0.12/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.17 % Command : eprover-ho %s --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --free-numbers -auto-schedule -p --cpu-limit=%d --neg-ext=all --pos-ext=all --ext-sup-max-depth=2 --schedule-kind=CASC 0.16/0.38 % Computer : n012.cluster.edu 0.16/0.38 % Model : x86_64 x86_64 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.16/0.38 % Memory : 8042.1875MB 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64 0.16/0.38 % CPULimit : 1200 0.16/0.38 % WCLimit : 120 0.16/0.38 % DateTime : Tue Jul 13 12:15:21 EDT 2021 0.16/0.38 % CPUTime : 0.16/0.38 % Number of cores: 8 0.16/0.38 % Python version: Python 3.6.8 0.16/0.39 # Version: 2.6rc1-ho 0.16/0.40 # No SInE strategy applied 0.16/0.40 # Trying AutoSched0 for 59 seconds 59.21/59.46 # AutoSched0-Mode selected heuristic G_E___303_C18_F1_URBAN_S0Y 59.21/59.46 # and selection function SelectMaxLComplexAvoidPosPred. 59.21/59.46 # 59.21/59.46 # Preprocessing time : 0.170 s 59.21/59.47 # No success with AutoSched0 59.21/59.47 # Trying AutoSched1 for 26 seconds 85.20/85.48 # AutoSched1-Mode selected heuristic G_E___008_C45_F1_PI_SE_Q4_CS_SP_S4SI 85.20/85.48 # and selection function SelectNewComplexAHPNS. 85.20/85.48 # 85.20/85.48 # Preprocessing time : 0.109 s 85.30/85.57 # No success with AutoSched1 85.30/85.57 # Trying AutoSched2 for 8 seconds 85.96/86.20 # AutoSched2-Mode selected heuristic U_____100_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_ND_S04AN 85.96/86.20 # and selection function SelectComplexExceptUniqMaxHorn. 85.96/86.20 # 85.96/86.20 # Preprocessing time : 0.053 s 85.96/86.20 # Presaturation interreduction done 85.96/86.20 85.96/86.20 # Proof found! 85.96/86.20 # SZS status Theorem 85.96/86.20 # SZS output start CNFRefutation 85.96/86.20 thf(breln1, axiom, (breln1)=(^[X4:$i, X33:$i]:subset @ X33 @ (cartprod @ X4 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln1)). 85.96/86.20 thf(breln, axiom, (breln)=(^[X4:$i, X5:$i, X7:$i]:subset @ X7 @ (cartprod @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln)). 85.96/86.20 thf(replAx, axiom, (replAx<=>![X6:$i > $i > $o, X4:$i]:(![X2:$i]:(in @ X2 @ X4=>exu @ (^[X3:$i]:X6 @ X2 @ X3))=>?[X5:$i]:![X2:$i]:(in @ X2 @ X5<=>?[X3:$i]:(in @ X3 @ X4&X6 @ X3 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', replAx)). 85.96/86.20 thf(exu, axiom, (exu)=(^[X1:$i > $o]:?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exu)). 85.96/86.20 thf(descrp, axiom, (descrp<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>X1 @ (descr @ (^[X2:$i]:X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', descrp)). 85.96/86.20 thf(exuE1, axiom, (exuE1<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuE1)). 85.96/86.20 thf(exuE3e, axiom, (exuE3e<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>?[X2:$i]:X1 @ X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuE3e)). 85.96/86.20 thf(nonemptyE1, axiom, (nonemptyE1<=>![X4:$i]:(nonempty @ X4=>?[X2:$i]:in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyE1)). 85.96/86.20 thf(nonempty, axiom, (nonempty)=(^[X2:$i]:(X2)!=(emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonempty)). 85.96/86.20 thf(nonemptyI, axiom, (nonemptyI<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyI)). 85.96/86.20 thf(nonemptyI1, axiom, (nonemptyI1<=>![X4:$i]:(?[X2:$i]:in @ X2 @ X4=>nonempty @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyI1)). 85.96/86.20 thf(exuE2, axiom, (exuE2<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuE2)). 85.96/86.20 thf(nonemptyImpWitness, axiom, (nonemptyImpWitness<=>![X4:$i]:(nonempty @ X4=>?[X2:$i]:(in @ X2 @ X4&$true))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyImpWitness)). 85.96/86.20 thf(exuI1, axiom, (exuI1<=>![X1:$i > $o]:(?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3)))=>exu @ (^[X2:$i]:X1 @ X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuI1)). 85.96/86.20 thf(exuI3, axiom, (exuI3<=>![X1:$i > $o]:(?[X2:$i]:X1 @ X2=>(![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3)))=>exu @ (^[X2:$i]:X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuI3)). 85.96/86.20 thf(exuI2, axiom, (exuI2<=>![X1:$i > $o]:(?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2))=>exu @ (^[X2:$i]:X1 @ X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuI2)). 85.96/86.20 thf(exuE3u, axiom, (exuE3u<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuE3u)). 85.96/86.20 thf(exu__Cong, axiom, (exu__Cong<=>![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(exu @ (^[X2:$i]:X1 @ X2)<=>exu @ (^[X2:$i]:X17 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exu__Cong)). 85.96/86.20 thf(exuEu, axiom, (exuEu<=>![X1:$i > $o]:(exu @ (^[X2:$i]:X1 @ X2)=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuEu)). 85.96/86.20 thf(descr__Cong, axiom, (descr__Cong<=>![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(exu @ (^[X2:$i]:X1 @ X2)=>(exu @ (^[X2:$i]:X17 @ X2)=>(descr @ (^[X2:$i]:X1 @ X2))=(descr @ (^[X2:$i]:X17 @ X2)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', descr__Cong)). 85.96/86.20 thf(setOfPairsIsBReln, axiom, (setOfPairsIsBReln<=>![X4:$i, X5:$i, X24:$i > $i > $o]:breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:X24 @ X2 @ X3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setOfPairsIsBReln)). 85.96/86.20 thf(brelnall1, axiom, (brelnall1<=>![X4:$i, X5:$i, X33:$i]:(breln @ X4 @ X5 @ X33=>![X1:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ X33=>X1 @ (kpair @ X2 @ X3))))=>![X2:$i]:(in @ X2 @ X33=>X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', brelnall1)). 85.96/86.20 thf(brelnall2, axiom, (brelnall2<=>![X4:$i, X5:$i, X33:$i]:(breln @ X4 @ X5 @ X33=>![X1:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ X33=>X1 @ (kpair @ X2 @ X3))))=>![X2:$i]:(in @ X2 @ X33=>X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', brelnall2)). 85.96/86.20 thf(subbreln, axiom, (subbreln<=>![X4:$i, X5:$i, X33:$i]:(breln @ X4 @ X5 @ X33=>![X35:$i]:(breln @ X4 @ X5 @ X35=>(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ X33=>in @ (kpair @ X2 @ X3) @ X35)))=>subset @ X33 @ X35)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subbreln)). 85.96/86.20 thf(eqbreln, axiom, (eqbreln<=>![X4:$i, X5:$i, X33:$i]:(breln @ X4 @ X5 @ X33=>![X35:$i]:(breln @ X4 @ X5 @ X35=>(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ X33=>in @ (kpair @ X2 @ X3) @ X35)))=>(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ X35=>in @ (kpair @ X2 @ X3) @ X33)))=>(X33)=(X35)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqbreln)). 85.96/86.20 thf(breln1all2, axiom, (breln1all2<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X1:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(in @ (kpair @ X2 @ X3) @ X33=>X1 @ (kpair @ X2 @ X3))))=>![X2:$i]:(in @ X2 @ X33=>X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln1all2)). 85.96/86.20 thf(breln1SetBreln1, axiom, (breln1SetBreln1<=>![X4:$i, X33:$i]:(in @ X33 @ (breln1Set @ X4)=>breln1 @ X4 @ X33)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln1SetBreln1)). 85.96/86.20 thf(setOfPairsIsBReln1, axiom, (setOfPairsIsBReln1<=>![X4:$i, X53:$i > $i > $o]:breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:X53 @ X2 @ X3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setOfPairsIsBReln1)). 85.96/86.20 thf(breln1all1, axiom, (breln1all1<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X1:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(in @ (kpair @ X2 @ X3) @ X33=>X1 @ (kpair @ X2 @ X3))))=>![X2:$i]:(in @ X2 @ X33=>X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln1all1)). 85.96/86.20 thf(subbreln1, axiom, (subbreln1<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X35:$i]:(breln1 @ X4 @ X35=>(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(in @ (kpair @ X2 @ X3) @ X33=>in @ (kpair @ X2 @ X3) @ X35)))=>subset @ X33 @ X35)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subbreln1)). 85.96/86.20 thf(eqbreln1, axiom, (eqbreln1<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X35:$i]:(breln1 @ X4 @ X35=>(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(in @ (kpair @ X2 @ X3) @ X33=>in @ (kpair @ X2 @ X3) @ X35)))=>(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(in @ (kpair @ X2 @ X3) @ X35=>in @ (kpair @ X2 @ X3) @ X33)))=>(X33)=(X35)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqbreln1)). 85.96/86.20 thf(breln1invprop, axiom, (breln1invprop<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>breln1 @ X4 @ (breln1invset @ X4 @ X33))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln1invprop)). 85.96/86.20 thf(breln1invI, axiom, (breln1invI<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(in @ (kpair @ X2 @ X3) @ X33=>in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln1invI)). 85.96/86.20 thf(breln1invE, axiom, (breln1invE<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33)=>in @ (kpair @ X2 @ X3) @ X33))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln1invE)). 85.96/86.20 thf(breln1compprop, axiom, (breln1compprop<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X35:$i]:(breln1 @ X4 @ X35=>breln1 @ X4 @ (breln1compset @ X4 @ X33 @ X35)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln1compprop)). 85.96/86.20 thf(breln1compI, axiom, (breln1compI<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X35:$i]:(breln1 @ X4 @ X35=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>![X14:$i]:(in @ X14 @ X4=>(in @ (kpair @ X2 @ X14) @ X33=>(in @ (kpair @ X14 @ X3) @ X35=>in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln1compI)). 85.96/86.20 thf(breln1compE, axiom, (breln1compE<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X35:$i]:(breln1 @ X4 @ X35=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35)=>?[X14:$i]:((in @ X14 @ X4&in @ (kpair @ X2 @ X14) @ X33)&in @ (kpair @ X14 @ X3) @ X35))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln1compE)). 85.96/86.20 thf(breln1compEex, axiom, (breln1compEex<=>![X4:$i, X33:$i]:(breln1 @ X4 @ X33=>![X35:$i]:(breln1 @ X4 @ X35=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35)=>![X54:$o]:(![X14:$i]:(in @ X14 @ X4=>(in @ (kpair @ X2 @ X14) @ X33=>(in @ (kpair @ X14 @ X3) @ X35=>X54)))=>X54))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln1compEex)). 85.96/86.20 thf(breln1unionprop, conjecture, ((emptysetAx=>(setadjoinAx=>(powersetAx=>(setunionAx=>(((((((descrp=>(dsetconstrI=>((((prop2setE=>(emptysetE=>((((((noeltsimpempty=>(setbeta=>((nonemptyI=>(((emptyinunitempty=>(setadjoinIR=>((((((emptyInPowerset=>(powersetE=>((setunionE=>((exuE2=>(((((singletonsswitch=>(upairsetE=>(((emptyE1=>(((quantDeMorgan2=>(quantDeMorgan3=>((prop2setI=>(prop2set2propI=>((notdallE=>(exuI1=>((exuI2=>(inCongP=>(in__Cong=>((exu__Cong=>(emptyset__Cong=>((((omega__Cong=>(exuEu=>(descr__Cong=>(((eqimpsubset2=>(eqimpsubset1=>(subsetI2=>(emptysetsubset=>(subsetE=>(subsetE2=>(((notequalI2=>((subsetTrans=>((setadjoinSub2=>(subset2powerset=>(setextsub=>(subsetemptysetimpeq=>(powersetI1=>((inPowerset=>(powersetsubset=>(sepInPowerset=>(sepSubset=>(binunionIL=>((((((binunionRsub=>(binintersectI=>(binintersectSubset5=>(binintersectEL=>(binintersectLsub=>(binintersectSubset2=>(((disjointsetsI1=>(((binintersectSubset1=>((setminusI=>(((((setminusELneg=>(setminusILneg=>(((setminusSubset1=>((((symdiffIneg1=>(((setukpairIL=>((kpairiskpair=>(kpairp=>(singletonsubset=>(((upairset2E=>((upairinpowunion=>((ubforcartprodlem2=>(ubforcartprodlem3=>((cartprodmempair1=>(((((setunionsingleton=>((ex1E1=>(ex1I=>(ex1I2=>(((kfstsingleton=>(((cartprodfstin=>((setukpairinjL=>((((((((((cartprodsndin=>(cartprodpairmemEL=>((cartprodmempaircEq=>((((dpsetconstrI=>((setOfPairsIsBReln=>((((dpsetconstrER=>((((infuncsetfunc=>(((lamProp=>(lamp=>(((brelnall2=>(ex1E2=>(funcGraphProp1=>((((funcGraphProp4=>(subbreln=>((funcext=>(((ap2apEq2=>(beta1=>((lam2lamEq=>(((((iftrueProp1=>((ifSingleton=>(ifp=>(((iffalse=>((binintersectT_lem=>(((((setextT=>(((powersetTE1=>(complementTI1=>((binintersectTELcontra=>(binintersectTERcontra=>(contrasubsetT=>(contrasubsetT1=>(((doubleComplementI1=>((doubleComplementSub1=>(doubleComplementSub2=>(doubleComplementEq=>((complementImpComplementIntersect=>(complementSubsetComplementIntersect=>((contraSubsetComplement=>(complementTcontraSubset=>((((((((inComplementUnionImpInComplement1=>(binunionTE=>((demorgan2a1=>(complementUnionInPowersetComplement=>(demorgan2a2=>(demorgan1a=>(demorgan1b=>(demorgan1=>((demorgan2b2=>(demorgan2b=>((((woz13rule2=>(woz13rule3=>(woz13rule4=>(woz1_1=>(woz1_2=>((woz1_4=>(((breln1SetBreln1=>((setOfPairsIsBReln1=>((((breln1invprop=>(breln1invI=>((((breln1compE=>(![X4:$i, X33:$i]:(![X35:$i]:(breln1 @ X4 @ X35=>breln1 @ X4 @ (binunion @ X33 @ X35))<=breln1 @ X4 @ X33)<=breln1compEex))<=breln1compI)<=breln1compprop)<=breln1invE)))<=eqbreln1)<=subbreln1)<=breln1all1))<=choice2fnsingleton))<=breln1all2)<=woz1_5))<=woz1_3))))))<=woz13rule1)<=woz13rule0)<=demorgan2)))<=demorgan2a)))))))<=binunionTEcontra)))<=inComplementUnionImpNotIn1)<=intersectInPowersetIntersectUnions)<=inIntersectImpInIntersectUnions)<=inIntersectImpInUnion2)<=inIntersectImpInUnion)<=binunionTIRcontra)<=binunionTILcontra)))<=complementInPowersetComplementIntersect)))<=complementTnotintersectT))))<=doubleComplementE1))<=contrasubsetT3)<=contrasubsetT2)))))<=complementTE1)))<=powersetTI1)<=subsetTI))<=complementT_lem)<=setminusT_lem)<=powersetT_lem)<=binunionT_lem))<=iftrueorfalse))<=iftrue)<=theeq)))<=iftrueProp2))<=iffalseProp2)<=iffalseProp1)<=eta2)<=beta2))<=eta1)))<=ap2apEq1)<=funcext2))<=eqbreln)))<=funcextLem)<=funcGraphProp2)<=funcGraphProp3))))<=brelnall1)<=lam2p)))<=funcinfuncset)<=ap2p))<=app)<=apProp)<=funcImageSingleton))<=dpsetconstrEL2)<=dpsetconstrEL1)<=dpsetconstrERa))<=dpsetconstrSub))<=cartprodpairsurjEq)<=cartprodsndpairEq)<=cartprodfstpairEq))<=cartprodpairmemER)))<=kpairsurjEq)<=ksndpairEq)<=ksndsingleton)<=setukpairinjR)<=setukpairinjR2)<=upairequniteq)<=setukpairinjR1)<=setukpairinjR12)<=setukpairinjR11))<=setukpairinjL2))<=kfstpairEq)<=theprop))<=setukpairinjL1)<=singletonsuniq))))<=singletonprop))<=setunionsingleton2)<=setunionsingleton1)<=setunionE2)<=cartprodmempair))<=cartprodpairin)))<=ubforcartprodlem1))<=upairsubunion))<=singletoninpowunion)<=singletoninpowerset))))<=setukpairIR))<=secondinupair)<=symdiffIneg2))<=symdiffI2)<=symdiffI1)<=symdiffE))<=setminusLsub)<=setminusIRneg)))<=setminusERneg)<=setminusSubset2)<=setminusER)<=setminusEL))<=bs114d))<=binintersectSubset4)<=binintersectRsub))<=binintersectER)<=binintersectSubset3)))))))<=binunionLsub)<=binunionE)<=binunionEcases)<=binunionIR)<=upairset2IR))))))<=powersetE1))))))<=setadjoinSub))<=subsetRefl))<=notequalI1)<=notsubsetI)))))))<=subsetI1)<=dsetconstr__Cong))))<=setunion__Cong)<=powerset__Cong)<=setadjoin__Cong)))<=exuE3u))))<=exuI3)))<=notdexE)))<=quantDeMorgan4)))<=quantDeMorgan1)<=vacuousDall))<=upairsetIR)<=upairsetIL)))<=eqinunit)<=notinsingleton)<=uniqinunit)<=nonemptyImpWitness))<=subPowSU))<=setunionI)))<=emptyinPowerset)<=powersetI)<=setoftrueEq)<=setadjoinOr)<=setadjoinE)))<=setadjoinIL)<=nonemptyI1))<=nonemptyE1)))<=emptyI)<=setext)<=exuE3e)<=notinemptyset)<=emptysetimpfalse)))<=exuE1)<=dsetconstrER)<=dsetconstrEL)))<=wellorderingAx)<=foundationAx)<=replAx)<=omegaIndAx)<=omegaSAx)<=omega0Ax)))))<=setextAx), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln1unionprop)). 85.96/86.20 thf(setextAx, axiom, (setextAx<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4<=>in @ X2 @ X5)=>(X4)=(X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setextAx)). 85.96/86.20 thf(emptysetAx, axiom, (emptysetAx<=>![X2:$i]:~(in @ X2 @ emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetAx)). 85.96/86.20 thf(setadjoinAx, axiom, (setadjoinAx<=>![X2:$i, X4:$i, X3:$i]:(in @ X3 @ (setadjoin @ X2 @ X4)<=>((X3)=(X2)|in @ X3 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinAx)). 85.96/86.20 thf(powersetAx, axiom, (powersetAx<=>![X4:$i, X5:$i]:(in @ X5 @ (powerset @ X4)<=>![X2:$i]:(in @ X2 @ X5=>in @ X2 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetAx)). 85.96/86.20 thf(setunionAx, axiom, (setunionAx<=>![X4:$i, X2:$i]:(in @ X2 @ (setunion @ X4)<=>?[X5:$i]:(in @ X2 @ X5&in @ X5 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionAx)). 85.96/86.20 thf(omega0Ax, axiom, (omega0Ax<=>in @ emptyset @ omega), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omega0Ax)). 85.96/86.20 thf(omegaSAx, axiom, (omegaSAx<=>![X2:$i]:(in @ X2 @ omega=>in @ (setadjoin @ X2 @ X2) @ omega)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omegaSAx)). 85.96/86.20 thf(omegaIndAx, axiom, (omegaIndAx<=>![X4:$i]:((in @ emptyset @ X4&![X2:$i]:((in @ X2 @ omega&in @ X2 @ X4)=>in @ (setadjoin @ X2 @ X2) @ X4))=>![X2:$i]:(in @ X2 @ omega=>in @ X2 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omegaIndAx)). 85.96/86.20 thf(foundationAx, axiom, (foundationAx<=>![X4:$i]:(?[X2:$i]:in @ X2 @ X4=>?[X5:$i]:(in @ X5 @ X4&~(?[X2:$i]:(in @ X2 @ X5&in @ X2 @ X4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', foundationAx)). 85.96/86.20 thf(wellorderingAx, axiom, (wellorderingAx<=>![X4:$i]:?[X5:$i]:(((![X7:$i]:(in @ X7 @ X5=>![X2:$i]:(in @ X2 @ X7=>in @ X2 @ X4))&![X2:$i, X3:$i]:((in @ X2 @ X4&in @ X3 @ X4)=>(![X7:$i]:(in @ X7 @ X5=>(in @ X2 @ X7<=>in @ X3 @ X7))=>(X2)=(X3))))&![X7:$i, X8:$i]:((in @ X7 @ X5&in @ X8 @ X5)=>(![X2:$i]:(in @ X2 @ X7=>in @ X2 @ X8)|![X2:$i]:(in @ X2 @ X8=>in @ X2 @ X7))))&![X7:$i]:((![X2:$i]:(in @ X2 @ X7=>in @ X2 @ X4)&?[X2:$i]:in @ X2 @ X7)=>?[X8:$i, X2:$i]:(((in @ X8 @ X5&in @ X2 @ X7)&~(?[X3:$i]:(in @ X3 @ X8&in @ X3 @ X7)))&![X9:$i]:(in @ X9 @ X5=>(![X3:$i]:(in @ X3 @ X9=>in @ X3 @ X8)|in @ X2 @ X9)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', wellorderingAx)). 85.96/86.20 thf(dsetconstrI, axiom, (dsetconstrI<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstrI)). 85.96/86.20 thf(dsetconstrEL, axiom, (dsetconstrEL<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))=>in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstrEL)). 85.96/86.20 thf(dsetconstrER, axiom, (dsetconstrER<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))=>X1 @ X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstrER)). 85.96/86.20 thf(prop2setE, axiom, (prop2setE<=>![X10:$o, X2:$i]:(in @ X2 @ (prop2set @ (X10))=>X10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prop2setE)). 85.96/86.20 thf(emptysetE, axiom, (emptysetE<=>![X2:$i]:(in @ X2 @ emptyset=>![X11:$o]:X11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetE)). 85.96/86.20 thf(emptysetimpfalse, axiom, (emptysetimpfalse<=>![X2:$i]:(in @ X2 @ emptyset=>~$true)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetimpfalse)). 85.96/86.20 thf(notinemptyset, axiom, (notinemptyset<=>![X2:$i]:~(in @ X2 @ emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notinemptyset)). 85.96/86.20 thf(setext, axiom, (setext<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4=>in @ X2 @ X5)=>(![X2:$i]:(in @ X2 @ X5=>in @ X2 @ X4)=>(X4)=(X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setext)). 85.96/86.20 thf(emptyI, axiom, (emptyI<=>![X4:$i]:(![X2:$i]:~(in @ X2 @ X4)=>(X4)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyI)). 85.96/86.20 thf(noeltsimpempty, axiom, (noeltsimpempty<=>![X4:$i]:(![X2:$i]:~(in @ X2 @ X4)=>(X4)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', noeltsimpempty)). 85.96/86.20 thf(setbeta, axiom, (setbeta<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))<=>X1 @ X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setbeta)). 85.96/86.20 thf(setadjoinIL, axiom, (setadjoinIL<=>![X2:$i, X3:$i]:in @ X2 @ (setadjoin @ X2 @ X3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinIL)). 85.96/86.20 thf(emptyinunitempty, axiom, (emptyinunitempty<=>in @ emptyset @ (setadjoin @ emptyset @ emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyinunitempty)). 85.96/86.20 thf(setadjoinIR, axiom, (setadjoinIR<=>![X2:$i, X4:$i, X3:$i]:(in @ X3 @ X4=>in @ X3 @ (setadjoin @ X2 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinIR)). 85.96/86.20 thf(setadjoinE, axiom, (setadjoinE<=>![X2:$i, X4:$i, X3:$i]:(in @ X3 @ (setadjoin @ X2 @ X4)=>![X12:$o]:(((X3)=(X2)=>X12)=>((in @ X3 @ X4=>X12)=>X12)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinE)). 85.96/86.20 thf(setadjoinOr, axiom, (setadjoinOr<=>![X2:$i, X4:$i, X3:$i]:(in @ X3 @ (setadjoin @ X2 @ X4)=>((X3)=(X2)|in @ X3 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinOr)). 85.96/86.20 thf(setoftrueEq, axiom, (setoftrueEq<=>![X4:$i]:(dsetconstr @ X4 @ (^[X2:$i]:$true))=(X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setoftrueEq)). 85.96/86.20 thf(powersetI, axiom, (powersetI<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X5=>in @ X2 @ X4)=>in @ X5 @ (powerset @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetI)). 85.96/86.20 thf(emptyinPowerset, axiom, (emptyinPowerset<=>![X4:$i]:in @ emptyset @ (powerset @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyinPowerset)). 85.96/86.20 thf(emptyInPowerset, axiom, (emptyInPowerset<=>![X4:$i]:in @ emptyset @ (powerset @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyInPowerset)). 85.96/86.20 thf(powersetE, axiom, (powersetE<=>![X4:$i, X5:$i, X2:$i]:(in @ X5 @ (powerset @ X4)=>(in @ X2 @ X5=>in @ X2 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetE)). 85.96/86.20 thf(setunionI, axiom, (setunionI<=>![X4:$i, X2:$i, X5:$i]:(in @ X2 @ X5=>(in @ X5 @ X4=>in @ X2 @ (setunion @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionI)). 85.96/86.20 thf(setunionE, axiom, (setunionE<=>![X4:$i, X2:$i]:(in @ X2 @ (setunion @ X4)=>![X13:$o]:(![X5:$i]:(in @ X2 @ X5=>(in @ X5 @ X4=>X13))=>X13))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionE)). 85.96/86.20 thf(subPowSU, axiom, (subPowSU<=>![X4:$i, X2:$i]:(in @ X2 @ X4=>in @ X2 @ (powerset @ (setunion @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subPowSU)). 85.96/86.20 thf(uniqinunit, axiom, (uniqinunit<=>![X2:$i, X3:$i]:(in @ X2 @ (setadjoin @ X3 @ emptyset)=>(X2)=(X3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', uniqinunit)). 85.96/86.20 thf(notinsingleton, axiom, (notinsingleton<=>![X2:$i, X3:$i]:((X2)!=(X3)=>~(in @ X3 @ (setadjoin @ X2 @ emptyset)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notinsingleton)). 85.96/86.20 thf(eqinunit, axiom, (eqinunit<=>![X2:$i, X3:$i]:((X2)=(X3)=>in @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqinunit)). 85.96/86.20 thf(singletonsswitch, axiom, (singletonsswitch<=>![X2:$i, X3:$i]:(in @ X2 @ (setadjoin @ X3 @ emptyset)=>in @ X3 @ (setadjoin @ X2 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletonsswitch)). 85.96/86.20 thf(upairsetE, axiom, (upairsetE<=>![X2:$i, X3:$i, X14:$i]:(in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=>((X14)=(X2)|(X14)=(X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsetE)). 85.96/86.20 thf(upairsetIL, axiom, (upairsetIL<=>![X2:$i, X3:$i]:in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsetIL)). 85.96/86.20 thf(upairsetIR, axiom, (upairsetIR<=>![X2:$i, X3:$i]:in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsetIR)). 85.96/86.20 thf(emptyE1, axiom, (emptyE1<=>![X4:$i, X1:$i > $o]:(?[X2:$i]:(in @ X2 @ X4&X1 @ X2)=>((dsetconstr @ X4 @ (^[X2:$i]:X1 @ X2))=(emptyset)=>~$true))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyE1)). 85.96/86.20 thf(vacuousDall, axiom, (vacuousDall<=>![X1:$i > $o, X2:$i]:(in @ X2 @ emptyset=>X1 @ X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', vacuousDall)). 85.96/86.20 thf(quantDeMorgan1, axiom, (quantDeMorgan1<=>![X4:$i, X1:$i > $o]:(~(![X2:$i]:(in @ X2 @ X4=>X1 @ X2))=>?[X2:$i]:(in @ X2 @ X4&~(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan1)). 85.96/86.20 thf(quantDeMorgan2, axiom, (quantDeMorgan2<=>![X4:$i, X1:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>~(X1 @ X2))=>~(?[X2:$i]:(in @ X2 @ X4&X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan2)). 85.96/86.20 thf(quantDeMorgan3, axiom, (quantDeMorgan3<=>![X4:$i, X1:$i > $o]:(~(?[X2:$i]:(in @ X2 @ X4&X1 @ X2))=>![X2:$i]:(in @ X2 @ X4=>~(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan3)). 85.96/86.20 thf(quantDeMorgan4, axiom, (quantDeMorgan4<=>![X4:$i, X1:$i > $o]:(?[X2:$i]:(in @ X2 @ X4&~(X1 @ X2))=>~(![X2:$i]:(in @ X2 @ X4=>X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan4)). 85.96/86.20 thf(prop2setI, axiom, (prop2setI<=>![X15:$o]:(X15=>in @ emptyset @ (prop2set @ (X15)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prop2setI)). 85.96/86.20 thf(prop2set2propI, axiom, (prop2set2propI<=>![X16:$o]:(X16=>set2prop @ (prop2set @ (X16)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prop2set2propI)). 85.96/86.20 thf(notdexE, axiom, (notdexE<=>![X4:$i, X1:$i > $o]:(~(?[X2:$i]:(in @ X2 @ X4&X1 @ X2))=>![X2:$i]:(in @ X2 @ X4=>~(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notdexE)). 85.96/86.20 thf(notdallE, axiom, (notdallE<=>![X4:$i, X1:$i > $o]:(~(![X2:$i]:(in @ X2 @ X4=>X1 @ X2))=>?[X2:$i]:(in @ X2 @ X4&~(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notdallE)). 85.96/86.20 thf(inCongP, axiom, (inCongP<=>![X4:$i, X5:$i]:((X4)=(X5)=>![X2:$i, X3:$i]:((X2)=(X3)=>(in @ X2 @ X4=>in @ X3 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', inCongP)). 85.96/86.20 thf(in__Cong, axiom, (in__Cong<=>![X4:$i, X5:$i]:((X4)=(X5)=>![X2:$i, X3:$i]:((X2)=(X3)=>(in @ X2 @ X4<=>in @ X3 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', in__Cong)). 85.96/86.20 thf(emptyset__Cong, axiom, (emptyset__Cong<=>(emptyset)=(emptyset)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyset__Cong)). 85.96/86.20 thf(setadjoin__Cong, axiom, (setadjoin__Cong<=>![X2:$i, X3:$i]:((X2)=(X3)=>![X14:$i, X18:$i]:((X14)=(X18)=>(setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoin__Cong)). 85.96/86.20 thf(powerset__Cong, axiom, (powerset__Cong<=>![X4:$i, X5:$i]:((X4)=(X5)=>(powerset @ X4)=(powerset @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powerset__Cong)). 85.96/86.20 thf(setunion__Cong, axiom, (setunion__Cong<=>![X4:$i, X5:$i]:((X4)=(X5)=>(setunion @ X4)=(setunion @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunion__Cong)). 85.96/86.20 thf(omega__Cong, axiom, (omega__Cong<=>(omega)=(omega)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omega__Cong)). 85.96/86.20 thf(dsetconstr__Cong, axiom, (dsetconstr__Cong<=>![X4:$i, X5:$i]:((X4)=(X5)=>![X1:$i > $o, X17:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))))=>(dsetconstr @ X4 @ (^[X2:$i]:X1 @ X2))=(dsetconstr @ X5 @ (^[X2:$i]:X17 @ X2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstr__Cong)). 85.96/86.20 thf(subsetI1, axiom, (subsetI1<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4=>in @ X2 @ X5)=>subset @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetI1)). 85.96/86.20 thf(eqimpsubset2, axiom, (eqimpsubset2<=>![X4:$i, X5:$i]:((X4)=(X5)=>subset @ X5 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqimpsubset2)). 85.96/86.20 thf(eqimpsubset1, axiom, (eqimpsubset1<=>![X4:$i, X5:$i]:((X4)=(X5)=>subset @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqimpsubset1)). 85.96/86.20 thf(subsetI2, axiom, (subsetI2<=>![X4:$i, X5:$i]:(![X2:$i]:(in @ X2 @ X4=>in @ X2 @ X5)=>subset @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetI2)). 85.96/86.20 thf(emptysetsubset, axiom, (emptysetsubset<=>![X4:$i]:subset @ emptyset @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetsubset)). 85.96/86.20 thf(subsetE, axiom, (subsetE<=>![X4:$i, X5:$i, X2:$i]:(subset @ X4 @ X5=>(in @ X2 @ X4=>in @ X2 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetE)). 85.96/86.20 thf(subsetE2, axiom, (subsetE2<=>![X4:$i, X5:$i, X2:$i]:(subset @ X4 @ X5=>(~(in @ X2 @ X5)=>~(in @ X2 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetE2)). 85.96/86.20 thf(notsubsetI, axiom, (notsubsetI<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X5)=>~(subset @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notsubsetI)). 85.96/86.20 thf(notequalI1, axiom, (notequalI1<=>![X4:$i, X5:$i]:(~(subset @ X4 @ X5)=>(X4)!=(X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notequalI1)). 85.96/86.20 thf(notequalI2, axiom, (notequalI2<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X5)=>(X4)!=(X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notequalI2)). 85.96/86.20 thf(subsetRefl, axiom, (subsetRefl<=>![X4:$i]:subset @ X4 @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetRefl)). 85.96/86.20 thf(subsetTrans, axiom, (subsetTrans<=>![X4:$i, X5:$i, X7:$i]:(subset @ X4 @ X5=>(subset @ X5 @ X7=>subset @ X4 @ X7))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetTrans)). 85.96/86.20 thf(setadjoinSub, axiom, (setadjoinSub<=>![X2:$i, X4:$i]:subset @ X4 @ (setadjoin @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinSub)). 85.96/86.20 thf(setadjoinSub2, axiom, (setadjoinSub2<=>![X4:$i, X2:$i, X5:$i]:(subset @ X4 @ X5=>subset @ X4 @ (setadjoin @ X2 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinSub2)). 85.96/86.20 thf(subset2powerset, axiom, (subset2powerset<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>in @ X4 @ (powerset @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subset2powerset)). 85.96/86.20 thf(setextsub, axiom, (setextsub<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>(subset @ X5 @ X4=>(X4)=(X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setextsub)). 85.96/86.20 thf(subsetemptysetimpeq, axiom, (subsetemptysetimpeq<=>![X4:$i]:(subset @ X4 @ emptyset=>(X4)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetemptysetimpeq)). 85.96/86.20 thf(powersetI1, axiom, (powersetI1<=>![X4:$i, X5:$i]:(subset @ X5 @ X4=>in @ X5 @ (powerset @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetI1)). 85.96/86.20 thf(powersetE1, axiom, (powersetE1<=>![X4:$i, X5:$i]:(in @ X5 @ (powerset @ X4)=>subset @ X5 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetE1)). 85.96/86.20 thf(inPowerset, axiom, (inPowerset<=>![X4:$i]:in @ X4 @ (powerset @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', inPowerset)). 85.96/86.20 thf(powersetsubset, axiom, (powersetsubset<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>subset @ (powerset @ X4) @ (powerset @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetsubset)). 85.96/86.20 thf(sepInPowerset, axiom, (sepInPowerset<=>![X4:$i, X1:$i > $o]:in @ (dsetconstr @ X4 @ (^[X2:$i]:X1 @ X2)) @ (powerset @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sepInPowerset)). 85.96/86.20 thf(sepSubset, axiom, (sepSubset<=>![X4:$i, X1:$i > $o]:subset @ (dsetconstr @ X4 @ (^[X2:$i]:X1 @ X2)) @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sepSubset)). 85.96/86.20 thf(binunionIL, axiom, (binunionIL<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>in @ X2 @ (binunion @ X4 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionIL)). 85.96/86.20 thf(upairset2IR, axiom, (upairset2IR<=>![X2:$i, X3:$i]:in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairset2IR)). 85.96/86.20 thf(binunionIR, axiom, (binunionIR<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X5=>in @ X2 @ (binunion @ X4 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionIR)). 85.96/86.20 thf(binunionEcases, axiom, (binunionEcases<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(in @ X2 @ (binunion @ X4 @ X5)=>((in @ X2 @ X4=>X19)=>((in @ X2 @ X5=>X19)=>X19)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionEcases)). 85.96/86.20 thf(binunionE, axiom, (binunionE<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (binunion @ X4 @ X5)=>(in @ X2 @ X4|in @ X2 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionE)). 85.96/86.20 thf(binunionLsub, axiom, (binunionLsub<=>![X4:$i, X5:$i]:subset @ X4 @ (binunion @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionLsub)). 85.96/86.20 thf(binunionRsub, axiom, (binunionRsub<=>![X4:$i, X5:$i]:subset @ X5 @ (binunion @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionRsub)). 85.96/86.20 thf(binintersectI, axiom, (binintersectI<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X5=>in @ X2 @ (binintersect @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectI)). 85.96/86.20 thf(binintersectSubset5, axiom, (binintersectSubset5<=>![X4:$i, X5:$i, X7:$i]:(subset @ X7 @ X4=>(subset @ X7 @ X5=>subset @ X7 @ (binintersect @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset5)). 85.96/86.20 thf(binintersectEL, axiom, (binintersectEL<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (binintersect @ X4 @ X5)=>in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectEL)). 85.96/86.20 thf(binintersectLsub, axiom, (binintersectLsub<=>![X4:$i, X5:$i]:subset @ (binintersect @ X4 @ X5) @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectLsub)). 85.96/86.20 thf(binintersectSubset2, axiom, (binintersectSubset2<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>(binintersect @ X4 @ X5)=(X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset2)). 85.96/86.20 thf(binintersectSubset3, axiom, (binintersectSubset3<=>![X4:$i, X5:$i]:((binintersect @ X4 @ X5)=(X5)=>subset @ X5 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset3)). 85.96/86.20 thf(binintersectER, axiom, (binintersectER<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (binintersect @ X4 @ X5)=>in @ X2 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectER)). 85.96/86.20 thf(disjointsetsI1, axiom, (disjointsetsI1<=>![X4:$i, X5:$i]:(~(?[X2:$i]:(in @ X2 @ X4&in @ X2 @ X5))=>(binintersect @ X4 @ X5)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', disjointsetsI1)). 85.96/86.20 thf(binintersectRsub, axiom, (binintersectRsub<=>![X4:$i, X5:$i]:subset @ (binintersect @ X4 @ X5) @ X5), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectRsub)). 85.96/86.20 thf(binintersectSubset4, axiom, (binintersectSubset4<=>![X4:$i, X5:$i]:(subset @ X5 @ X4=>(binintersect @ X4 @ X5)=(X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset4)). 85.96/86.20 thf(binintersectSubset1, axiom, (binintersectSubset1<=>![X4:$i, X5:$i]:((binintersect @ X4 @ X5)=(X4)=>subset @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset1)). 85.96/86.20 thf(bs114d, axiom, (bs114d<=>![X4:$i, X5:$i, X7:$i]:(binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', bs114d)). 85.96/86.20 thf(setminusI, axiom, (setminusI<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X5)=>in @ X2 @ (setminus @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusI)). 85.96/86.20 thf(setminusEL, axiom, (setminusEL<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (setminus @ X4 @ X5)=>in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusEL)). 85.96/86.20 thf(setminusER, axiom, (setminusER<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (setminus @ X4 @ X5)=>~(in @ X2 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusER)). 85.96/86.20 thf(setminusSubset2, axiom, (setminusSubset2<=>![X4:$i, X5:$i]:(subset @ X4 @ X5=>(setminus @ X4 @ X5)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusSubset2)). 85.96/86.20 thf(setminusERneg, axiom, (setminusERneg<=>![X4:$i, X5:$i, X2:$i]:(~(in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4=>in @ X2 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusERneg)). 85.96/86.20 thf(setminusELneg, axiom, (setminusELneg<=>![X4:$i, X5:$i, X2:$i]:(~(in @ X2 @ (setminus @ X4 @ X5))=>(~(in @ X2 @ X5)=>~(in @ X2 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusELneg)). 85.96/86.20 thf(setminusILneg, axiom, (setminusILneg<=>![X4:$i, X5:$i, X2:$i]:(~(in @ X2 @ X4)=>~(in @ X2 @ (setminus @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusILneg)). 85.96/86.20 thf(setminusIRneg, axiom, (setminusIRneg<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X5=>~(in @ X2 @ (setminus @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusIRneg)). 85.96/86.20 thf(setminusLsub, axiom, (setminusLsub<=>![X4:$i, X5:$i]:subset @ (setminus @ X4 @ X5) @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusLsub)). 85.96/86.20 thf(setminusSubset1, axiom, (setminusSubset1<=>![X4:$i, X5:$i]:((setminus @ X4 @ X5)=(emptyset)=>subset @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusSubset1)). 85.96/86.20 thf(symdiffE, axiom, (symdiffE<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ (symdiff @ X4 @ X5)=>![X20:$o]:((in @ X2 @ X4=>(~(in @ X2 @ X5)=>X20))=>((~(in @ X2 @ X4)=>(in @ X2 @ X5=>X20))=>X20)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', symdiffE)). 85.96/86.20 thf(symdiffI1, axiom, (symdiffI1<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X5)=>in @ X2 @ (symdiff @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', symdiffI1)). 85.96/86.20 thf(symdiffI2, axiom, (symdiffI2<=>![X4:$i, X5:$i, X2:$i]:(~(in @ X2 @ X4)=>(in @ X2 @ X5=>in @ X2 @ (symdiff @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', symdiffI2)). 85.96/86.20 thf(symdiffIneg1, axiom, (symdiffIneg1<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X5=>~(in @ X2 @ (symdiff @ X4 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', symdiffIneg1)). 85.96/86.20 thf(symdiffIneg2, axiom, (symdiffIneg2<=>![X4:$i, X5:$i, X2:$i]:(~(in @ X2 @ X4)=>(~(in @ X2 @ X5)=>~(in @ X2 @ (symdiff @ X4 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', symdiffIneg2)). 85.96/86.20 thf(secondinupair, axiom, (secondinupair<=>![X2:$i, X3:$i]:in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', secondinupair)). 85.96/86.20 thf(setukpairIL, axiom, (setukpairIL<=>![X2:$i, X3:$i]:in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairIL)). 85.96/86.20 thf(setukpairIR, axiom, (setukpairIR<=>![X2:$i, X3:$i]:in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairIR)). 85.96/86.20 thf(kpairiskpair, axiom, (kpairiskpair<=>![X2:$i, X3:$i]:iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', kpairiskpair)). 85.96/86.20 thf(kpairp, axiom, (kpairp<=>![X2:$i, X3:$i]:iskpair @ (kpair @ X2 @ X3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', kpairp)). 85.96/86.20 thf(singletonsubset, axiom, (singletonsubset<=>![X4:$i, X2:$i]:(in @ X2 @ X4=>subset @ (setadjoin @ X2 @ emptyset) @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletonsubset)). 85.96/86.20 thf(singletoninpowerset, axiom, (singletoninpowerset<=>![X4:$i, X2:$i]:(in @ X2 @ X4=>in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletoninpowerset)). 85.96/86.20 thf(singletoninpowunion, axiom, (singletoninpowunion<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletoninpowunion)). 85.96/86.20 thf(upairset2E, axiom, (upairset2E<=>![X2:$i, X3:$i, X14:$i]:(in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=>((X14)=(X2)|(X14)=(X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairset2E)). 85.96/86.20 thf(upairsubunion, axiom, (upairsubunion<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsubunion)). 85.96/86.20 thf(upairinpowunion, axiom, (upairinpowunion<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairinpowunion)). 85.96/86.20 thf(ubforcartprodlem1, axiom, (ubforcartprodlem1<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ubforcartprodlem1)). 85.96/86.20 thf(ubforcartprodlem2, axiom, (ubforcartprodlem2<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ubforcartprodlem2)). 85.96/86.20 thf(ubforcartprodlem3, axiom, (ubforcartprodlem3<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ubforcartprodlem3)). 85.96/86.20 thf(cartprodpairin, axiom, (cartprodpairin<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodpairin)). 85.96/86.20 thf(cartprodmempair1, axiom, (cartprodmempair1<=>![X4:$i, X5:$i, X18:$i]:(in @ X18 @ (cartprod @ X4 @ X5)=>?[X2:$i]:(in @ X2 @ X4&?[X3:$i]:(in @ X3 @ X5&(X18)=(kpair @ X2 @ X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodmempair1)). 85.96/86.20 thf(cartprodmempair, axiom, (cartprodmempair<=>![X4:$i, X5:$i, X18:$i]:(in @ X18 @ (cartprod @ X4 @ X5)=>iskpair @ X18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodmempair)). 85.96/86.20 thf(setunionE2, axiom, (setunionE2<=>![X4:$i, X2:$i]:(in @ X2 @ (setunion @ X4)=>?[X21:$i]:(in @ X21 @ X4&in @ X2 @ X21))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionE2)). 85.96/86.20 thf(setunionsingleton1, axiom, (setunionsingleton1<=>![X4:$i]:subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionsingleton1)). 85.96/86.20 thf(setunionsingleton2, axiom, (setunionsingleton2<=>![X4:$i]:subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionsingleton2)). 85.96/86.20 thf(setunionsingleton, axiom, (setunionsingleton<=>![X2:$i]:(setunion @ (setadjoin @ X2 @ emptyset))=(X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionsingleton)). 85.96/86.20 thf(singletonprop, axiom, (singletonprop<=>![X4:$i, X1:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(X1 @ X2=>(X1 @ X3=>(X2)=(X3)))))=>(?[X2:$i]:(in @ X2 @ X4&X1 @ X2)=>singleton @ (dsetconstr @ X4 @ (^[X2:$i]:X1 @ X2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletonprop)). 85.96/86.20 thf(ex1E1, axiom, (ex1E1<=>![X4:$i, X1:$i > $o]:(ex1 @ X4 @ (^[X2:$i]:X1 @ X2)=>?[X2:$i]:(in @ X2 @ X4&X1 @ X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ex1E1)). 85.96/86.20 thf(ex1I, axiom, (ex1I<=>![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>(![X3:$i]:(in @ X3 @ X4=>(X1 @ X3=>(X3)=(X2)))=>ex1 @ X4 @ (^[X3:$i]:X1 @ X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ex1I)). 85.96/86.20 thf(ex1I2, axiom, (ex1I2<=>![X4:$i, X1:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(X1 @ X2=>(X1 @ X3=>(X2)=(X3)))))=>(?[X2:$i]:(in @ X2 @ X4&X1 @ X2)=>ex1 @ X4 @ (^[X2:$i]:X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ex1I2)). 85.96/86.20 thf(singletonsuniq, axiom, (singletonsuniq<=>![X2:$i, X3:$i]:((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset)=>(X2)=(X3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletonsuniq)). 85.96/86.20 thf(setukpairinjL1, axiom, (setukpairinjL1<=>![X2:$i, X3:$i, X14:$i]:(in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=>(X2)=(X14))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairinjL1)). 85.96/86.20 thf(kfstsingleton, axiom, (kfstsingleton<=>![X18:$i]:(iskpair @ X18=>singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:in @ (setadjoin @ X2 @ emptyset) @ X18)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', kfstsingleton)). 85.96/86.20 thf(theprop, axiom, (theprop<=>![X21:$i]:(singleton @ X21=>in @ (setunion @ X21) @ X21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', theprop)). 85.96/86.20 thf(kfstpairEq, axiom, (kfstpairEq<=>![X2:$i, X3:$i]:(kfst @ (kpair @ X2 @ X3))=(X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', kfstpairEq)). 85.96/86.20 thf(cartprodfstin, axiom, (cartprodfstin<=>![X4:$i, X5:$i, X18:$i]:(in @ X18 @ (cartprod @ X4 @ X5)=>in @ (kfst @ X18) @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodfstin)). 85.96/86.20 thf(setukpairinjL2, axiom, (setukpairinjL2<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset))=>(X2)=(X14))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairinjL2)). 85.96/86.20 thf(setukpairinjL, axiom, (setukpairinjL<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((kpair @ X2 @ X3)=(kpair @ X14 @ X18)=>(X2)=(X14))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairinjL)). 85.96/86.20 thf(setukpairinjR11, axiom, (setukpairinjR11<=>![X2:$i, X3:$i]:((X2)=(X3)=>(setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairinjR11)). 85.96/86.20 thf(setukpairinjR12, axiom, (setukpairinjR12<=>![X2:$i, X3:$i]:((X2)=(X3)=>(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairinjR12)). 85.96/86.20 thf(setukpairinjR1, axiom, (setukpairinjR1<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset))=>((X14)=(X18)=>(X3)=(X18)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairinjR1)). 85.96/86.20 thf(upairequniteq, axiom, (upairequniteq<=>![X2:$i, X3:$i, X14:$i]:((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset)=>(X2)=(X3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairequniteq)). 85.96/86.20 thf(setukpairinjR2, axiom, (setukpairinjR2<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset))=>(X3)=(X18))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairinjR2)). 85.96/86.20 thf(setukpairinjR, axiom, (setukpairinjR<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((kpair @ X2 @ X3)=(kpair @ X14 @ X18)=>(X3)=(X18))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairinjR)). 85.96/86.20 thf(ksndsingleton, axiom, (ksndsingleton<=>![X18:$i]:(iskpair @ X18=>singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(X18)=(kpair @ (kfst @ X18) @ X2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ksndsingleton)). 85.96/86.20 thf(ksndpairEq, axiom, (ksndpairEq<=>![X2:$i, X3:$i]:(ksnd @ (kpair @ X2 @ X3))=(X3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ksndpairEq)). 85.96/86.20 thf(kpairsurjEq, axiom, (kpairsurjEq<=>![X18:$i]:(iskpair @ X18=>(kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', kpairsurjEq)). 85.96/86.20 thf(cartprodsndin, axiom, (cartprodsndin<=>![X4:$i, X5:$i, X18:$i]:(in @ X18 @ (cartprod @ X4 @ X5)=>in @ (ksnd @ X18) @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodsndin)). 85.96/86.20 thf(cartprodpairmemEL, axiom, (cartprodpairmemEL<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5)=>in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodpairmemEL)). 85.96/86.20 thf(cartprodpairmemER, axiom, (cartprodpairmemER<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5)=>in @ X3 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodpairmemER)). 85.96/86.20 thf(cartprodmempaircEq, axiom, (cartprodmempaircEq<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(kpair @ X2 @ X3)=(kpair @ X2 @ X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodmempaircEq)). 85.96/86.20 thf(cartprodfstpairEq, axiom, (cartprodfstpairEq<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodfstpairEq)). 85.96/86.20 thf(cartprodsndpairEq, axiom, (cartprodsndpairEq<=>![X4:$i, X5:$i, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodsndpairEq)). 85.96/86.20 thf(cartprodpairsurjEq, axiom, (cartprodpairsurjEq<=>![X4:$i, X5:$i, X18:$i]:(in @ X18 @ (cartprod @ X4 @ X5)=>(kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodpairsurjEq)). 85.96/86.20 thf(dpsetconstrI, axiom, (dpsetconstrI<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(X22 @ X2 @ X3=>in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:X22 @ X14 @ X18)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dpsetconstrI)). 85.96/86.20 thf(dpsetconstrSub, axiom, (dpsetconstrSub<=>![X4:$i, X5:$i, X23:$i > $i > $o]:subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:X23 @ X2 @ X3)) @ (cartprod @ X4 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dpsetconstrSub)). 85.96/86.20 thf(dpsetconstrERa, axiom, (dpsetconstrERa<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:X25 @ X14 @ X18))=>X25 @ X2 @ X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dpsetconstrERa)). 85.96/86.20 thf(dpsetconstrEL1, axiom, (dpsetconstrEL1<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:X26 @ X14 @ X18))=>in @ X2 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dpsetconstrEL1)). 85.96/86.20 thf(dpsetconstrEL2, axiom, (dpsetconstrEL2<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:X27 @ X14 @ X18))=>in @ X3 @ X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dpsetconstrEL2)). 85.96/86.20 thf(dpsetconstrER, axiom, (dpsetconstrER<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:X28 @ X14 @ X18))=>X28 @ X2 @ X3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dpsetconstrER)). 85.96/86.20 thf(funcImageSingleton, axiom, (funcImageSingleton<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>![X2:$i]:(in @ X2 @ X4=>singleton @ (dsetconstr @ X5 @ (^[X3:$i]:in @ (kpair @ X2 @ X3) @ X29))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', funcImageSingleton)). 85.96/86.20 thf(apProp, axiom, (apProp<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>![X2:$i]:(in @ X2 @ X4=>in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:in @ (kpair @ X2 @ X3) @ X29))) @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', apProp)). 85.96/86.20 thf(app, axiom, (app<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>![X2:$i]:(in @ X2 @ X4=>in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', app)). 85.96/86.20 thf(infuncsetfunc, axiom, (infuncsetfunc<=>![X4:$i, X5:$i, X29:$i]:(in @ X29 @ (funcSet @ X4 @ X5)=>func @ X4 @ X5 @ X29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', infuncsetfunc)). 85.96/86.20 thf(ap2p, axiom, (ap2p<=>![X4:$i, X5:$i, X29:$i]:(in @ X29 @ (funcSet @ X4 @ X5)=>![X2:$i]:(in @ X2 @ X4=>in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ap2p)). 85.96/86.20 thf(funcinfuncset, axiom, (funcinfuncset<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>in @ X29 @ (funcSet @ X4 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', funcinfuncset)). 85.96/86.20 thf(lamProp, axiom, (lamProp<=>![X4:$i, X5:$i, X30:$i > $i]:(![X2:$i]:(in @ X2 @ X4=>in @ (X30 @ X2) @ X5)=>func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(X30 @ X2)=(X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', lamProp)). 85.96/86.20 thf(lamp, axiom, (lamp<=>![X4:$i, X5:$i, X31:$i > $i]:(![X2:$i]:(in @ X2 @ X4=>in @ (X31 @ X2) @ X5)=>func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:X31 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', lamp)). 85.96/86.20 thf(lam2p, axiom, (lam2p<=>![X4:$i, X5:$i, X32:$i > $i]:(![X2:$i]:(in @ X2 @ X4=>in @ (X32 @ X2) @ X5)=>in @ (lam @ X4 @ X5 @ (^[X2:$i]:X32 @ X2)) @ (funcSet @ X4 @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', lam2p)). 85.96/86.20 thf(ex1E2, axiom, (ex1E2<=>![X4:$i, X1:$i > $o]:(ex1 @ X4 @ (^[X2:$i]:X1 @ X2)=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ex1E2)). 85.96/86.20 thf(funcGraphProp1, axiom, (funcGraphProp1<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>![X2:$i]:(in @ X2 @ X4=>in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', funcGraphProp1)). 85.96/86.20 thf(funcGraphProp3, axiom, (funcGraphProp3<=>![X4:$i, X5:$i, X29:$i]:(in @ X29 @ (funcSet @ X4 @ X5)=>![X2:$i]:(in @ X2 @ X4=>in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', funcGraphProp3)). 85.96/86.20 thf(funcGraphProp2, axiom, (funcGraphProp2<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ X29=>(ap @ X4 @ X5 @ X29 @ X2)=(X3)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', funcGraphProp2)). 85.96/86.20 thf(funcextLem, axiom, (funcextLem<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>![X34:$i]:(func @ X4 @ X5 @ X34=>(![X2:$i]:(in @ X2 @ X4=>(ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ X34=>in @ (kpair @ X2 @ X3) @ X29))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', funcextLem)). 85.96/86.20 thf(funcGraphProp4, axiom, (funcGraphProp4<=>![X4:$i, X5:$i, X29:$i]:(in @ X29 @ (funcSet @ X4 @ X5)=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ X29=>(ap @ X4 @ X5 @ X29 @ X2)=(X3)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', funcGraphProp4)). 85.96/86.20 thf(funcext, axiom, (funcext<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>![X34:$i]:(func @ X4 @ X5 @ X34=>(![X2:$i]:(in @ X2 @ X4=>(ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))=>(X29)=(X34))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', funcext)). 85.96/86.20 thf(funcext2, axiom, (funcext2<=>![X4:$i, X5:$i, X29:$i]:(in @ X29 @ (funcSet @ X4 @ X5)=>![X34:$i]:(in @ X34 @ (funcSet @ X4 @ X5)=>(![X2:$i]:(in @ X2 @ X4=>(ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))=>(X29)=(X34))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', funcext2)). 85.96/86.20 thf(ap2apEq1, axiom, (ap2apEq1<=>![X4:$i, X5:$i, X29:$i]:(in @ X29 @ (funcSet @ X4 @ X5)=>![X2:$i]:(in @ X2 @ X4=>(ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ap2apEq1)). 85.96/86.20 thf(ap2apEq2, axiom, (ap2apEq2<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>![X2:$i]:(in @ X2 @ X4=>(ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ap2apEq2)). 85.96/86.20 thf(beta1, axiom, (beta1<=>![X4:$i, X5:$i, X36:$i > $i]:(![X2:$i]:(in @ X2 @ X4=>in @ (X36 @ X2) @ X5)=>![X2:$i]:(in @ X2 @ X4=>(ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:X36 @ X3)) @ X2)=(X36 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', beta1)). 85.96/86.20 thf(eta1, axiom, (eta1<=>![X4:$i, X5:$i, X29:$i]:(func @ X4 @ X5 @ X29=>(lam @ X4 @ X5 @ (^[X2:$i]:ap @ X4 @ X5 @ X29 @ X2))=(X29))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eta1)). 85.96/86.20 thf(lam2lamEq, axiom, (lam2lamEq<=>![X4:$i, X5:$i, X37:$i > $i]:(![X2:$i]:(in @ X2 @ X4=>in @ (X37 @ X2) @ X5)=>(lam @ X4 @ X5 @ (^[X2:$i]:X37 @ X2))=(lam @ X4 @ X5 @ (^[X2:$i]:X37 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', lam2lamEq)). 85.96/86.20 thf(beta2, axiom, (beta2<=>![X4:$i, X5:$i, X38:$i > $i]:(![X2:$i]:(in @ X2 @ X4=>in @ (X38 @ X2) @ X5)=>![X2:$i]:(in @ X2 @ X4=>(ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:X38 @ X3)) @ X2)=(X38 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', beta2)). 85.96/86.20 thf(eta2, axiom, (eta2<=>![X4:$i, X5:$i, X29:$i]:(in @ X29 @ (funcSet @ X4 @ X5)=>(lam @ X4 @ X5 @ (^[X2:$i]:ap @ X4 @ X5 @ X29 @ X2))=(X29))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eta2)). 85.96/86.20 thf(iffalseProp1, axiom, (iffalseProp1<=>![X4:$i, X39:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(~(X39)=>in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((X39&(X14)=(X2))|(~(X39)&(X14)=(X3))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', iffalseProp1)). 85.96/86.20 thf(iffalseProp2, axiom, (iffalseProp2<=>![X4:$i, X40:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(~(X40)=>(dsetconstr @ X4 @ (^[X14:$i]:((X40&(X14)=(X2))|(~(X40)&(X14)=(X3)))))=(setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', iffalseProp2)). 85.96/86.20 thf(iftrueProp1, axiom, (iftrueProp1<=>![X4:$i, X41:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(X41=>in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((X41&(X14)=(X2))|(~(X41)&(X14)=(X3))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', iftrueProp1)). 85.96/86.20 thf(iftrueProp2, axiom, (iftrueProp2<=>![X4:$i, X42:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(X42=>(dsetconstr @ X4 @ (^[X14:$i]:((X42&(X14)=(X2))|(~(X42)&(X14)=(X3)))))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', iftrueProp2)). 85.96/86.20 thf(ifSingleton, axiom, (ifSingleton<=>![X4:$i, X43:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((X43&(X14)=(X2))|(~(X43)&(X14)=(X3)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ifSingleton)). 85.96/86.20 thf(ifp, axiom, (ifp<=>![X4:$i, X44:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>in @ (if @ X4 @ (X44) @ X2 @ X3) @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ifp)). 85.96/86.20 thf(theeq, axiom, (theeq<=>![X21:$i]:(singleton @ X21=>![X2:$i]:(in @ X2 @ X21=>(setunion @ X21)=(X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', theeq)). 85.96/86.20 thf(iftrue, axiom, (iftrue<=>![X4:$i, X45:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(X45=>(if @ X4 @ (X45) @ X2 @ X3)=(X2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', iftrue)). 85.96/86.20 thf(iffalse, axiom, (iffalse<=>![X4:$i, X46:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(~(X46)=>(if @ X4 @ (X46) @ X2 @ X3)=(X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', iffalse)). 85.96/86.20 thf(iftrueorfalse, axiom, (iftrueorfalse<=>![X4:$i, X47:$o, X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>in @ (if @ X4 @ (X47) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', iftrueorfalse)). 85.96/86.20 thf(binintersectT_lem, axiom, (binintersectT_lem<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>in @ (binintersect @ X21 @ X48) @ (powerset @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectT_lem)). 85.96/86.20 thf(binunionT_lem, axiom, (binunionT_lem<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>in @ (binunion @ X21 @ X48) @ (powerset @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionT_lem)). 85.96/86.20 thf(powersetT_lem, axiom, (powersetT_lem<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetT_lem)). 85.96/86.20 thf(setminusT_lem, axiom, (setminusT_lem<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>in @ (setminus @ X21 @ X48) @ (powerset @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusT_lem)). 85.96/86.20 thf(complementT_lem, axiom, (complementT_lem<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>in @ (setminus @ X4 @ X21) @ (powerset @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', complementT_lem)). 85.96/86.20 thf(setextT, axiom, (setextT<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>(![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X21=>in @ X2 @ X48))=>(![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X48=>in @ X2 @ X21))=>(X21)=(X48)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setextT)). 85.96/86.20 thf(subsetTI, axiom, (subsetTI<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>(![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X21=>in @ X2 @ X48))=>subset @ X21 @ X48)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetTI)). 85.96/86.20 thf(powersetTI1, axiom, (powersetTI1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>(![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X21=>in @ X2 @ X48))=>in @ X21 @ (powerset @ X48))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetTI1)). 85.96/86.20 thf(powersetTE1, axiom, (powersetTE1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X21 @ (powerset @ X48)=>(in @ X2 @ X21=>in @ X2 @ X48)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetTE1)). 85.96/86.20 thf(complementTI1, axiom, (complementTI1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X21=>~(in @ X2 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', complementTI1)). 85.96/86.20 thf(complementTE1, axiom, (complementTE1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ (setminus @ X4 @ X21))=>in @ X2 @ X21)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', complementTE1)). 85.96/86.20 thf(binintersectTELcontra, axiom, (binintersectTELcontra<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X21)=>~(in @ X2 @ (binintersect @ X21 @ X48))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectTELcontra)). 85.96/86.20 thf(binintersectTERcontra, axiom, (binintersectTERcontra<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X48)=>~(in @ X2 @ (binintersect @ X21 @ X48))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectTERcontra)). 85.96/86.20 thf(contrasubsetT, axiom, (contrasubsetT<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(subset @ X21 @ (setminus @ X4 @ X48)=>(in @ X2 @ X48=>~(in @ X2 @ X21))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', contrasubsetT)). 85.96/86.20 thf(contrasubsetT1, axiom, (contrasubsetT1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(subset @ X21 @ X48=>(~(in @ X2 @ X48)=>~(in @ X2 @ X21))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', contrasubsetT1)). 85.96/86.20 thf(contrasubsetT2, axiom, (contrasubsetT2<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>(subset @ X21 @ X48=>subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', contrasubsetT2)). 85.96/86.20 thf(contrasubsetT3, axiom, (contrasubsetT3<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)=>subset @ X21 @ X48)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', contrasubsetT3)). 85.96/86.20 thf(doubleComplementI1, axiom, (doubleComplementI1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X21=>in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', doubleComplementI1)). 85.96/86.20 thf(doubleComplementE1, axiom, (doubleComplementE1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))=>in @ X2 @ X21)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', doubleComplementE1)). 85.96/86.20 thf(doubleComplementSub1, axiom, (doubleComplementSub1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', doubleComplementSub1)). 85.96/86.20 thf(doubleComplementSub2, axiom, (doubleComplementSub2<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', doubleComplementSub2)). 85.96/86.20 thf(doubleComplementEq, axiom, (doubleComplementEq<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>(X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', doubleComplementEq)). 85.96/86.20 thf(complementTnotintersectT, axiom, (complementTnotintersectT<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (setminus @ X4 @ X21)=>~(in @ X2 @ (binintersect @ X21 @ X48))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', complementTnotintersectT)). 85.96/86.20 thf(complementImpComplementIntersect, axiom, (complementImpComplementIntersect<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (setminus @ X4 @ X21)=>in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', complementImpComplementIntersect)). 85.96/86.20 thf(complementSubsetComplementIntersect, axiom, (complementSubsetComplementIntersect<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', complementSubsetComplementIntersect)). 85.96/86.20 thf(complementInPowersetComplementIntersect, axiom, (complementInPowersetComplementIntersect<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', complementInPowersetComplementIntersect)). 85.96/86.20 thf(contraSubsetComplement, axiom, (contraSubsetComplement<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>(subset @ X21 @ (setminus @ X4 @ X48)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ X48=>in @ X2 @ (setminus @ X4 @ X21))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', contraSubsetComplement)). 85.96/86.20 thf(complementTcontraSubset, axiom, (complementTcontraSubset<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>(subset @ X21 @ (setminus @ X4 @ X48)=>subset @ X48 @ (setminus @ X4 @ X21))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', complementTcontraSubset)). 85.96/86.20 thf(binunionTILcontra, axiom, (binunionTILcontra<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ (binunion @ X21 @ X48))=>~(in @ X2 @ X21)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionTILcontra)). 85.96/86.20 thf(binunionTIRcontra, axiom, (binunionTIRcontra<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ (binunion @ X21 @ X48))=>~(in @ X2 @ X48)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionTIRcontra)). 85.96/86.20 thf(inIntersectImpInUnion, axiom, (inIntersectImpInUnion<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X49:$i]:(in @ X49 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (binintersect @ X21 @ X48)=>in @ X2 @ (binunion @ X21 @ X49))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', inIntersectImpInUnion)). 85.96/86.20 thf(inIntersectImpInUnion2, axiom, (inIntersectImpInUnion2<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X49:$i]:(in @ X49 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (binintersect @ X21 @ X48)=>in @ X2 @ (binunion @ X48 @ X49))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', inIntersectImpInUnion2)). 85.96/86.20 thf(inIntersectImpInIntersectUnions, axiom, (inIntersectImpInIntersectUnions<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X49:$i]:(in @ X49 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (binintersect @ X21 @ X48)=>in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', inIntersectImpInIntersectUnions)). 85.96/86.20 thf(intersectInPowersetIntersectUnions, axiom, (intersectInPowersetIntersectUnions<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X49:$i]:(in @ X49 @ (powerset @ X4)=>in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', intersectInPowersetIntersectUnions)). 85.96/86.20 thf(inComplementUnionImpNotIn1, axiom, (inComplementUnionImpNotIn1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))=>~(in @ X2 @ X21)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', inComplementUnionImpNotIn1)). 85.96/86.20 thf(inComplementUnionImpInComplement1, axiom, (inComplementUnionImpInComplement1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))=>in @ X2 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', inComplementUnionImpInComplement1)). 85.96/86.20 thf(binunionTE, axiom, (binunionTE<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X50:$o, X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (binunion @ X21 @ X48)=>((in @ X2 @ X21=>X50)=>((in @ X2 @ X48=>X50)=>X50))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionTE)). 85.96/86.20 thf(binunionTEcontra, axiom, (binunionTEcontra<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(~(in @ X2 @ X21)=>(~(in @ X2 @ X48)=>~(in @ X2 @ (binunion @ X21 @ X48)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionTEcontra)). 85.96/86.20 thf(demorgan2a1, axiom, (demorgan2a1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))=>in @ X2 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', demorgan2a1)). 85.96/86.20 thf(complementUnionInPowersetComplement, axiom, (complementUnionInPowersetComplement<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', complementUnionInPowersetComplement)). 85.96/86.20 thf(demorgan2a2, axiom, (demorgan2a2<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))=>in @ X2 @ (setminus @ X4 @ X48)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', demorgan2a2)). 85.96/86.20 thf(demorgan1a, axiom, (demorgan1a<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))=>in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', demorgan1a)). 85.96/86.20 thf(demorgan1b, axiom, (demorgan1b<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))=>in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', demorgan1b)). 85.96/86.20 thf(demorgan1, axiom, (demorgan1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>(setminus @ X4 @ (binintersect @ X21 @ X48))=(binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', demorgan1)). 85.96/86.20 thf(demorgan2a, axiom, (demorgan2a<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))=>in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', demorgan2a)). 85.96/86.20 thf(demorgan2b2, axiom, (demorgan2b2<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (setminus @ X4 @ X21)=>(in @ X2 @ (setminus @ X4 @ X48)=>in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', demorgan2b2)). 85.96/86.20 thf(demorgan2b, axiom, (demorgan2b<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ X4=>(in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))=>in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', demorgan2b)). 85.96/86.20 thf(demorgan2, axiom, (demorgan2<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>(setminus @ X4 @ (binunion @ X21 @ X48))=(binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', demorgan2)). 85.96/86.20 thf(woz13rule0, axiom, (woz13rule0<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X2:$i]:(in @ X2 @ (binintersect @ X21 @ X48)=>in @ X2 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', woz13rule0)). 85.96/86.20 thf(woz13rule1, axiom, (woz13rule1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X49:$i]:(in @ X49 @ (powerset @ X4)=>(subset @ X21 @ X49=>subset @ (binintersect @ X21 @ X48) @ X49))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', woz13rule1)). 85.96/86.20 thf(woz13rule2, axiom, (woz13rule2<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X49:$i]:(in @ X49 @ (powerset @ X4)=>(subset @ X48 @ X49=>subset @ (binintersect @ X21 @ X48) @ X49))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', woz13rule2)). 85.96/86.20 thf(woz13rule3, axiom, (woz13rule3<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X49:$i]:(in @ X49 @ (powerset @ X4)=>(subset @ X21 @ X48=>(subset @ X21 @ X49=>subset @ X21 @ (binintersect @ X48 @ X49))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', woz13rule3)). 85.96/86.20 thf(woz13rule4, axiom, (woz13rule4<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X49:$i]:(in @ X49 @ (powerset @ X4)=>![X51:$i]:(in @ X51 @ (powerset @ X4)=>(subset @ X21 @ X49=>(subset @ X48 @ X51=>subset @ (binintersect @ X21 @ X48) @ (binintersect @ X49 @ X51)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', woz13rule4)). 85.96/86.20 thf(woz1_1, axiom, (woz1_1<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', woz1_1)). 85.96/86.20 thf(woz1_2, axiom, (woz1_2<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X49:$i]:(in @ X49 @ (powerset @ X4)=>![X51:$i]:(in @ X51 @ (powerset @ X4)=>(setminus @ X4 @ (binintersect @ (binunion @ X21 @ X48) @ (binunion @ X49 @ X51)))=(binunion @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)) @ (binintersect @ (setminus @ X4 @ X49) @ (setminus @ X4 @ X51)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', woz1_2)). 85.96/86.20 thf(woz1_3, axiom, (woz1_3<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X49:$i]:(in @ X49 @ (powerset @ X4)=>in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', woz1_3)). 85.96/86.20 thf(woz1_4, axiom, (woz1_4<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>(subset @ X21 @ (setminus @ X4 @ X48)=>subset @ X48 @ (setminus @ X4 @ X21))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', woz1_4)). 85.96/86.20 thf(woz1_5, axiom, (woz1_5<=>![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', woz1_5)). 85.96/86.20 thf(choice2fnsingleton, axiom, (choice2fnsingleton<=>![X4:$i, X5:$i, X52:$i > $i > $o]:(![X2:$i]:(in @ X2 @ X4=>?[X3:$i]:(in @ X3 @ X5&X52 @ X2 @ X3))=>![X33:$i]:(in @ X33 @ (breln1Set @ X5)=>(reflwellordering @ X5 @ X33=>![X2:$i]:(in @ X2 @ X4=>singleton @ (dsetconstr @ X5 @ (^[X3:$i]:(X52 @ X2 @ X3&![X14:$i]:(in @ X14 @ X5=>(X52 @ X2 @ X14=>in @ (kpair @ X3 @ X14) @ X33)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', choice2fnsingleton)). 85.96/86.20 thf(c_0_303, axiom, (breln1)=(^[X4:$i, X33:$i]:subset @ X33 @ (cartprod @ X4 @ X4)), inference(apply_def,[status(thm)],[breln1, breln])). 85.96/86.20 thf(c_0_304, axiom, (replAx)=(![X6:$i > $i > $o, X4:$i]:(![X2:$i]:(in @ X2 @ X4=>?[X1032:$i]:(X6 @ X2 @ X1032&![X1034:$i]:(X6 @ X2 @ X1034=>(X1032)=(X1034))))=>?[X5:$i]:![X2:$i]:(in @ X2 @ X5<=>?[X3:$i]:(in @ X3 @ X4&X6 @ X3 @ X2)))), inference(apply_def,[status(thm)],[replAx, exu])). 85.96/86.20 thf(c_0_305, axiom, (descrp)=(![X1:$i > $o]:(?[X1035:$i]:(X1 @ X1035&![X1036:$i]:(X1 @ X1036=>(X1035)=(X1036)))=>X1 @ (descr @ (^[X2:$i]:X1 @ X2)))), inference(apply_def,[status(thm)],[descrp, exu])). 85.96/86.20 thf(c_0_306, axiom, (exuE1)=(![X1:$i > $o]:(?[X1037:$i]:(X1 @ X1037&![X1038:$i]:(X1 @ X1038=>(X1037)=(X1038)))=>?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3))))), inference(apply_def,[status(thm)],[exuE1, exu])). 85.96/86.20 thf(c_0_307, axiom, (exuE3e)=(![X1:$i > $o]:(?[X1039:$i]:(X1 @ X1039&![X1040:$i]:(X1 @ X1040=>(X1039)=(X1040)))=>?[X2:$i]:X1 @ X2)), inference(apply_def,[status(thm)],[exuE3e, exu])). 85.96/86.20 thf(c_0_308, axiom, (nonemptyE1)=(![X4:$i]:((X4)!=(emptyset)=>?[X2:$i]:in @ X2 @ X4)), inference(apply_def,[status(thm)],[nonemptyE1, nonempty])). 85.96/86.20 thf(c_0_309, axiom, (nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(in @ X2 @ X4=>(X1 @ X2=>(dsetconstr @ X4 @ (^[X3:$i]:X1 @ X3))!=(emptyset)))), inference(apply_def,[status(thm)],[nonemptyI, nonempty])). 85.96/86.20 thf(c_0_310, axiom, (nonemptyI1)=(![X4:$i]:(?[X2:$i]:in @ X2 @ X4=>(X4)!=(emptyset))), inference(apply_def,[status(thm)],[nonemptyI1, nonempty])). 85.96/86.20 thf(c_0_311, axiom, (exuE2)=(![X1:$i > $o]:(?[X1041:$i]:(X1 @ X1041&![X1042:$i]:(X1 @ X1042=>(X1041)=(X1042)))=>?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2)))), inference(apply_def,[status(thm)],[exuE2, exu])). 85.96/86.20 thf(c_0_312, axiom, (nonemptyImpWitness)=(![X4:$i]:((X4)!=(emptyset)=>?[X2:$i]:(in @ X2 @ X4&$true))), inference(apply_def,[status(thm)],[nonemptyImpWitness, nonempty])). 85.96/86.20 thf(c_0_313, axiom, (exuI1)=(![X1:$i > $o]:(?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3)))=>?[X1043:$i]:(X1 @ X1043&![X1044:$i]:(X1 @ X1044=>(X1043)=(X1044))))), inference(apply_def,[status(thm)],[exuI1, exu])). 85.96/86.20 thf(c_0_314, axiom, (exuI3)=(![X1:$i > $o]:(?[X2:$i]:X1 @ X2=>(![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3)))=>?[X1045:$i]:(X1 @ X1045&![X1046:$i]:(X1 @ X1046=>(X1045)=(X1046)))))), inference(apply_def,[status(thm)],[exuI3, exu])). 85.96/86.20 thf(c_0_315, axiom, (exuI2)=(![X1:$i > $o]:(?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2))=>?[X1047:$i]:(X1 @ X1047&![X1048:$i]:(X1 @ X1048=>(X1047)=(X1048))))), inference(apply_def,[status(thm)],[exuI2, exu])). 85.96/86.20 thf(c_0_316, axiom, (exuE3u)=(![X1:$i > $o]:(?[X1049:$i]:(X1 @ X1049&![X1050:$i]:(X1 @ X1050=>(X1049)=(X1050)))=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))), inference(apply_def,[status(thm)],[exuE3u, exu])). 85.96/86.20 thf(c_0_317, axiom, (exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(?[X1051:$i]:(X1 @ X1051&![X1052:$i]:(X1 @ X1052=>(X1051)=(X1052)))<=>?[X1053:$i]:(X17 @ X1053&![X1054:$i]:(X17 @ X1054=>(X1053)=(X1054)))))), inference(apply_def,[status(thm)],[exu__Cong, exu])). 85.96/86.20 thf(c_0_318, axiom, (exuEu)=(![X1:$i > $o]:(?[X1055:$i]:(X1 @ X1055&![X1056:$i]:(X1 @ X1056=>(X1055)=(X1056)))=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))), inference(apply_def,[status(thm)],[exuEu, exu])). 85.96/86.20 thf(c_0_319, axiom, (descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(?[X1057:$i]:(X1 @ X1057&![X1058:$i]:(X1 @ X1058=>(X1057)=(X1058)))=>(?[X1059:$i]:(X17 @ X1059&![X1060:$i]:(X17 @ X1060=>(X1059)=(X1060)))=>(descr @ (^[X2:$i]:X1 @ X2))=(descr @ (^[X2:$i]:X17 @ X2)))))), inference(apply_def,[status(thm)],[descr__Cong, exu])). 85.96/86.20 thf(c_0_320, axiom, (setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:X24 @ X2 @ X3)) @ (cartprod @ X4 @ X5)), inference(apply_def,[status(thm)],[setOfPairsIsBReln, breln])). 85.96/86.20 thf(c_0_321, axiom, (brelnall1)=(![X4:$i, X5:$i, X33:$i]:(subset @ X33 @ (cartprod @ X4 @ X5)=>![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)))), inference(apply_def,[status(thm)],[brelnall1, breln])). 85.96/86.20 thf(c_0_322, axiom, (brelnall2)=(![X4:$i, X5:$i, X33:$i]:(subset @ X33 @ (cartprod @ X4 @ X5)=>![X1:$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)))), inference(apply_def,[status(thm)],[brelnall2, breln])). 85.96/86.20 thf(c_0_323, axiom, (subbreln)=(![X4:$i, X5:$i, X33:$i]:(subset @ X33 @ (cartprod @ X4 @ X5)=>![X35:$i]:(subset @ X35 @ (cartprod @ X4 @ X5)=>(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>(in @ (kpair @ X2 @ X3) @ X33=>in @ (kpair @ X2 @ X3) @ X35)))=>subset @ X33 @ X35)))), inference(apply_def,[status(thm)],[subbreln, breln])). 85.96/86.20 thf(c_0_324, axiom, (eqbreln)=(![X4:$i, X5:$i, X33:$i]:(subset @ X33 @ (cartprod @ X4 @ X5)=>![X35:$i]:(subset @ X35 @ (cartprod @ X4 @ X5)=>(![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)))))), inference(apply_def,[status(thm)],[eqbreln, breln])). 85.96/86.20 thf(c_0_325, axiom, (breln1all2)=(![X4:$i, X33:$i]:(subset @ X33 @ (cartprod @ X4 @ X4)=>![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)))), inference(apply_def,[status(thm)],[breln1all2, c_0_303])). 85.96/86.20 thf(c_0_326, axiom, (breln1SetBreln1)=(![X4:$i, X33:$i]:(in @ X33 @ (breln1Set @ X4)=>subset @ X33 @ (cartprod @ X4 @ X4))), inference(apply_def,[status(thm)],[breln1SetBreln1, c_0_303])). 85.96/86.20 thf(c_0_327, axiom, (setOfPairsIsBReln1)=(![X4:$i, X53:$i > $i > $o]:subset @ (dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:X53 @ X2 @ X3)) @ (cartprod @ X4 @ X4)), inference(apply_def,[status(thm)],[setOfPairsIsBReln1, c_0_303])). 85.96/86.20 thf(c_0_328, axiom, (breln1all1)=(![X4:$i, X33:$i]:(subset @ X33 @ (cartprod @ X4 @ X4)=>![X1:$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)))), inference(apply_def,[status(thm)],[breln1all1, c_0_303])). 85.96/86.20 thf(c_0_329, axiom, (subbreln1)=(![X4:$i, X33:$i]:(subset @ X33 @ (cartprod @ X4 @ X4)=>![X35:$i]:(subset @ X35 @ (cartprod @ X4 @ X4)=>(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(in @ (kpair @ X2 @ X3) @ X33=>in @ (kpair @ X2 @ X3) @ X35)))=>subset @ X33 @ X35)))), inference(apply_def,[status(thm)],[subbreln1, c_0_303])). 85.96/86.20 thf(c_0_330, axiom, (eqbreln1)=(![X4:$i, X33:$i]:(subset @ X33 @ (cartprod @ X4 @ X4)=>![X35:$i]:(subset @ X35 @ (cartprod @ X4 @ X4)=>(![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)))))), inference(apply_def,[status(thm)],[eqbreln1, c_0_303])). 85.96/86.20 thf(c_0_331, axiom, (breln1invprop)=(![X4:$i, X33:$i]:(subset @ X33 @ (cartprod @ X4 @ X4)=>subset @ (breln1invset @ X4 @ X33) @ (cartprod @ X4 @ X4))), inference(apply_def,[status(thm)],[breln1invprop, c_0_303])). 85.96/86.20 thf(c_0_332, axiom, (breln1invI)=(![X4:$i, X33:$i]:(subset @ X33 @ (cartprod @ X4 @ X4)=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(in @ (kpair @ X2 @ X3) @ X33=>in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33)))))), inference(apply_def,[status(thm)],[breln1invI, c_0_303])). 85.96/86.20 thf(c_0_333, axiom, (breln1invE)=(![X4:$i, X33:$i]:(subset @ X33 @ (cartprod @ X4 @ X4)=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33)=>in @ (kpair @ X2 @ X3) @ X33))))), inference(apply_def,[status(thm)],[breln1invE, c_0_303])). 85.96/86.20 thf(c_0_334, axiom, (breln1compprop)=(![X4:$i, X33:$i]:(subset @ X33 @ (cartprod @ X4 @ X4)=>![X35:$i]:(subset @ X35 @ (cartprod @ X4 @ X4)=>subset @ (breln1compset @ X4 @ X33 @ X35) @ (cartprod @ X4 @ X4)))), inference(apply_def,[status(thm)],[breln1compprop, c_0_303])). 85.96/86.20 thf(c_0_335, axiom, (breln1compI)=(![X4:$i, X33:$i]:(subset @ X33 @ (cartprod @ X4 @ X4)=>![X35:$i]:(subset @ X35 @ (cartprod @ X4 @ X4)=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>![X14:$i]:(in @ X14 @ X4=>(in @ (kpair @ X2 @ X14) @ X33=>(in @ (kpair @ X14 @ X3) @ X35=>in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))))))))), inference(apply_def,[status(thm)],[breln1compI, c_0_303])). 85.96/86.20 thf(c_0_336, axiom, (breln1compE)=(![X4:$i, X33:$i]:(subset @ X33 @ (cartprod @ X4 @ X4)=>![X35:$i]:(subset @ X35 @ (cartprod @ X4 @ X4)=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35)=>?[X14:$i]:((in @ X14 @ X4&in @ (kpair @ X2 @ X14) @ X33)&in @ (kpair @ X14 @ X3) @ X35))))))), inference(apply_def,[status(thm)],[breln1compE, c_0_303])). 85.96/86.20 thf(c_0_337, axiom, (breln1compEex)=(![X4:$i, X33:$i]:(subset @ X33 @ (cartprod @ X4 @ X4)=>![X35:$i]:(subset @ X35 @ (cartprod @ X4 @ X4)=>![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))))))), inference(apply_def,[status(thm)],[breln1compEex, c_0_303])). 85.96/86.20 thf(c_0_338, plain, ![X2:$i, X1:$i > $o]:(epred1_2 @ X1 @ X2<=>X1 @ X2), introduced(definition)). 85.96/86.20 thf(c_0_339, plain, ![X2:$i]:epred9_1 @ X2, inference(fof_simplification,[status(thm)],[introduced(definition)])). 85.96/86.20 thf(c_0_340, plain, ![X2:$i, X18:$i]:(epred8_2 @ X18 @ X2<=>(X18)=(kpair @ (kfst @ X18) @ X2)), introduced(definition)). 85.96/86.20 thf(c_0_341, plain, ![X18:$i, X14:$i, X22:$i > $i > $o]:(epred3_3 @ X22 @ X14 @ X18<=>X22 @ X14 @ X18), introduced(definition)). 85.96/86.20 thf(c_0_342, plain, ![X3:$i, X29:$i, X2:$i]:(epred7_3 @ X2 @ X29 @ X3<=>in @ (kpair @ X2 @ X3) @ X29), introduced(definition)). 85.96/86.20 thf(c_0_343, plain, ![X2:$i, X31:$i > $i]:(esk1_2 @ X31 @ X2)=(X31 @ X2), introduced(definition)). 85.96/86.20 thf(c_0_344, plain, ![X14:$i, X2:$i, X41:$o, X3:$i]:(epred5_4 @ X3 @ X41 @ X2 @ X14<=>((X41&(X14)=(X2))|(~X41&(X14)=(X3)))), inference(fof_simplification,[status(thm)],[introduced(definition)])). 85.96/86.20 thf(c_0_345, plain, ![X3:$i, X52:$i > $i > $o, X33:$i, X5:$i, X2:$i]:(epred6_5 @ X2 @ X5 @ X33 @ X52 @ X3<=>(X52 @ X2 @ X3&![X14:$i]:(in @ X14 @ X5=>(X52 @ X2 @ X14=>in @ (kpair @ X3 @ X14) @ X33)))), introduced(definition)). 85.96/86.20 thf(c_0_346, plain, ![X3:$i, X2:$i, X30:$i > $i]:(epred4_3 @ X30 @ X2 @ X3<=>(X30 @ X2)=(X3)), introduced(definition)). 85.96/86.20 thf(c_0_347, plain, ![X2:$i, X18:$i]:(epred2_2 @ X18 @ X2<=>in @ (setadjoin @ X2 @ emptyset) @ X18), introduced(definition)). 85.96/86.20 thf(c_0_348, plain, (epred10_0<=>![X4:$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)). 85.96/86.20 thf(c_0_349, 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:$i]:(in @ X2 @ X4=>?[X1032:$i]:(X6 @ X2 @ X1032&![X1034:$i]:(X6 @ X2 @ X1034=>(X1032)=(X1034))))=>?[X5:$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 > $o]:(?[X1035:$i]:(X1 @ X1035&![X1036:$i]:(X1 @ X1036=>(X1035)=(X1036)))=>X1 @ (descr @ (epred1_2 @ X1)))=>(![X4:$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 > $o]:(?[X1037:$i]:(X1 @ X1037&![X1038:$i]:(X1 @ X1038=>(X1037)=(X1038)))=>?[X2:$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 > $o]:(?[X1039:$i]:(X1 @ X1039&![X1040:$i]:(X1 @ X1040=>(X1039)=(X1040)))=>?[X2:$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 > $o]:(?[X1041:$i]:(X1 @ X1041&![X1042:$i]:(X1 @ X1042=>(X1041)=(X1042)))=>?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2)))=>(![X4:$i]:((X4)!=(emptyset)=>?[X2:$i]:in @ X2 @ X4)=>(![X2:$i, X3:$i]:(in @ X2 @ (setadjoin @ X3 @ emptyset)=>(X2)=(X3))=>(![X2:$i, X3:$i]:((X2)!=(X3)=>~in @ X3 @ (setadjoin @ X2 @ emptyset))=>(![X2:$i, X3:$i]:((X2)=(X3)=>in @ X2 @ (setadjoin @ X3 @ emptyset))=>(![X2:$i, X3:$i]:(in @ X2 @ (setadjoin @ X3 @ emptyset)=>in @ X3 @ (setadjoin @ X2 @ emptyset))=>(![X2:$i, X3:$i, X14:$i]:(in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=>((X14)=(X2)|(X14)=(X3)))=>(![X2:$i, X3:$i]:in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=>(![X2:$i, X3:$i]:in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=>(![X4:$i, X1:$i > $o]:(?[X2:$i]:(in @ X2 @ X4&X1 @ X2)=>(dsetconstr @ X4 @ (epred1_2 @ X1))!=(emptyset))=>(![X1:$i > $o, X2:$i]:(in @ X2 @ emptyset=>X1 @ X2)=>(![X4:$i, X1:$i > $o]:(~(![X2:$i]:(in @ X2 @ X4=>X1 @ X2))=>?[X2:$i]:(in @ X2 @ X4&~X1 @ X2))=>(![X4:$i, X1:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>~X1 @ X2)=>~(?[X2:$i]:(in @ X2 @ X4&X1 @ X2)))=>(![X4:$i, X1:$i > $o]:(~(?[X2:$i]:(in @ X2 @ X4&X1 @ X2))=>![X2:$i]:(in @ X2 @ X4=>~X1 @ X2))=>(![X4:$i, X1:$i > $o]:(?[X2:$i]:(in @ X2 @ X4&~X1 @ X2)=>~(![X2:$i]:(in @ X2 @ X4=>X1 @ X2)))=>(![X15:$o]:(X15=>((~X15|in @ emptyset @ (prop2set @ $true))&(X15|in @ emptyset @ (prop2set @ $false))))=>(![X16:$o]:(X16=>((~X16|set2prop @ (prop2set @ $true))&(X16|set2prop @ (prop2set @ $false))))=>(![X4:$i, X1:$i > $o]:(~(?[X2:$i]:(in @ X2 @ X4&X1 @ X2))=>![X2:$i]:(in @ X2 @ X4=>~X1 @ X2))=>(![X4:$i, X1:$i > $o]:(~(![X2:$i]:(in @ X2 @ X4=>X1 @ X2))=>?[X2:$i]:(in @ X2 @ X4&~X1 @ X2))=>(![X1:$i > $o]:(?[X2:$i]:(X1 @ X2&![X3:$i]:(X1 @ X3=>(X2)=(X3)))=>?[X1043:$i]:(X1 @ X1043&![X1044:$i]:(X1 @ X1044=>(X1043)=(X1044))))=>(![X1:$i > $o]:(?[X2:$i]:X1 @ X2=>(![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3)))=>?[X1045:$i]:(X1 @ X1045&![X1046:$i]:(X1 @ X1046=>(X1045)=(X1046)))))=>(![X1:$i > $o]:(?[X2:$i]:![X3:$i]:(X1 @ X3<=>(X3)=(X2))=>?[X1047:$i]:(X1 @ X1047&![X1048:$i]:(X1 @ X1048=>(X1047)=(X1048))))=>(![X4:$i, X5:$i]:((X4)=(X5)=>![X2:$i, X3:$i]:((X2)=(X3)=>(in @ X2 @ X4=>in @ X3 @ X5)))=>(![X4:$i, X5:$i]:((X4)=(X5)=>![X2:$i, X3:$i]:((X2)=(X3)=>(in @ X2 @ X4<=>in @ X3 @ X5)))=>(![X1:$i > $o]:(?[X1049:$i]:(X1 @ X1049&![X1050:$i]:(X1 @ X1050=>(X1049)=(X1050)))=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))=>(![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(?[X1051:$i]:(X1 @ X1051&![X1052:$i]:(X1 @ X1052=>(X1051)=(X1052)))<=>?[X1053:$i]:(X17 @ X1053&![X1054:$i]:(X17 @ X1054=>(X1053)=(X1054)))))=>((emptyset)=(emptyset)=>(![X2:$i, X3:$i]:((X2)=(X3)=>![X14:$i, X18:$i]:((X14)=(X18)=>(setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18)))=>(![X4:$i, X5:$i]:((X4)=(X5)=>(powerset @ X4)=(powerset @ X5))=>(![X4:$i, X5:$i]:((X4)=(X5)=>(setunion @ X4)=(setunion @ X5))=>((omega)=(omega)=>(![X1:$i > $o]:(?[X1055:$i]:(X1 @ X1055&![X1056:$i]:(X1 @ X1056=>(X1055)=(X1056)))=>![X2:$i, X3:$i]:(X1 @ X2=>(X1 @ X3=>(X2)=(X3))))=>(![X1:$i > $o, X17:$i > $o]:(![X2:$i, X3:$i]:((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))=>(?[X1057:$i]:(X1 @ X1057&![X1058:$i]:(X1 @ X1058=>(X1057)=(X1058)))=>(?[X1059:$i]:(X17 @ X1059&![X1060:$i]:(X17 @ X1060=>(X1059)=(X1060)))=>(descr @ (epred1_2 @ X1))=(descr @ (epred1_2 @ X17)))))=>(![X4:$i, X5:$i]:((X4)=(X5)=>![X1:$i > $o, X17:$i > $o]:(![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X5=>((X2)=(X3)=>(X1 @ X2<=>X17 @ X3))))=>(dsetconstr @ X4 @ (epred1_2 @ X1))=(dsetconstr @ X5 @ (epred1_2 @ 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X48 @ (powerset @ X4)=>![X49:$i]:(in @ X49 @ (powerset @ X4)=>![X51:$i]:(in @ X51 @ (powerset @ X4)=>(setminus @ X4 @ (binintersect @ (binunion @ X21 @ X48) @ (binunion @ X49 @ X51)))=(binunion @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)) @ (binintersect @ (setminus @ X4 @ X49) @ (setminus @ X4 @ X51)))))))=>(![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>![X49:$i]:(in @ X49 @ (powerset @ X4)=>in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))=>(![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>(subset @ X21 @ (setminus @ X4 @ X48)=>subset @ X48 @ (setminus @ X4 @ X21))))=>(![X4:$i, X21:$i]:(in @ X21 @ (powerset @ X4)=>![X48:$i]:(in @ X48 @ (powerset @ X4)=>in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21))))=>(![X4:$i, X33:$i]:(subset @ X33 @ (cartprod @ X4 @ X4)=>![X1:$i > $o]:(![X2:$i]:(in @ X2 @ 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X35)))=>subset @ X33 @ X35)))=>(![X4:$i, X33:$i]:(subset @ X33 @ (cartprod @ X4 @ X4)=>![X35:$i]:(subset @ X35 @ (cartprod @ X4 @ X4)=>(![X2:$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:$i]:(in @ X3 @ X4=>(in @ (kpair @ X2 @ X3) @ X35=>in @ (kpair @ X2 @ X3) @ X33)))=>(X33)=(X35)))))=>(![X4:$i, X33:$i]:(subset @ X33 @ (cartprod @ X4 @ X4)=>subset @ (breln1invset @ X4 @ X33) @ (cartprod @ X4 @ X4))=>(![X4:$i, X33:$i]:(subset @ X33 @ (cartprod @ X4 @ X4)=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(in @ (kpair @ X2 @ X3) @ X33=>in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33)))))=>(![X4:$i, X33:$i]:(subset @ X33 @ (cartprod @ X4 @ X4)=>![X2:$i]:(in @ X2 @ X4=>![X3:$i]:(in @ X3 @ X4=>(in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33)=>in @ (kpair @ X2 @ X3) @ X33))))=>(![X4:$i, X33:$i]:(subset @ X33 @ (cartprod @ X4 @ X4)=>![X35:$i]:(subset @ X35 @ (cartprod @ X4 @ X4)=>subset @ 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X35=>X54)))=>X54))))))=>![X4:$i, X33:$i]:(subset @ X33 @ (cartprod @ X4 @ X4)=>![X35:$i]:(subset @ X35 @ (cartprod @ X4 @ X4)=>subset @ (binunion @ X33 @ X35) @ (cartprod @ X4 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_304]), foundationAx]), wellorderingAx]), c_0_305]), dsetconstrI]), dsetconstrEL]), dsetconstrER]), c_0_306]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_307]), setext]), emptyI]), noeltsimpempty]), setbeta]), c_0_308]), c_0_309]), c_0_310]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), setoftrueEq]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_311]), c_0_312]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), emptyE1]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_313]), c_0_314]), c_0_315]), inCongP]), in__Cong]), c_0_316]), c_0_317]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_318]), c_0_319]), 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]), c_0_320]), dpsetconstrERa]), dpsetconstrEL1]), dpsetconstrEL2]), dpsetconstrER]), funcImageSingleton]), apProp]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), lamProp]), lamp]), lam2p]), c_0_321]), c_0_322]), ex1E2]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), c_0_323]), c_0_324]), 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]), c_0_303]), c_0_325]), c_0_326]), choice2fnsingleton]), c_0_327]), c_0_328]), c_0_329]), c_0_330]), c_0_331]), c_0_332]), c_0_333]), c_0_334]), c_0_335]), c_0_336]), c_0_337]), c_0_338]), c_0_338]), c_0_339]), c_0_338]), c_0_338]), c_0_338]), c_0_340]), c_0_341]), c_0_341]), c_0_341]), c_0_341]), c_0_342]), c_0_342]), c_0_343]), c_0_343]), c_0_343]), c_0_343]), c_0_344]), c_0_344]), c_0_344]), c_0_345]), c_0_341]), c_0_344]), c_0_344]), c_0_343]), c_0_343]), c_0_343]), c_0_338]), c_0_343]), c_0_346]), c_0_341]), c_0_341]), c_0_341]), c_0_347]), c_0_338]), c_0_338]), c_0_338]), c_0_338]), c_0_338]), c_0_338]), c_0_338]), c_0_338]), c_0_338]), c_0_338]), c_0_338]), c_0_338])])]), c_0_348])). 85.96/86.20 thf(c_0_350, negated_conjecture, ![X1061:$i, X1062:$i, X1064:$i, X1065:$i, X1066:$i, X1067:$i, X1068:$i, X1069:$i, X1070:$i, X1071:$i, X1072:$i, X1074:$i, X1075:$i, X1077:$i, X1078:$i, X1079:$i, X1080:$i, X1081:$i, X1083:$i, X1084:$i > $i > $o, X1085:$i, X1087:$i, X1090:$i, X1092:$i, X1093:$i, X1094:$i, X1095:$i, X1097:$i, X1098:$i > $o, X1099:$i, X1101:$i, X1102:$i > $o, X1103:$i, X1104:$i, X1105:$i > $o, X1106:$i, X1107:$i, X1108:$i > $o, X1109:$i, X1110:$i > $o, X1111:$i, X1114:$i, X1115:$o, X1116:$i, X1117:$i, X1118:$o, X1119:$i, X1120:$i, X1121:$i > $o, X1122:$i, X1125:$i, X1126:$i, X1129:$i, X1131:$i, X1133:$i, X1134:$i > $o, X1135:$i, X1136:$i, X1138:$i, X1139:$i > $o, X1140:$i, X1141:$i, X1142:$i, X1143:$i, X1144:$i, X1145:$i, X1146:$i, X1147:$i, X1148:$i, X1149:$i, X1150:$i, X1151:$o, X1152:$i, X1153:$i, X1154:$i, X1155:$i, X1156:$i, X1157:$i, X1159:$i, X1160:$i, X1161:$i, X1162:$i, X1163:$i, X1164:$i, X1165:$i, X1166:$i, X1167:$i, X1168:$i, X1169:$o, X1171:$i, X1172:$i, X1173:$i > $o, X1174:$i, X1177:$i, X1178:$i, X1179:$i, X1181:$i, X1182:$i, X1183:$i, X1184:$i, X1185:$i, X1186:$i, X1187:$i, X1188:$i, X1189:$i, X1190:$i, X1191:$i, X1192:$i, X1193:$i, X1194:$i, X1195:$i, X1196:$i, X1197:$i > $o, X1198:$i, X1199:$i > $o, X1200:$i, X1201:$i, X1202:$i > $o, X1203:$i, X1205:$i, X1206:$i > $o, X1208:$i, X1209:$i, X1210:$i > $o, X1212:$i, X1213:$i, X1214:$i > $o, X1215:$i, X1217:$o, X1218:$o, X1219:$i, X1220:$i > $o, X1222:$i, X1223:$i, X1224:$i > $o, X1225:$i, X1227:$i > $o, X1228:$i, X1231:$i, X1232:$i > $o, X1233:$i, X1237:$i, X1238:$i > $o, X1239:$i, X1242:$i, X1243:$i, X1244:$i, X1245:$i, X1246:$i, X1247:$i, X1248:$i, X1249:$i, X1250:$i, X1251:$i > $o, X1252:$i, X1254:$i, X1255:$i, X1256:$i > $o, X1257:$i > $o, X1260:$i, X1263:$i, X1264:$i, X1267:$i, X1268:$i, X1269:$i, X1270:$i, X1271:$i, X1272:$i, X1273:$i, X1274:$i, X1275:$i, X1276:$i > $o, X1277:$i, X1279:$i, X1280:$i, X1281:$i > $o, X1282:$i > $o, X1285:$i, X1287:$i, X1289:$i, X1290:$i, X1291:$i > $o, X1292:$i > $o, X1295:$i, X1296:$i, X1298:$i, X1299:$i, X1300:$i, X1301:$i, X1302:$i, X1303:$i, X1305:$i, X1306:$i, X1307:$i, X1308:$i, X1309:$i, X1310:$i, X1311:$i, X1312:$i, X1313:$i, X1314:$i, X1315:$i, X1316:$i, X1317:$i, X1318:$i, X1319:$i, X1320:$i, X1321:$i, X1322:$i, X1323:$i, X1324:$i, X1325:$i, X1326:$i, X1327:$i, X1328:$i, X1329:$i, X1330:$i, X1331:$i, X1332:$i, X1333:$i, X1334:$i, X1335:$i, X1336:$i, X1337:$i, X1338:$i, X1339:$i, X1340:$i, X1341:$i, X1342:$i > $o, X1343:$i, X1344:$i > $o, X1345:$i, X1346:$i, X1347:$i, X1348:$i, X1349:$i, X1350:$i, X1351:$i, X1352:$i, X1353:$i, X1354:$i, X1355:$i, X1356:$o, X1357:$i, X1358:$i, X1359:$i, X1360:$i, X1361:$i, X1362:$i, X1363:$i, X1364:$i, X1365:$i, X1366:$i, X1367:$i, X1368:$i, X1369:$i, X1370:$i, X1371:$i, X1372:$i, X1373:$i, X1374:$i, X1375:$i, X1376:$i, X1377:$i, X1378:$i, X1379:$i, X1380:$i, X1381:$i, X1382:$i, X1383:$i, X1385:$i, X1386:$i, X1387:$i, X1388:$i, X1389:$i, X1390:$i, X1391:$i, X1392:$i, X1393:$i, X1394:$i, X1395:$i, X1396:$i, X1397:$i, X1398:$i, X1399:$i, X1400:$i, X1401:$i, X1402:$i, X1403:$i, X1404:$i, X1405:$i, X1406:$i, X1407:$i, X1408:$i, X1409:$i, X1410:$i, X1411:$i, X1412:$i, X1413:$i, X1414:$i, X1415:$i, X1416:$i, X1417:$i, X1418:$i, X1419:$i, X1420:$i, X1421:$i, X1422:$i, X1423:$i, X1424:$o, 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, X1455:$i, X1456:$i, X1457:$i, X1458:$i, X1459:$i, X1460:$i, X1461:$i, X1462:$i, X1463:$i, X1464:$i, X1465:$i, X1466:$i, X1467:$i, X1468:$i, 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:$i, X1486:$i, X1487:$i, X1488:$i, X1489:$i, X1490:$i, X1492:$i, X1493:$i, X1494:$i, X1495:$i, X1496:$i > $o, X1499:$i, X1500:$i, X1501:$i > $o, X1503:$i, X1504:$i > $o, X1505:$i, X1507:$i, X1508:$i > $o, X1511:$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:$i, X1537:$i, X1538:$i, X1539:$i, X1540:$i, X1541:$i, X1542:$i, X1543:$i, X1544:$i, X1545:$i, X1546:$i, X1547:$i, X1548:$i, X1549:$i, X1550:$i, X1551:$i, X1552:$i, X1553:$i, X1554:$i, X1555:$i, X1556:$i, X1557:$i, X1558:$i, X1559:$i, X1560:$i, X1561:$i, X1562:$i, X1563:$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 > $i > $o, X1584:$i, X1585:$i, X1586:$i, X1587:$i, X1588:$i > $i > $o, X1589:$i, X1590:$i, X1591:$i > $i > $o, X1592:$i, X1593:$i, X1594:$i > $i > $o, X1595:$i, X1596:$i, X1597:$i, X1598:$i, X1599:$i > $i > $o, X1600:$i, X1601:$i, X1602:$i, X1603:$i, X1604:$i > $i > $o, X1605:$i, X1606:$i, X1607:$i, X1608:$i, X1609:$i > $i > $o, X1610:$i, X1611:$i, X1612:$i, X1613:$i, X1614:$i, X1615:$i, X1616:$i, X1617:$i, X1618:$i, X1619:$i, X1620:$i, X1621:$i, X1622:$i, X1623:$i, X1624:$i, X1625:$i, X1626:$i, X1627:$i, X1628:$i, X1629:$i, X1630:$i, X1631:$i, X1632:$i, X1633:$i, X1634:$i, X1635:$i, X1636:$i > $i, X1638:$i, X1639:$i, X1640:$i > $i, X1642:$i, X1643:$i, X1644:$i > $i, X1646:$i, X1647:$i, X1648:$i, X1649:$i > $o, X1652:$i, X1653:$i, X1654:$i, X1655:$i, X1656:$i > $o, X1659:$i, X1660:$i, X1661:$i > $o, X1662:$i, 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X1237|(esk36_1 @ X1232)=(X1237)|(esk34_1 @ X1232)!=(esk35_1 @ X1232)|~X1232 @ X1233))))&((((X1238 @ (esk38_1 @ X1238)|(~X1238 @ (esk37_2 @ X1238 @ X1239)|(esk37_2 @ X1238 @ X1239)!=(X1239)))&(~X1238 @ X1242|(esk38_1 @ X1238)=(X1242)|(~X1238 @ (esk37_2 @ X1238 @ X1239)|(esk37_2 @ X1238 @ X1239)!=(X1239))))&((X1238 @ (esk38_1 @ X1238)|(X1238 @ (esk37_2 @ X1238 @ X1239)|(esk37_2 @ X1238 @ X1239)=(X1239)))&(~X1238 @ X1242|(esk38_1 @ X1238)=(X1242)|(X1238 @ (esk37_2 @ X1238 @ X1239)|(esk37_2 @ X1238 @ X1239)=(X1239)))))&(((X1243)!=(X1244)|((X1245)!=(X1246)|(~in @ X1245 @ X1243|in @ X1246 @ X1244)))&(((~in @ X1249 @ X1247|in @ X1250 @ X1248|(X1249)!=(X1250)|(X1247)!=(X1248))&(~in @ X1250 @ X1248|in @ X1249 @ X1247|(X1249)!=(X1250)|(X1247)!=(X1248)))&(((X1251 @ (esk39_2 @ X1251 @ X1252)|~X1251 @ X1252|(~X1251 @ X1254|(~X1251 @ X1255|(X1254)=(X1255))))&((X1252)!=(esk39_2 @ X1251 @ X1252)|~X1251 @ X1252|(~X1251 @ X1254|(~X1251 @ X1255|(X1254)=(X1255)))))&((((((X1257 @ (esk43_2 @ X1256 @ X1257)|(X1256 @ (esk42_3 @ X1256 @ X1257 @ X1260)|~X1256 @ X1260)|(esk40_2 @ X1256 @ X1257)=(esk41_2 @ X1256 @ X1257))&(~X1257 @ X1263|(esk43_2 @ X1256 @ X1257)=(X1263)|(X1256 @ (esk42_3 @ X1256 @ X1257 @ X1260)|~X1256 @ X1260)|(esk40_2 @ X1256 @ X1257)=(esk41_2 @ X1256 @ X1257)))&((X1257 @ (esk43_2 @ X1256 @ X1257)|((X1260)!=(esk42_3 @ X1256 @ X1257 @ X1260)|~X1256 @ X1260)|(esk40_2 @ X1256 @ X1257)=(esk41_2 @ X1256 @ X1257))&(~X1257 @ X1263|(esk43_2 @ X1256 @ X1257)=(X1263)|((X1260)!=(esk42_3 @ X1256 @ X1257 @ X1260)|~X1256 @ X1260)|(esk40_2 @ X1256 @ X1257)=(esk41_2 @ X1256 @ X1257))))&(((X1256 @ (esk45_2 @ X1256 @ X1257)|(X1257 @ (esk44_3 @ X1256 @ X1257 @ X1264)|~X1257 @ X1264)|(esk40_2 @ X1256 @ X1257)=(esk41_2 @ X1256 @ X1257))&(~X1256 @ X1267|(esk45_2 @ X1256 @ X1257)=(X1267)|(X1257 @ (esk44_3 @ X1256 @ X1257 @ X1264)|~X1257 @ X1264)|(esk40_2 @ X1256 @ X1257)=(esk41_2 @ X1256 @ X1257)))&((X1256 @ (esk45_2 @ X1256 @ X1257)|((X1264)!=(esk44_3 @ X1256 @ X1257 @ X1264)|~X1257 @ X1264)|(esk40_2 @ X1256 @ X1257)=(esk41_2 @ X1256 @ X1257))&(~X1256 @ X1267|(esk45_2 @ X1256 @ X1257)=(X1267)|((X1264)!=(esk44_3 @ X1256 @ X1257 @ X1264)|~X1257 @ X1264)|(esk40_2 @ X1256 @ X1257)=(esk41_2 @ X1256 @ X1257)))))&(((((X1257 @ (esk43_2 @ X1256 @ X1257)|(X1256 @ (esk42_3 @ X1256 @ X1257 @ X1260)|~X1256 @ X1260)|(~X1256 @ (esk40_2 @ X1256 @ X1257)|~X1257 @ (esk41_2 @ X1256 @ X1257)))&(~X1257 @ X1263|(esk43_2 @ X1256 @ X1257)=(X1263)|(X1256 @ (esk42_3 @ X1256 @ X1257 @ X1260)|~X1256 @ X1260)|(~X1256 @ (esk40_2 @ X1256 @ X1257)|~X1257 @ (esk41_2 @ X1256 @ X1257))))&((X1257 @ (esk43_2 @ X1256 @ X1257)|((X1260)!=(esk42_3 @ X1256 @ X1257 @ X1260)|~X1256 @ X1260)|(~X1256 @ (esk40_2 @ X1256 @ X1257)|~X1257 @ (esk41_2 @ X1256 @ X1257)))&(~X1257 @ X1263|(esk43_2 @ X1256 @ X1257)=(X1263)|((X1260)!=(esk42_3 @ X1256 @ X1257 @ X1260)|~X1256 @ X1260)|(~X1256 @ (esk40_2 @ X1256 @ X1257)|~X1257 @ (esk41_2 @ X1256 @ X1257)))))&(((X1256 @ (esk45_2 @ X1256 @ X1257)|(X1257 @ (esk44_3 @ X1256 @ X1257 @ X1264)|~X1257 @ X1264)|(~X1256 @ (esk40_2 @ X1256 @ X1257)|~X1257 @ (esk41_2 @ X1256 @ X1257)))&(~X1256 @ X1267|(esk45_2 @ X1256 @ X1257)=(X1267)|(X1257 @ (esk44_3 @ X1256 @ X1257 @ X1264)|~X1257 @ X1264)|(~X1256 @ (esk40_2 @ X1256 @ X1257)|~X1257 @ (esk41_2 @ X1256 @ X1257))))&((X1256 @ (esk45_2 @ X1256 @ X1257)|((X1264)!=(esk44_3 @ X1256 @ X1257 @ X1264)|~X1257 @ X1264)|(~X1256 @ (esk40_2 @ X1256 @ X1257)|~X1257 @ (esk41_2 @ X1256 @ X1257)))&(~X1256 @ X1267|(esk45_2 @ X1256 @ X1257)=(X1267)|((X1264)!=(esk44_3 @ X1256 @ X1257 @ X1264)|~X1257 @ X1264)|(~X1256 @ (esk40_2 @ X1256 @ X1257)|~X1257 @ (esk41_2 @ X1256 @ X1257))))))&((((X1257 @ (esk43_2 @ X1256 @ X1257)|(X1256 @ (esk42_3 @ X1256 @ X1257 @ X1260)|~X1256 @ X1260)|(X1256 @ (esk40_2 @ X1256 @ X1257)|X1257 @ (esk41_2 @ X1256 @ X1257)))&(~X1257 @ X1263|(esk43_2 @ X1256 @ X1257)=(X1263)|(X1256 @ (esk42_3 @ X1256 @ X1257 @ X1260)|~X1256 @ X1260)|(X1256 @ (esk40_2 @ X1256 @ X1257)|X1257 @ (esk41_2 @ X1256 @ X1257))))&((X1257 @ (esk43_2 @ X1256 @ X1257)|((X1260)!=(esk42_3 @ X1256 @ X1257 @ X1260)|~X1256 @ X1260)|(X1256 @ (esk40_2 @ X1256 @ X1257)|X1257 @ (esk41_2 @ X1256 @ X1257)))&(~X1257 @ X1263|(esk43_2 @ X1256 @ X1257)=(X1263)|((X1260)!=(esk42_3 @ X1256 @ X1257 @ X1260)|~X1256 @ X1260)|(X1256 @ (esk40_2 @ X1256 @ X1257)|X1257 @ (esk41_2 @ X1256 @ X1257)))))&(((X1256 @ (esk45_2 @ X1256 @ X1257)|(X1257 @ (esk44_3 @ X1256 @ X1257 @ X1264)|~X1257 @ X1264)|(X1256 @ (esk40_2 @ X1256 @ X1257)|X1257 @ (esk41_2 @ X1256 @ X1257)))&(~X1256 @ X1267|(esk45_2 @ X1256 @ X1257)=(X1267)|(X1257 @ (esk44_3 @ X1256 @ X1257 @ X1264)|~X1257 @ X1264)|(X1256 @ (esk40_2 @ X1256 @ X1257)|X1257 @ (esk41_2 @ X1256 @ X1257))))&((X1256 @ (esk45_2 @ X1256 @ X1257)|((X1264)!=(esk44_3 @ X1256 @ X1257 @ X1264)|~X1257 @ X1264)|(X1256 @ (esk40_2 @ X1256 @ X1257)|X1257 @ (esk41_2 @ X1256 @ X1257)))&(~X1256 @ X1267|(esk45_2 @ X1256 @ X1257)=(X1267)|((X1264)!=(esk44_3 @ X1256 @ X1257 @ X1264)|~X1257 @ X1264)|(X1256 @ (esk40_2 @ X1256 @ X1257)|X1257 @ (esk41_2 @ X1256 @ X1257))))))))&((emptyset)=(emptyset)&(((X1268)!=(X1269)|((X1270)!=(X1271)|(setadjoin @ X1268 @ X1270)=(setadjoin @ X1269 @ X1271)))&(((X1272)!=(X1273)|(powerset @ X1272)=(powerset @ X1273))&(((X1274)!=(X1275)|(setunion @ X1274)=(setunion @ X1275))&((omega)=(omega)&(((X1276 @ (esk46_2 @ X1276 @ X1277)|~X1276 @ X1277|(~X1276 @ X1279|(~X1276 @ X1280|(X1279)=(X1280))))&((X1277)!=(esk46_2 @ X1276 @ X1277)|~X1276 @ X1277|(~X1276 @ X1279|(~X1276 @ X1280|(X1279)=(X1280)))))&(((((X1282 @ (esk50_3 @ X1281 @ X1282 @ X1287)|~X1282 @ X1287|(descr @ (epred1_2 @ X1281))=(descr @ (epred1_2 @ X1282))|(X1281 @ (esk49_3 @ X1281 @ X1282 @ X1285)|~X1281 @ X1285)|(esk47_2 @ X1281 @ X1282)=(esk48_2 @ X1281 @ X1282))&((X1287)!=(esk50_3 @ X1281 @ X1282 @ X1287)|~X1282 @ X1287|(descr @ (epred1_2 @ X1281))=(descr @ (epred1_2 @ X1282))|(X1281 @ (esk49_3 @ X1281 @ X1282 @ X1285)|~X1281 @ X1285)|(esk47_2 @ X1281 @ X1282)=(esk48_2 @ X1281 @ X1282)))&((X1282 @ (esk50_3 @ X1281 @ X1282 @ X1287)|~X1282 @ X1287|(descr @ (epred1_2 @ X1281))=(descr @ (epred1_2 @ X1282))|((X1285)!=(esk49_3 @ X1281 @ X1282 @ X1285)|~X1281 @ X1285)|(esk47_2 @ X1281 @ X1282)=(esk48_2 @ X1281 @ X1282))&((X1287)!=(esk50_3 @ X1281 @ X1282 @ X1287)|~X1282 @ X1287|(descr @ (epred1_2 @ X1281))=(descr @ (epred1_2 @ X1282))|((X1285)!=(esk49_3 @ X1281 @ X1282 @ X1285)|~X1281 @ X1285)|(esk47_2 @ X1281 @ X1282)=(esk48_2 @ X1281 @ X1282))))&((((X1282 @ (esk50_3 @ X1281 @ X1282 @ X1287)|~X1282 @ X1287|(descr @ (epred1_2 @ X1281))=(descr @ (epred1_2 @ X1282))|(X1281 @ (esk49_3 @ X1281 @ X1282 @ X1285)|~X1281 @ X1285)|(~X1281 @ (esk47_2 @ X1281 @ X1282)|~X1282 @ (esk48_2 @ X1281 @ X1282)))&((X1287)!=(esk50_3 @ X1281 @ X1282 @ X1287)|~X1282 @ X1287|(descr @ (epred1_2 @ X1281))=(descr @ (epred1_2 @ X1282))|(X1281 @ (esk49_3 @ X1281 @ X1282 @ X1285)|~X1281 @ X1285)|(~X1281 @ (esk47_2 @ X1281 @ X1282)|~X1282 @ (esk48_2 @ X1281 @ X1282))))&((X1282 @ (esk50_3 @ X1281 @ X1282 @ X1287)|~X1282 @ X1287|(descr 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(epred1_2 @ X1281))=(descr @ (epred1_2 @ X1282))|((X1285)!=(esk49_3 @ X1281 @ X1282 @ X1285)|~X1281 @ X1285)|(X1281 @ (esk47_2 @ X1281 @ X1282)|X1282 @ (esk48_2 @ X1281 @ X1282)))&((X1287)!=(esk50_3 @ X1281 @ X1282 @ X1287)|~X1282 @ X1287|(descr @ (epred1_2 @ X1281))=(descr @ (epred1_2 @ X1282))|((X1285)!=(esk49_3 @ X1281 @ X1282 @ X1285)|~X1281 @ X1285)|(X1281 @ (esk47_2 @ X1281 @ X1282)|X1282 @ (esk48_2 @ X1281 @ X1282)))))))&(((in @ (esk51_4 @ X1289 @ X1290 @ X1291 @ X1292) @ X1289|(dsetconstr @ X1289 @ (epred1_2 @ X1291))=(dsetconstr @ X1290 @ (epred1_2 @ X1292))|(X1289)!=(X1290))&((in @ (esk52_4 @ X1289 @ X1290 @ X1291 @ X1292) @ X1290|(dsetconstr @ X1289 @ (epred1_2 @ X1291))=(dsetconstr @ X1290 @ (epred1_2 @ X1292))|(X1289)!=(X1290))&(((esk51_4 @ X1289 @ X1290 @ X1291 @ X1292)=(esk52_4 @ X1289 @ X1290 @ X1291 @ X1292)|(dsetconstr @ X1289 @ (epred1_2 @ X1291))=(dsetconstr @ X1290 @ (epred1_2 @ X1292))|(X1289)!=(X1290))&((~X1291 @ (esk51_4 @ X1289 @ X1290 @ X1291 @ X1292)|~X1292 @ (esk52_4 @ X1289 @ X1290 @ X1291 @ X1292)|(dsetconstr @ X1289 @ (epred1_2 @ X1291))=(dsetconstr @ X1290 @ (epred1_2 @ X1292))|(X1289)!=(X1290))&(X1291 @ (esk51_4 @ X1289 @ X1290 @ X1291 @ X1292)|X1292 @ (esk52_4 @ X1289 @ X1290 @ X1291 @ X1292)|(dsetconstr @ X1289 @ (epred1_2 @ X1291))=(dsetconstr @ X1290 @ (epred1_2 @ X1292))|(X1289)!=(X1290))))))&(((in @ (esk53_2 @ X1295 @ X1296) @ X1295|subset @ X1295 @ X1296)&(~in @ (esk53_2 @ X1295 @ X1296) @ X1296|subset @ X1295 @ X1296))&(((X1298)!=(X1299)|subset @ X1299 @ X1298)&(((X1300)!=(X1301)|subset @ X1300 @ X1301)&(((in @ (esk54_2 @ X1302 @ X1303) @ X1302|subset @ X1302 @ X1303)&(~in @ (esk54_2 @ X1302 @ X1303) @ X1303|subset @ X1302 @ X1303))&(subset @ emptyset @ X1305&((~subset @ X1306 @ X1307|(~in @ X1308 @ X1306|in @ X1308 @ X1307))&((~subset @ X1309 @ X1310|(in @ X1311 @ X1310|~in @ X1311 @ X1309))&((~in @ X1314 @ X1312|(in @ X1314 @ X1313|~subset @ X1312 @ X1313))&((subset @ X1315 @ X1316|(X1315)!=(X1316))&((~in @ X1319 @ X1317|(in @ X1319 @ X1318|(X1317)!=(X1318)))&(subset @ X1320 @ X1320&((~subset @ X1321 @ X1322|(~subset @ X1322 @ X1323|subset @ X1321 @ X1323))&(subset @ X1325 @ (setadjoin @ X1324 @ X1325)&((~subset @ X1326 @ X1328|subset @ X1326 @ (setadjoin @ X1327 @ X1328))&((~subset @ X1329 @ X1330|in @ X1329 @ (powerset @ X1330))&((~subset @ X1331 @ X1332|(~subset @ X1332 @ X1331|(X1331)=(X1332)))&((~subset @ X1333 @ emptyset|(X1333)=(emptyset))&((~subset @ X1335 @ X1334|in @ X1335 @ (powerset @ X1334))&((~in @ X1337 @ (powerset @ X1336)|subset @ X1337 @ X1336)&(in @ X1338 @ (powerset @ X1338)&((~subset @ X1339 @ X1340|subset @ (powerset @ X1339) @ (powerset @ X1340))&(in @ (dsetconstr @ X1341 @ (epred1_2 @ X1342)) @ (powerset @ X1341)&(subset @ (dsetconstr @ X1343 @ (epred1_2 @ X1344)) @ X1343&((~in @ X1347 @ X1345|in @ X1347 @ (binunion @ X1345 @ X1346))&(in @ X1349 @ (setadjoin @ X1348 @ (setadjoin @ X1349 @ emptyset))&((~in @ X1352 @ X1351|in @ X1352 @ (binunion @ X1350 @ X1351))&((((in @ X1355 @ 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(cartprod @ X2044 @ X2044)|~subset @ X2045 @ (cartprod @ X2044 @ X2044)))&(in @ (kpair @ (esk99_5 @ X2044 @ X2045 @ X2046 @ X2047 @ X2048) @ X2048) @ X2046|~in @ (kpair @ X2047 @ X2048) @ (breln1compset @ X2044 @ X2045 @ X2046)|~in @ X2048 @ X2044|~in @ X2047 @ X2044|~subset @ X2046 @ (cartprod @ X2044 @ X2044)|~subset @ X2045 @ (cartprod @ X2044 @ X2044)))&(((in @ (esk100_6 @ X2050 @ X2051 @ X2052 @ X2053 @ X2054 @ X2055) @ X2050|X2055|~in @ (kpair @ X2053 @ X2054) @ (breln1compset @ X2050 @ X2051 @ X2052)|~in @ X2054 @ X2050|~in @ X2053 @ X2050|~subset @ X2052 @ (cartprod @ X2050 @ X2050)|~subset @ X2051 @ (cartprod @ X2050 @ X2050))&((in @ (kpair @ X2053 @ (esk100_6 @ X2050 @ X2051 @ X2052 @ X2053 @ X2054 @ X2055)) @ X2051|X2055|~in @ (kpair @ X2053 @ X2054) @ (breln1compset @ X2050 @ X2051 @ X2052)|~in @ X2054 @ X2050|~in @ X2053 @ X2050|~subset @ X2052 @ (cartprod @ X2050 @ X2050)|~subset @ X2051 @ (cartprod @ X2050 @ X2050))&((in @ (kpair @ (esk100_6 @ X2050 @ X2051 @ X2052 @ X2053 @ X2054 @ X2055) @ X2054) @ X2052|X2055|~in @ (kpair @ X2053 @ X2054) @ (breln1compset @ X2050 @ X2051 @ X2052)|~in @ X2054 @ X2050|~in @ X2053 @ X2050|~subset @ X2052 @ (cartprod @ X2050 @ X2050)|~subset @ X2051 @ (cartprod @ X2050 @ X2050))&(~X2055|X2055|~in @ (kpair @ X2053 @ X2054) @ (breln1compset @ X2050 @ X2051 @ X2052)|~in @ X2054 @ X2050|~in @ X2053 @ X2050|~subset @ X2052 @ (cartprod @ X2050 @ X2050)|~subset @ X2051 @ (cartprod @ X2050 @ X2050)))))&(subset @ esk102_0 @ (cartprod @ esk101_0 @ esk101_0)&(subset @ esk103_0 @ (cartprod @ esk101_0 @ esk101_0)&~subset @ (binunion @ esk102_0 @ esk103_0) @ (cartprod @ esk101_0 @ esk101_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_349])])])])])])). 85.96/86.20 thf(c_0_351, negated_conjecture, ![X2:$i, X3:$i]:((binintersect @ X3 @ X2)=(X2)|~subset @ X2 @ X3), inference(split_conjunct,[status(thm)],[c_0_350])). 85.96/86.20 thf(c_0_352, negated_conjecture, subset @ esk103_0 @ (cartprod @ esk101_0 @ esk101_0), inference(split_conjunct,[status(thm)],[c_0_350])). 85.96/86.20 thf(c_0_353, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(binintersect @ X2 @ (binunion @ X3 @ X4))=(binunion @ (binintersect @ X2 @ X3) @ (binintersect @ X2 @ X4)), inference(split_conjunct,[status(thm)],[c_0_350])). 85.96/86.20 thf(c_0_354, negated_conjecture, (binintersect @ (cartprod @ esk101_0 @ esk101_0) @ esk103_0)=(esk103_0), inference(spm,[status(thm)],[c_0_351, c_0_352])). 85.96/86.20 thf(c_0_355, negated_conjecture, subset @ esk102_0 @ (cartprod @ esk101_0 @ esk101_0), inference(split_conjunct,[status(thm)],[c_0_350])). 85.96/86.20 thf(c_0_356, negated_conjecture, ~subset @ (binunion @ esk102_0 @ esk103_0) @ (cartprod @ esk101_0 @ esk101_0), inference(split_conjunct,[status(thm)],[c_0_350])). 85.96/86.20 thf(c_0_357, negated_conjecture, ![X2:$i, X3:$i]:(subset @ X3 @ X2|(binintersect @ X2 @ X3)!=(X3)), inference(split_conjunct,[status(thm)],[c_0_350])). 85.96/86.20 thf(c_0_358, negated_conjecture, ![X2:$i]:(binunion @ (binintersect @ (cartprod @ esk101_0 @ esk101_0) @ X2) @ esk103_0)=(binintersect @ (cartprod @ esk101_0 @ esk101_0) @ (binunion @ X2 @ esk103_0)), inference(spm,[status(thm)],[c_0_353, c_0_354])). 85.96/86.20 thf(c_0_359, negated_conjecture, (binintersect @ (cartprod @ esk101_0 @ esk101_0) @ esk102_0)=(esk102_0), inference(spm,[status(thm)],[c_0_351, c_0_355])). 85.96/86.20 thf(c_0_360, negated_conjecture, (binintersect @ (cartprod @ esk101_0 @ esk101_0) @ (binunion @ esk102_0 @ esk103_0))!=(binunion @ esk102_0 @ esk103_0), inference(spm,[status(thm)],[c_0_356, c_0_357])). 85.96/86.20 thf(c_0_361, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_358, c_0_359]), c_0_360]), ['proof']). 85.96/86.20 # SZS output end CNFRefutation 85.96/86.20 # Proof object total steps : 362 85.96/86.20 # Proof object clause steps : 11 85.96/86.20 # Proof object formula steps : 351 85.96/86.20 # Proof object conjectures : 14 85.96/86.20 # Proof object clause conjectures : 11 85.96/86.20 # Proof object formula conjectures : 3 85.96/86.20 # Proof object initial clauses used : 6 85.96/86.20 # Proof object initial formulas used : 303 85.96/86.20 # Proof object generating inferences : 5 85.96/86.20 # Proof object simplifying inferences : 1 85.96/86.20 # Training examples: 0 positive, 0 negative 85.96/86.20 # Parsed axioms : 649 85.96/86.20 # Removed by relevancy pruning/SinE : 0 85.96/86.20 # Initial clauses : 894 85.96/86.20 # Removed in clause preprocessing : 385 85.96/86.20 # Initial clauses in saturation : 509 85.96/86.20 # Processed clauses : 5396 85.96/86.20 # ...of these trivial : 38 85.96/86.20 # ...subsumed : 2750 85.96/86.20 # ...remaining for further processing : 2608 85.96/86.20 # Other redundant clauses eliminated : 2776 85.96/86.20 # Clauses deleted for lack of memory : 0 85.96/86.20 # Backward-subsumed : 109 85.96/86.20 # Backward-rewritten : 124 85.96/86.20 # Generated clauses : 52026 85.96/86.20 # ...of the previous two non-trivial : 44759 85.96/86.20 # Contextual simplify-reflections : 16 85.96/86.20 # Paramodulations : 44024 85.96/86.20 # Factorizations : 2 85.96/86.20 # NegExts : 36 85.96/86.20 # Equation resolutions : 2782 85.96/86.20 # Propositional unsat checks : 0 85.96/86.20 # Propositional check models : 0 85.96/86.20 # Propositional check unsatisfiable : 0 85.96/86.20 # Propositional clauses : 0 85.96/86.20 # Propositional clauses after purity: 0 85.96/86.20 # Propositional unsat core size : 0 85.96/86.20 # Propositional preprocessing time : 0.000 85.96/86.20 # Propositional encoding time : 0.000 85.96/86.20 # Propositional solver time : 0.000 85.96/86.20 # Success case prop preproc time : 0.000 85.96/86.20 # Success case prop encoding time : 0.000 85.96/86.20 # Success case prop solver time : 0.000 85.96/86.20 # Current number of processed clauses : 1872 85.96/86.20 # Positive orientable unit clauses : 165 85.96/86.20 # Positive unorientable unit clauses: 0 85.96/86.20 # Negative unit clauses : 37 85.96/86.20 # Non-unit-clauses : 1670 85.96/86.20 # Current number of unprocessed clauses: 40254 85.96/86.20 # ...number of literals in the above : 172356 85.96/86.20 # Current number of archived formulas : 0 85.96/86.20 # Current number of archived clauses : 717 85.96/86.20 # Clause-clause subsumption calls (NU) : 340675 85.96/86.20 # Rec. Clause-clause subsumption calls : 182075 85.96/86.20 # Non-unit clause-clause subsumptions : 1634 85.96/86.20 # Unit Clause-clause subsumption calls : 16392 85.96/86.20 # Rewrite failures with RHS unbound : 0 85.96/86.20 # BW rewrite match attempts : 262 85.96/86.20 # BW rewrite match successes : 21 85.96/86.20 # Condensation attempts : 0 85.96/86.20 # Condensation successes : 0 85.96/86.20 # Termbank termtop insertions : 1003050 85.96/86.21 85.96/86.21 # ------------------------------------------------- 85.96/86.21 # User time : 84.594 s 85.96/86.21 # System time : 1.150 s 85.96/86.21 # Total time : 85.744 s 85.96/86.21 # Maximum resident set size: 2396 pages 85.96/86.21 EOF