $o, X1763:$i, X1764:$i, X1765:$i, X1766:$i, X1767:$i > $i > $o, X1768:$i, X1769:$i, X1770:$i > $i > $o, X1771:$i, X1772:$i, X1773:$i > $i > $o, X1774:$i, X1775:$i, X1776:$i, X1777:$i, X1778:$i > $i > $o, X1779:$i, X1780:$i, X1781:$i, X1782:$i, X1783:$i > $i > $o, X1784:$i, X1785:$i, X1786:$i, X1787:$i, X1788:$i > $i > $o, X1789:$i, X1790:$i, X1791:$i, X1792:$i, X1793:$i, X1794:$i, X1795:$i, X1796:$i, X1797:$i, X1798:$i, X1799:$i, X1800:$i, X1801:$i, X1802:$i, X1803:$i, X1804:$i, X1805:$i, X1806:$i, X1807:$i, X1808:$i, X1809:$i, X1810:$i, X1811:$i, X1812:$i, X1813:$i, X1814:$i, X1815:$i > $i, X1817:$i, X1818:$i, X1819:$i > $i, X1821:$i, X1822:$i, X1823:$i > $i, X1825:$i, X1826:$i, X1827:$i, X1828:$i > $o, X1831:$i, X1832:$i, X1833:$i, X1834:$i, X1835:$i > $o, X1838:$i, X1839:$i, X1840:$i > $o, X1841:$i, X1842:$i, X1843:$i, X1844:$i, X1845:$i, X1846:$i, X1847:$i, X1848:$i, X1849:$i, X1850:$i, X1851:$i, X1852:$i, X1853:$i, X1854:$i, X1855:$i, X1856:$i, X1857:$i, X1858:$i, X1859:$i, X1861:$i, X1862:$i, X1863:$i, X1864:$i, X1865:$i, X1866:$i, X1867:$i, X1868:$i, X1869:$i, X1870:$i, X1871:$i, X1874:$i, X1875:$i, X1876:$i, X1877:$i, X1882:$i, X1883:$i, X1884:$i, X1885:$i, X1887:$i, X1888:$i, X1889:$i, X1890:$i, X1892:$i, X1893:$i, X1894:$i, X1895:$i, X1896:$i, X1897:$i, X1898:$i, X1899:$i, X1900:$i, X1901:$i, X1902:$i > $i, X1904:$i, X1905:$i, X1906:$i, X1907:$i, X1908:$i, X1909:$i, X1910:$i > $i, X1912:$i, X1913:$i, X1914:$i > $i, X1916:$i, X1917:$i, X1918:$i, X1919:$i, X1920:$i, X1921:$o, X1922:$i, X1923:$i, X1924:$i, X1925:$o, X1926:$i, X1927:$i, X1928:$i, X1929:$o, X1930:$i, X1931:$i, X1932:$i, X1933:$o, X1934:$i, X1935:$i, X1936:$i, X1937:$o, X1938:$i, X1939:$i, X1940:$i, X1941:$o, X1942:$i, X1943:$i, X1944:$i, X1945:$i, X1946:$i, X1947:$o, X1948:$i, X1949:$i, X1950:$i, X1951:$o, X1952:$i, X1953:$i, X1954:$i, X1955:$o, X1956:$i, X1957:$i, X1958:$i, X1959:$i, X1960:$i, X1961:$i, X1962:$i, X1963:$i, X1964:$i, X1965:$i, X1966:$i, X1967:$i, X1968:$i, X1969:$i, X1970:$i, X1971:$i, X1972:$i, X1973:$i, X1976:$i, X1977:$i, X1978:$i, X1980:$i, X1981:$i, X1982:$i, X1984:$i, X1985:$i, X1986:$i, X1987:$i, X1988:$i, X1989:$i, X1990:$i, X1991:$i, X1992:$i, X1993:$i, X1994:$i, X1995:$i, X1996:$i, X1997:$i, X1998:$i, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$i, X2004:$i, X2005:$i, X2006:$i, X2007:$i, X2008:$i, X2009:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2015:$i, X2016:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$i, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2025:$i, X2026:$i, X2027:$i, X2028:$i, X2029:$i, X2030:$i, X2031:$i, X2032:$i, X2033:$i, X2034:$i, X2035:$i, X2036:$i, X2037:$i, X2038:$i, X2039:$i, X2040:$i, X2041:$i, X2042:$i, X2043:$i, X2044:$i, X2045:$i, X2046:$i, X2047:$i, X2048:$i, X2049:$i, X2050:$i, X2051:$i, X2052:$i, X2053:$i, X2054:$i, X2055:$i, X2056:$i, X2057:$i, X2058:$i, X2059:$i, X2060:$i, X2061:$i, X2062:$i, X2063:$i, X2064:$i, X2065:$i, X2066:$i, X2067:$i, X2068:$i, X2069:$i, X2070:$i, X2071:$i, X2072:$i, X2073:$i, X2074:$i, X2075:$i, X2076:$i, X2077:$i, X2078:$i, X2079:$i, X2080:$i, X2081:$i, X2082:$i, X2083:$i, X2084:$i, X2085:$i, X2086:$i, X2087:$o, X2088:$i, X2089:$i, X2090:$i, X2091:$i, X2092:$i, X2093:$i, X2094:$i, X2095:$i, X2096:$i, X2097:$i, X2098:$i, X2099:$i, X2100:$i, X2101:$i, X2102:$i, X2103:$i, X2104:$i, X2105:$i, X2106:$i, X2107:$i, X2108:$i, X2109:$i, X2110:$i, X2111:$i, X2112:$i, X2113:$i, X2114:$i, X2115:$i, X2116:$i, X2117:$i, X2118:$i, X2119:$i, X2120:$i, X2121:$i, X2122:$i, X2123:$i, X2124:$i, X2125:$i, X2126:$i, X2127:$i, X2128:$i, X2129:$i, X2130:$i, X2131:$i, X2132:$i, X2133:$i, X2134:$i, X2135:$i, X2136:$i, X2137:$i, X2138:$i, X2139:$i, X2140:$i, X2141:$i, X2142:$i, X2143:$i, X2144:$i, X2145:$i, X2146:$i, X2147:$i, X2148:$i, X2149:$i, X2150:$i, X2151:$i, X2152:$i, X2153:$i, X2154:$i, X2155:$i, X2156:$i, X2157:$i, X2158:$i, X2159:$i, X2160:$i, X2161:$i, X2162:$i, X2163:$i, X2164:$i, X2165:$i, X2166:$i, X2167:$i, X2168:$i, X2169:$i, X2170:$i, X2171:$i > $o, X2174:$i, X2175:$i, X2176:$i, X2177:$i, X2178:$i, X2179:$i > $i > $o, X2181:$i, X2182:$i, X2183:$i, X2184:$i, X2185:$i > $i > $o, X2186:$i, X2187:$i, X2188:$i > $o, X2191:$i, X2192:$i, X2193:$i, X2194:$i, X2197:$i, X2198:$i, X2199:$i, X2204:$i, X2205:$i, X2206:$i, X2207:$i, X2208:$i, X2209:$i, X2210:$i, X2211:$i, X2212:$i, X2213:$i, X2214:$i, X2215:$i, X2216:$i, X2217:$i, X2218:$i, X2219:$i, X2220:$i, X2221:$i, X2222:$i, X2223:$i, X2224:$i, X2225:$i, X2226:$i, X2227:$i, X2229:$i, X2230:$i, X2231:$i, X2232:$i, X2233:$i, X2234:$o, X2236:$i, X2237:$i, X2238:$i, X2239:$i, X2240:$i, X2241:$i, X2242:$i, X2243:$i, X2244:$i, X2245:$i, X2246:$i, X2247:$i, X2248:$i, X2249:$i, X2250:$i, X2251:$i, X2252:$i, X2253:$i, X2254:$i, X2255:$i, X2256:$i, X2257:$i, X2258:$i, X2259:$i, X2260:$i, X2261:$i, X2262:$i, X2263:$i, X2264:$o, X2265:$i, X2266:$i, X2267:$i, X2268:$i, X2269:$i, X2270:$i, X2271:$i, X2272:$i, X2273:$i, X2274:$i, X2275:$i, X2276:$i, X2277:$i, X2278:$i, X2279:$i, X2280:$i, X2281:$i, X2282:$i > $i, X2284:$i, X2286:$i, X2287:$i, X2288:$i, X2289:$i > $i, X2291:$i, X2293:$i, X2294:$i, X2295:$i, X2297:$i, X2299:$i, X2300:$i > $i, X2301:$i, X2303:$i, X2304:$i > $i, X2305:$i, X2306:$i, X2307:$i, X2308:$i > $i, X2309:$i, X2311:$i, X2312:$i > $i, X2313:$i, X2314:$i, X2315:$i, X2316:$i, X2317:$i, X2318:$i, X2319:$i, X2320:$i, X2321:$i, X2322:$i, X2323:$i, X2324:$i, X2325:$i, X2326:$i, X2327:$i, X2328:$i, X2329:$i, X2330:$i, X2331:$i, X2332:$i > $i, X2334:$i, X2336:$i, X2337:$i, X2338:$i, X2340:$i, X2341:$i, X2342:$i, X2343:$i, X2344:$i, X2345:$i, X2346:$i, X2347:$i, X2348:$i, X2350:$i, X2351:$i, X2353:$i, X2355:$i, X2356:$i, X2358:$i, X2359:$i, X2360:$i, X2363:$i, X2364:$i, X2368:$i, X2370:$i, X2374:$i, X2376:$i]:(((~in @ (esk2_2 @ X1240 @ X1241) @ X1240|~in @ (esk2_2 @ X1240 @ X1241) @ X1241|(X1240)=(X1241))&(in @ (esk2_2 @ X1240 @ X1241) @ X1240|in @ (esk2_2 @ X1240 @ X1241) @ X1241|(X1240)=(X1241)))&(~in @ X1243 @ emptyset&(((~in @ X1246 @ (setadjoin @ X1244 @ X1245)|((X1246)=(X1244)|in @ X1246 @ X1245))&(((X1246)!=(X1244)|in @ X1246 @ (setadjoin @ X1244 @ X1245))&(~in @ X1246 @ X1245|in @ X1246 @ (setadjoin @ X1244 @ X1245))))&(((~in @ X1248 @ (powerset @ X1247)|(~in @ X1249 @ X1248|in @ X1249 @ X1247))&((in @ (esk3_2 @ X1250 @ X1251) @ X1251|in @ X1251 @ (powerset @ X1250))&(~in @ (esk3_2 @ X1250 @ X1251) @ X1250|in @ X1251 @ (powerset @ X1250))))&((((in @ X1254 @ (esk4_2 @ X1253 @ X1254)|~in @ X1254 @ (setunion @ X1253))&(in @ (esk4_2 @ X1253 @ X1254) @ X1253|~in @ X1254 @ (setunion @ X1253)))&(~in @ X1257 @ X1258|~in @ X1258 @ X1256|in @ X1257 @ (setunion @ X1256)))&(in @ emptyset @ omega&((~in @ X1259 @ omega|in @ (setadjoin @ X1259 @ X1259) @ omega)&((((in @ (esk5_1 @ X1260) @ omega|~in @ emptyset @ X1260|(~in @ X1262 @ omega|in @ X1262 @ X1260))&(in @ (esk5_1 @ X1260) @ X1260|~in @ emptyset @ X1260|(~in @ X1262 @ omega|in @ X1262 @ X1260)))&(~in @ (setadjoin @ (esk5_1 @ X1260) @ (esk5_1 @ X1260)) @ X1260|~in @ emptyset @ X1260|(~in @ X1262 @ omega|in @ X1262 @ X1260)))&(((((in @ (esk9_3 @ X1263 @ X1264 @ X1269) @ X1264|~in @ X1269 @ (esk8_2 @ X1263 @ X1264)|in @ (esk6_2 @ X1263 @ X1264) @ X1264)&(X1263 @ (esk9_3 @ X1263 @ X1264 @ X1269) @ X1269|~in @ X1269 @ (esk8_2 @ X1263 @ X1264)|in @ (esk6_2 @ X1263 @ X1264) @ X1264))&(~in @ X1272 @ X1264|~X1263 @ X1272 @ X1271|in @ X1271 @ (esk8_2 @ X1263 @ X1264)|in @ (esk6_2 @ X1263 @ X1264) @ X1264))&((((in @ (esk9_3 @ X1263 @ X1264 @ X1269) @ X1264|~in @ X1269 @ (esk8_2 @ X1263 @ X1264)|(X1263 @ (esk6_2 @ X1263 @ X1264) @ (esk7_3 @ X1263 @ X1264 @ X1266)|~X1263 @ (esk6_2 @ X1263 @ X1264) @ X1266))&(X1263 @ (esk9_3 @ X1263 @ X1264 @ X1269) @ X1269|~in @ X1269 @ (esk8_2 @ X1263 @ X1264)|(X1263 @ (esk6_2 @ X1263 @ X1264) @ (esk7_3 @ X1263 @ X1264 @ X1266)|~X1263 @ (esk6_2 @ X1263 @ X1264) @ X1266)))&(~in @ X1272 @ X1264|~X1263 @ X1272 @ X1271|in @ X1271 @ (esk8_2 @ X1263 @ X1264)|(X1263 @ (esk6_2 @ X1263 @ X1264) @ (esk7_3 @ X1263 @ X1264 @ X1266)|~X1263 @ 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X1464)|~X1460 @ X1464)|(esk47_2 @ X1460 @ X1461)=(esk48_2 @ X1460 @ X1461)))&((X1461 @ (esk50_3 @ X1460 @ X1461 @ X1466)|~X1461 @ X1466|(descr @ (epred1_2 @ X1460))=(descr @ (epred1_2 @ X1461))|((X1464)!=(esk49_3 @ X1460 @ X1461 @ X1464)|~X1460 @ X1464)|(esk47_2 @ X1460 @ X1461)=(esk48_2 @ X1460 @ X1461))&((X1466)!=(esk50_3 @ X1460 @ X1461 @ X1466)|~X1461 @ X1466|(descr @ (epred1_2 @ X1460))=(descr @ (epred1_2 @ X1461))|((X1464)!=(esk49_3 @ X1460 @ X1461 @ X1464)|~X1460 @ X1464)|(esk47_2 @ X1460 @ X1461)=(esk48_2 @ X1460 @ X1461))))&((((X1461 @ (esk50_3 @ X1460 @ X1461 @ X1466)|~X1461 @ X1466|(descr @ (epred1_2 @ X1460))=(descr @ (epred1_2 @ X1461))|(X1460 @ (esk49_3 @ X1460 @ X1461 @ X1464)|~X1460 @ X1464)|(~X1460 @ (esk47_2 @ X1460 @ X1461)|~X1461 @ (esk48_2 @ X1460 @ X1461)))&((X1466)!=(esk50_3 @ X1460 @ X1461 @ X1466)|~X1461 @ X1466|(descr @ (epred1_2 @ X1460))=(descr @ (epred1_2 @ X1461))|(X1460 @ (esk49_3 @ X1460 @ X1461 @ X1464)|~X1460 @ X1464)|(~X1460 @ (esk47_2 @ X1460 @ X1461)|~X1461 @ (esk48_2 @ X1460 @ X1461))))&((X1461 @ (esk50_3 @ X1460 @ X1461 @ X1466)|~X1461 @ X1466|(descr @ (epred1_2 @ X1460))=(descr @ (epred1_2 @ X1461))|((X1464)!=(esk49_3 @ X1460 @ X1461 @ X1464)|~X1460 @ X1464)|(~X1460 @ (esk47_2 @ X1460 @ X1461)|~X1461 @ (esk48_2 @ X1460 @ X1461)))&((X1466)!=(esk50_3 @ X1460 @ X1461 @ X1466)|~X1461 @ X1466|(descr @ (epred1_2 @ X1460))=(descr @ (epred1_2 @ X1461))|((X1464)!=(esk49_3 @ X1460 @ X1461 @ X1464)|~X1460 @ X1464)|(~X1460 @ (esk47_2 @ X1460 @ X1461)|~X1461 @ (esk48_2 @ X1460 @ X1461)))))&(((X1461 @ (esk50_3 @ X1460 @ X1461 @ X1466)|~X1461 @ X1466|(descr @ (epred1_2 @ X1460))=(descr @ (epred1_2 @ X1461))|(X1460 @ (esk49_3 @ X1460 @ X1461 @ X1464)|~X1460 @ X1464)|(X1460 @ (esk47_2 @ X1460 @ X1461)|X1461 @ (esk48_2 @ X1460 @ X1461)))&((X1466)!=(esk50_3 @ X1460 @ X1461 @ X1466)|~X1461 @ X1466|(descr @ (epred1_2 @ X1460))=(descr @ (epred1_2 @ X1461))|(X1460 @ (esk49_3 @ X1460 @ X1461 @ X1464)|~X1460 @ X1464)|(X1460 @ (esk47_2 @ X1460 @ X1461)|X1461 @ (esk48_2 @ X1460 @ X1461))))&((X1461 @ (esk50_3 @ X1460 @ X1461 @ X1466)|~X1461 @ X1466|(descr @ (epred1_2 @ X1460))=(descr @ (epred1_2 @ X1461))|((X1464)!=(esk49_3 @ X1460 @ X1461 @ X1464)|~X1460 @ X1464)|(X1460 @ (esk47_2 @ X1460 @ X1461)|X1461 @ (esk48_2 @ X1460 @ X1461)))&((X1466)!=(esk50_3 @ X1460 @ X1461 @ X1466)|~X1461 @ X1466|(descr @ (epred1_2 @ X1460))=(descr @ (epred1_2 @ X1461))|((X1464)!=(esk49_3 @ X1460 @ X1461 @ X1464)|~X1460 @ X1464)|(X1460 @ (esk47_2 @ X1460 @ X1461)|X1461 @ (esk48_2 @ X1460 @ X1461)))))))&(((in @ (esk51_4 @ X1468 @ X1469 @ X1470 @ X1471) @ X1468|(dsetconstr @ X1468 @ (epred1_2 @ X1470))=(dsetconstr @ X1469 @ (epred1_2 @ X1471))|(X1468)!=(X1469))&((in @ (esk52_4 @ X1468 @ X1469 @ X1470 @ X1471) @ X1469|(dsetconstr @ X1468 @ (epred1_2 @ X1470))=(dsetconstr @ X1469 @ (epred1_2 @ X1471))|(X1468)!=(X1469))&(((esk51_4 @ X1468 @ X1469 @ X1470 @ X1471)=(esk52_4 @ X1468 @ X1469 @ X1470 @ X1471)|(dsetconstr @ X1468 @ (epred1_2 @ X1470))=(dsetconstr @ X1469 @ (epred1_2 @ X1471))|(X1468)!=(X1469))&((~X1470 @ (esk51_4 @ X1468 @ X1469 @ X1470 @ X1471)|~X1471 @ (esk52_4 @ X1468 @ X1469 @ X1470 @ X1471)|(dsetconstr @ X1468 @ (epred1_2 @ X1470))=(dsetconstr @ X1469 @ (epred1_2 @ X1471))|(X1468)!=(X1469))&(X1470 @ (esk51_4 @ X1468 @ X1469 @ X1470 @ X1471)|X1471 @ (esk52_4 @ X1468 @ X1469 @ X1470 @ X1471)|(dsetconstr @ X1468 @ (epred1_2 @ X1470))=(dsetconstr @ X1469 @ (epred1_2 @ X1471))|(X1468)!=(X1469))))))&(((in @ (esk53_2 @ X1474 @ X1475) @ X1474|subset @ X1474 @ X1475)&(~in @ (esk53_2 @ X1474 @ X1475) @ X1475|subset @ X1474 @ X1475))&(((X1477)!=(X1478)|subset @ X1478 @ X1477)&(((X1479)!=(X1480)|subset @ X1479 @ X1480)&(((in @ (esk54_2 @ X1481 @ X1482) @ X1481|subset @ X1481 @ X1482)&(~in @ (esk54_2 @ X1481 @ X1482) @ X1482|subset @ X1481 @ X1482))&(subset @ emptyset @ X1484&((~subset @ X1485 @ X1486|(~in @ X1487 @ X1485|in @ X1487 @ X1486))&((~subset @ X1488 @ X1489|(in @ X1490 @ X1489|~in @ X1490 @ X1488))&((~in @ X1493 @ X1491|(in @ X1493 @ X1492|~subset @ X1491 @ X1492))&((subset @ X1494 @ X1495|(X1494)!=(X1495))&((~in @ X1498 @ X1496|(in @ X1498 @ X1497|(X1496)!=(X1497)))&(subset @ X1499 @ X1499&((~subset @ X1500 @ X1501|(~subset @ X1501 @ X1502|subset @ X1500 @ X1502))&(subset @ X1504 @ (setadjoin @ X1503 @ X1504)&((~subset @ X1505 @ X1507|subset @ X1505 @ (setadjoin @ X1506 @ X1507))&((~subset @ X1508 @ X1509|in @ X1508 @ (powerset @ X1509))&((~subset @ X1510 @ X1511|(~subset @ X1511 @ X1510|(X1510)=(X1511)))&((~subset @ X1512 @ emptyset|(X1512)=(emptyset))&((~subset @ X1514 @ X1513|in @ X1514 @ (powerset @ X1513))&((~in @ X1516 @ (powerset @ X1515)|subset @ X1516 @ X1515)&(in @ X1517 @ (powerset @ X1517)&((~subset @ X1518 @ X1519|subset @ (powerset @ X1518) @ (powerset @ X1519))&(in @ (dsetconstr @ X1520 @ (epred1_2 @ X1521)) @ (powerset @ X1520)&(subset @ (dsetconstr @ X1522 @ (epred1_2 @ X1523)) @ X1522&((~in @ X1526 @ X1524|in @ X1526 @ (binunion @ X1524 @ X1525))&(in @ X1528 @ 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X2364))&((in @ (esk125_3 @ X2364 @ X2370 @ X2374) @ (esk124_2 @ X2364 @ X2370)|~in @ X2374 @ (esk124_2 @ X2364 @ X2370)|(in @ (esk123_2 @ X2364 @ X2370) @ X2370|~epred12_1 @ X2370)|~subset @ (esk122_2 @ X2364 @ X2370) @ X2370|(~in @ X2376 @ (binintersect @ X2364 @ X2370)|subset @ X2376 @ (binintersect @ X2364 @ X2370))|((X2368)!=(esk121_2 @ X2364 @ X2368)|~in @ X2368 @ (esk120_1 @ X2364)|(in @ (esk119_1 @ X2364) @ (esk119_1 @ X2364)|~epred11_1 @ X2364)|~subset @ (esk118_1 @ X2364) @ X2364))&(((X2374)!=(esk125_3 @ X2364 @ X2370 @ X2374)|~in @ X2374 @ (esk124_2 @ X2364 @ X2370)|(in @ (esk123_2 @ X2364 @ X2370) @ X2370|~epred12_1 @ X2370)|~subset @ (esk122_2 @ X2364 @ X2370) @ X2370|(~in @ X2376 @ (binintersect @ X2364 @ X2370)|subset @ X2376 @ (binintersect @ X2364 @ X2370))|((X2368)!=(esk121_2 @ X2364 @ X2368)|~in @ X2368 @ (esk120_1 @ X2364)|(in @ (esk119_1 @ X2364) @ (esk119_1 @ X2364)|~epred11_1 @ X2364)|~subset @ (esk118_1 @ X2364) @ X2364))&(~in @ X2374 @ (esk125_3 @ X2364 @ X2370 @ X2374)|~in @ X2374 @ (esk124_2 @ X2364 @ X2370)|(in @ (esk123_2 @ X2364 @ X2370) @ X2370|~epred12_1 @ X2370)|~subset @ (esk122_2 @ X2364 @ X2370) @ X2370|(~in @ X2376 @ (binintersect @ X2364 @ X2370)|subset @ X2376 @ (binintersect @ X2364 @ X2370))|((X2368)!=(esk121_2 @ X2364 @ X2368)|~in @ X2368 @ (esk120_1 @ X2364)|(in @ (esk119_1 @ X2364) @ (esk119_1 @ X2364)|~epred11_1 @ X2364)|~subset @ (esk118_1 @ X2364) @ X2364))))))&((in @ (esk124_2 @ X2364 @ X2370) @ (powerset @ X2370)|(in @ (esk123_2 @ X2364 @ X2370) @ (esk123_2 @ X2364 @ X2370)|~epred12_1 @ X2370)|~subset @ (esk122_2 @ X2364 @ X2370) @ X2370|(~in @ X2376 @ (binintersect @ X2364 @ X2370)|subset @ X2376 @ (binintersect @ X2364 @ X2370))|((X2368)!=(esk121_2 @ X2364 @ X2368)|~in @ X2368 @ (esk120_1 @ X2364)|(in @ (esk119_1 @ X2364) @ (esk119_1 @ X2364)|~epred11_1 @ X2364)|~subset @ (esk118_1 @ X2364) @ X2364))&(((esk124_2 @ X2364 @ X2370)!=(emptyset)|(in @ (esk123_2 @ X2364 @ X2370) @ (esk123_2 @ X2364 @ X2370)|~epred12_1 @ X2370)|~subset @ (esk122_2 @ X2364 @ X2370) @ X2370|(~in @ X2376 @ (binintersect @ X2364 @ X2370)|subset @ X2376 @ (binintersect @ X2364 @ X2370))|((X2368)!=(esk121_2 @ X2364 @ X2368)|~in @ X2368 @ (esk120_1 @ X2364)|(in @ (esk119_1 @ X2364) @ (esk119_1 @ X2364)|~epred11_1 @ X2364)|~subset @ (esk118_1 @ X2364) @ X2364))&((in @ (esk125_3 @ X2364 @ X2370 @ X2374) @ (esk124_2 @ X2364 @ X2370)|~in @ X2374 @ (esk124_2 @ X2364 @ X2370)|(in @ (esk123_2 @ X2364 @ X2370) @ (esk123_2 @ X2364 @ X2370)|~epred12_1 @ X2370)|~subset @ (esk122_2 @ X2364 @ X2370) @ X2370|(~in @ X2376 @ (binintersect @ X2364 @ X2370)|subset @ X2376 @ (binintersect @ X2364 @ X2370))|((X2368)!=(esk121_2 @ X2364 @ X2368)|~in @ X2368 @ (esk120_1 @ X2364)|(in @ (esk119_1 @ X2364) @ (esk119_1 @ X2364)|~epred11_1 @ X2364)|~subset @ (esk118_1 @ X2364) @ X2364))&(((X2374)!=(esk125_3 @ X2364 @ X2370 @ X2374)|~in @ X2374 @ (esk124_2 @ X2364 @ X2370)|(in @ (esk123_2 @ X2364 @ X2370) @ (esk123_2 @ X2364 @ X2370)|~epred12_1 @ X2370)|~subset @ (esk122_2 @ X2364 @ X2370) @ X2370|(~in @ X2376 @ (binintersect @ X2364 @ X2370)|subset @ X2376 @ (binintersect @ X2364 @ X2370))|((X2368)!=(esk121_2 @ X2364 @ X2368)|~in @ X2368 @ (esk120_1 @ X2364)|(in @ (esk119_1 @ X2364) @ (esk119_1 @ X2364)|~epred11_1 @ X2364)|~subset @ (esk118_1 @ X2364) @ X2364))&(~in @ X2374 @ (esk125_3 @ X2364 @ X2370 @ X2374)|~in @ X2374 @ (esk124_2 @ X2364 @ X2370)|(in @ (esk123_2 @ X2364 @ X2370) @ (esk123_2 @ X2364 @ X2370)|~epred12_1 @ X2370)|~subset @ (esk122_2 @ X2364 @ X2370) @ X2370|(~in @ X2376 @ (binintersect @ X2364 @ X2370)|subset @ X2376 @ (binintersect @ X2364 @ X2370))|((X2368)!=(esk121_2 @ X2364 @ X2368)|~in @ X2368 @ (esk120_1 @ X2364)|(in @ (esk119_1 @ X2364) @ (esk119_1 @ X2364)|~epred11_1 @ X2364)|~subset @ (esk118_1 @ X2364) @ X2364))))))))&((((in @ (esk124_2 @ X2364 @ X2370) @ (powerset @ X2370)|(in @ (esk123_2 @ X2364 @ X2370) @ X2370|~epred12_1 @ X2370)|in @ (esk122_2 @ X2364 @ X2370) @ X2370|(~in @ X2376 @ (binintersect @ X2364 @ X2370)|subset @ X2376 @ (binintersect @ X2364 @ X2370))|(~in @ X2368 @ (esk121_2 @ X2364 @ X2368)|~in @ X2368 @ (esk120_1 @ X2364)|(in @ (esk119_1 @ X2364) @ (esk119_1 @ X2364)|~epred11_1 @ X2364)|~subset @ (esk118_1 @ X2364) @ X2364))&(((esk124_2 @ X2364 @ X2370)!=(emptyset)|(in @ (esk123_2 @ X2364 @ X2370) @ X2370|~epred12_1 @ X2370)|in @ (esk122_2 @ X2364 @ X2370) @ X2370|(~in @ X2376 @ (binintersect @ X2364 @ X2370)|subset @ X2376 @ (binintersect @ X2364 @ X2370))|(~in @ X2368 @ (esk121_2 @ X2364 @ X2368)|~in @ X2368 @ (esk120_1 @ X2364)|(in @ (esk119_1 @ X2364) @ (esk119_1 @ X2364)|~epred11_1 @ X2364)|~subset @ (esk118_1 @ X2364) @ X2364))&((in @ (esk125_3 @ X2364 @ X2370 @ X2374) @ (esk124_2 @ X2364 @ X2370)|~in @ X2374 @ (esk124_2 @ X2364 @ X2370)|(in @ (esk123_2 @ X2364 @ X2370) @ X2370|~epred12_1 @ X2370)|in @ (esk122_2 @ X2364 @ X2370) @ X2370|(~in @ X2376 @ (binintersect @ X2364 @ X2370)|subset @ X2376 @ (binintersect @ X2364 @ X2370))|(~in @ X2368 @ (esk121_2 @ X2364 @ X2368)|~in @ X2368 @ (esk120_1 @ X2364)|(in @ (esk119_1 @ X2364) @ (esk119_1 @ X2364)|~epred11_1 @ X2364)|~subset @ (esk118_1 @ X2364) @ X2364))&(((X2374)!=(esk125_3 @ X2364 @ X2370 @ X2374)|~in @ X2374 @ (esk124_2 @ X2364 @ X2370)|(in @ (esk123_2 @ X2364 @ X2370) @ X2370|~epred12_1 @ X2370)|in @ (esk122_2 @ X2364 @ X2370) @ X2370|(~in @ X2376 @ (binintersect @ X2364 @ X2370)|subset @ X2376 @ (binintersect @ X2364 @ X2370))|(~in @ X2368 @ (esk121_2 @ X2364 @ X2368)|~in @ X2368 @ (esk120_1 @ X2364)|(in @ (esk119_1 @ X2364) @ (esk119_1 @ X2364)|~epred11_1 @ X2364)|~subset @ (esk118_1 @ X2364) @ X2364))&(~in @ X2374 @ (esk125_3 @ X2364 @ X2370 @ X2374)|~in @ X2374 @ (esk124_2 @ X2364 @ X2370)|(in @ (esk123_2 @ X2364 @ X2370) @ X2370|~epred12_1 @ X2370)|in @ (esk122_2 @ X2364 @ X2370) @ X2370|(~in @ X2376 @ (binintersect @ X2364 @ X2370)|subset @ X2376 @ (binintersect @ X2364 @ X2370))|(~in @ X2368 @ (esk121_2 @ X2364 @ X2368)|~in @ X2368 @ (esk120_1 @ X2364)|(in @ (esk119_1 @ X2364) @ (esk119_1 @ X2364)|~epred11_1 @ X2364)|~subset @ (esk118_1 @ X2364) @ X2364))))))&((in @ (esk124_2 @ X2364 @ X2370) @ (powerset @ X2370)|(in @ (esk123_2 @ X2364 @ X2370) @ (esk123_2 @ X2364 @ X2370)|~epred12_1 @ X2370)|in @ (esk122_2 @ X2364 @ X2370) @ X2370|(~in @ X2376 @ (binintersect @ X2364 @ X2370)|subset @ X2376 @ (binintersect @ X2364 @ X2370))|(~in @ X2368 @ (esk121_2 @ X2364 @ X2368)|~in @ X2368 @ (esk120_1 @ X2364)|(in @ (esk119_1 @ X2364) @ (esk119_1 @ X2364)|~epred11_1 @ X2364)|~subset @ (esk118_1 @ X2364) @ X2364))&(((esk124_2 @ X2364 @ X2370)!=(emptyset)|(in @ (esk123_2 @ X2364 @ X2370) @ (esk123_2 @ X2364 @ X2370)|~epred12_1 @ X2370)|in @ (esk122_2 @ X2364 @ X2370) @ X2370|(~in @ X2376 @ (binintersect @ X2364 @ X2370)|subset @ X2376 @ (binintersect @ X2364 @ X2370))|(~in @ X2368 @ (esk121_2 @ X2364 @ X2368)|~in @ X2368 @ (esk120_1 @ X2364)|(in @ (esk119_1 @ X2364) @ (esk119_1 @ X2364)|~epred11_1 @ X2364)|~subset @ (esk118_1 @ X2364) @ X2364))&((in @ (esk125_3 @ X2364 @ X2370 @ X2374) @ (esk124_2 @ X2364 @ X2370)|~in @ X2374 @ (esk124_2 @ X2364 @ X2370)|(in @ (esk123_2 @ X2364 @ X2370) @ (esk123_2 @ X2364 @ X2370)|~epred12_1 @ X2370)|in @ (esk122_2 @ X2364 @ X2370) @ X2370|(~in @ X2376 @ (binintersect @ X2364 @ X2370)|subset @ X2376 @ (binintersect @ X2364 @ X2370))|(~in @ X2368 @ (esk121_2 @ X2364 @ X2368)|~in @ X2368 @ (esk120_1 @ X2364)|(in @ (esk119_1 @ X2364) @ (esk119_1 @ X2364)|~epred11_1 @ X2364)|~subset @ (esk118_1 @ X2364) @ X2364))&(((X2374)!=(esk125_3 @ X2364 @ X2370 @ X2374)|~in @ X2374 @ (esk124_2 @ X2364 @ X2370)|(in @ (esk123_2 @ X2364 @ X2370) @ (esk123_2 @ X2364 @ X2370)|~epred12_1 @ X2370)|in @ (esk122_2 @ X2364 @ X2370) @ X2370|(~in @ X2376 @ (binintersect @ X2364 @ X2370)|subset @ X2376 @ (binintersect @ X2364 @ X2370))|(~in @ X2368 @ (esk121_2 @ X2364 @ X2368)|~in @ X2368 @ (esk120_1 @ X2364)|(in @ (esk119_1 @ X2364) @ (esk119_1 @ X2364)|~epred11_1 @ X2364)|~subset @ (esk118_1 @ X2364) @ X2364))&(~in @ X2374 @ (esk125_3 @ X2364 @ X2370 @ X2374)|~in @ X2374 @ (esk124_2 @ X2364 @ X2370)|(in @ (esk123_2 @ X2364 @ X2370) @ (esk123_2 @ X2364 @ X2370)|~epred12_1 @ X2370)|in @ (esk122_2 @ X2364 @ X2370) @ X2370|(~in @ X2376 @ (binintersect @ X2364 @ X2370)|subset @ X2376 @ (binintersect @ X2364 @ X2370))|(~in @ X2368 @ (esk121_2 @ X2364 @ X2368)|~in @ X2368 @ (esk120_1 @ X2364)|(in @ (esk119_1 @ X2364) @ (esk119_1 @ X2364)|~epred11_1 @ X2364)|~subset @ (esk118_1 @ X2364) @ X2364)))))))&(((in @ (esk124_2 @ X2364 @ X2370) @ (powerset @ X2370)|(in @ (esk123_2 @ X2364 @ X2370) @ X2370|~epred12_1 @ X2370)|~subset @ (esk122_2 @ X2364 @ X2370) @ X2370|(~in @ X2376 @ (binintersect @ X2364 @ X2370)|subset @ X2376 @ (binintersect @ X2364 @ X2370))|(~in @ X2368 @ (esk121_2 @ X2364 @ X2368)|~in @ X2368 @ (esk120_1 @ X2364)|(in @ (esk119_1 @ X2364) @ (esk119_1 @ X2364)|~epred11_1 @ X2364)|~subset @ (esk118_1 @ X2364) @ X2364))&(((esk124_2 @ X2364 @ X2370)!=(emptyset)|(in @ (esk123_2 @ X2364 @ X2370) @ X2370|~epred12_1 @ X2370)|~subset @ (esk122_2 @ X2364 @ X2370) @ X2370|(~in @ X2376 @ (binintersect @ X2364 @ X2370)|subset @ X2376 @ (binintersect @ X2364 @ X2370))|(~in @ X2368 @ (esk121_2 @ X2364 @ X2368)|~in @ X2368 @ (esk120_1 @ X2364)|(in @ (esk119_1 @ X2364) @ (esk119_1 @ X2364)|~epred11_1 @ X2364)|~subset @ (esk118_1 @ X2364) @ X2364))&((in @ (esk125_3 @ X2364 @ X2370 @ X2374) @ (esk124_2 @ X2364 @ X2370)|~in @ X2374 @ (esk124_2 @ X2364 @ X2370)|(in @ (esk123_2 @ X2364 @ X2370) @ X2370|~epred12_1 @ X2370)|~subset @ (esk122_2 @ X2364 @ X2370) @ X2370|(~in @ X2376 @ (binintersect @ X2364 @ X2370)|subset @ X2376 @ (binintersect @ X2364 @ X2370))|(~in @ X2368 @ (esk121_2 @ X2364 @ X2368)|~in @ X2368 @ (esk120_1 @ X2364)|(in @ (esk119_1 @ X2364) @ (esk119_1 @ X2364)|~epred11_1 @ X2364)|~subset @ (esk118_1 @ X2364) @ X2364))&(((X2374)!=(esk125_3 @ X2364 @ X2370 @ X2374)|~in @ X2374 @ (esk124_2 @ X2364 @ X2370)|(in @ (esk123_2 @ X2364 @ X2370) @ X2370|~epred12_1 @ X2370)|~subset @ (esk122_2 @ X2364 @ X2370) @ X2370|(~in @ X2376 @ (binintersect @ X2364 @ X2370)|subset @ X2376 @ (binintersect @ X2364 @ X2370))|(~in @ X2368 @ (esk121_2 @ X2364 @ X2368)|~in @ X2368 @ (esk120_1 @ X2364)|(in @ (esk119_1 @ X2364) @ (esk119_1 @ X2364)|~epred11_1 @ X2364)|~subset @ (esk118_1 @ X2364) @ X2364))&(~in @ X2374 @ (esk125_3 @ X2364 @ X2370 @ X2374)|~in @ X2374 @ (esk124_2 @ X2364 @ X2370)|(in @ (esk123_2 @ X2364 @ X2370) @ X2370|~epred12_1 @ X2370)|~subset @ (esk122_2 @ X2364 @ X2370) @ X2370|(~in @ X2376 @ (binintersect @ X2364 @ X2370)|subset @ X2376 @ (binintersect @ X2364 @ X2370))|(~in @ X2368 @ (esk121_2 @ X2364 @ X2368)|~in @ X2368 @ (esk120_1 @ X2364)|(in @ (esk119_1 @ X2364) @ (esk119_1 @ X2364)|~epred11_1 @ X2364)|~subset @ (esk118_1 @ X2364) @ X2364))))))&((in @ (esk124_2 @ X2364 @ X2370) @ (powerset @ X2370)|(in @ (esk123_2 @ X2364 @ X2370) @ (esk123_2 @ X2364 @ X2370)|~epred12_1 @ X2370)|~subset @ (esk122_2 @ X2364 @ X2370) @ X2370|(~in @ X2376 @ (binintersect @ X2364 @ X2370)|subset @ X2376 @ (binintersect @ X2364 @ X2370))|(~in @ X2368 @ (esk121_2 @ X2364 @ X2368)|~in @ X2368 @ (esk120_1 @ X2364)|(in @ (esk119_1 @ X2364) @ (esk119_1 @ X2364)|~epred11_1 @ X2364)|~subset @ (esk118_1 @ X2364) @ X2364))&(((esk124_2 @ X2364 @ X2370)!=(emptyset)|(in @ (esk123_2 @ X2364 @ X2370) @ (esk123_2 @ X2364 @ X2370)|~epred12_1 @ X2370)|~subset @ (esk122_2 @ X2364 @ X2370) @ X2370|(~in @ X2376 @ (binintersect @ X2364 @ X2370)|subset @ X2376 @ (binintersect @ X2364 @ X2370))|(~in @ X2368 @ (esk121_2 @ X2364 @ X2368)|~in @ X2368 @ (esk120_1 @ X2364)|(in @ (esk119_1 @ X2364) @ (esk119_1 @ X2364)|~epred11_1 @ X2364)|~subset @ (esk118_1 @ X2364) @ X2364))&((in @ (esk125_3 @ X2364 @ X2370 @ X2374) @ (esk124_2 @ X2364 @ X2370)|~in @ X2374 @ (esk124_2 @ X2364 @ X2370)|(in @ (esk123_2 @ X2364 @ X2370) @ (esk123_2 @ X2364 @ X2370)|~epred12_1 @ X2370)|~subset @ (esk122_2 @ X2364 @ X2370) @ X2370|(~in @ X2376 @ (binintersect @ X2364 @ X2370)|subset @ X2376 @ (binintersect @ X2364 @ X2370))|(~in @ X2368 @ (esk121_2 @ X2364 @ X2368)|~in @ X2368 @ (esk120_1 @ X2364)|(in @ (esk119_1 @ X2364) @ (esk119_1 @ X2364)|~epred11_1 @ X2364)|~subset @ (esk118_1 @ X2364) @ X2364))&(((X2374)!=(esk125_3 @ X2364 @ X2370 @ X2374)|~in @ X2374 @ (esk124_2 @ X2364 @ X2370)|(in @ (esk123_2 @ X2364 @ X2370) @ (esk123_2 @ X2364 @ X2370)|~epred12_1 @ X2370)|~subset @ (esk122_2 @ X2364 @ X2370) @ X2370|(~in @ X2376 @ (binintersect @ X2364 @ X2370)|subset @ X2376 @ (binintersect @ X2364 @ X2370))|(~in @ X2368 @ (esk121_2 @ X2364 @ X2368)|~in @ X2368 @ (esk120_1 @ X2364)|(in @ (esk119_1 @ X2364) @ (esk119_1 @ X2364)|~epred11_1 @ X2364)|~subset @ (esk118_1 @ X2364) @ X2364))&(~in @ X2374 @ (esk125_3 @ X2364 @ X2370 @ X2374)|~in @ X2374 @ (esk124_2 @ X2364 @ X2370)|(in @ (esk123_2 @ X2364 @ X2370) @ (esk123_2 @ X2364 @ X2370)|~epred12_1 @ X2370)|~subset @ (esk122_2 @ X2364 @ X2370) @ X2370|(~in @ X2376 @ (binintersect @ X2364 @ X2370)|subset @ X2376 @ (binintersect @ X2364 @ X2370))|(~in @ X2368 @ (esk121_2 @ X2364 @ X2368)|~in @ X2368 @ (esk120_1 @ X2364)|(in @ (esk119_1 @ X2364) @ (esk119_1 @ X2364)|~epred11_1 @ X2364)|~subset @ (esk118_1 @ X2364) @ X2364))))))))))))))&(epred13_1 @ esk126_0&(in @ esk128_0 @ esk126_0&(in @ esk127_0 @ esk128_0&~in @ esk127_0 @ esk126_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_380])])])])])])). 1.33/1.50 thf(c_0_383, plain, ![X2:$i, X3:$i]:(subset @ X2 @ X3|~in @ X2 @ X3|~epred13_1 @ X3), inference(split_conjunct,[status(thm)],[c_0_381])). 1.33/1.50 thf(c_0_384, negated_conjecture, in @ esk128_0 @ esk126_0, inference(split_conjunct,[status(thm)],[c_0_382])). 1.33/1.50 thf(c_0_385, negated_conjecture, epred13_1 @ esk126_0, inference(split_conjunct,[status(thm)],[c_0_382])). 1.33/1.50 thf(c_0_386, negated_conjecture, ![X2:$i, X3:$i]:((binintersect @ X3 @ X2)=(X2)|~subset @ X2 @ X3), inference(split_conjunct,[status(thm)],[c_0_382])). 1.33/1.50 thf(c_0_387, negated_conjecture, subset @ esk128_0 @ esk126_0, inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_383, c_0_384]), c_0_385])])). 1.33/1.50 thf(c_0_388, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(in @ X2 @ X3|~in @ X2 @ (binintersect @ X3 @ X4)), inference(split_conjunct,[status(thm)],[c_0_382])). 1.33/1.50 thf(c_0_389, negated_conjecture, (binintersect @ esk126_0 @ esk128_0)=(esk128_0), inference(spm,[status(thm)],[c_0_386, c_0_387])). 1.33/1.50 thf(c_0_390, negated_conjecture, ![X2:$i]:(in @ X2 @ esk126_0|~in @ X2 @ esk128_0), inference(spm,[status(thm)],[c_0_388, c_0_389])). 1.33/1.50 thf(c_0_391, negated_conjecture, in @ esk127_0 @ esk128_0, inference(split_conjunct,[status(thm)],[c_0_382])). 1.33/1.50 thf(c_0_392, negated_conjecture, ~in @ esk127_0 @ esk126_0, inference(split_conjunct,[status(thm)],[c_0_382])). 1.33/1.50 thf(c_0_393, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_390, c_0_391]), c_0_392]), ['proof']). 1.33/1.50 # SZS output end CNFRefutation 1.33/1.50 # Proof object total steps : 394 1.33/1.50 # Proof object clause steps : 11 1.33/1.50 # Proof object formula steps : 383 1.33/1.50 # Proof object conjectures : 13 1.33/1.50 # Proof object clause conjectures : 10 1.33/1.50 # Proof object formula conjectures : 3 1.33/1.50 # Proof object initial clauses used : 7 1.33/1.50 # Proof object initial formulas used : 340 1.33/1.50 # Proof object generating inferences : 4 1.33/1.50 # Proof object simplifying inferences : 3 1.33/1.50 # Training examples: 0 positive, 0 negative 1.33/1.50 # Parsed axioms : 736 1.33/1.50 # Removed by relevancy pruning/SinE : 0 1.33/1.50 # Initial clauses : 1470 1.33/1.50 # Removed in clause preprocessing : 438 1.33/1.50 # Initial clauses in saturation : 1032 1.33/1.50 # Processed clauses : 4968 1.33/1.50 # ...of these trivial : 38 1.33/1.50 # ...subsumed : 1564 1.33/1.50 # ...remaining for further processing : 3366 1.33/1.50 # Other redundant clauses eliminated : 594 1.33/1.50 # Clauses deleted for lack of memory : 0 1.33/1.50 # Backward-subsumed : 315 1.33/1.50 # Backward-rewritten : 17 1.33/1.50 # Generated clauses : 63162 1.33/1.50 # ...of the previous two non-trivial : 38247 1.33/1.50 # Contextual simplify-reflections : 15 1.33/1.50 # Paramodulations : 39191 1.33/1.50 # Factorizations : 2 1.33/1.50 # NegExts : 1 1.33/1.50 # Equation resolutions : 600 1.33/1.50 # Propositional unsat checks : 0 1.33/1.50 # Propositional check models : 0 1.33/1.50 # Propositional check unsatisfiable : 0 1.33/1.50 # Propositional clauses : 0 1.33/1.50 # Propositional clauses after purity: 0 1.33/1.50 # Propositional unsat core size : 0 1.33/1.50 # Propositional preprocessing time : 0.000 1.33/1.50 # Propositional encoding time : 0.000 1.33/1.50 # Propositional solver time : 0.000 1.33/1.50 # Success case prop preproc time : 0.000 1.33/1.50 # Success case prop encoding time : 0.000 1.33/1.50 # Success case prop solver time : 0.000 1.33/1.50 # Current number of processed clauses : 2348 1.33/1.50 # Positive orientable unit clauses : 853 1.33/1.50 # Positive unorientable unit clauses: 0 1.33/1.50 # Negative unit clauses : 652 1.33/1.50 # Non-unit-clauses : 843 1.33/1.50 # Current number of unprocessed clauses: 34746 1.33/1.50 # ...number of literals in the above : 98300 1.33/1.50 # Current number of archived formulas : 0 1.33/1.50 # Current number of archived clauses : 996 1.33/1.50 # Clause-clause subsumption calls (NU) : 1118904 1.33/1.50 # Rec. Clause-clause subsumption calls : 101849 1.33/1.50 # Non-unit clause-clause subsumptions : 648 1.33/1.50 # Unit Clause-clause subsumption calls : 83855 1.33/1.50 # Rewrite failures with RHS unbound : 0 1.33/1.50 # BW rewrite match attempts : 1189 1.33/1.50 # BW rewrite match successes : 17 1.33/1.50 # Condensation attempts : 0 1.33/1.50 # Condensation successes : 0 1.33/1.50 # Termbank termtop insertions : 1343349 1.35/1.51 1.35/1.51 # ------------------------------------------------- 1.35/1.51 # User time : 1.088 s 1.35/1.51 # System time : 0.035 s 1.35/1.51 # Total time : 1.123 s 1.35/1.51 # Maximum resident set size: 2512 pages 1.35/1.51 EOF