0.07/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.13/0.18 % 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 0.17/0.39 % Computer : n013.cluster.edu 0.17/0.39 % Model : x86_64 x86_64 0.17/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.17/0.39 % Memory : 8042.1875MB 0.17/0.39 % OS : Linux 3.10.0-693.el7.x86_64 0.17/0.39 % CPULimit : 1200 0.17/0.39 % WCLimit : 120 0.17/0.39 % DateTime : Tue Jul 13 15:49:33 EDT 2021 0.17/0.39 % CPUTime : 0.17/0.40 % Number of cores: 8 0.17/0.40 % Python version: Python 3.6.8 0.17/0.40 # Version: 2.6rc1-ho 0.26/0.42 # No SInE strategy applied 0.26/0.42 # Trying AutoSched0 for 59 seconds 59.23/59.42 # AutoSched0-Mode selected heuristic G_E___303_C18_F1_URBAN_S0Y 59.23/59.42 # and selection function SelectMaxLComplexAvoidPosPred. 59.23/59.42 # 59.23/59.42 # Preprocessing time : 0.167 s 59.23/59.43 # No success with AutoSched0 59.23/59.43 # Trying AutoSched1 for 26 seconds 85.26/85.43 # AutoSched1-Mode selected heuristic G_E___008_C45_F1_PI_SE_Q4_CS_SP_S4SI 85.26/85.43 # and selection function SelectNewComplexAHPNS. 85.26/85.43 # 85.26/85.43 # Preprocessing time : 0.056 s 85.33/85.51 # No success with AutoSched1 85.33/85.51 # Trying AutoSched2 for 8 seconds 93.29/93.51 # AutoSched2-Mode selected heuristic U_____100_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_ND_S04AN 93.29/93.51 # and selection function SelectComplexExceptUniqMaxHorn. 93.29/93.51 # 93.29/93.51 # Preprocessing time : 0.054 s 93.29/93.51 # Presaturation interreduction done 93.29/93.54 # No success with AutoSched2 93.29/93.54 # Trying AutoSched3 for 7 seconds 100.30/100.54 # AutoSched3-Mode selected heuristic G_E___300_C01_S5PRR_S00 100.30/100.54 # and selection function NoSelection. 100.30/100.54 # 100.30/100.54 # Preprocessing time : 0.059 s 100.38/100.57 # No success with AutoSched3 100.38/100.57 # Trying AutoSched4 for 5 seconds 105.31/105.57 # AutoSched4-Mode selected heuristic G_E___207_C18_F1_SE_CS_SP_PI_PS_S2SI 105.31/105.57 # and selection function SelectNewComplexAHP. 105.31/105.57 # 105.31/105.57 # Preprocessing time : 0.056 s 105.31/105.57 # Presaturation interreduction done 105.31/105.60 # No success with AutoSched4 105.31/105.60 # Trying AutoSched5 for 3 seconds 108.41/108.60 # AutoSched5-Mode selected heuristic G_E___207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y 108.41/108.60 # and selection function SelectMaxLComplexAvoidPosPred. 108.41/108.60 # 108.41/108.60 # Preprocessing time : 0.059 s 108.41/108.61 # No success with AutoSched5 108.41/108.61 # Trying AutoSched6 for 1 seconds 109.35/109.61 # AutoSched6-Mode selected heuristic U_____207d_10_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN 109.35/109.61 # and selection function SelectComplexExceptUniqMaxHorn. 109.35/109.61 # 109.35/109.61 # Preprocessing time : 0.056 s 109.35/109.61 # Presaturation interreduction done 109.35/109.62 # No success with AutoSched6 109.35/109.62 # Trying AutoSched7 for 1 seconds 110.41/110.62 # AutoSched7-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_S2v 110.41/110.62 # and selection function SelectCQArNTNp. 110.41/110.62 # 110.41/110.62 # Preprocessing time : 0.056 s 110.41/110.62 # Presaturation interreduction done 110.41/110.62 # No success with AutoSched7 110.41/110.62 # Trying AutoSched8 for 1 seconds 111.39/111.62 # AutoSched8-Mode selected heuristic G_E___107_C00_02_nc_F1_PI_AE_Q4_CS_SP_PS_S08BN 111.39/111.62 # and selection function SelectCQPrecWNTNp. 111.39/111.62 # 111.39/111.62 # Preprocessing time : 0.057 s 111.39/111.62 # Presaturation interreduction done 111.39/111.63 # No success with AutoSched8 111.39/111.63 # Trying AutoSched9 for 8 seconds 117.41/117.61 # AutoSched9-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S05CN 117.41/117.61 # and selection function PSelectUnlessUniqMaxSmallestOrientable. 117.41/117.61 # 117.41/117.61 # Preprocessing time : 0.057 s 117.41/117.61 # Presaturation interreduction done 117.41/117.61 117.41/117.61 # Proof found! 117.41/117.61 # SZS status Theorem 117.41/117.61 # SZS output start CNFRefutation 117.41/117.61 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:$i]:(in @ X3 @ X4&X6 @ X3 @ X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', replAx)). 117.41/117.61 thf(exu, axiom, (exu)=(^[X1:$i > $o]:?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exu)). 117.41/117.61 thf(descrp, axiom, (descrp<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>X1 @ (descr @ (^[X2:$i]:X1 @ X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', descrp)). 117.41/117.61 thf(exuE1, axiom, (exuE1<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuE1)). 117.41/117.61 thf(exuE3e, axiom, (exuE3e<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>?[X2:$i]:X1 @ X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuE3e)). 117.41/117.61 thf(nonemptyE1, axiom, (nonemptyE1<=>![X4:$i]:(nonempty @ X4=>?[X2:$i]:in @ X2 @ X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', nonemptyE1)). 117.41/117.61 thf(nonempty, axiom, (nonempty)=(^[X2:$i]:(X2)!=(emptyset)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', nonempty)). 117.41/117.61 thf(nonemptyI, axiom, (nonemptyI<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', nonemptyI)). 117.41/117.61 thf(nonemptyI1, axiom, (nonemptyI1<=>![X4:$i]:(?[X2:$i]:in @ X2 @ X4=>nonempty @ X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', nonemptyI1)). 117.41/117.61 thf(exuE2, axiom, (exuE2<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuE2)). 117.41/117.61 thf(nonemptyImpWitness, axiom, (nonemptyImpWitness<=>![X4:$i]:(nonempty @ X4=>?[X2:$i]:(in @ X2 @ X4&$true))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', nonemptyImpWitness)). 117.41/117.61 thf(exuI1, axiom, (exuI1<=>![X1:$i > $o]:(?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3)))=>exu @ (^[X2:$i]:X1 @ X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuI1)). 117.41/117.61 thf(exuI3, axiom, (exuI3<=>![X1:$i > $o]:(?[X2:$i]:X1 @ X2=>(![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3)))=>exu @ (^[X2:$i]:X1 @ X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuI3)). 117.41/117.61 thf(exuI2, axiom, (exuI2<=>![X1:$i > $o]:(?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2))=>exu @ (^[X2:$i]:X1 @ X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuI2)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', exuE3u)). 117.41/117.61 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:$i]:X17 @ X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exu__Cong)). 117.41/117.61 thf(exuEu, axiom, (exuEu<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuEu)). 117.41/117.61 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:$i]:X17 @ X2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', descr__Cong)). 117.41/117.61 thf(image1Ex1, axiom, (image1Ex1<=>![X4:$i, X58:$i > $i]:exu @ (^[X5:$i]:![X2:$i]:(in @ X2 @ X5<=>?[X3:$i]:(in @ X3 @ X4&(X2)=(X58 @ X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', image1Ex1)). 117.41/117.61 thf(foundation2, axiom, (foundation2<=>![X4:$i]:(nonempty @ X4=>?[X21:$i]:(in @ X21 @ X4&(binintersect @ X21 @ X4)=(emptyset)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', foundation2)). 117.41/117.61 thf(peanoSinj, conjecture, (setextAx=>(((powersetAx=>((((((foundationAx=>(wellorderingAx=>((dsetconstrI=>(dsetconstrEL=>(dsetconstrER=>(exuE1=>(prop2setE=>((emptysetimpfalse=>(notinemptyset=>(exuE3e=>(setext=>(emptyI=>(noeltsimpempty=>(setbeta=>((nonemptyI=>(nonemptyI1=>(setadjoinIL=>(emptyinunitempty=>((setadjoinE=>(setadjoinOr=>((powersetI=>(emptyinPowerset=>(emptyInPowerset=>((((subPowSU=>(exuE2=>((uniqinunit=>(notinsingleton=>((singletonsswitch=>(upairsetE=>((upairsetIR=>((vacuousDall=>(quantDeMorgan1=>((quantDeMorgan3=>(quantDeMorgan4=>(prop2setI=>(((notdallE=>(exuI1=>(((inCongP=>(((((((setunion__Cong=>(omega__Cong=>(exuEu=>(descr__Cong=>(dsetconstr__Cong=>(((eqimpsubset1=>(((subsetE=>(subsetE2=>(notsubsetI=>(notequalI1=>((subsetRefl=>(subsetTrans=>(setadjoinSub=>((subset2powerset=>((subsetemptysetimpeq=>(powersetI1=>(powersetE1=>((powersetsubset=>(sepInPowerset=>(sepSubset=>(binunionIL=>(((binunionEcases=>(binunionE=>(binunionLsub=>(binunionRsub=>(binintersectI=>(binintersectSubset5=>(binintersectEL=>(binintersectLsub=>(((binintersectER=>((((((setminusI=>((setminusER=>((((setminusILneg=>((((((symdiffI2=>((symdiffIneg2=>(secondinupair=>(setukpairIL=>(setukpairIR=>(kpairiskpair=>(kpairp=>((singletoninpowerset=>(singletoninpowunion=>(upairset2E=>(upairsubunion=>(upairinpowunion=>(ubforcartprodlem1=>(ubforcartprodlem2=>((cartprodpairin=>(((setunionE2=>((((singletonprop=>((ex1I=>(ex1I2=>((setukpairinjL1=>(kfstsingleton=>(theprop=>((cartprodfstin=>((setukpairinjL=>(setukpairinjR11=>(setukpairinjR12=>(setukpairinjR1=>((setukpairinjR2=>((ksndsingleton=>(ksndpairEq=>((cartprodsndin=>((cartprodpairmemER=>(cartprodmempaircEq=>(cartprodfstpairEq=>(cartprodsndpairEq=>(cartprodpairsurjEq=>(dpsetconstrI=>(dpsetconstrSub=>((dpsetconstrERa=>((((((app=>(infuncsetfunc=>((funcinfuncset=>((lamp=>(((brelnall2=>((funcGraphProp1=>(funcGraphProp3=>(funcGraphProp2=>(((subbreln=>((funcext=>(((ap2apEq2=>((eta1=>(lam2lamEq=>(beta2=>((iffalseProp1=>(iffalseProp2=>(((ifSingleton=>(ifp=>((((iftrueorfalse=>((((setminusT_lem=>(((subsetTI=>(powersetTI1=>(powersetTE1=>((complementTE1=>((binintersectTERcontra=>(contrasubsetT=>(((((doubleComplementE1=>(doubleComplementSub1=>(((((complementSubsetComplementIntersect=>((((((((inIntersectImpInIntersectUnions=>((inComplementUnionImpNotIn1=>(((((complementUnionInPowersetComplement=>((demorgan1a=>(demorgan1b=>(demorgan1=>((demorgan2b2=>(((((woz13rule2=>(woz13rule3=>((woz1_1=>(woz1_2=>((woz1_4=>((breln1all2=>(breln1SetBreln1=>((((subbreln1=>(eqbreln1=>((breln1invI=>((((breln1compE=>((breln1unionprop=>(((breln1unionI=>(((breln1unionCommutes=>((woz2W=>(woz2A=>((image1Ex=>(image1Ex1=>((((injFuncInInjFuncSet=>(injFuncSetFuncIn=>((((leftInvIsSurj=>(surjCantorThm=>(((notinself2=>(omegaSp=>(omegaSclos=>(![X2:$i]:(![X3:$i]:(((omegaS @ X2)=(omegaS @ X3)=>(X2)=(X3))<=in @ X3 @ omega)<=in @ X2 @ omega)<=peano0notS))))<=notinself)<=foundation2)))<=surjFuncSetFuncSurj)<=surjFuncSetFuncIn)<=injFuncSetFuncInj)))<=image1I)<=image1E)<=image1Equiv)))<=woz2B)))<=woz2Ex))<=breln1unionEcases)<=breln1unionE))<=breln1unionIR)<=breln1unionIL))<=breln1compEex))<=breln1compI)<=breln1compprop)<=breln1invE))<=breln1invprop)))<=breln1all1)<=setOfPairsIsBReln1)<=choice2fnsingleton)))<=woz1_5))<=woz1_3)))<=woz13rule4)))<=woz13rule1)<=woz13rule0)<=demorgan2)<=demorgan2b))<=demorgan2a))))<=demorgan2a2))<=demorgan2a1)<=binunionTEcontra)<=binunionTE)<=inComplementUnionImpInComplement1))<=intersectInPowersetIntersectUnions))<=inIntersectImpInUnion2)<=inIntersectImpInUnion)<=binunionTIRcontra)<=binunionTILcontra)<=complementTcontraSubset)<=contraSubsetComplement)<=complementInPowersetComplementIntersect))<=complementImpComplementIntersect)<=complementTnotintersectT)<=doubleComplementEq)<=doubleComplementSub2)))<=doubleComplementI1)<=contrasubsetT3)<=contrasubsetT2)<=contrasubsetT1)))<=binintersectTELcontra))<=complementTI1))))<=setextT)<=complementT_lem))<=powersetT_lem)<=binunionT_lem)<=binintersectT_lem))<=iffalse)<=iftrue)<=theeq)))<=iftrueProp2)<=iftrueProp1)))<=eta2))))<=beta1))<=ap2apEq1)<=funcext2))<=eqbreln))<=funcGraphProp4)<=funcextLem))))<=ex1E2))<=brelnall1)<=lam2p))<=lamProp))<=ap2p)))<=apProp)<=funcImageSingleton)<=dpsetconstrER)<=dpsetconstrEL2)<=dpsetconstrEL1))<=setOfPairsIsBReln))))))))<=cartprodpairmemEL))<=kpairsurjEq)))<=setukpairinjR))<=upairequniteq)))))<=setukpairinjL2))<=kfstpairEq))))<=singletonsuniq)))<=ex1E1))<=setunionsingleton)<=setunionsingleton2)<=setunionsingleton1))<=cartprodmempair)<=cartprodmempair1))<=ubforcartprodlem3))))))))<=singletonsubset)))))))<=symdiffIneg1))<=symdiffI1)<=symdiffE)<=setminusSubset1)<=setminusLsub)<=setminusIRneg))<=setminusELneg)<=setminusERneg)<=setminusSubset2))<=setminusEL))<=bs114d)<=binintersectSubset1)<=binintersectSubset4)<=binintersectRsub)<=disjointsetsI1))<=binintersectSubset3)<=binintersectSubset2)))))))))<=binunionIR)<=upairset2IR)))))<=inPowerset))))<=setextsub))<=setadjoinSub2))))<=notequalI2)))))<=emptysetsubset)<=subsetI2))<=eqimpsubset2)<=subsetI1))))))<=powerset__Cong)<=setadjoin__Cong)<=emptyset__Cong)<=exu__Cong)<=exuE3u)<=in__Cong))<=exuI2)<=exuI3)))<=notdexE)<=prop2set2propI))))<=quantDeMorgan2)))<=emptyE1))<=upairsetIL)))<=eqinunit)))<=nonemptyImpWitness)))<=setunionE)<=setunionI)<=powersetE))))<=setoftrueEq)))<=setadjoinIR)))))<=nonemptyE1))))))))<=emptysetE))))))<=descrp)))<=replAx)<=omegaIndAx)<=omegaSAx)<=omega0Ax)<=setunionAx))<=setadjoinAx)<=emptysetAx)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', peanoSinj)). 117.41/117.61 thf(setextAx, axiom, (setextAx<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4<=>in @ X2 @ X5)=>(X4)=(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setextAx)). 117.41/117.61 thf(emptysetAx, axiom, (emptysetAx<=>![X2:$i]:~(in @ X2 @ emptyset)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptysetAx)). 117.41/117.61 thf(setadjoinAx, axiom, (setadjoinAx<=>![X2:$i, X4:$i, X3:$i]:(in @ X3 @ (setadjoin @ X2 @ X4)<=>((X3)=(X2)|in @ X3 @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinAx)). 117.41/117.61 thf(powersetAx, axiom, (powersetAx<=>![X4:$i, X5:$i]:(in @ X5 @ (powerset @ X4)<=>![X2:$i]:(in @ X2 @ X5=>in @ X2 @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetAx)). 117.41/117.61 thf(setunionAx, axiom, (setunionAx<=>![X4:$i, X2:$i]:(in @ X2 @ (setunion @ X4)<=>?[X5:$i]:(in @ X2 @ X5&in @ X5 @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionAx)). 117.41/117.61 thf(omega0Ax, axiom, (omega0Ax<=>in @ emptyset @ omega), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', omega0Ax)). 117.41/117.61 thf(omegaSAx, axiom, (omegaSAx<=>![X2:$i]:(in @ X2 @ omega=>in @ (setadjoin @ X2 @ X2) @ omega)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', omegaSAx)). 117.41/117.61 thf(omegaIndAx, axiom, (omegaIndAx<=>![X4:$i]:((in @ emptyset @ X4&![X2:$i]:((in @ X2 @ omega&in @ X2 @ X4)=>in @ (setadjoin @ X2 @ X2) @ X4))=>![X2:$i]:(in @ X2 @ omega=>in @ X2 @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', omegaIndAx)). 117.41/117.61 thf(foundationAx, axiom, (foundationAx<=>![X4:$i]:(?[X2:$i]:in @ X2 @ X4=>?[X5:$i]:(in @ X5 @ X4&~(?[X2:$i]:(in @ X2 @ X5&in @ X2 @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', foundationAx)). 117.41/117.61 thf(wellorderingAx, axiom, (wellorderingAx<=>![X4:$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/sandbox2/benchmark/theBenchmark.p', wellorderingAx)). 117.41/117.61 thf(dsetconstrI, axiom, (dsetconstrI<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dsetconstrI)). 117.41/117.61 thf(dsetconstrEL, axiom, (dsetconstrEL<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))=>in @ X2 @ X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dsetconstrEL)). 117.41/117.61 thf(dsetconstrER, axiom, (dsetconstrER<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))=>X1 @ X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dsetconstrER)). 117.41/117.61 thf(prop2setE, axiom, (prop2setE<=>![X10:$o, X2:$i]:(in @ X2 @ (prop2set @ (X10))=>X10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', prop2setE)). 117.41/117.61 thf(emptysetE, axiom, (emptysetE<=>![X2:$i]:(in @ X2 @ emptyset=>![X11:$o]:X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptysetE)). 117.41/117.61 thf(emptysetimpfalse, axiom, (emptysetimpfalse<=>![X2:$i]:(in @ X2 @ emptyset=>~$true)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptysetimpfalse)). 117.41/117.61 thf(notinemptyset, axiom, (notinemptyset<=>![X2:$i]:~(in @ X2 @ emptyset)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notinemptyset)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', setext)). 117.41/117.61 thf(emptyI, axiom, (emptyI<=>![X4:$i]:(![X2:$i]:~(in @ X2 @ X4)=>(X4)=(emptyset))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyI)). 117.41/117.61 thf(noeltsimpempty, axiom, (noeltsimpempty<=>![X4:$i]:(![X2:$i]:~(in @ X2 @ X4)=>(X4)=(emptyset))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', noeltsimpempty)). 117.41/117.61 thf(setbeta, axiom, (setbeta<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))<=>X1 @ X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setbeta)). 117.41/117.61 thf(setadjoinIL, axiom, (setadjoinIL<=>![X2:$i, X3:$i]:in @ X2 @ (setadjoin @ X2 @ X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinIL)). 117.41/117.61 thf(emptyinunitempty, axiom, (emptyinunitempty<=>in @ emptyset @ (setadjoin @ emptyset @ emptyset)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyinunitempty)). 117.41/117.61 thf(setadjoinIR, axiom, (setadjoinIR<=>![X2:$i, X4:$i, X3:$i]:(in @ X3 @ X4=>in @ X3 @ (setadjoin @ X2 @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinIR)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', setadjoinE)). 117.41/117.61 thf(setadjoinOr, axiom, (setadjoinOr<=>![X2:$i, X4:$i, X3:$i]:(in @ X3 @ (setadjoin @ X2 @ X4)=>((X3)=(X2)|in @ X3 @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinOr)). 117.41/117.61 thf(setoftrueEq, axiom, (setoftrueEq<=>![X4:$i]:(dsetconstr @ X4 @ (^[X2:$i]:$true))=(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setoftrueEq)). 117.41/117.61 thf(powersetI, axiom, (powersetI<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X5=>in @ X2 @ X4)=>in @ X5 @ (powerset @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetI)). 117.41/117.61 thf(emptyinPowerset, axiom, (emptyinPowerset<=>![X4:$i]:in @ emptyset @ (powerset @ X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyinPowerset)). 117.41/117.61 thf(emptyInPowerset, axiom, (emptyInPowerset<=>![X4:$i]:in @ emptyset @ (powerset @ X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyInPowerset)). 117.41/117.61 thf(powersetE, axiom, (powersetE<=>![X4:$i, X5:$i, X2:$i]:(in @ X5 @ (powerset @ X4)=>(in @ X2 @ X5=>in @ X2 @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetE)). 117.41/117.61 thf(setunionI, axiom, (setunionI<=>![X4:$i, X2:$i, X5:$i]:(in @ X2 @ X5=>(in @ X5 @ X4=>in @ X2 @ (setunion @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionI)). 117.41/117.61 thf(setunionE, axiom, (setunionE<=>![X4:$i, X2:$i]:(in @ X2 @ (setunion @ X4)=>![X13:$o]:(![X5:$i]:(in @ X2 @ X5=>(in @ X5 @ X4=>X13))=>X13))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionE)). 117.41/117.61 thf(subPowSU, axiom, (subPowSU<=>![X4:$i, X2:$i]:(in @ X2 @ X4=>in @ X2 @ (powerset @ (setunion @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subPowSU)). 117.41/117.61 thf(uniqinunit, axiom, (uniqinunit<=>![X2:$i, X3:$i]:(in @ X2 @ (setadjoin @ X3 @ emptyset)=>(X2)=(X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', uniqinunit)). 117.41/117.61 thf(notinsingleton, axiom, (notinsingleton<=>![X2:$i, X3:$i]:((X2)!=(X3)=>~(in @ X3 @ (setadjoin @ X2 @ emptyset)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notinsingleton)). 117.41/117.61 thf(eqinunit, axiom, (eqinunit<=>![X2:$i, X3:$i]:((X2)=(X3)=>in @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', eqinunit)). 117.41/117.61 thf(singletonsswitch, axiom, (singletonsswitch<=>![X2:$i, X3:$i]:(in @ X2 @ (setadjoin @ X3 @ emptyset)=>in @ X3 @ (setadjoin @ X2 @ emptyset))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletonsswitch)). 117.41/117.61 thf(upairsetE, axiom, (upairsetE<=>![X2:$i, X3:$i, X14:$i]:(in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=>((X14)=(X2)|(X14)=(X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairsetE)). 117.41/117.61 thf(upairsetIL, axiom, (upairsetIL<=>![X2:$i, X3:$i]:in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairsetIL)). 117.41/117.61 thf(upairsetIR, axiom, (upairsetIR<=>![X2:$i, X3:$i]:in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairsetIR)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', emptyE1)). 117.41/117.61 thf(vacuousDall, axiom, (vacuousDall<=>![X1:$i > $o, X2:$i]:(in @ X2 @ emptyset=>X1 @ X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', vacuousDall)). 117.41/117.61 thf(quantDeMorgan1, axiom, (quantDeMorgan1<=>![X4:$i, X1:$i > $o]:(~(![X2:$i]:(in @ X2 @ X4=>X1 @ X2))=>?[X2:$i]:(in @ X2 @ X4&~(X1 @ X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', quantDeMorgan1)). 117.41/117.61 thf(quantDeMorgan2, axiom, (quantDeMorgan2<=>![X4:$i, X1:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>~(X1 @ X2))=>~(?[X2:$i]:(in @ X2 @ X4&X1 @ X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', quantDeMorgan2)). 117.41/117.61 thf(quantDeMorgan3, axiom, (quantDeMorgan3<=>![X4:$i, X1:$i > $o]:(~(?[X2:$i]:(in @ X2 @ X4&X1 @ X2))=>![X2:$i]:(in @ X2 @ X4=>~(X1 @ X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', quantDeMorgan3)). 117.41/117.61 thf(quantDeMorgan4, axiom, (quantDeMorgan4<=>![X4:$i, X1:$i > $o]:(?[X2:$i]:(in @ X2 @ X4&~(X1 @ X2))=>~(![X2:$i]:(in @ X2 @ X4=>X1 @ X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', quantDeMorgan4)). 117.41/117.61 thf(prop2setI, axiom, (prop2setI<=>![X15:$o]:(X15=>in @ emptyset @ (prop2set @ (X15)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', prop2setI)). 117.41/117.61 thf(prop2set2propI, axiom, (prop2set2propI<=>![X16:$o]:(X16=>set2prop @ (prop2set @ (X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', prop2set2propI)). 117.41/117.61 thf(notdexE, axiom, (notdexE<=>![X4:$i, X1:$i > $o]:(~(?[X2:$i]:(in @ X2 @ X4&X1 @ X2))=>![X2:$i]:(in @ X2 @ X4=>~(X1 @ X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notdexE)). 117.41/117.61 thf(notdallE, axiom, (notdallE<=>![X4:$i, X1:$i > $o]:(~(![X2:$i]:(in @ X2 @ X4=>X1 @ X2))=>?[X2:$i]:(in @ X2 @ X4&~(X1 @ X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notdallE)). 117.41/117.61 thf(inCongP, axiom, (inCongP<=>![X4:$i, X5:$i]:((X4)=(X5)=>![X2:$i, X3:$i]:((X2)=(X3)=>(in @ X2 @ X4=>in @ X3 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', inCongP)). 117.41/117.61 thf(in__Cong, axiom, (in__Cong<=>![X4:$i, X5:$i]:((X4)=(X5)=>![X2:$i, X3:$i]:((X2)=(X3)=>(in @ X2 @ X4<=>in @ X3 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', in__Cong)). 117.41/117.61 thf(emptyset__Cong, axiom, (emptyset__Cong<=>(emptyset)=(emptyset)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyset__Cong)). 117.41/117.61 thf(setadjoin__Cong, axiom, (setadjoin__Cong<=>![X2:$i, X3:$i]:((X2)=(X3)=>![X14:$i, X18:$i]:((X14)=(X18)=>(setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoin__Cong)). 117.41/117.61 thf(powerset__Cong, axiom, (powerset__Cong<=>![X4:$i, X5:$i]:((X4)=(X5)=>(powerset @ X4)=(powerset @ X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powerset__Cong)). 117.41/117.61 thf(setunion__Cong, axiom, (setunion__Cong<=>![X4:$i, X5:$i]:((X4)=(X5)=>(setunion @ X4)=(setunion @ X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunion__Cong)). 117.41/117.61 thf(omega__Cong, axiom, (omega__Cong<=>(omega)=(omega)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', omega__Cong)). 117.41/117.61 thf(dsetconstr__Cong, axiom, (dsetconstr__Cong<=>![X4:$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:$i]:X17 @ X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dsetconstr__Cong)). 117.41/117.61 thf(subsetI1, axiom, (subsetI1<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4=>in @ X2 @ X5)=>subset @ X4 @ X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetI1)). 117.41/117.61 thf(eqimpsubset2, axiom, (eqimpsubset2<=>![X4:$i, X5:$i]:((X4)=(X5)=>subset @ X5 @ X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', eqimpsubset2)). 117.41/117.61 thf(eqimpsubset1, axiom, (eqimpsubset1<=>![X4:$i, X5:$i]:((X4)=(X5)=>subset @ X4 @ X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', eqimpsubset1)). 117.41/117.61 thf(subsetI2, axiom, (subsetI2<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4=>in @ X2 @ X5)=>subset @ X4 @ X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetI2)). 117.41/117.61 thf(emptysetsubset, axiom, (emptysetsubset<=>![X4:$i]:subset @ emptyset @ X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptysetsubset)). 117.41/117.61 thf(subsetE, axiom, (subsetE<=>![X4:$i, X5:$i, X2:$i]:(subset @ X4 @ X5=>(in @ X2 @ X4=>in @ X2 @ X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetE)). 117.41/117.61 thf(subsetE2, axiom, (subsetE2<=>![X4:$i, X5:$i, X2:$i]:(subset @ X4 @ X5=>(~(in @ X2 @ X5)=>~(in @ X2 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetE2)). 117.41/117.61 thf(notsubsetI, axiom, (notsubsetI<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X5)=>~(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notsubsetI)). 117.41/117.61 thf(notequalI1, axiom, (notequalI1<=>![X4:$i, X5:$i]:(~(subset @ X4 @ X5)=>(X4)!=(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notequalI1)). 117.41/117.61 thf(notequalI2, axiom, (notequalI2<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X5)=>(X4)!=(X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notequalI2)). 117.41/117.61 thf(subsetRefl, axiom, (subsetRefl<=>![X4:$i]:subset @ X4 @ X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetRefl)). 117.41/117.61 thf(subsetTrans, axiom, (subsetTrans<=>![X4:$i, X5:$i, X7:$i]:(subset @ X4 @ X5=>(subset @ X5 @ X7=>subset @ X4 @ X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetTrans)). 117.41/117.61 thf(setadjoinSub, axiom, (setadjoinSub<=>![X2:$i, X4:$i]:subset @ X4 @ (setadjoin @ X2 @ X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinSub)). 117.41/117.61 thf(setadjoinSub2, axiom, (setadjoinSub2<=>![X4:$i, X2:$i, X5:$i]:(subset @ X4 @ X5=>subset @ X4 @ (setadjoin @ X2 @ X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinSub2)). 117.41/117.61 thf(subset2powerset, axiom, (subset2powerset<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>in @ X4 @ (powerset @ X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subset2powerset)). 117.41/117.61 thf(setextsub, axiom, (setextsub<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>(subset @ X5 @ X4=>(X4)=(X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setextsub)). 117.41/117.61 thf(subsetemptysetimpeq, axiom, (subsetemptysetimpeq<=>![X4:$i]:(subset @ X4 @ emptyset=>(X4)=(emptyset))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetemptysetimpeq)). 117.41/117.61 thf(powersetI1, axiom, (powersetI1<=>![X4:$i, X5:$i]:(subset @ X5 @ X4=>in @ X5 @ (powerset @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetI1)). 117.41/117.61 thf(powersetE1, axiom, (powersetE1<=>![X4:$i, X5:$i]:(in @ X5 @ (powerset @ X4)=>subset @ X5 @ X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetE1)). 117.41/117.61 thf(inPowerset, axiom, (inPowerset<=>![X4:$i]:in @ X4 @ (powerset @ X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', inPowerset)). 117.41/117.61 thf(powersetsubset, axiom, (powersetsubset<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>subset @ (powerset @ X4) @ (powerset @ X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetsubset)). 117.41/117.61 thf(sepInPowerset, axiom, (sepInPowerset<=>![X4:$i, X1:$i > $o]:in @ (dsetconstr @ X4 @ (^[X2:$i]:X1 @ X2)) @ (powerset @ X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', sepInPowerset)). 117.41/117.61 thf(sepSubset, axiom, (sepSubset<=>![X4:$i, X1:$i > $o]:subset @ (dsetconstr @ X4 @ (^[X2:$i]:X1 @ X2)) @ X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', sepSubset)). 117.41/117.61 thf(binunionIL, axiom, (binunionIL<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>in @ X2 @ (binunion @ X4 @ X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionIL)). 117.41/117.61 thf(upairset2IR, axiom, (upairset2IR<=>![X2:$i, X3:$i]:in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairset2IR)). 117.41/117.61 thf(binunionIR, axiom, (binunionIR<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X5=>in @ X2 @ (binunion @ X4 @ X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionIR)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', binunionEcases)). 117.41/117.61 thf(binunionE, axiom, (binunionE<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (binunion @ X4 @ X5)=>(in @ X2 @ X4|in @ X2 @ X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionE)). 117.41/117.61 thf(binunionLsub, axiom, (binunionLsub<=>![X4:$i, X5:$i]:subset @ X4 @ (binunion @ X4 @ X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionLsub)). 117.41/117.61 thf(binunionRsub, axiom, (binunionRsub<=>![X4:$i, X5:$i]:subset @ X5 @ (binunion @ X4 @ X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionRsub)). 117.41/117.61 thf(binintersectI, axiom, (binintersectI<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X5=>in @ X2 @ (binintersect @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectI)). 117.41/117.61 thf(binintersectSubset5, axiom, (binintersectSubset5<=>![X4:$i, X5:$i, X7:$i]:(subset @ X7 @ X4=>(subset @ X7 @ X5=>subset @ X7 @ (binintersect @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectSubset5)). 117.41/117.61 thf(binintersectEL, axiom, (binintersectEL<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (binintersect @ X4 @ X5)=>in @ X2 @ X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectEL)). 117.41/117.61 thf(binintersectLsub, axiom, (binintersectLsub<=>![X4:$i, X5:$i]:subset @ (binintersect @ X4 @ X5) @ X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectLsub)). 117.41/117.61 thf(binintersectSubset2, axiom, (binintersectSubset2<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>(binintersect @ X4 @ X5)=(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectSubset2)). 117.41/117.61 thf(binintersectSubset3, axiom, (binintersectSubset3<=>![X4:$i, X5:$i]:((binintersect @ X4 @ X5)=(X5)=>subset @ X5 @ X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectSubset3)). 117.41/117.61 thf(binintersectER, axiom, (binintersectER<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (binintersect @ X4 @ X5)=>in @ X2 @ X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectER)). 117.41/117.61 thf(disjointsetsI1, axiom, (disjointsetsI1<=>![X4:$i, X5:$i]:(~(?[X2:$i]:(in @ X2 @ X4&in @ X2 @ X5))=>(binintersect @ X4 @ X5)=(emptyset))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', disjointsetsI1)). 117.41/117.61 thf(binintersectRsub, axiom, (binintersectRsub<=>![X4:$i, X5:$i]:subset @ (binintersect @ X4 @ X5) @ X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectRsub)). 117.41/117.61 thf(binintersectSubset4, axiom, (binintersectSubset4<=>![X4:$i, X5:$i]:(subset @ X5 @ X4=>(binintersect @ X4 @ X5)=(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectSubset4)). 117.41/117.61 thf(binintersectSubset1, axiom, (binintersectSubset1<=>![X4:$i, X5:$i]:((binintersect @ X4 @ X5)=(X4)=>subset @ X4 @ X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectSubset1)). 117.41/117.61 thf(bs114d, axiom, (bs114d<=>![X4:$i, X5:$i, X7:$i]:(binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', bs114d)). 117.41/117.61 thf(setminusI, axiom, (setminusI<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X5)=>in @ X2 @ (setminus @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusI)). 117.41/117.61 thf(setminusEL, axiom, (setminusEL<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (setminus @ X4 @ X5)=>in @ X2 @ X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusEL)). 117.41/117.61 thf(setminusER, axiom, (setminusER<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (setminus @ X4 @ X5)=>~(in @ X2 @ X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusER)). 117.41/117.61 thf(setminusSubset2, axiom, (setminusSubset2<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>(setminus @ X4 @ X5)=(emptyset))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusSubset2)). 117.41/117.61 thf(setminusERneg, axiom, (setminusERneg<=>![X4:$i, X5:$i, X2:$i]:(~(in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4=>in @ X2 @ X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusERneg)). 117.41/117.61 thf(setminusELneg, axiom, (setminusELneg<=>![X4:$i, X5:$i, X2:$i]:(~(in @ X2 @ (setminus @ X4 @ X5))=>(~(in @ X2 @ X5)=>~(in @ X2 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusELneg)). 117.41/117.61 thf(setminusILneg, axiom, (setminusILneg<=>![X4:$i, X5:$i, X2:$i]:(~(in @ X2 @ X4)=>~(in @ X2 @ (setminus @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusILneg)). 117.41/117.61 thf(setminusIRneg, axiom, (setminusIRneg<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X5=>~(in @ X2 @ (setminus @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusIRneg)). 117.41/117.61 thf(setminusLsub, axiom, (setminusLsub<=>![X4:$i, X5:$i]:subset @ (setminus @ X4 @ X5) @ X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusLsub)). 117.41/117.61 thf(setminusSubset1, axiom, (setminusSubset1<=>![X4:$i, X5:$i]:((setminus @ X4 @ X5)=(emptyset)=>subset @ X4 @ X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusSubset1)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', symdiffE)). 117.41/117.61 thf(symdiffI1, axiom, (symdiffI1<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X5)=>in @ X2 @ (symdiff @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', symdiffI1)). 117.41/117.61 thf(symdiffI2, axiom, (symdiffI2<=>![X4:$i, X5:$i, X2:$i]:(~(in @ X2 @ X4)=>(in @ X2 @ X5=>in @ X2 @ (symdiff @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', symdiffI2)). 117.41/117.61 thf(symdiffIneg1, axiom, (symdiffIneg1<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X5=>~(in @ X2 @ (symdiff @ X4 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', symdiffIneg1)). 117.41/117.61 thf(symdiffIneg2, axiom, (symdiffIneg2<=>![X4:$i, X5:$i, X2:$i]:(~(in @ X2 @ X4)=>(~(in @ X2 @ X5)=>~(in @ X2 @ (symdiff @ X4 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', symdiffIneg2)). 117.41/117.61 thf(secondinupair, axiom, (secondinupair<=>![X2:$i, X3:$i]:in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', secondinupair)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', setukpairIL)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', setukpairIR)). 117.41/117.61 thf(kpairiskpair, axiom, (kpairiskpair<=>![X2:$i, X3:$i]:iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', kpairiskpair)). 117.41/117.61 thf(kpairp, axiom, (kpairp<=>![X2:$i, X3:$i]:iskpair @ (kpair @ X2 @ X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', kpairp)). 117.41/117.61 thf(singletonsubset, axiom, (singletonsubset<=>![X4:$i, X2:$i]:(in @ X2 @ X4=>subset @ (setadjoin @ X2 @ emptyset) @ X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletonsubset)). 117.41/117.61 thf(singletoninpowerset, axiom, (singletoninpowerset<=>![X4:$i, X2:$i]:(in @ X2 @ X4=>in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletoninpowerset)). 117.41/117.61 thf(singletoninpowunion, axiom, (singletoninpowunion<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletoninpowunion)). 117.41/117.61 thf(upairset2E, axiom, (upairset2E<=>![X2:$i, X3:$i, X14:$i]:(in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=>((X14)=(X2)|(X14)=(X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairset2E)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', upairsubunion)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', upairinpowunion)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', ubforcartprodlem1)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', ubforcartprodlem2)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', ubforcartprodlem3)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', cartprodpairin)). 117.41/117.61 thf(cartprodmempair1, axiom, (cartprodmempair1<=>![X4:$i, X5:$i, X18:$i]:(in @ X18 @ (cartprod @ X4 @ X5)=>?[X2:$i]:(in @ X2 @ X4&?[X3:$i]:(in @ X3 @ X5&(X18)=(kpair @ X2 @ X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodmempair1)). 117.41/117.61 thf(cartprodmempair, axiom, (cartprodmempair<=>![X4:$i, X5:$i, X18:$i]:(in @ X18 @ (cartprod @ X4 @ X5)=>iskpair @ X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodmempair)). 117.41/117.61 thf(setunionE2, axiom, (setunionE2<=>![X4:$i, X2:$i]:(in @ X2 @ (setunion @ X4)=>?[X21:$i]:(in @ X21 @ X4&in @ X2 @ X21))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionE2)). 117.41/117.61 thf(setunionsingleton1, axiom, (setunionsingleton1<=>![X4:$i]:subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionsingleton1)). 117.41/117.61 thf(setunionsingleton2, axiom, (setunionsingleton2<=>![X4:$i]:subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionsingleton2)). 117.41/117.61 thf(setunionsingleton, axiom, (setunionsingleton<=>![X2:$i]:(setunion @ (setadjoin @ X2 @ emptyset))=(X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionsingleton)). 117.41/117.61 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:$i]:X1 @ X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletonprop)). 117.41/117.61 thf(ex1E1, axiom, (ex1E1<=>![X4:$i, X1:$i > $o]:(ex1 @ X4 @ (^[X2:$i]:X1 @ X2)=>?[X2:$i]:(in @ X2 @ X4&X1 @ X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ex1E1)). 117.41/117.61 thf(ex1I, axiom, (ex1I<=>![X4:$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/sandbox2/benchmark/theBenchmark.p', ex1I)). 117.41/117.61 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:$i]:X1 @ X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ex1I2)). 117.41/117.61 thf(singletonsuniq, axiom, (singletonsuniq<=>![X2:$i, X3:$i]:((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset)=>(X2)=(X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletonsuniq)). 117.41/117.61 thf(setukpairinjL1, axiom, (setukpairinjL1<=>![X2:$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/sandbox2/benchmark/theBenchmark.p', setukpairinjL1)). 117.41/117.61 thf(kfstsingleton, axiom, (kfstsingleton<=>![X18:$i]:(iskpair @ X18=>singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:in @ (setadjoin @ X2 @ emptyset) @ X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', kfstsingleton)). 117.41/117.61 thf(theprop, axiom, (theprop<=>![X21:$i]:(singleton @ X21=>in @ (setunion @ X21) @ X21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', theprop)). 117.41/117.61 thf(kfstpairEq, axiom, (kfstpairEq<=>![X2:$i, X3:$i]:(kfst @ (kpair @ X2 @ X3))=(X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', kfstpairEq)). 117.41/117.61 thf(cartprodfstin, axiom, (cartprodfstin<=>![X4:$i, X5:$i, X18:$i]:(in @ X18 @ (cartprod @ X4 @ X5)=>in @ (kfst @ X18) @ X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodfstin)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', setukpairinjL2)). 117.41/117.61 thf(setukpairinjL, axiom, (setukpairinjL<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((kpair @ X2 @ X3)=(kpair @ X14 @ X18)=>(X2)=(X14))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjL)). 117.41/117.61 thf(setukpairinjR11, axiom, (setukpairinjR11<=>![X2:$i, X3:$i]:((X2)=(X3)=>(setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjR11)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', setukpairinjR12)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', setukpairinjR1)). 117.41/117.61 thf(upairequniteq, axiom, (upairequniteq<=>![X2:$i, X3:$i, X14:$i]:((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset)=>(X2)=(X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairequniteq)). 117.41/117.61 thf(setukpairinjR2, axiom, (setukpairinjR2<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset))=>(X3)=(X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjR2)). 117.41/117.61 thf(setukpairinjR, axiom, (setukpairinjR<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((kpair @ X2 @ X3)=(kpair @ X14 @ X18)=>(X3)=(X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjR)). 117.41/117.61 thf(ksndsingleton, axiom, (ksndsingleton<=>![X18:$i]:(iskpair @ X18=>singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(X18)=(kpair @ (kfst @ X18) @ X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ksndsingleton)). 117.41/117.61 thf(ksndpairEq, axiom, (ksndpairEq<=>![X2:$i, X3:$i]:(ksnd @ (kpair @ X2 @ X3))=(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ksndpairEq)). 117.41/117.61 thf(kpairsurjEq, axiom, (kpairsurjEq<=>![X18:$i]:(iskpair @ X18=>(kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', kpairsurjEq)). 117.41/117.61 thf(cartprodsndin, axiom, (cartprodsndin<=>![X4:$i, X5:$i, X18:$i]:(in @ X18 @ (cartprod @ X4 @ X5)=>in @ (ksnd @ X18) @ X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodsndin)). 117.41/117.61 thf(cartprodpairmemEL, axiom, (cartprodpairmemEL<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5)=>in @ X2 @ X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodpairmemEL)). 117.41/117.61 thf(cartprodpairmemER, axiom, (cartprodpairmemER<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5)=>in @ X3 @ X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodpairmemER)). 117.41/117.61 thf(cartprodmempaircEq, axiom, (cartprodmempaircEq<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(kpair @ X2 @ X3)=(kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodmempaircEq)). 117.41/117.61 thf(cartprodfstpairEq, axiom, (cartprodfstpairEq<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodfstpairEq)). 117.41/117.61 thf(cartprodsndpairEq, axiom, (cartprodsndpairEq<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodsndpairEq)). 117.41/117.61 thf(cartprodpairsurjEq, axiom, (cartprodpairsurjEq<=>![X4:$i, X5:$i, X18:$i]:(in @ X18 @ (cartprod @ X4 @ X5)=>(kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodpairsurjEq)). 117.41/117.61 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:$i]:X22 @ X14 @ X18)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dpsetconstrI)). 117.41/117.61 thf(dpsetconstrSub, axiom, (dpsetconstrSub<=>![X4:$i, X5:$i, X23:$i > $i > $o]:subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:X23 @ X2 @ X3)) @ (cartprod @ X4 @ X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dpsetconstrSub)). 117.41/117.61 thf(setOfPairsIsBReln, axiom, (setOfPairsIsBReln<=>![X4:$i, X5:$i, X24:$i > $i > $o]:breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:X24 @ X2 @ X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setOfPairsIsBReln)). 117.41/117.61 thf(dpsetconstrERa, axiom, (dpsetconstrERa<=>![X4:$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:$i]:X25 @ X14 @ X18))=>X25 @ X2 @ X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dpsetconstrERa)). 117.41/117.61 thf(dpsetconstrEL1, axiom, (dpsetconstrEL1<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:X26 @ X14 @ X18))=>in @ X2 @ X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dpsetconstrEL1)). 117.41/117.61 thf(dpsetconstrEL2, axiom, (dpsetconstrEL2<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:X27 @ X14 @ X18))=>in @ X3 @ X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dpsetconstrEL2)). 117.41/117.61 thf(dpsetconstrER, axiom, (dpsetconstrER<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:X28 @ X14 @ X18))=>X28 @ X2 @ X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dpsetconstrER)). 117.41/117.61 thf(funcImageSingleton, axiom, (funcImageSingleton<=>![X4:$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/sandbox2/benchmark/theBenchmark.p', funcImageSingleton)). 117.41/117.61 thf(apProp, axiom, (apProp<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>![X2:$i]:(in @ X2 @ X4=>in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:in @ (kpair @ X2 @ X3) @ X29))) @ X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', apProp)). 117.41/117.61 thf(app, axiom, (app<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>![X2:$i]:(in @ X2 @ X4=>in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', app)). 117.41/117.61 thf(infuncsetfunc, axiom, (infuncsetfunc<=>![X4:$i, X5:$i, X29:$i]:(in @ X29 @ (funcSet @ X4 @ X5)=>func @ X4 @ X5 @ X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', infuncsetfunc)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', ap2p)). 117.41/117.61 thf(funcinfuncset, axiom, (funcinfuncset<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>in @ X29 @ (funcSet @ X4 @ X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', funcinfuncset)). 117.41/117.61 thf(lamProp, axiom, (lamProp<=>![X4:$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/sandbox2/benchmark/theBenchmark.p', lamProp)). 117.41/117.61 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:$i]:X31 @ X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', lamp)). 117.41/117.61 thf(lam2p, axiom, (lam2p<=>![X4:$i, X5:$i, X32:$i > $i]:(![X2:$i]:(in @ X2 @ X4=>in @ (X32 @ X2) @ X5)=>in @ (lam @ X4 @ X5 @ (^[X2:$i]:X32 @ X2)) @ (funcSet @ X4 @ X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', lam2p)). 117.41/117.61 thf(brelnall1, axiom, (brelnall1<=>![X4:$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/sandbox2/benchmark/theBenchmark.p', brelnall1)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', brelnall2)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', ex1E2)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', funcGraphProp1)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', funcGraphProp3)). 117.41/117.61 thf(funcGraphProp2, axiom, (funcGraphProp2<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ X29=>(ap @ X4 @ X5 @ X29 @ X2)=(X3)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', funcGraphProp2)). 117.41/117.61 thf(funcextLem, axiom, (funcextLem<=>![X4:$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/sandbox2/benchmark/theBenchmark.p', funcextLem)). 117.41/117.61 thf(funcGraphProp4, axiom, (funcGraphProp4<=>![X4:$i, X5:$i, X29:$i]:(in @ X29 @ (funcSet @ X4 @ X5)=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ X29=>(ap @ X4 @ X5 @ X29 @ X2)=(X3)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', funcGraphProp4)). 117.41/117.61 thf(subbreln, axiom, (subbreln<=>![X4:$i, X5:$i, X33:$i]:(breln @ X4 @ X5 @ X33=>![X35:$i]:(breln @ X4 @ X5 @ X35=>(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ X33=>in @ (kpair @ X2 @ X3) @ X35)))=>subset @ X33 @ X35)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subbreln)). 117.41/117.61 thf(eqbreln, axiom, (eqbreln<=>![X4:$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:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ X35=>in @ (kpair @ X2 @ X3) @ X33)))=>(X33)=(X35)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', eqbreln)). 117.41/117.61 thf(funcext, axiom, (funcext<=>![X4:$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/sandbox2/benchmark/theBenchmark.p', funcext)). 117.41/117.61 thf(funcext2, axiom, (funcext2<=>![X4:$i, X5:$i, X29:$i]:(in @ X29 @ (funcSet @ X4 @ X5)=>![X34:$i]:(in @ X34 @ (funcSet @ X4 @ X5)=>(![X2:$i]:(in @ X2 @ X4=>(ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))=>(X29)=(X34))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', funcext2)). 117.41/117.61 thf(ap2apEq1, axiom, (ap2apEq1<=>![X4:$i, X5:$i, X29:$i]:(in @ X29 @ (funcSet @ X4 @ X5)=>![X2:$i]:(in @ X2 @ X4=>(ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ap2apEq1)). 117.41/117.61 thf(ap2apEq2, axiom, (ap2apEq2<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>![X2:$i]:(in @ X2 @ X4=>(ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ap2apEq2)). 117.41/117.61 thf(beta1, axiom, (beta1<=>![X4:$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/sandbox2/benchmark/theBenchmark.p', beta1)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', eta1)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', lam2lamEq)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', beta2)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', eta2)). 117.41/117.61 thf(iffalseProp1, axiom, (iffalseProp1<=>![X4:$i, X39:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(~(X39)=>in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((X39&(X14)=(X2))|(~(X39)&(X14)=(X3))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', iffalseProp1)). 117.41/117.61 thf(iffalseProp2, axiom, (iffalseProp2<=>![X4:$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/sandbox2/benchmark/theBenchmark.p', iffalseProp2)). 117.41/117.61 thf(iftrueProp1, axiom, (iftrueProp1<=>![X4:$i, X41:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(X41=>in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((X41&(X14)=(X2))|(~(X41)&(X14)=(X3))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', iftrueProp1)). 117.41/117.61 thf(iftrueProp2, axiom, (iftrueProp2<=>![X4:$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/sandbox2/benchmark/theBenchmark.p', iftrueProp2)). 117.41/117.61 thf(ifSingleton, axiom, (ifSingleton<=>![X4:$i, X43:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((X43&(X14)=(X2))|(~(X43)&(X14)=(X3)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ifSingleton)). 117.41/117.61 thf(ifp, axiom, (ifp<=>![X4:$i, X44:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>in @ (if @ X4 @ (X44) @ X2 @ X3) @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ifp)). 117.41/117.61 thf(theeq, axiom, (theeq<=>![X21:$i]:(singleton @ X21=>![X2:$i]:(in @ X2 @ X21=>(setunion @ X21)=(X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', theeq)). 117.41/117.61 thf(iftrue, axiom, (iftrue<=>![X4:$i, X45:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(X45=>(if @ X4 @ (X45) @ X2 @ X3)=(X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', iftrue)). 117.41/117.61 thf(iffalse, axiom, (iffalse<=>![X4:$i, X46:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(~(X46)=>(if @ X4 @ (X46) @ X2 @ X3)=(X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', iffalse)). 117.41/117.61 thf(iftrueorfalse, axiom, (iftrueorfalse<=>![X4:$i, X47:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>in @ (if @ X4 @ (X47) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', iftrueorfalse)). 117.41/117.61 thf(binintersectT_lem, axiom, (binintersectT_lem<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>in @ (binintersect @ X21 @ X48) @ (powerset @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectT_lem)). 117.41/117.61 thf(binunionT_lem, axiom, (binunionT_lem<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>in @ (binunion @ X21 @ X48) @ (powerset @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionT_lem)). 117.41/117.61 thf(powersetT_lem, axiom, (powersetT_lem<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetT_lem)). 117.41/117.61 thf(setminusT_lem, axiom, (setminusT_lem<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>in @ (setminus @ X21 @ X48) @ (powerset @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusT_lem)). 117.41/117.61 thf(complementT_lem, axiom, (complementT_lem<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>in @ (setminus @ X4 @ X21) @ (powerset @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', complementT_lem)). 117.41/117.61 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:$i]:(in @ X2 @ X4=>(in @ X2 @ X48=>in @ X2 @ X21))=>(X21)=(X48)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setextT)). 117.41/117.61 thf(subsetTI, axiom, (subsetTI<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>(![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X21=>in @ X2 @ X48))=>subset @ X21 @ X48)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetTI)). 117.41/117.61 thf(powersetTI1, axiom, (powersetTI1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>(![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X21=>in @ X2 @ X48))=>in @ X21 @ (powerset @ X48))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetTI1)). 117.41/117.61 thf(powersetTE1, axiom, (powersetTE1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X21 @ (powerset @ X48)=>(in @ X2 @ X21=>in @ X2 @ X48)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetTE1)). 117.41/117.61 thf(complementTI1, axiom, (complementTI1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X21=>~(in @ X2 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', complementTI1)). 117.41/117.61 thf(complementTE1, axiom, (complementTE1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ (setminus @ X4 @ X21))=>in @ X2 @ X21)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', complementTE1)). 117.41/117.61 thf(binintersectTELcontra, axiom, (binintersectTELcontra<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X21)=>~(in @ X2 @ (binintersect @ X21 @ X48))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectTELcontra)). 117.41/117.61 thf(binintersectTERcontra, axiom, (binintersectTERcontra<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X48)=>~(in @ X2 @ (binintersect @ X21 @ X48))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectTERcontra)). 117.41/117.61 thf(contrasubsetT, axiom, (contrasubsetT<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(subset @ X21 @ (setminus @ X4 @ X48)=>(in @ X2 @ X48=>~(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', contrasubsetT)). 117.41/117.61 thf(contrasubsetT1, axiom, (contrasubsetT1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(subset @ X21 @ X48=>(~(in @ X2 @ X48)=>~(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', contrasubsetT1)). 117.41/117.61 thf(contrasubsetT2, axiom, (contrasubsetT2<=>![X4:$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/sandbox2/benchmark/theBenchmark.p', contrasubsetT2)). 117.41/117.61 thf(contrasubsetT3, axiom, (contrasubsetT3<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)=>subset @ X21 @ X48)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', contrasubsetT3)). 117.41/117.61 thf(doubleComplementI1, axiom, (doubleComplementI1<=>![X4:$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/sandbox2/benchmark/theBenchmark.p', doubleComplementI1)). 117.41/117.61 thf(doubleComplementE1, axiom, (doubleComplementE1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))=>in @ X2 @ X21)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', doubleComplementE1)). 117.41/117.61 thf(doubleComplementSub1, axiom, (doubleComplementSub1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', doubleComplementSub1)). 117.41/117.61 thf(doubleComplementSub2, axiom, (doubleComplementSub2<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', doubleComplementSub2)). 117.41/117.61 thf(doubleComplementEq, axiom, (doubleComplementEq<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>(X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', doubleComplementEq)). 117.41/117.61 thf(complementTnotintersectT, axiom, (complementTnotintersectT<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (setminus @ X4 @ X21)=>~(in @ X2 @ (binintersect @ X21 @ X48))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', complementTnotintersectT)). 117.41/117.61 thf(complementImpComplementIntersect, axiom, (complementImpComplementIntersect<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (setminus @ X4 @ X21)=>in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', complementImpComplementIntersect)). 117.41/117.61 thf(complementSubsetComplementIntersect, axiom, (complementSubsetComplementIntersect<=>![X4:$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/sandbox2/benchmark/theBenchmark.p', complementSubsetComplementIntersect)). 117.41/117.61 thf(complementInPowersetComplementIntersect, axiom, (complementInPowersetComplementIntersect<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', complementInPowersetComplementIntersect)). 117.41/117.61 thf(contraSubsetComplement, axiom, (contraSubsetComplement<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>(subset @ X21 @ (setminus @ X4 @ X48)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X48=>in @ X2 @ (setminus @ X4 @ X21))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', contraSubsetComplement)). 117.41/117.61 thf(complementTcontraSubset, axiom, (complementTcontraSubset<=>![X4:$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/sandbox2/benchmark/theBenchmark.p', complementTcontraSubset)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', binunionTILcontra)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', binunionTIRcontra)). 117.41/117.61 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:$i]:(in @ X2 @ X4=>(in @ X2 @ (binintersect @ X21 @ X48)=>in @ X2 @ (binunion @ X21 @ X49))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', inIntersectImpInUnion)). 117.41/117.61 thf(inIntersectImpInUnion2, axiom, (inIntersectImpInUnion2<=>![X4:$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/sandbox2/benchmark/theBenchmark.p', inIntersectImpInUnion2)). 117.41/117.61 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:$i]:(in @ X2 @ X4=>(in @ X2 @ (binintersect @ X21 @ X48)=>in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', inIntersectImpInIntersectUnions)). 117.41/117.61 thf(intersectInPowersetIntersectUnions, axiom, (intersectInPowersetIntersectUnions<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X49:$i]:(in @ X49 @ (powerset @ X4)=>in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', intersectInPowersetIntersectUnions)). 117.41/117.61 thf(inComplementUnionImpNotIn1, axiom, (inComplementUnionImpNotIn1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))=>~(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', inComplementUnionImpNotIn1)). 117.41/117.61 thf(inComplementUnionImpInComplement1, axiom, (inComplementUnionImpInComplement1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))=>in @ X2 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', inComplementUnionImpInComplement1)). 117.41/117.61 thf(binunionTE, axiom, (binunionTE<=>![X4:$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/sandbox2/benchmark/theBenchmark.p', binunionTE)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', binunionTEcontra)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', demorgan2a1)). 117.41/117.61 thf(complementUnionInPowersetComplement, axiom, (complementUnionInPowersetComplement<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', complementUnionInPowersetComplement)). 117.41/117.61 thf(demorgan2a2, axiom, (demorgan2a2<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))=>in @ X2 @ (setminus @ X4 @ X48)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', demorgan2a2)). 117.41/117.61 thf(demorgan1a, axiom, (demorgan1a<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))=>in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', demorgan1a)). 117.41/117.61 thf(demorgan1b, axiom, (demorgan1b<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))=>in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', demorgan1b)). 117.41/117.61 thf(demorgan1, axiom, (demorgan1<=>![X4:$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/sandbox2/benchmark/theBenchmark.p', demorgan1)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', demorgan2a)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', demorgan2b2)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', demorgan2b)). 117.41/117.61 thf(demorgan2, axiom, (demorgan2<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>(setminus @ X4 @ (binunion @ X21 @ X48))=(binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', demorgan2)). 117.41/117.61 thf(woz13rule0, axiom, (woz13rule0<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ (binintersect @ X21 @ X48)=>in @ X2 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', woz13rule0)). 117.41/117.61 thf(woz13rule1, axiom, (woz13rule1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X49:$i]:(in @ X49 @ (powerset @ X4)=>(subset @ X21 @ X49=>subset @ (binintersect @ X21 @ X48) @ X49))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', woz13rule1)). 117.41/117.61 thf(woz13rule2, axiom, (woz13rule2<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X49:$i]:(in @ X49 @ (powerset @ X4)=>(subset @ X48 @ X49=>subset @ (binintersect @ X21 @ X48) @ X49))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', woz13rule2)). 117.41/117.61 thf(woz13rule3, axiom, (woz13rule3<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X49:$i]:(in @ X49 @ (powerset @ X4)=>(subset @ X21 @ X48=>(subset @ X21 @ X49=>subset @ X21 @ (binintersect @ X48 @ X49))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', woz13rule3)). 117.41/117.61 thf(woz13rule4, axiom, (woz13rule4<=>![X4:$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/sandbox2/benchmark/theBenchmark.p', woz13rule4)). 117.41/117.61 thf(woz1_1, axiom, (woz1_1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', woz1_1)). 117.41/117.61 thf(woz1_2, axiom, (woz1_2<=>![X4:$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/sandbox2/benchmark/theBenchmark.p', woz1_2)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', woz1_3)). 117.41/117.61 thf(woz1_4, axiom, (woz1_4<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>(subset @ X21 @ (setminus @ X4 @ X48)=>subset @ X48 @ (setminus @ X4 @ X21))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', woz1_4)). 117.41/117.61 thf(woz1_5, axiom, (woz1_5<=>![X4:$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/sandbox2/benchmark/theBenchmark.p', woz1_5)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', breln1all2)). 117.41/117.61 thf(breln1SetBreln1, axiom, (breln1SetBreln1<=>![X4:$i, X33:$i]:(in @ X33 @ (breln1Set @ X4)=>breln1 @ X4 @ X33)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', breln1SetBreln1)). 117.41/117.61 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:$i]:(in @ X14 @ X5=>(X52 @ X2 @ X14=>in @ (kpair @ X3 @ X14) @ X33)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', choice2fnsingleton)). 117.41/117.61 thf(setOfPairsIsBReln1, axiom, (setOfPairsIsBReln1<=>![X4:$i, X53:$i > $i > $o]:breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:X53 @ X2 @ X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setOfPairsIsBReln1)). 117.41/117.61 thf(breln1all1, axiom, (breln1all1<=>![X4:$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/sandbox2/benchmark/theBenchmark.p', breln1all1)). 117.41/117.61 thf(subbreln1, axiom, (subbreln1<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X35:$i]:(breln1 @ X4 @ X35=>(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(in @ (kpair @ X2 @ X3) @ X33=>in @ (kpair @ X2 @ X3) @ X35)))=>subset @ X33 @ X35)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subbreln1)). 117.41/117.61 thf(eqbreln1, axiom, (eqbreln1<=>![X4:$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/sandbox2/benchmark/theBenchmark.p', eqbreln1)). 117.41/117.61 thf(breln1invprop, axiom, (breln1invprop<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>breln1 @ X4 @ (breln1invset @ X4 @ X33))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', breln1invprop)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', breln1invI)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', breln1invE)). 117.41/117.61 thf(breln1compprop, axiom, (breln1compprop<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X35:$i]:(breln1 @ X4 @ X35=>breln1 @ X4 @ (breln1compset @ X4 @ X33 @ X35)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', breln1compprop)). 117.41/117.61 thf(breln1compI, axiom, (breln1compI<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X35:$i]:(breln1 @ X4 @ X35=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>![X14:$i]:(in @ X14 @ X4=>(in @ (kpair @ X2 @ X14) @ X33=>(in @ (kpair @ X14 @ X3) @ X35=>in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', breln1compI)). 117.41/117.61 thf(breln1compE, axiom, (breln1compE<=>![X4:$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:$i]:((in @ X14 @ X4&in @ (kpair @ X2 @ X14) @ X33)&in @ (kpair @ X14 @ X3) @ X35))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', breln1compE)). 117.41/117.61 thf(breln1compEex, axiom, (breln1compEex<=>![X4:$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/sandbox2/benchmark/theBenchmark.p', breln1compEex)). 117.41/117.61 thf(breln1unionprop, axiom, (breln1unionprop<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X35:$i]:(breln1 @ X4 @ X35=>breln1 @ X4 @ (binunion @ X33 @ X35)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', breln1unionprop)). 117.41/117.61 thf(breln1unionIL, axiom, (breln1unionIL<=>![X4:$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/sandbox2/benchmark/theBenchmark.p', breln1unionIL)). 117.41/117.61 thf(breln1unionIR, axiom, (breln1unionIR<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X35:$i]:(breln1 @ X4 @ X35=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(in @ (kpair @ X2 @ X3) @ X35=>in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', breln1unionIR)). 117.41/117.61 thf(breln1unionI, axiom, (breln1unionI<=>![X4:$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/sandbox2/benchmark/theBenchmark.p', breln1unionI)). 117.41/117.61 thf(breln1unionE, axiom, (breln1unionE<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X35:$i]:(breln1 @ X4 @ X35=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)=>(in @ (kpair @ X2 @ X3) @ X33|in @ (kpair @ X2 @ X3) @ X35))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', breln1unionE)). 117.41/117.61 thf(breln1unionEcases, axiom, (breln1unionEcases<=>![X4:$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:$o]:((in @ (kpair @ X2 @ X3) @ X33=>X55)=>((in @ (kpair @ X2 @ X3) @ X35=>X55)=>X55)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', breln1unionEcases)). 117.41/117.61 thf(breln1unionCommutes, axiom, (breln1unionCommutes<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X35:$i]:(breln1 @ X4 @ X35=>(binunion @ X33 @ X35)=(binunion @ X35 @ X33)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', breln1unionCommutes)). 117.41/117.61 thf(woz2Ex, axiom, (woz2Ex<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>(X33)=(breln1invset @ X4 @ (breln1invset @ X4 @ X33)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', woz2Ex)). 117.41/117.61 thf(woz2W, axiom, (woz2W<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X35:$i]:(breln1 @ X4 @ X35=>(breln1invset @ X4 @ (breln1compset @ X4 @ X33 @ X35))=(breln1compset @ X4 @ (breln1invset @ X4 @ X35) @ (breln1invset @ X4 @ X33))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', woz2W)). 117.41/117.61 thf(woz2A, axiom, (woz2A<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X35:$i]:(breln1 @ X4 @ X35=>![X56:$i]:(breln1 @ X4 @ X56=>(breln1compset @ X4 @ (binunion @ X33 @ X35) @ X56)=(binunion @ (breln1compset @ X4 @ X33 @ X56) @ (breln1compset @ X4 @ X35 @ X56)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', woz2A)). 117.41/117.61 thf(woz2B, axiom, (woz2B<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X35:$i]:(breln1 @ X4 @ X35=>![X56:$i]:(breln1 @ X4 @ X56=>(breln1compset @ X4 @ (binunion @ X33 @ X35) @ X56)=(binunion @ (breln1invset @ X4 @ (breln1compset @ X4 @ (breln1invset @ X4 @ X56) @ (breln1invset @ X4 @ X35))) @ (breln1invset @ X4 @ (breln1compset @ X4 @ (breln1invset @ X4 @ X56) @ (breln1invset @ X4 @ X33)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', woz2B)). 117.41/117.61 thf(image1Ex, axiom, (image1Ex<=>![X4:$i, X57:$i > $i]:?[X5:$i]:![X2:$i]:(in @ X2 @ X5<=>?[X3:$i]:(in @ X3 @ X4&(X2)=(X57 @ X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', image1Ex)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', image1Equiv)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', image1E)). 117.41/117.61 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/sandbox2/benchmark/theBenchmark.p', image1I)). 117.41/117.61 thf(injFuncInInjFuncSet, axiom, (injFuncInInjFuncSet<=>![X4:$i, X5:$i, X29:$i]:(in @ X29 @ (funcSet @ X4 @ X5)=>(injective @ X4 @ X5 @ X29=>in @ X29 @ (injFuncSet @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', injFuncInInjFuncSet)). 117.41/117.61 thf(injFuncSetFuncIn, axiom, (injFuncSetFuncIn<=>![X4:$i, X5:$i, X29:$i]:(in @ X29 @ (injFuncSet @ X4 @ X5)=>in @ X29 @ (funcSet @ X4 @ X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', injFuncSetFuncIn)). 117.41/117.61 thf(injFuncSetFuncInj, axiom, (injFuncSetFuncInj<=>![X2:$i, X3:$i, X29:$i]:(in @ X29 @ (injFuncSet @ X2 @ X3)=>injective @ X2 @ X3 @ X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', injFuncSetFuncInj)). 117.41/117.61 thf(surjFuncSetFuncIn, axiom, (surjFuncSetFuncIn<=>![X4:$i, X5:$i, X29:$i]:(in @ X29 @ (surjFuncSet @ X4 @ X5)=>in @ X29 @ (funcSet @ X4 @ X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', surjFuncSetFuncIn)). 117.41/117.61 thf(surjFuncSetFuncSurj, axiom, (surjFuncSetFuncSurj<=>![X2:$i, X3:$i, X29:$i]:(in @ X29 @ (surjFuncSet @ X2 @ X3)=>surjective @ X2 @ X3 @ X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', surjFuncSetFuncSurj)). 117.41/117.61 thf(leftInvIsSurj, axiom, (leftInvIsSurj<=>![X4:$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/sandbox2/benchmark/theBenchmark.p', leftInvIsSurj)). 117.41/117.61 thf(surjCantorThm, axiom, (surjCantorThm<=>![X4:$i, X29:$i]:(in @ X29 @ (funcSet @ X4 @ (powerset @ X4))=>~(surjective @ X4 @ (powerset @ X4) @ X29))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', surjCantorThm)). 117.41/117.61 thf(notinself, axiom, (notinself<=>![X4:$i]:~(in @ X4 @ X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notinself)). 117.41/117.61 thf(notinself2, axiom, (notinself2<=>![X4:$i, X5:$i]:(in @ X4 @ X5=>~(in @ X5 @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notinself2)). 117.41/117.61 thf(omegaSp, axiom, (omegaSp<=>![X2:$i]:(in @ X2 @ omega=>in @ (omegaS @ X2) @ omega)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', omegaSp)). 117.41/117.61 thf(omegaSclos, axiom, (omegaSclos<=>![X2:$i]:(in @ X2 @ omega=>in @ (setadjoin @ X2 @ X2) @ omega)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', omegaSclos)). 117.41/117.61 thf(peano0notS, axiom, (peano0notS<=>![X2:$i]:(in @ X2 @ omega=>(omegaS @ X2)!=(emptyset))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', peano0notS)). 117.41/117.61 thf(omegaS, axiom, (omegaS)=(^[X2:$i]:setadjoin @ X2 @ X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', omegaS)). 117.41/117.61 thf(c_0_331, axiom, (replAx)=(![X6:$i > $i > $o, X4:$i]:(![X2:$i]:(in @ X2 @ X4=>?[X1134:$i]:(X6 @ X2 @ X1134&![X1136:$i]:(X6 @ X2 @ X1136=>(X1134)=(X1136))))=>?[X5:$i]:![X2:$i]:(in @ X2 @ X5<=>?[X3:$i]:(in @ X3 @ X4&X6 @ X3 @ X2)))), inference(apply_def,[status(thm)],[replAx, exu])). 117.41/117.61 thf(c_0_332, axiom, (descrp)=(![X1:$i > $o]:(?[X1137:$i]:(X1 @ X1137&![X1138:$i]:(X1 @ X1138=>(X1137)=(X1138)))=>X1 @ (descr @ (^[X2:$i]:X1 @ X2)))), inference(apply_def,[status(thm)],[descrp, exu])). 117.41/117.61 thf(c_0_333, axiom, (exuE1)=(![X1:$i > $o]:(?[X1139:$i]:(X1 @ X1139&![X1140:$i]:(X1 @ X1140=>(X1139)=(X1140)))=>?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3))))), inference(apply_def,[status(thm)],[exuE1, exu])). 117.41/117.61 thf(c_0_334, axiom, (exuE3e)=(![X1:$i > $o]:(?[X1141:$i]:(X1 @ X1141&![X1142:$i]:(X1 @ X1142=>(X1141)=(X1142)))=>?[X2:$i]:X1 @ X2)), inference(apply_def,[status(thm)],[exuE3e, exu])). 117.41/117.61 thf(c_0_335, axiom, (nonemptyE1)=(![X4:$i]:((X4)!=(emptyset)=>?[X2:$i]:in @ X2 @ X4)), inference(apply_def,[status(thm)],[nonemptyE1, nonempty])). 117.41/117.61 thf(c_0_336, axiom, (nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>(dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))!=(emptyset)))), inference(apply_def,[status(thm)],[nonemptyI, nonempty])). 117.41/117.61 thf(c_0_337, axiom, (nonemptyI1)=(![X4:$i]:(?[X2:$i]:in @ X2 @ X4=>(X4)!=(emptyset))), inference(apply_def,[status(thm)],[nonemptyI1, nonempty])). 117.41/117.61 thf(c_0_338, axiom, (exuE2)=(![X1:$i > $o]:(?[X1143:$i]:(X1 @ X1143&![X1144:$i]:(X1 @ X1144=>(X1143)=(X1144)))=>?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2)))), inference(apply_def,[status(thm)],[exuE2, exu])). 117.41/117.61 thf(c_0_339, axiom, (nonemptyImpWitness)=(![X4:$i]:((X4)!=(emptyset)=>?[X2:$i]:(in @ X2 @ X4&$true))), inference(apply_def,[status(thm)],[nonemptyImpWitness, nonempty])). 117.41/117.61 thf(c_0_340, axiom, (exuI1)=(![X1:$i > $o]:(?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3)))=>?[X1145:$i]:(X1 @ X1145&![X1146:$i]:(X1 @ X1146=>(X1145)=(X1146))))), inference(apply_def,[status(thm)],[exuI1, exu])). 117.41/117.61 thf(c_0_341, axiom, (exuI3)=(![X1:$i > $o]:(?[X2:$i]:X1 @ X2=>(![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3)))=>?[X1147:$i]:(X1 @ X1147&![X1148:$i]:(X1 @ X1148=>(X1147)=(X1148)))))), inference(apply_def,[status(thm)],[exuI3, exu])). 117.41/117.61 thf(c_0_342, axiom, (exuI2)=(![X1:$i > $o]:(?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2))=>?[X1149:$i]:(X1 @ X1149&![X1150:$i]:(X1 @ X1150=>(X1149)=(X1150))))), inference(apply_def,[status(thm)],[exuI2, exu])). 117.41/117.61 thf(c_0_343, axiom, (exuE3u)=(![X1:$i > $o]:(?[X1151:$i]:(X1 @ X1151&![X1152:$i]:(X1 @ X1152=>(X1151)=(X1152)))=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))), inference(apply_def,[status(thm)],[exuE3u, exu])). 117.41/117.61 thf(c_0_344, axiom, (exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(?[X1153:$i]:(X1 @ X1153&![X1154:$i]:(X1 @ X1154=>(X1153)=(X1154)))<=>?[X1155:$i]:(X17 @ X1155&![X1156:$i]:(X17 @ X1156=>(X1155)=(X1156)))))), inference(apply_def,[status(thm)],[exu__Cong, exu])). 117.41/117.61 thf(c_0_345, axiom, (exuEu)=(![X1:$i > $o]:(?[X1157:$i]:(X1 @ X1157&![X1158:$i]:(X1 @ X1158=>(X1157)=(X1158)))=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))), inference(apply_def,[status(thm)],[exuEu, exu])). 117.41/117.61 thf(c_0_346, axiom, (descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(?[X1159:$i]:(X1 @ X1159&![X1160:$i]:(X1 @ X1160=>(X1159)=(X1160)))=>(?[X1161:$i]:(X17 @ X1161&![X1162:$i]:(X17 @ X1162=>(X1161)=(X1162)))=>(descr @ (^[X2:$i]:X1 @ X2))=(descr @ (^[X2:$i]:X17 @ X2)))))), inference(apply_def,[status(thm)],[descr__Cong, exu])). 117.41/117.61 thf(c_0_347, axiom, (image1Ex1)=(![X4:$i, X58:$i > $i]:?[X1163:$i]:(![X1168:$i]:(in @ X1168 @ X1163<=>?[X1169:$i]:(in @ X1169 @ X4&(X1168)=(X58 @ X1169)))&![X1166:$i]:(![X1170:$i]:(in @ X1170 @ X1166<=>?[X1171:$i]:(in @ X1171 @ X4&(X1170)=(X58 @ X1171)))=>(X1163)=(X1166)))), inference(apply_def,[status(thm)],[image1Ex1, exu])). 117.41/117.61 thf(c_0_348, axiom, (foundation2)=(![X4:$i]:((X4)!=(emptyset)=>?[X21:$i]:(in @ X21 @ X4&(binintersect @ X21 @ X4)=(emptyset)))), inference(apply_def,[status(thm)],[foundation2, nonempty])). 117.41/117.61 thf(c_0_349, plain, ![X3:$i, X1:$i > $o]:(epred1_2 @ X1 @ X3<=>X1 @ X3), introduced(definition)). 117.41/117.61 thf(c_0_350, plain, ![X2:$i]:epred9_1 @ X2, inference(fof_simplification,[status(thm)],[introduced(definition)])). 117.41/117.61 thf(c_0_351, plain, ![X18:$i, X14:$i, X22:$i > $i > $o]:(epred4_3 @ X22 @ X14 @ X18<=>X22 @ X14 @ X18), introduced(definition)). 117.41/117.61 thf(c_0_352, plain, ![X3:$i, X29:$i, X2:$i]:(epred8_3 @ X2 @ X29 @ X3<=>in @ (kpair @ X2 @ X3) @ X29), introduced(definition)). 117.41/117.61 thf(c_0_353, plain, ![X3:$i, X2:$i, X30:$i > $i]:(epred7_3 @ X30 @ X2 @ X3<=>(X30 @ X2)=(X3)), introduced(definition)). 117.41/117.61 thf(c_0_354, plain, ![X2:$i, X31:$i > $i]:(esk1_2 @ X31 @ X2)=(X31 @ X2), introduced(definition)). 117.41/117.61 thf(c_0_355, plain, ![X14:$i, X2:$i, X39:$o, X3:$i]:(epred5_4 @ X3 @ X39 @ X2 @ X14<=>((X39&(X14)=(X2))|(~X39&(X14)=(X3)))), inference(fof_simplification,[status(thm)],[introduced(definition)])). 117.41/117.61 thf(c_0_356, plain, ![X3:$i, X52:$i > $i > $o, X33:$i, X5:$i, X2:$i]:(epred6_5 @ X2 @ X5 @ X33 @ X52 @ X3<=>(X52 @ X2 @ X3&![X14:$i]:(in @ X14 @ X5=>(X52 @ X2 @ X14=>in @ (kpair @ X3 @ X14) @ X33)))), introduced(definition)). 117.41/117.61 thf(c_0_357, plain, ![X2:$i, X18:$i]:(epred3_2 @ X18 @ X2<=>(X18)=(kpair @ (kfst @ X18) @ X2)), introduced(definition)). 117.41/117.61 thf(c_0_358, plain, ![X2:$i, X18:$i]:(epred2_2 @ X18 @ X2<=>in @ (setadjoin @ X2 @ emptyset) @ X18), introduced(definition)). 117.41/117.61 thf(c_0_359, plain, (epred10_0<=>![X4:$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)). 117.41/117.61 thf(c_0_360, 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:$i]:(in @ X2 @ X4=>?[X1134:$i]:(X6 @ X2 @ X1134&![X1136:$i]:(X6 @ X2 @ X1136=>(X1134)=(X1136))))=>?[X5:$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 > $o]:(?[X1137:$i]:(X1 @ X1137&![X1138:$i]:(X1 @ X1138=>(X1137)=(X1138)))=>X1 @ (descr @ (epred1_2 @ X1)))=>(![X4:$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 > $o]:(?[X1139:$i]:(X1 @ X1139&![X1140:$i]:(X1 @ X1140=>(X1139)=(X1140)))=>?[X2:$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 > $o]:(?[X1141:$i]:(X1 @ X1141&![X1142:$i]:(X1 @ X1142=>(X1141)=(X1142)))=>?[X2:$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:$i]:(dsetconstr @ X4 @ epred9_1)=(X4)=>(![X4:$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 > $o]:(?[X1143:$i]:(X1 @ X1143&![X1144:$i]:(X1 @ X1144=>(X1143)=(X1144)))=>?[X2:$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 @ 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setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_331]), foundationAx]), wellorderingAx]), c_0_332]), dsetconstrI]), dsetconstrEL]), dsetconstrER]), c_0_333]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_334]), setext]), emptyI]), noeltsimpempty]), setbeta]), c_0_335]), c_0_336]), c_0_337]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), setoftrueEq]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_338]), c_0_339]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), emptyE1]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_340]), c_0_341]), c_0_342]), inCongP]), in__Cong]), c_0_343]), c_0_344]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_345]), c_0_346]), 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_347]), image1Equiv]), image1E]), image1I]), injFuncInInjFuncSet]), injFuncSetFuncIn]), injFuncSetFuncInj]), surjFuncSetFuncIn]), surjFuncSetFuncSurj]), leftInvIsSurj]), surjCantorThm]), c_0_348]), notinself]), notinself2]), omegaSp]), omegaSclos]), peano0notS]), c_0_349]), c_0_350]), c_0_349]), c_0_349]), c_0_351]), c_0_351]), c_0_351]), c_0_351]), c_0_352]), c_0_352]), c_0_353]), c_0_354]), c_0_349]), c_0_354]), c_0_354]), c_0_355]), c_0_355]), c_0_356]), c_0_351]), c_0_354]), c_0_354]), c_0_354]), c_0_355]), c_0_355]), c_0_355]), c_0_354]), c_0_354]), c_0_354]), c_0_354]), c_0_354]), c_0_351]), c_0_351]), c_0_351]), c_0_357]), c_0_358]), c_0_349]), c_0_349]), c_0_349]), c_0_349]), c_0_349]), c_0_349]), c_0_349]), c_0_349]), c_0_349]), c_0_349]), c_0_349]), c_0_349]), c_0_349]), c_0_349])])]), c_0_359])). 117.41/117.61 thf(c_0_361, plain, ![X2:$i]:(omegaS @ X2)=(setadjoin @ X2 @ X2), inference(fof_simplification,[status(thm)],[omegaS])). 117.41/117.61 thf(c_0_362, negated_conjecture, ![X1173:$i, X1174:$i, X1176:$i, X1177:$i, X1178:$i, X1179:$i, X1180:$i, X1181:$i, X1182:$i, X1183:$i, X1184:$i, X1186:$i, X1187:$i, X1189:$i, X1190:$i, X1191:$i, X1192:$i, X1193:$i, X1195:$i, X1196:$i > $i > $o, X1197:$i, X1199:$i, X1202:$i, X1204:$i, X1205:$i, X1206:$i, X1207:$i, X1209:$i, X1210:$i > $o, X1211:$i, X1213:$i, X1214:$i > $o, X1215:$i, X1216:$i, X1217:$i > $o, X1218:$i, X1219:$i, X1220:$i > $o, X1221:$i, X1222:$i > $o, X1223:$i, X1226:$i, X1227:$o, X1228:$i, X1229:$i, X1230:$o, X1231:$i, X1232:$i, X1233:$i > $o, X1234:$i, X1237:$i, X1238:$i, X1241:$i, X1243:$i, X1245:$i, X1246:$i > $o, X1247:$i, X1248:$i, X1250:$i, X1251:$i > $o, X1252:$i, X1253:$i, X1254:$i, X1255:$i, X1256:$i, X1257:$i, X1258:$i, X1259:$i, X1260:$i, X1261:$i, X1262:$i, X1263:$o, X1264:$i, X1265:$i, X1266:$i, X1267:$i, X1268:$i, X1269:$i, X1271:$i, X1272:$i, X1273:$i, X1274:$i, X1275:$i, X1276:$i, X1277:$i, X1278:$i, X1279:$i, X1280:$i, X1281:$o, X1283:$i, X1284:$i, X1285:$i > $o, X1286:$i, X1289:$i, X1290:$i, X1291:$i, X1293:$i, X1294:$i, X1295:$i, X1296:$i, X1297:$i, X1298:$i, X1299:$i, X1300:$i, X1301:$i, X1302:$i, X1303:$i, X1304:$i, X1305:$i, X1306:$i, X1307:$i, X1308:$i, X1309:$i > $o, X1310:$i, X1311:$i > $o, X1312:$i, X1313:$i, X1314:$i > $o, X1315:$i, X1317:$i, X1318:$i > $o, X1320:$i, X1321:$i, X1322:$i > $o, X1324:$i, X1325:$i, X1326:$i > $o, X1327:$i, X1329:$o, X1330:$o, X1331:$i, X1332:$i > $o, X1334:$i, X1335:$i, X1336:$i > $o, X1337:$i, X1339:$i > $o, X1340:$i, X1343:$i, X1344:$i > $o, X1345:$i, X1349:$i, X1350:$i > $o, X1351:$i, X1354:$i, X1355:$i, X1356:$i, X1357:$i, X1358:$i, X1359:$i, X1360:$i, X1361:$i, X1362:$i, X1363:$i > $o, X1364:$i, X1366:$i, X1367:$i, X1368:$i > $o, X1369:$i > $o, X1372:$i, X1375:$i, X1376:$i, X1379:$i, X1380:$i, X1381:$i, X1382:$i, X1383:$i, X1384:$i, X1385:$i, X1386:$i, X1387:$i, X1388:$i > $o, X1389:$i, X1391:$i, X1392:$i, X1393:$i > $o, X1394:$i > $o, X1397:$i, X1399:$i, X1401:$i, X1402:$i, X1403:$i > $o, X1404:$i > $o, X1407:$i, X1408:$i, X1410:$i, X1411:$i, X1412:$i, X1413:$i, X1414:$i, X1415:$i, X1417:$i, X1418:$i, X1419:$i, X1420:$i, X1421:$i, X1422:$i, X1423:$i, X1424:$i, X1425:$i, X1426:$i, X1427:$i, X1428:$i, X1429:$i, X1430:$i, X1431:$i, X1432:$i, X1433:$i, X1434:$i, X1435:$i, X1436:$i, X1437:$i, X1438:$i, X1439:$i, X1440:$i, X1441:$i, X1442:$i, X1443:$i, X1444:$i, X1445:$i, X1446:$i, X1447:$i, X1448:$i, X1449:$i, X1450:$i, X1451:$i, X1452:$i, X1453:$i, X1454:$i > $o, X1455:$i, X1456:$i > $o, X1457:$i, X1458:$i, X1459:$i, X1460:$i, X1461:$i, X1462:$i, X1463:$i, X1464:$i, X1465:$i, X1466:$i, X1467:$i, X1468:$o, X1469:$i, X1470:$i, X1471:$i, X1472:$i, X1473:$i, X1474:$i, X1475:$i, X1476:$i, X1477:$i, X1478:$i, X1479:$i, X1480:$i, X1481:$i, X1482:$i, X1483:$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, 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:$i, X1522:$i, X1523:$i, X1524:$i, X1525:$i, X1526:$i, X1527:$i, X1528:$i, X1529:$i, X1530:$i, X1531:$i, X1532:$i, X1533:$i, X1534:$i, X1535:$i, X1536:$o, 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, X1563:$i, X1564:$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:$i, X1598:$i, X1599:$i, X1600:$i, X1601:$i, X1602:$i, X1604:$i, X1605:$i, X1606:$i, X1607:$i, X1608:$i > $o, X1611:$i, X1612:$i, X1613:$i > $o, X1615:$i, X1616:$i > $o, X1617:$i, X1619:$i, X1620:$i > $o, X1623:$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:$i, X1663:$i, X1664:$i, X1665:$i, X1666:$i, X1667:$i, X1668:$i, X1669:$i, X1670:$i, X1671:$i, X1672:$i, X1673:$i, X1674:$i, X1675:$i, X1676:$i, X1677:$i, X1678:$i, X1679:$i, X1680:$i, X1681:$i, X1682:$i, X1683:$i, X1684:$i, X1685:$i, X1686:$i, X1687:$i, X1688:$i, X1689:$i, X1690:$i, X1691:$i, X1692:$i, X1693:$i, X1694:$i, X1695:$i > $i > $o, X1696:$i, X1697:$i, X1698:$i, X1699:$i, X1700:$i > $i > $o, X1701:$i, X1702:$i, X1703:$i > $i > $o, X1704:$i, X1705:$i, X1706:$i > $i > $o, X1707:$i, X1708:$i, X1709:$i, X1710:$i, X1711:$i > $i > $o, X1712:$i, X1713:$i, X1714:$i, X1715:$i, X1716:$i > $i > $o, X1717:$i, X1718:$i, X1719:$i, X1720:$i, X1721:$i > $i > $o, X1722:$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 > $i, X1750:$i, X1751:$i, X1752:$i > $i, X1754:$i, X1755:$i, X1756:$i > $i, X1758:$i, X1759:$i, X1760:$i, X1761:$i > $o, X1764:$i, X1765:$i, X1766:$i, X1767:$i, X1768:$i > $o, X1771:$i, X1772:$i, X1773:$i > $o, X1774:$i, X1775:$i, X1776:$i, X1777:$i, X1778:$i, X1779:$i, X1780:$i, X1781:$i, X1782:$i, X1783:$i, X1784:$i, X1785:$i, X1786:$i, X1787:$i, X1788:$i, X1789:$i, X1790:$i, X1791:$i, X1792:$i, X1794:$i, X1795:$i, X1796:$i, X1797:$i, X1798:$i, X1799:$i, X1800:$i, X1801:$i, X1802:$i, X1803:$i, X1804:$i, X1807:$i, X1808:$i, X1809:$i, X1810:$i, X1815:$i, X1816:$i, X1817:$i, X1818:$i, X1820:$i, X1821:$i, X1822:$i, X1823:$i, X1825:$i, X1826:$i, X1827:$i, X1828:$i, X1829:$i, X1830:$i, X1831:$i, X1832:$i, X1833:$i, X1834:$i, X1835:$i > $i, X1837:$i, X1838:$i, X1839:$i, X1840:$i, X1841:$i, X1842:$i, X1843:$i > $i, X1845:$i, X1846:$i, X1847:$i > $i, X1849:$i, X1850:$i, X1851:$i, X1852:$i, X1853:$i, X1854:$o, X1855:$i, X1856:$i, X1857:$i, X1858:$o, X1859:$i, X1860:$i, X1861:$i, X1862:$o, X1863:$i, X1864:$i, X1865:$i, X1866:$o, X1867:$i, X1868:$i, X1869:$i, X1870:$o, X1871:$i, X1872:$i, X1873:$i, X1874:$o, X1875:$i, X1876:$i, X1877:$i, X1878:$i, X1879:$i, X1880:$o, X1881:$i, X1882:$i, X1883:$i, X1884:$o, X1885:$i, X1886:$i, X1887:$i, X1888:$o, X1889:$i, X1890:$i, X1891:$i, X1892:$i, X1893:$i, X1894:$i, X1895:$i, X1896:$i, X1897:$i, X1898:$i, X1899:$i, X1900:$i, X1901:$i, X1902:$i, X1903:$i, X1904:$i, X1905:$i, X1906:$i, X1909:$i, X1910:$i, X1911:$i, X1913:$i, X1914:$i, X1915:$i, X1917:$i, X1918:$i, X1919:$i, X1920:$i, X1921:$i, X1922:$i, X1923:$i, X1924:$i, X1925:$i, X1926:$i, X1927:$i, X1928:$i, X1929:$i, X1930:$i, X1931:$i, X1932:$i, X1933:$i, X1934:$i, X1935:$i, X1936:$i, X1937:$i, X1938:$i, X1939:$i, X1940:$i, X1941:$i, X1942:$i, X1943:$i, X1944:$i, X1945:$i, X1946:$i, X1947:$i, X1948:$i, X1949:$i, X1950:$i, X1951:$i, X1952:$i, X1953:$i, X1954:$i, X1955:$i, 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, X1974:$i, X1975:$i, X1976:$i, X1977:$i, X1978:$i, X1979:$i, X1980:$i, X1981:$i, X1982:$i, X1983:$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:$o, X2021:$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:$i, X2087:$i, 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 > $o, X2107:$i, X2108:$i, X2109:$i, X2110:$i, X2111:$i, X2112:$i > $i > $o, X2114:$i, X2115:$i, X2116:$i, X2117:$i, X2118:$i > $i > $o, X2119:$i, X2120:$i, X2121:$i > $o, X2124:$i, X2125:$i, X2126:$i, X2127:$i, X2130:$i, X2131:$i, X2132:$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, X2162:$i, X2163:$i, X2164:$i, X2165:$i, X2166:$i, X2167:$o, X2169:$i, X2170:$i, X2171:$i, X2172:$i, X2173:$i, X2174:$i, X2175:$i, X2176:$i, X2177:$i, X2178:$i, X2179:$i, X2180:$i, X2181:$i, X2182:$i, X2183:$i, X2184:$i, X2185:$i, X2186:$i, X2187:$i, X2188:$i, X2189:$i, X2190:$i, X2191:$i, X2192:$i, X2193:$i, X2194:$i, X2195:$i, X2196:$i, X2197:$o, X2198:$i, X2199:$i, X2200:$i, X2201:$i, X2202:$i, X2203:$i, X2204:$i, X2205:$i, X2206:$i, X2207:$i, X2208:$i, X2209:$i, X2210:$i, X2211:$i, X2212:$i, X2213:$i, X2214:$i, X2215:$i > $i, X2217:$i, X2219:$i, X2220:$i, X2221:$i, X2222:$i > $i, X2224:$i, X2226:$i, X2227:$i, X2228:$i, X2230:$i, X2232:$i, X2233:$i > $i, X2234:$i, X2236:$i, X2237:$i > $i, X2238:$i, X2239:$i, X2240:$i, X2241:$i > $i, X2242:$i, X2244:$i, X2245:$i > $i, X2246:$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:$i, X2264:$i, X2265:$i > $i, X2267:$i, X2269:$i, X2270:$i, X2271:$i, X2273:$i, X2274:$i, X2275:$i, X2276:$i, X2277:$i, X2278:$i]:(((~in @ (esk2_2 @ X1173 @ X1174) @ X1173|~in @ (esk2_2 @ X1173 @ X1174) @ X1174|(X1173)=(X1174))&(in @ (esk2_2 @ X1173 @ X1174) @ X1173|in @ (esk2_2 @ X1173 @ X1174) @ X1174|(X1173)=(X1174)))&(~in @ X1176 @ emptyset&(((~in @ X1179 @ (setadjoin @ X1177 @ X1178)|((X1179)=(X1177)|in @ X1179 @ X1178))&(((X1179)!=(X1177)|in @ X1179 @ (setadjoin @ X1177 @ X1178))&(~in @ X1179 @ X1178|in @ X1179 @ (setadjoin @ X1177 @ X1178))))&(((~in @ X1181 @ (powerset @ X1180)|(~in @ X1182 @ X1181|in @ X1182 @ X1180))&((in @ (esk3_2 @ X1183 @ X1184) @ X1184|in @ X1184 @ (powerset @ X1183))&(~in @ (esk3_2 @ X1183 @ X1184) @ X1183|in @ X1184 @ (powerset @ X1183))))&((((in @ X1187 @ (esk4_2 @ X1186 @ X1187)|~in @ X1187 @ (setunion @ X1186))&(in @ (esk4_2 @ X1186 @ X1187) @ X1186|~in @ X1187 @ (setunion @ X1186)))&(~in @ X1190 @ X1191|~in @ X1191 @ X1189|in @ X1190 @ (setunion @ X1189)))&(in @ emptyset @ omega&((~in @ X1192 @ omega|in @ (setadjoin @ X1192 @ X1192) @ omega)&((((in @ (esk5_1 @ X1193) @ omega|~in @ emptyset @ X1193|(~in @ X1195 @ omega|in @ X1195 @ X1193))&(in @ (esk5_1 @ X1193) @ X1193|~in @ emptyset @ X1193|(~in @ X1195 @ omega|in @ X1195 @ X1193)))&(~in @ (setadjoin @ (esk5_1 @ X1193) @ (esk5_1 @ X1193)) @ X1193|~in @ emptyset @ X1193|(~in @ X1195 @ omega|in @ X1195 @ X1193)))&(((((in @ (esk9_3 @ X1196 @ X1197 @ X1202) @ X1197|~in @ X1202 @ (esk8_2 @ X1196 @ X1197)|in @ (esk6_2 @ X1196 @ X1197) @ X1197)&(X1196 @ (esk9_3 @ X1196 @ X1197 @ X1202) @ X1202|~in @ X1202 @ (esk8_2 @ X1196 @ X1197)|in @ (esk6_2 @ X1196 @ X1197) @ X1197))&(~in @ X1205 @ X1197|~X1196 @ X1205 @ X1204|in @ X1204 @ (esk8_2 @ X1196 @ X1197)|in @ (esk6_2 @ X1196 @ X1197) @ X1197))&((((in @ (esk9_3 @ X1196 @ X1197 @ X1202) @ X1197|~in @ X1202 @ (esk8_2 @ X1196 @ X1197)|(X1196 @ (esk6_2 @ X1196 @ X1197) @ (esk7_3 @ X1196 @ X1197 @ X1199)|~X1196 @ (esk6_2 @ X1196 @ X1197) @ X1199))&(X1196 @ (esk9_3 @ X1196 @ X1197 @ X1202) @ X1202|~in @ X1202 @ (esk8_2 @ X1196 @ X1197)|(X1196 @ (esk6_2 @ X1196 @ X1197) @ (esk7_3 @ X1196 @ X1197 @ X1199)|~X1196 @ (esk6_2 @ X1196 @ X1197) @ X1199)))&(~in @ X1205 @ X1197|~X1196 @ X1205 @ X1204|in @ X1204 @ (esk8_2 @ X1196 @ X1197)|(X1196 @ (esk6_2 @ X1196 @ X1197) @ (esk7_3 @ X1196 @ X1197 @ X1199)|~X1196 @ (esk6_2 @ X1196 @ X1197) @ X1199)))&(((in @ (esk9_3 @ X1196 @ X1197 @ X1202) @ X1197|~in @ X1202 @ (esk8_2 @ X1196 @ X1197)|((X1199)!=(esk7_3 @ X1196 @ X1197 @ X1199)|~X1196 @ (esk6_2 @ X1196 @ X1197) @ X1199))&(X1196 @ (esk9_3 @ X1196 @ X1197 @ X1202) @ X1202|~in @ X1202 @ (esk8_2 @ X1196 @ X1197)|((X1199)!=(esk7_3 @ 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X2127|~breln1 @ X2125 @ X2126)&(~in @ (kpair @ (esk93_3 @ X2125 @ X2126 @ X2127) @ (esk94_3 @ X2125 @ X2126 @ X2127)) @ X2127|subset @ X2126 @ X2127|~breln1 @ X2125 @ X2127|~breln1 @ X2125 @ X2126))))&((((in @ (esk97_3 @ X2130 @ X2131 @ X2132) @ X2130|(X2131)=(X2132)|in @ (esk95_3 @ X2130 @ X2131 @ X2132) @ X2130|~breln1 @ X2130 @ X2132|~breln1 @ X2130 @ X2131)&((in @ (esk98_3 @ X2130 @ X2131 @ X2132) @ X2130|(X2131)=(X2132)|in @ (esk95_3 @ X2130 @ X2131 @ X2132) @ X2130|~breln1 @ X2130 @ X2132|~breln1 @ X2130 @ X2131)&((in @ (kpair @ (esk97_3 @ X2130 @ X2131 @ X2132) @ (esk98_3 @ X2130 @ X2131 @ X2132)) @ X2132|(X2131)=(X2132)|in @ (esk95_3 @ X2130 @ X2131 @ X2132) @ X2130|~breln1 @ X2130 @ X2132|~breln1 @ X2130 @ X2131)&(~in @ (kpair @ (esk97_3 @ X2130 @ X2131 @ X2132) @ (esk98_3 @ X2130 @ X2131 @ X2132)) @ X2131|(X2131)=(X2132)|in @ (esk95_3 @ X2130 @ X2131 @ X2132) @ X2130|~breln1 @ X2130 @ X2132|~breln1 @ X2130 @ X2131))))&(((in @ (esk97_3 @ X2130 @ X2131 @ X2132) @ X2130|(X2131)=(X2132)|in @ (esk96_3 @ X2130 @ X2131 @ X2132) @ X2130|~breln1 @ X2130 @ X2132|~breln1 @ X2130 @ X2131)&((in @ (esk98_3 @ X2130 @ X2131 @ X2132) @ X2130|(X2131)=(X2132)|in @ (esk96_3 @ X2130 @ X2131 @ X2132) @ X2130|~breln1 @ X2130 @ X2132|~breln1 @ X2130 @ X2131)&((in @ (kpair @ (esk97_3 @ X2130 @ X2131 @ X2132) @ (esk98_3 @ X2130 @ X2131 @ X2132)) @ X2132|(X2131)=(X2132)|in @ (esk96_3 @ X2130 @ X2131 @ X2132) @ X2130|~breln1 @ X2130 @ X2132|~breln1 @ X2130 @ X2131)&(~in @ (kpair @ (esk97_3 @ X2130 @ X2131 @ X2132) @ (esk98_3 @ X2130 @ X2131 @ X2132)) @ X2131|(X2131)=(X2132)|in @ (esk96_3 @ X2130 @ X2131 @ X2132) @ X2130|~breln1 @ X2130 @ X2132|~breln1 @ X2130 @ X2131))))&(((in @ (esk97_3 @ X2130 @ X2131 @ X2132) @ X2130|(X2131)=(X2132)|in @ (kpair @ (esk95_3 @ X2130 @ X2131 @ X2132) @ (esk96_3 @ X2130 @ X2131 @ X2132)) @ X2131|~breln1 @ X2130 @ X2132|~breln1 @ X2130 @ X2131)&((in @ (esk98_3 @ X2130 @ X2131 @ X2132) @ X2130|(X2131)=(X2132)|in @ (kpair @ (esk95_3 @ X2130 @ X2131 @ X2132) @ (esk96_3 @ X2130 @ X2131 @ X2132)) @ X2131|~breln1 @ X2130 @ X2132|~breln1 @ X2130 @ X2131)&((in @ (kpair @ (esk97_3 @ X2130 @ X2131 @ X2132) @ (esk98_3 @ X2130 @ X2131 @ X2132)) @ X2132|(X2131)=(X2132)|in @ (kpair @ (esk95_3 @ X2130 @ X2131 @ X2132) @ (esk96_3 @ X2130 @ X2131 @ X2132)) @ X2131|~breln1 @ X2130 @ X2132|~breln1 @ X2130 @ X2131)&(~in @ (kpair @ (esk97_3 @ X2130 @ X2131 @ X2132) @ (esk98_3 @ X2130 @ X2131 @ X2132)) @ X2131|(X2131)=(X2132)|in @ (kpair @ (esk95_3 @ X2130 @ X2131 @ X2132) @ (esk96_3 @ X2130 @ X2131 @ X2132)) @ X2131|~breln1 @ X2130 @ X2132|~breln1 @ X2130 @ X2131))))&((in @ (esk97_3 @ X2130 @ X2131 @ X2132) @ X2130|(X2131)=(X2132)|~in @ (kpair @ (esk95_3 @ X2130 @ X2131 @ X2132) @ (esk96_3 @ X2130 @ X2131 @ X2132)) @ X2132|~breln1 @ X2130 @ X2132|~breln1 @ X2130 @ X2131)&((in @ (esk98_3 @ X2130 @ X2131 @ X2132) @ X2130|(X2131)=(X2132)|~in @ (kpair @ (esk95_3 @ X2130 @ X2131 @ X2132) @ (esk96_3 @ X2130 @ X2131 @ X2132)) @ X2132|~breln1 @ X2130 @ X2132|~breln1 @ X2130 @ X2131)&((in @ (kpair @ (esk97_3 @ X2130 @ X2131 @ X2132) @ (esk98_3 @ X2130 @ X2131 @ X2132)) @ X2132|(X2131)=(X2132)|~in @ (kpair @ (esk95_3 @ X2130 @ X2131 @ X2132) @ (esk96_3 @ X2130 @ X2131 @ X2132)) @ X2132|~breln1 @ X2130 @ X2132|~breln1 @ X2130 @ X2131)&(~in @ (kpair @ (esk97_3 @ X2130 @ X2131 @ X2132) @ (esk98_3 @ X2130 @ X2131 @ X2132)) @ X2131|(X2131)=(X2132)|~in @ (kpair @ (esk95_3 @ X2130 @ X2131 @ X2132) @ (esk96_3 @ X2130 @ X2131 @ X2132)) @ X2132|~breln1 @ X2130 @ X2132|~breln1 @ X2130 @ X2131)))))))&((~breln1 @ X2137 @ X2138|breln1 @ X2137 @ (breln1invset @ X2137 @ X2138))&((~breln1 @ X2139 @ X2140|(~in @ X2141 @ X2139|(~in @ X2142 @ X2139|(~in @ (kpair @ X2141 @ X2142) @ X2140|in @ (kpair @ X2142 @ X2141) @ (breln1invset @ X2139 @ X2140)))))&((~breln1 @ X2143 @ X2144|(~in @ X2145 @ X2143|(~in @ X2146 @ X2143|(~in @ (kpair @ X2146 @ X2145) @ (breln1invset @ X2143 @ X2144)|in @ (kpair @ X2145 @ X2146) @ X2144))))&((~breln1 @ X2147 @ X2148|(~breln1 @ X2147 @ X2149|breln1 @ X2147 @ (breln1compset @ X2147 @ X2148 @ X2149)))&((~breln1 @ X2150 @ X2151|(~breln1 @ X2150 @ X2152|(~in @ X2153 @ X2150|(~in @ X2154 @ X2150|(~in @ X2155 @ X2150|(~in @ (kpair @ X2153 @ X2155) @ X2151|(~in @ (kpair @ X2155 @ X2154) @ X2152|in @ (kpair @ X2153 @ X2154) @ (breln1compset @ X2150 @ X2151 @ X2152))))))))&((((in @ (esk99_5 @ X2156 @ X2157 @ X2158 @ X2159 @ X2160) @ X2156|~in @ (kpair @ X2159 @ X2160) @ (breln1compset @ X2156 @ X2157 @ X2158)|~in @ X2160 @ X2156|~in @ X2159 @ X2156|~breln1 @ X2156 @ X2158|~breln1 @ X2156 @ X2157)&(in @ (kpair @ X2159 @ (esk99_5 @ X2156 @ X2157 @ X2158 @ X2159 @ X2160)) @ X2157|~in @ (kpair @ X2159 @ X2160) @ (breln1compset @ X2156 @ X2157 @ X2158)|~in @ X2160 @ X2156|~in @ X2159 @ X2156|~breln1 @ X2156 @ X2158|~breln1 @ X2156 @ X2157))&(in @ (kpair @ (esk99_5 @ X2156 @ X2157 @ X2158 @ X2159 @ X2160) @ X2160) @ X2158|~in @ (kpair @ X2159 @ X2160) @ (breln1compset @ X2156 @ X2157 @ X2158)|~in @ X2160 @ X2156|~in @ X2159 @ X2156|~breln1 @ X2156 @ X2158|~breln1 @ X2156 @ X2157))&(((in @ (esk100_6 @ X2162 @ X2163 @ X2164 @ X2165 @ X2166 @ X2167) @ X2162|X2167|~in @ (kpair @ X2165 @ X2166) @ (breln1compset @ X2162 @ X2163 @ X2164)|~in @ X2166 @ X2162|~in @ X2165 @ X2162|~breln1 @ X2162 @ X2164|~breln1 @ X2162 @ X2163)&((in @ (kpair @ X2165 @ (esk100_6 @ X2162 @ X2163 @ X2164 @ X2165 @ X2166 @ X2167)) @ X2163|X2167|~in @ (kpair @ X2165 @ X2166) @ (breln1compset @ X2162 @ X2163 @ X2164)|~in @ X2166 @ X2162|~in @ X2165 @ X2162|~breln1 @ X2162 @ X2164|~breln1 @ X2162 @ X2163)&((in @ (kpair @ (esk100_6 @ X2162 @ X2163 @ X2164 @ X2165 @ X2166 @ X2167) @ X2166) @ X2164|X2167|~in @ (kpair @ X2165 @ X2166) @ (breln1compset @ X2162 @ X2163 @ X2164)|~in @ X2166 @ X2162|~in @ X2165 @ X2162|~breln1 @ X2162 @ X2164|~breln1 @ X2162 @ X2163)&(~X2167|X2167|~in @ (kpair @ X2165 @ X2166) @ (breln1compset @ X2162 @ X2163 @ X2164)|~in @ X2166 @ X2162|~in @ X2165 @ X2162|~breln1 @ X2162 @ X2164|~breln1 @ X2162 @ X2163))))&((~breln1 @ X2169 @ X2170|(~breln1 @ X2169 @ X2171|breln1 @ X2169 @ (binunion @ X2170 @ X2171)))&((~breln1 @ X2172 @ X2173|(~breln1 @ X2172 @ X2174|(~in @ X2175 @ X2172|(~in @ X2176 @ X2172|(~in @ (kpair @ X2175 @ X2176) @ X2173|in @ (kpair @ X2175 @ X2176) @ (binunion @ X2173 @ X2174))))))&((~breln1 @ X2177 @ X2178|(~breln1 @ X2177 @ X2179|(~in @ X2180 @ X2177|(~in @ X2181 @ X2177|(~in @ (kpair @ X2180 @ X2181) @ X2179|in @ (kpair @ X2180 @ X2181) @ (binunion @ X2178 @ X2179))))))&(((~in @ (kpair @ X2185 @ X2186) @ X2183|in @ (kpair @ X2185 @ X2186) @ (binunion @ X2183 @ X2184)|~in @ X2186 @ X2182|~in @ X2185 @ X2182|~breln1 @ X2182 @ X2184|~breln1 @ X2182 @ X2183)&(~in @ (kpair @ X2185 @ X2186) @ X2184|in @ (kpair @ X2185 @ X2186) @ (binunion @ X2183 @ X2184)|~in @ X2186 @ X2182|~in @ X2185 @ X2182|~breln1 @ X2182 @ X2184|~breln1 @ X2182 @ X2183))&((~breln1 @ X2187 @ X2188|(~breln1 @ X2187 @ X2189|(~in @ X2190 @ X2187|(~in @ X2191 @ X2187|(~in @ (kpair @ X2190 @ X2191) @ (binunion @ X2188 @ X2189)|(in @ (kpair @ X2190 @ X2191) @ X2188|in @ (kpair @ X2190 @ X2191) @ X2189))))))&((((in @ (kpair @ X2195 @ X2196) @ X2194|X2197|in @ (kpair @ X2195 @ X2196) @ X2193|~in @ (kpair @ X2195 @ X2196) @ (binunion @ X2193 @ X2194)|~in @ X2196 @ X2192|~in @ X2195 @ X2192|~breln1 @ X2192 @ X2194|~breln1 @ X2192 @ X2193)&(~X2197|X2197|in @ (kpair @ X2195 @ X2196) @ X2193|~in @ (kpair @ X2195 @ X2196) @ (binunion @ X2193 @ X2194)|~in @ X2196 @ X2192|~in @ X2195 @ X2192|~breln1 @ X2192 @ X2194|~breln1 @ X2192 @ X2193))&((in @ (kpair @ X2195 @ X2196) @ X2194|X2197|~X2197|~in @ (kpair @ X2195 @ X2196) @ (binunion @ X2193 @ X2194)|~in @ X2196 @ X2192|~in @ X2195 @ X2192|~breln1 @ X2192 @ X2194|~breln1 @ X2192 @ X2193)&(~X2197|X2197|~X2197|~in @ (kpair @ X2195 @ X2196) @ (binunion @ X2193 @ X2194)|~in @ X2196 @ X2192|~in @ X2195 @ X2192|~breln1 @ X2192 @ X2194|~breln1 @ X2192 @ X2193)))&((~breln1 @ X2198 @ X2199|(~breln1 @ X2198 @ X2200|(binunion @ X2199 @ X2200)=(binunion @ X2200 @ X2199)))&((~breln1 @ X2201 @ X2202|(X2202)=(breln1invset @ X2201 @ (breln1invset @ X2201 @ X2202)))&((~breln1 @ X2203 @ X2204|(~breln1 @ X2203 @ X2205|(breln1invset @ X2203 @ (breln1compset @ X2203 @ X2204 @ X2205))=(breln1compset @ X2203 @ (breln1invset @ X2203 @ X2205) @ (breln1invset @ X2203 @ X2204))))&((~breln1 @ X2206 @ X2207|(~breln1 @ X2206 @ X2208|(~breln1 @ X2206 @ X2209|(breln1compset @ X2206 @ (binunion @ X2207 @ X2208) @ X2209)=(binunion @ (breln1compset @ X2206 @ X2207 @ X2209) @ (breln1compset @ X2206 @ X2208 @ X2209)))))&((~breln1 @ X2210 @ X2211|(~breln1 @ X2210 @ X2212|(~breln1 @ X2210 @ X2213|(breln1compset @ X2210 @ (binunion @ X2211 @ X2212) @ X2213)=(binunion @ (breln1invset @ X2210 @ (breln1compset @ X2210 @ (breln1invset @ X2210 @ X2213) @ (breln1invset @ X2210 @ X2212))) @ (breln1invset @ X2210 @ (breln1compset @ X2210 @ (breln1invset @ X2210 @ X2213) @ (breln1invset @ X2210 @ X2211)))))))&((((in @ (esk102_3 @ X2214 @ X2215 @ X2217) @ X2214|~in @ X2217 @ (esk101_2 @ X2214 @ X2215))&((X2217)=(X2215 @ (esk102_3 @ X2214 @ X2215 @ X2217))|~in @ X2217 @ (esk101_2 @ X2214 @ X2215)))&(~in @ X2220 @ X2214|(X2219)!=(X2215 @ X2220)|in @ X2219 @ (esk101_2 @ X2214 @ X2215)))&(((((in @ (esk104_3 @ X2221 @ X2222 @ X2224) @ X2221|~in @ X2224 @ (esk103_2 @ X2221 @ X2222))&((X2224)=(X2222 @ (esk104_3 @ X2221 @ X2222 @ X2224))|~in @ X2224 @ (esk103_2 @ X2221 @ X2222)))&(~in @ X2227 @ X2221|(X2226)!=(X2222 @ X2227)|in @ X2226 @ (esk103_2 @ X2221 @ X2222)))&((~in @ (esk105_3 @ X2221 @ X2222 @ X2228) @ X2228|(~in @ X2230 @ X2221|(esk105_3 @ X2221 @ X2222 @ X2228)!=(X2222 @ X2230))|(esk103_2 @ X2221 @ X2222)=(X2228))&((in @ (esk106_3 @ X2221 @ X2222 @ X2228) @ X2221|in @ (esk105_3 @ X2221 @ X2222 @ X2228) @ X2228|(esk103_2 @ X2221 @ X2222)=(X2228))&((esk105_3 @ X2221 @ X2222 @ X2228)=(X2222 @ (esk106_3 @ X2221 @ X2222 @ X2228))|in @ (esk105_3 @ X2221 @ X2222 @ X2228) @ X2228|(esk103_2 @ X2221 @ X2222)=(X2228)))))&((((in @ (esk107_3 @ X2232 @ X2233 @ X2234) @ X2232|~in @ X2234 @ (image1 @ X2232 @ (esk1_2 @ X2233)))&((X2234)=(X2233 @ (esk107_3 @ X2232 @ X2233 @ X2234))|~in @ X2234 @ (image1 @ X2232 @ (esk1_2 @ X2233))))&(~in @ X2239 @ X2236|(X2238)!=(X2237 @ X2239)|in @ X2238 @ (image1 @ X2236 @ (esk1_2 @ X2237))))&(((in @ (esk108_3 @ X2240 @ X2241 @ X2242) @ X2240|~in @ X2242 @ (image1 @ X2240 @ (esk1_2 @ X2241)))&((X2242)=(X2241 @ (esk108_3 @ X2240 @ X2241 @ X2242))|~in @ X2242 @ (image1 @ X2240 @ (esk1_2 @ X2241))))&((~in @ X2247 @ X2244|(X2246)!=(X2245 @ X2247)|in @ X2246 @ (image1 @ X2244 @ (esk1_2 @ X2245)))&((~in @ X2250 @ (funcSet @ X2248 @ X2249)|(~injective @ X2248 @ X2249 @ X2250|in @ X2250 @ (injFuncSet @ X2248 @ X2249)))&((~in @ X2253 @ (injFuncSet @ X2251 @ X2252)|in @ X2253 @ (funcSet @ X2251 @ X2252))&((~in @ X2256 @ (injFuncSet @ X2254 @ X2255)|injective @ X2254 @ X2255 @ X2256)&((~in @ X2259 @ (surjFuncSet @ X2257 @ X2258)|in @ X2259 @ (funcSet @ X2257 @ X2258))&((~in @ X2262 @ (surjFuncSet @ X2260 @ X2261)|surjective @ X2260 @ X2261 @ X2262)&((((in @ (esk110_4 @ X2263 @ X2264 @ X2265 @ X2267) @ X2263|surjective @ X2264 @ X2263 @ X2267|~in @ X2267 @ (funcSet @ X2264 @ X2263)|in @ (esk109_3 @ X2263 @ X2264 @ X2265) @ X2263)&((ap @ X2264 @ X2263 @ X2267 @ (X2265 @ (esk110_4 @ X2263 @ X2264 @ X2265 @ X2267)))!=(esk110_4 @ X2263 @ X2264 @ X2265 @ X2267)|surjective @ X2264 @ X2263 @ X2267|~in @ X2267 @ (funcSet @ X2264 @ X2263)|in @ (esk109_3 @ X2263 @ X2264 @ X2265) @ X2263))&((in @ (esk110_4 @ X2263 @ X2264 @ X2265 @ X2267) @ X2263|surjective @ X2264 @ X2263 @ X2267|~in @ X2267 @ (funcSet @ X2264 @ X2263)|~in @ (X2265 @ (esk109_3 @ X2263 @ X2264 @ X2265)) @ X2264)&((ap @ X2264 @ X2263 @ X2267 @ (X2265 @ (esk110_4 @ X2263 @ X2264 @ X2265 @ X2267)))!=(esk110_4 @ X2263 @ X2264 @ X2265 @ X2267)|surjective @ X2264 @ X2263 @ X2267|~in @ X2267 @ (funcSet @ X2264 @ X2263)|~in @ (X2265 @ (esk109_3 @ X2263 @ X2264 @ X2265)) @ X2264)))&((~in @ X2270 @ (funcSet @ X2269 @ (powerset @ X2269))|~surjective @ X2269 @ (powerset @ X2269) @ X2270)&(((in @ (esk111_1 @ X2271) @ X2271|(X2271)=(emptyset))&((binintersect @ (esk111_1 @ X2271) @ X2271)=(emptyset)|(X2271)=(emptyset)))&(~in @ X2273 @ X2273&((~in @ X2274 @ X2275|~in @ X2275 @ X2274)&((~in @ X2276 @ omega|in @ (omegaS @ X2276) @ omega)&((~in @ X2277 @ omega|in @ (setadjoin @ X2277 @ X2277) @ omega)&((~in @ X2278 @ omega|(omegaS @ X2278)!=(emptyset))&(in @ esk112_0 @ omega&(in @ esk113_0 @ omega&((omegaS @ esk112_0)=(omegaS @ esk113_0)&(esk112_0)!=(esk113_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_360])])])])])])). 117.41/117.62 thf(c_0_363, plain, ![X1172:$i]:(omegaS @ X1172)=(setadjoin @ X1172 @ X1172), inference(variable_rename,[status(thm)],[c_0_361])). 117.41/117.62 thf(c_0_364, negated_conjecture, (omegaS @ esk112_0)=(omegaS @ esk113_0), inference(split_conjunct,[status(thm)],[c_0_362])). 117.41/117.62 thf(c_0_365, plain, ![X2:$i]:(omegaS @ X2)=(setadjoin @ X2 @ X2), inference(split_conjunct,[status(thm)],[c_0_363])). 117.41/117.62 thf(c_0_366, negated_conjecture, ![X2:$i, X3:$i]:in @ X2 @ (setadjoin @ X2 @ X3), inference(split_conjunct,[status(thm)],[c_0_362])). 117.41/117.62 thf(c_0_367, negated_conjecture, (setadjoin @ esk112_0 @ esk112_0)=(setadjoin @ esk113_0 @ esk113_0), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_364, c_0_365]), c_0_365])). 117.41/117.62 thf(c_0_368, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(in @ X2 @ X3|(X2)=(X4)|~in @ X2 @ (setadjoin @ X4 @ X3)), inference(eliminate_boolean_vars,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_362])])])). 117.41/117.62 thf(c_0_369, negated_conjecture, in @ esk112_0 @ (setadjoin @ esk113_0 @ esk113_0), inference(spm,[status(thm)],[c_0_366, c_0_367])). 117.41/117.62 thf(c_0_370, negated_conjecture, (esk112_0)!=(esk113_0), inference(split_conjunct,[status(thm)],[c_0_362])). 117.41/117.62 thf(c_0_371, negated_conjecture, ![X3:$i, X2:$i]:(~in @ X2 @ X3|~in @ X3 @ X2), inference(split_conjunct,[status(thm)],[c_0_362])). 117.41/117.62 thf(c_0_372, negated_conjecture, in @ esk112_0 @ esk113_0, inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_368, c_0_369]), c_0_370])). 117.41/117.62 thf(c_0_373, negated_conjecture, ![X2:$i]:((X2)=(esk112_0)|in @ X2 @ esk112_0|~in @ X2 @ (setadjoin @ esk113_0 @ esk113_0)), inference(spm,[status(thm)],[c_0_368, c_0_367])). 117.41/117.62 thf(c_0_374, negated_conjecture, ~in @ esk113_0 @ esk112_0, inference(spm,[status(thm)],[c_0_371, c_0_372])). 117.41/117.62 thf(c_0_375, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_373, c_0_366]), c_0_370]), c_0_374]), ['proof']). 117.41/117.62 # SZS output end CNFRefutation 117.41/117.62 # Proof object total steps : 376 117.41/117.62 # Proof object clause steps : 12 117.41/117.62 # Proof object formula steps : 364 117.41/117.62 # Proof object conjectures : 14 117.41/117.62 # Proof object clause conjectures : 11 117.41/117.62 # Proof object formula conjectures : 3 117.41/117.62 # Proof object initial clauses used : 6 117.41/117.62 # Proof object initial formulas used : 331 117.41/117.62 # Proof object generating inferences : 5 117.41/117.62 # Proof object simplifying inferences : 6 117.41/117.62 # Training examples: 0 positive, 0 negative 117.41/117.62 # Parsed axioms : 715 117.41/117.62 # Removed by relevancy pruning/SinE : 0 117.41/117.62 # Initial clauses : 981 117.41/117.62 # Removed in clause preprocessing : 426 117.41/117.62 # Initial clauses in saturation : 555 117.41/117.62 # Processed clauses : 33985 117.41/117.62 # ...of these trivial : 781 117.41/117.62 # ...subsumed : 25515 117.41/117.62 # ...remaining for further processing : 7689 117.41/117.62 # Other redundant clauses eliminated : 34623 117.41/117.62 # Clauses deleted for lack of memory : 0 117.41/117.62 # Backward-subsumed : 122 117.41/117.62 # Backward-rewritten : 86 117.41/117.62 # Generated clauses : 562947 117.41/117.62 # ...of the previous two non-trivial : 515091 117.41/117.62 # Contextual simplify-reflections : 20 117.41/117.62 # Paramodulations : 495901 117.41/117.62 # Factorizations : 33 117.41/117.62 # NegExts : 954 117.41/117.62 # Equation resolutions : 34630 117.41/117.62 # Propositional unsat checks : 0 117.41/117.62 # Propositional check models : 0 117.41/117.62 # Propositional check unsatisfiable : 0 117.41/117.62 # Propositional clauses : 0 117.41/117.62 # Propositional clauses after purity: 0 117.41/117.62 # Propositional unsat core size : 0 117.41/117.62 # Propositional preprocessing time : 0.000 117.41/117.62 # Propositional encoding time : 0.000 117.41/117.62 # Propositional solver time : 0.000 117.41/117.62 # Success case prop preproc time : 0.000 117.41/117.62 # Success case prop encoding time : 0.000 117.41/117.62 # Success case prop solver time : 0.000 117.41/117.62 # Current number of processed clauses : 6953 117.41/117.62 # Positive orientable unit clauses : 569 117.41/117.62 # Positive unorientable unit clauses: 1 117.41/117.62 # Negative unit clauses : 2643 117.41/117.62 # Non-unit-clauses : 3740 117.41/117.62 # Current number of unprocessed clauses: 481153 117.41/117.62 # ...number of literals in the above : 1597593 117.41/117.62 # Current number of archived formulas : 0 117.41/117.62 # Current number of archived clauses : 714 117.41/117.62 # Clause-clause subsumption calls (NU) : 1221211 117.41/117.62 # Rec. Clause-clause subsumption calls : 842010 117.41/117.62 # Non-unit clause-clause subsumptions : 2810 117.41/117.62 # Unit Clause-clause subsumption calls : 1378642 117.41/117.62 # Rewrite failures with RHS unbound : 0 117.41/117.62 # BW rewrite match attempts : 2104 117.41/117.62 # BW rewrite match successes : 66 117.41/117.62 # Condensation attempts : 0 117.41/117.62 # Condensation successes : 0 117.41/117.62 # Termbank termtop insertions : 8964330 117.41/117.64 117.41/117.64 # ------------------------------------------------- 117.41/117.64 # User time : 114.726 s 117.41/117.64 # System time : 2.503 s 117.41/117.64 # Total time : 117.229 s 117.41/117.64 # Maximum resident set size: 2528 pages 117.41/117.64 EOF