0.13/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.13/0.14 % Command : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.cdBSZNGCOj 0.14/0.35 % Computer : n004.cluster.edu 0.14/0.35 % Model : x86_64 x86_64 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.35 % Memory : 8042.1875MB 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.35 % CPULimit : 180 0.14/0.35 % DateTime : Thu Aug 29 16:59:08 EDT 2019 0.14/0.35 % CPUTime : 164.12/165.22 % Running portfolio for 180 s 164.12/165.22 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 164.12/165.22 % TempDir : /export/starexec/sandbox2/tmp/tmp.cdBSZNGCOj 164.12/165.22 % Recognized as monomorphic HO. 164.12/165.22 % Running /export/starexec/sandbox2/solver/bin/competitive.sh for 18 164.12/165.22 % Running /export/starexec/sandbox2/solver/bin/competitive.2.sh for 13 164.12/165.22 % Running /export/starexec/sandbox2/solver/bin/competitive.3.sh for 3 164.12/165.22 % Running /export/starexec/sandbox2/solver/bin/pragmatic.rudimentary.sh for 28 164.12/165.22 % Running /export/starexec/sandbox2/solver/bin/pragmatic.rudimentary.1.sh for 12 164.12/165.22 % Running /export/starexec/sandbox2/solver/bin/pragmatic.rudimentary.2.sh for 7 164.12/165.22 % Running /export/starexec/sandbox2/solver/bin/pragmatic.shallow.sh for 3 164.12/165.22 % Running /export/starexec/sandbox2/solver/bin/pragmatic.shallow.1.sh for 14 164.12/165.22 % Running /export/starexec/sandbox2/solver/bin/pragmatic.shallow.2.sh for 12 164.12/165.22 % Running /export/starexec/sandbox2/solver/bin/pragmatic.ll.e.sh for 19 164.12/165.22 % Running /export/starexec/sandbox2/solver/bin/pragmatic.bools.sh for 13 164.12/165.22 % Running /export/starexec/sandbox2/solver/bin/pragmatic.bools.1.sh for 10 164.12/165.22 % Running /export/starexec/sandbox2/solver/bin/pragmatic.rudimentary.e.sh for 8 164.12/165.22 % Running /export/starexec/sandbox2/solver/bin/competitive.strong.sh for 20 164.12/165.22 % Solved by: competitive.strong.sh 164.12/165.22 % Running : timeout 12 /export/starexec/sandbox2/solver/bin/eprover-ho /export/starexec/sandbox2/tmp/tmp.cdBSZNGCOj/e_input937670 --cpu-limit=10 --auto-schedule -s -p. 164.12/165.22 % done 1018 iterations in 16.161s 164.12/165.22 % hashcons stats for terms: size 9223, num 32276, sum length 68190, buckets: small 0, median 7, big 22 164.12/165.22 % proof state stats: {active 462, passive 4207, simpl 0} 164.12/165.22 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 164.12/165.22 % SZS output start Refutation 164.12/165.22 tff(setunionTransitive, conjecture, 164.12/165.22 (setextAx => 164.12/165.22 (emptysetAx => 164.12/165.22 (setadjoinAx => 164.12/165.22 (powersetAx => 164.12/165.22 (setunionAx => 164.12/165.22 (omega0Ax => 164.12/165.22 (omegaSAx => 164.12/165.22 (omegaIndAx => 164.12/165.22 (replAx => 164.12/165.22 (foundationAx => 164.12/165.22 (wellorderingAx => 164.12/165.22 (descrp => 164.12/165.22 (dsetconstrI => 164.12/165.22 (dsetconstrEL => 164.12/165.22 (dsetconstrER => 164.12/165.22 (exuE1 => 164.12/165.22 (prop2setE => 164.12/165.22 (emptysetE => 164.12/165.22 (emptysetimpfalse => 164.12/165.22 (notinemptyset => 164.12/165.22 (exuE3e => 164.12/165.22 (setext => 164.12/165.22 (emptyI => 164.12/165.22 (noeltsimpempty => 164.12/165.22 (setbeta => 164.12/165.22 (nonemptyE1 => 164.12/165.22 (nonemptyI => 164.12/165.22 (nonemptyI1 => 164.12/165.22 (setadjoinIL => 164.12/165.22 (emptyinunitempty => 164.12/165.22 (setadjoinIR => 164.12/165.22 (setadjoinE => 164.12/165.22 (setadjoinOr => 164.12/165.22 (setoftrueEq => 164.12/165.22 (powersetI => 164.12/165.22 (emptyinPowerset => 164.12/165.22 (emptyInPowerset => 164.12/165.22 (powersetE => 164.12/165.22 (setunionI => 164.12/165.22 (setunionE => 164.12/165.22 (subPowSU => 164.12/165.22 (exuE2 => 164.12/165.22 (nonemptyImpWitness => 164.12/165.22 (uniqinunit => 164.12/165.22 (notinsingleton => 164.12/165.22 (eqinunit => 164.12/165.22 (singletonsswitch => 164.12/165.22 (upairsetE => 164.12/165.22 (upairsetIL => 164.12/165.22 (upairsetIR => 164.12/165.22 (emptyE1 => 164.12/165.22 (vacuousDall => 164.12/165.22 (quantDeMorgan1 => 164.12/165.22 (quantDeMorgan2 => 164.12/165.22 (quantDeMorgan3 => 164.12/165.22 (quantDeMorgan4 => 164.12/165.22 (prop2setI => 164.12/165.22 (prop2set2propI => 164.12/165.22 (notdexE => 164.12/165.22 (notdallE => 164.12/165.22 (exuI1 => 164.12/165.22 (exuI3 => 164.12/165.22 (exuI2 => 164.12/165.22 (inCongP => 164.12/165.22 (in__Cong => 164.12/165.22 (exuE3u => 164.12/165.22 ( 164.12/165.22 exu__Cong => 164.12/165.22 ( 164.12/165.22 emptyset__Cong => 164.12/165.22 ( 164.12/165.22 setadjoin__Cong => 164.12/165.22 ( 164.12/165.22 powerset__Cong => 164.12/165.22 ( 164.12/165.22 setunion__Cong => 164.12/165.22 ( 164.12/165.22 omega__Cong => 164.12/165.22 ( 164.12/165.22 exuEu => 164.12/165.22 ( 164.12/165.22 descr__Cong => 164.12/165.22 ( 164.12/165.22 dsetconstr__Cong => 164.12/165.22 ( 164.12/165.22 subsetI1 => 164.12/165.22 ( 164.12/165.22 eqimpsubset2 => 164.12/165.22 ( 164.12/165.22 eqimpsubset1 => 164.12/165.22 ( 164.12/165.22 subsetI2 => 164.12/165.22 ( 164.12/165.22 emptysetsubset => 164.12/165.22 ( 164.12/165.22 subsetE => 164.12/165.22 ( 164.12/165.22 subsetE2 => 164.12/165.22 ( 164.12/165.22 notsubsetI => 164.12/165.22 ( 164.12/165.22 notequalI1 => 164.12/165.22 ( 164.12/165.22 notequalI2 => 164.12/165.22 ( 164.12/165.22 subsetRefl => 164.12/165.22 ( 164.12/165.22 subsetTrans => 164.12/165.22 ( 164.12/165.22 setadjoinSub => 164.12/165.22 ( 164.12/165.22 setadjoinSub2 => 164.12/165.22 ( 164.12/165.22 subset2powerset => 164.12/165.22 ( 164.12/165.22 setextsub => 164.12/165.22 ( 164.12/165.22 subsetemptysetimpeq => 164.12/165.22 ( 164.12/165.22 powersetI1 => 164.12/165.22 ( 164.12/165.22 powersetE1 => 164.12/165.22 ( 164.12/165.22 inPowerset => 164.12/165.22 ( 164.12/165.22 powersetsubset => 164.12/165.22 ( 164.12/165.22 sepInPowerset => 164.12/165.22 ( 164.12/165.22 sepSubset => 164.12/165.22 ( 164.12/165.22 binunionIL => 164.12/165.22 ( 164.12/165.22 upairset2IR => 164.12/165.22 ( 164.12/165.22 binunionIR => 164.12/165.22 ( 164.12/165.22 binunionEcases => 164.12/165.22 ( 164.12/165.22 binunionE => 164.12/165.22 ( 164.12/165.22 binunionLsub => 164.12/165.22 ( 164.12/165.22 binunionRsub => 164.12/165.22 ( 164.12/165.22 binintersectI => 164.12/165.22 ( 164.12/165.22 binintersectSubset5 => 164.12/165.22 ( 164.12/165.22 binintersectEL => 164.12/165.22 ( 164.12/165.22 binintersectLsub => 164.12/165.22 ( 164.12/165.22 binintersectSubset2 => 164.12/165.22 ( 164.12/165.22 binintersectSubset3 => 164.12/165.22 ( 164.12/165.22 binintersectER => 164.12/165.22 ( 164.12/165.22 disjointsetsI1 => 164.12/165.22 ( 164.12/165.22 binintersectRsub => 164.12/165.22 ( 164.12/165.22 binintersectSubset4 => 164.12/165.22 ( 164.12/165.22 binintersectSubset1 => 164.12/165.22 ( 164.12/165.22 bs114d => 164.12/165.22 ( 164.12/165.22 setminusI => 164.12/165.22 ( 164.12/165.22 setminusEL => 164.12/165.22 ( 164.12/165.22 setminusER => 164.12/165.22 ( 164.12/165.22 setminusSubset2 => 164.12/165.22 ( 164.12/165.22 setminusERneg => 164.12/165.22 ( 164.12/165.22 setminusELneg => 164.12/165.22 ( 164.12/165.22 setminusILneg => 164.12/165.22 ( 164.12/165.22 setminusIRneg => 164.12/165.22 ( 164.12/165.22 setminusLsub => 164.12/165.22 ( 164.12/165.22 setminusSubset1 => 164.12/165.22 ( 164.12/165.22 symdiffE => 164.12/165.22 ( 164.12/165.22 symdiffI1 => 164.12/165.22 ( 164.12/165.22 symdiffI2 => 164.12/165.22 ( 164.12/165.22 symdiffIneg1 => 164.12/165.22 ( 164.12/165.22 symdiffIneg2 => 164.12/165.22 ( 164.12/165.22 secondinupair => 164.12/165.22 ( 164.12/165.22 setukpairIL => 164.12/165.22 ( 164.12/165.22 setukpairIR => 164.12/165.22 ( 164.12/165.22 kpairiskpair => 164.12/165.22 ( 164.12/165.22 kpairp => 164.12/165.22 ( 164.12/165.22 singletonsubset => 164.12/165.22 ( 164.12/165.22 singletoninpowerset => 164.12/165.22 ( 164.12/165.22 singletoninpowunion => 164.12/165.22 ( 164.12/165.22 upairset2E => 164.12/165.22 ( 164.12/165.22 upairsubunion => 164.12/165.22 ( 164.12/165.22 upairinpowunion => 164.12/165.22 ( 164.12/165.22 ubforcartprodlem1 => 164.12/165.22 ( 164.12/165.22 ubforcartprodlem2 => 164.12/165.22 ( 164.12/165.22 ubforcartprodlem3 => 164.12/165.22 ( 164.12/165.22 cartprodpairin => 164.12/165.22 ( 164.12/165.22 cartprodmempair1 => 164.12/165.22 ( 164.12/165.22 cartprodmempair => 164.12/165.22 ( 164.12/165.22 setunionE2 => 164.12/165.22 ( 164.12/165.22 setunionsingleton1 => 164.12/165.22 ( 164.12/165.22 setunionsingleton2 => 164.12/165.22 ( 164.12/165.22 setunionsingleton => 164.12/165.22 ( 164.12/165.22 singletonprop => 164.12/165.22 ( 164.12/165.22 ex1E1 => 164.12/165.22 ( 164.12/165.22 ex1I => 164.12/165.22 ( 164.12/165.22 ex1I2 => 164.12/165.22 ( 164.12/165.22 singletonsuniq => 164.12/165.22 ( 164.12/165.22 setukpairinjL1 => 164.12/165.22 ( 164.12/165.22 kfstsingleton => 164.12/165.22 ( 164.12/165.22 theprop => 164.12/165.22 ( 164.12/165.22 kfstpairEq => 164.12/165.22 ( 164.12/165.22 cartprodfstin => 164.12/165.22 ( 164.12/165.22 setukpairinjL2 => 164.12/165.22 ( 164.12/165.22 setukpairinjL => 164.12/165.22 ( 164.12/165.22 setukpairinjR11 => 164.12/165.22 ( 164.12/165.22 setukpairinjR12 => 164.12/165.22 ( 164.12/165.22 setukpairinjR1 => 164.12/165.22 ( 164.12/165.22 upairequniteq => 164.12/165.22 ( 164.12/165.22 setukpairinjR2 => 164.12/165.22 ( 164.12/165.22 setukpairinjR => 164.12/165.22 ( 164.12/165.22 ksndsingleton => 164.12/165.22 ( 164.12/165.22 ksndpairEq => 164.12/165.22 ( 164.12/165.22 kpairsurjEq => 164.12/165.22 ( 164.12/165.22 cartprodsndin => 164.12/165.22 ( 164.12/165.22 cartprodpairmemEL => 164.12/165.22 ( 164.12/165.22 cartprodpairmemER => 164.12/165.22 ( 164.12/165.22 cartprodmempaircEq => 164.12/165.22 ( 164.12/165.22 cartprodfstpairEq => 164.12/165.22 ( 164.12/165.22 cartprodsndpairEq => 164.12/165.22 ( 164.12/165.22 cartprodpairsurjEq => 164.12/165.22 ( 164.12/165.22 dpsetconstrI => 164.12/165.22 ( 164.12/165.22 dpsetconstrSub => 164.12/165.22 ( 164.12/165.22 setOfPairsIsBReln => 164.12/165.22 ( 164.12/165.22 dpsetconstrERa => 164.12/165.22 ( 164.12/165.22 dpsetconstrEL1 => 164.12/165.22 ( 164.12/165.22 dpsetconstrEL2 => 164.12/165.22 ( 164.12/165.22 dpsetconstrER => 164.12/165.22 ( 164.12/165.22 funcImageSingleton => 164.12/165.22 ( 164.12/165.22 apProp => 164.12/165.22 ( 164.12/165.22 app => 164.12/165.22 ( 164.12/165.22 infuncsetfunc => 164.12/165.22 ( 164.12/165.22 ap2p => 164.12/165.22 ( 164.12/165.22 funcinfuncset => 164.12/165.22 ( 164.12/165.22 lamProp => 164.12/165.22 ( 164.12/165.22 lamp => 164.12/165.22 ( 164.12/165.22 lam2p => 164.12/165.22 ( 164.12/165.22 brelnall1 => 164.12/165.22 ( 164.12/165.22 brelnall2 => 164.12/165.22 ( 164.12/165.22 ex1E2 => 164.12/165.22 ( 164.12/165.22 funcGraphProp1 => 164.12/165.22 ( 164.12/165.22 funcGraphProp3 => 164.12/165.22 ( 164.12/165.22 funcGraphProp2 => 164.12/165.22 ( 164.12/165.22 funcextLem => 164.12/165.22 ( 164.12/165.22 funcGraphProp4 => 164.12/165.22 ( 164.12/165.22 subbreln => 164.12/165.22 ( 164.12/165.22 eqbreln => 164.12/165.22 ( 164.12/165.22 funcext => 164.12/165.22 ( 164.12/165.22 funcext2 => 164.12/165.22 ( 164.12/165.22 ap2apEq1 => 164.12/165.22 ( 164.12/165.22 ap2apEq2 => 164.12/165.22 ( 164.12/165.22 beta1 => 164.12/165.22 ( 164.12/165.22 eta1 => 164.12/165.22 ( 164.12/165.22 lam2lamEq => 164.12/165.22 ( 164.12/165.22 beta2 => 164.12/165.22 ( 164.12/165.22 eta2 => 164.12/165.22 ( 164.12/165.22 iffalseProp1 => 164.12/165.22 ( 164.12/165.22 iffalseProp2 => 164.12/165.22 ( 164.12/165.22 iftrueProp1 => 164.12/165.22 ( 164.12/165.22 iftrueProp2 => 164.12/165.22 ( 164.12/165.22 ifSingleton => 164.12/165.22 ( 164.12/165.22 ifp => 164.12/165.22 ( 164.12/165.22 theeq => 164.12/165.22 ( 164.12/165.22 iftrue => 164.12/165.22 ( 164.12/165.22 iffalse => 164.12/165.22 ( 164.12/165.22 iftrueorfalse => 164.12/165.22 ( 164.12/165.22 binintersectT_lem => 164.12/165.22 ( 164.12/165.22 binunionT_lem => 164.12/165.22 ( 164.12/165.22 powersetT_lem => 164.12/165.22 ( 164.12/165.22 setminusT_lem => 164.12/165.22 ( 164.12/165.22 complementT_lem => 164.12/165.22 ( 164.12/165.22 setextT => 164.12/165.22 ( 164.12/165.22 subsetTI => 164.12/165.22 ( 164.12/165.22 powersetTI1 => 164.12/165.22 ( 164.12/165.22 powersetTE1 => 164.12/165.22 ( 164.12/165.22 complementTI1 => 164.12/165.22 ( 164.12/165.22 complementTE1 => 164.12/165.22 ( 164.12/165.22 binintersectTELcontra => 164.12/165.22 ( 164.12/165.22 binintersectTERcontra => 164.12/165.22 ( 164.12/165.22 contrasubsetT => 164.12/165.22 ( 164.12/165.22 contrasubsetT1 => 164.12/165.22 ( 164.12/165.22 contrasubsetT2 => 164.12/165.22 ( 164.12/165.22 contrasubsetT3 => 164.12/165.22 ( 164.12/165.22 doubleComplementI1 => 164.12/165.22 ( 164.12/165.22 doubleComplementE1 => 164.12/165.22 ( 164.12/165.22 doubleComplementSub1 => 164.12/165.22 ( 164.12/165.22 doubleComplementSub2 => 164.12/165.22 ( 164.12/165.22 doubleComplementEq => 164.12/165.22 ( 164.12/165.22 complementTnotintersectT => 164.12/165.22 ( 164.12/165.22 complementImpComplementIntersect => 164.12/165.22 ( 164.12/165.22 complementSubsetComplementIntersect => 164.12/165.22 ( 164.12/165.22 complementInPowersetComplementIntersect => 164.12/165.22 ( 164.12/165.22 contraSubsetComplement => 164.12/165.22 ( 164.12/165.22 complementTcontraSubset => 164.12/165.22 ( 164.12/165.22 binunionTILcontra => 164.12/165.22 ( 164.12/165.22 binunionTIRcontra => 164.12/165.22 ( 164.12/165.22 inIntersectImpInUnion => 164.12/165.22 ( 164.12/165.22 inIntersectImpInUnion2 => 164.12/165.22 ( 164.12/165.22 inIntersectImpInIntersectUnions => 164.12/165.22 ( 164.12/165.22 intersectInPowersetIntersectUnions => 164.12/165.22 ( 164.12/165.22 inComplementUnionImpNotIn1 => 164.12/165.22 ( 164.12/165.22 inComplementUnionImpInComplement1 => 164.12/165.22 ( 164.12/165.22 binunionTE => 164.12/165.22 ( 164.12/165.22 binunionTEcontra => 164.12/165.22 ( 164.12/165.22 demorgan2a1 => 164.12/165.22 ( 164.12/165.22 complementUnionInPowersetComplement => 164.12/165.22 ( 164.12/165.22 demorgan2a2 => 164.12/165.22 ( 164.12/165.22 demorgan1a => 164.12/165.22 ( 164.12/165.22 demorgan1b => 164.12/165.22 ( 164.12/165.22 demorgan1 => 164.12/165.22 ( 164.12/165.22 demorgan2a => 164.12/165.22 ( 164.12/165.22 demorgan2b2 => 164.12/165.22 ( 164.12/165.22 demorgan2b => 164.12/165.22 ( 164.12/165.22 demorgan2 => 164.12/165.22 ( 164.12/165.22 woz13rule0 => 164.12/165.22 ( 164.12/165.22 woz13rule1 => 164.12/165.22 ( 164.12/165.22 woz13rule2 => 164.12/165.22 ( 164.12/165.22 woz13rule3 => 164.12/165.22 ( 164.12/165.22 woz13rule4 => 164.12/165.22 ( 164.12/165.22 woz1_1 => 164.12/165.22 ( 164.12/165.22 woz1_2 => 164.12/165.22 ( 164.12/165.22 woz1_3 => 164.12/165.22 ( 164.12/165.22 woz1_4 => 164.12/165.22 ( 164.12/165.22 woz1_5 => 164.12/165.22 ( 164.12/165.22 breln1all2 => 164.12/165.22 ( 164.12/165.22 breln1SetBreln1 => 164.12/165.22 ( 164.12/165.22 choice2fnsingleton => 164.12/165.22 ( 164.12/165.22 setOfPairsIsBReln1 => 164.12/165.22 ( 164.12/165.22 breln1all1 => 164.12/165.22 ( 164.12/165.22 subbreln1 => 164.12/165.22 ( 164.12/165.22 eqbreln1 => 164.12/165.22 ( 164.12/165.22 breln1invprop => 164.12/165.22 ( 164.12/165.22 breln1invI => 164.12/165.22 ( 164.12/165.22 breln1invE => 164.12/165.22 ( 164.12/165.22 breln1compprop => 164.12/165.22 ( 164.12/165.22 breln1compI => 164.12/165.22 ( 164.12/165.22 breln1compE => 164.12/165.22 ( 164.12/165.22 breln1compEex => 164.12/165.22 ( 164.12/165.22 breln1unionprop => 164.12/165.22 ( 164.12/165.22 breln1unionIL => 164.12/165.22 ( 164.12/165.22 breln1unionIR => 164.12/165.22 ( 164.12/165.22 breln1unionI => 164.12/165.22 ( 164.12/165.22 breln1unionE => 164.12/165.22 ( 164.12/165.22 breln1unionEcases => 164.12/165.22 ( 164.12/165.22 breln1unionCommutes => 164.12/165.22 ( 164.12/165.22 woz2Ex => 164.12/165.22 ( 164.12/165.22 woz2W => 164.12/165.22 ( 164.12/165.22 woz2A => 164.12/165.22 ( 164.12/165.22 woz2B => 164.12/165.22 ( 164.12/165.22 image1Ex => 164.12/165.22 ( 164.12/165.22 image1Ex1 => 164.12/165.22 ( 164.12/165.22 image1Equiv => 164.12/165.22 ( 164.12/165.22 image1E => 164.12/165.22 ( 164.12/165.22 image1I => 164.12/165.22 ( 164.12/165.22 injFuncInInjFuncSet => 164.12/165.22 ( 164.12/165.22 injFuncSetFuncIn => 164.12/165.22 ( 164.12/165.22 injFuncSetFuncInj => 164.12/165.22 ( 164.12/165.22 surjFuncSetFuncIn => 164.12/165.22 ( 164.12/165.22 surjFuncSetFuncSurj => 164.12/165.22 ( 164.12/165.22 leftInvIsSurj => 164.12/165.22 ( 164.12/165.22 surjCantorThm => 164.12/165.22 ( 164.12/165.22 foundation2 => 164.12/165.22 ( 164.12/165.22 notinself => 164.12/165.22 ( 164.12/165.22 notinself2 => 164.12/165.22 ( 164.12/165.22 omegaSp => 164.12/165.22 ( 164.12/165.22 omegaSclos => 164.12/165.22 ( 164.12/165.22 peano0notS => 164.12/165.22 ( 164.12/165.22 peanoSinj => 164.12/165.22 ( 164.12/165.22 transitivesetOp1 => 164.12/165.22 ( 164.12/165.22 binintTransitive => 164.12/165.22 ( 164.12/165.22 transitivesetOp2 => 164.12/165.22 ( 164.12/165.22 ![X]: 164.12/165.22 (( 164.12/165.22 ![Xx]: 164.12/165.22 (in(Xx,X) => 164.12/165.22 transitiveset( 164.12/165.22 Xx))) => 164.12/165.22 transitiveset( 164.12/165.22 setunion( 164.12/165.22 X)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 164.12/165.22 tff(zf_stmt_0, negated_conjecture, 164.12/165.22 (~ 164.12/165.22 (setextAx => 164.12/165.22 (emptysetAx => 164.12/165.22 (setadjoinAx => 164.12/165.22 (powersetAx => 164.12/165.22 (setunionAx => 164.12/165.22 (omega0Ax => 164.12/165.22 (omegaSAx => 164.12/165.22 (omegaIndAx => 164.12/165.22 (replAx => 164.12/165.22 (foundationAx => 164.12/165.22 (wellorderingAx => 164.12/165.22 (descrp => 164.12/165.22 (dsetconstrI => 164.12/165.22 (dsetconstrEL => 164.12/165.22 (dsetconstrER => 164.12/165.22 (exuE1 => 164.12/165.22 (prop2setE => 164.12/165.22 (emptysetE => 164.12/165.22 (emptysetimpfalse => 164.12/165.22 (notinemptyset => 164.12/165.22 (exuE3e => 164.12/165.22 (setext => 164.12/165.22 (emptyI => 164.12/165.22 (noeltsimpempty => 164.12/165.22 (setbeta => 164.12/165.22 (nonemptyE1 => 164.12/165.22 (nonemptyI => 164.12/165.22 (nonemptyI1 => 164.12/165.22 (setadjoinIL => 164.12/165.22 (emptyinunitempty => 164.12/165.22 (setadjoinIR => 164.12/165.22 (setadjoinE => 164.12/165.22 (setadjoinOr => 164.12/165.22 (setoftrueEq => 164.12/165.22 (powersetI => 164.12/165.22 (emptyinPowerset => 164.12/165.22 (emptyInPowerset => 164.12/165.22 (powersetE => 164.12/165.22 (setunionI => 164.12/165.22 (setunionE => 164.12/165.22 (subPowSU => 164.12/165.22 (exuE2 => 164.12/165.22 (nonemptyImpWitness => 164.12/165.22 (uniqinunit => 164.12/165.22 (notinsingleton => 164.12/165.22 (eqinunit => 164.12/165.22 (singletonsswitch => 164.12/165.22 (upairsetE => 164.12/165.22 (upairsetIL => 164.12/165.22 (upairsetIR => 164.12/165.22 (emptyE1 => 164.12/165.22 (vacuousDall => 164.12/165.22 (quantDeMorgan1 => 164.12/165.22 (quantDeMorgan2 => 164.12/165.22 (quantDeMorgan3 => 164.12/165.22 (quantDeMorgan4 => 164.12/165.22 (prop2setI => 164.12/165.22 (prop2set2propI => 164.12/165.22 (notdexE => 164.12/165.22 (notdallE => 164.12/165.22 (exuI1 => 164.12/165.22 (exuI3 => 164.12/165.22 (exuI2 => 164.12/165.22 (inCongP => 164.12/165.22 ( 164.12/165.22 in__Cong => 164.12/165.22 ( 164.12/165.22 exuE3u => 164.12/165.22 ( 164.12/165.22 exu__Cong => 164.12/165.22 ( 164.12/165.22 emptyset__Cong => 164.12/165.22 ( 164.12/165.22 setadjoin__Cong => 164.12/165.22 ( 164.12/165.22 powerset__Cong => 164.12/165.22 ( 164.12/165.22 setunion__Cong => 164.12/165.22 ( 164.12/165.22 omega__Cong => 164.12/165.22 ( 164.12/165.22 exuEu => 164.12/165.22 ( 164.12/165.22 descr__Cong => 164.12/165.22 ( 164.12/165.22 dsetconstr__Cong => 164.12/165.22 ( 164.12/165.22 subsetI1 => 164.12/165.22 ( 164.12/165.22 eqimpsubset2 => 164.12/165.22 ( 164.12/165.22 eqimpsubset1 => 164.12/165.22 ( 164.12/165.22 subsetI2 => 164.12/165.22 ( 164.12/165.22 emptysetsubset => 164.12/165.22 ( 164.12/165.22 subsetE => 164.12/165.22 ( 164.12/165.22 subsetE2 => 164.12/165.22 ( 164.12/165.22 notsubsetI => 164.12/165.22 ( 164.12/165.22 notequalI1 => 164.12/165.22 ( 164.12/165.22 notequalI2 => 164.12/165.22 ( 164.12/165.22 subsetRefl => 164.12/165.22 ( 164.12/165.22 subsetTrans => 164.12/165.22 ( 164.12/165.22 setadjoinSub => 164.12/165.22 ( 164.12/165.22 setadjoinSub2 => 164.12/165.22 ( 164.12/165.22 subset2powerset => 164.12/165.22 ( 164.12/165.22 setextsub => 164.12/165.22 ( 164.12/165.22 subsetemptysetimpeq => 164.12/165.22 ( 164.12/165.22 powersetI1 => 164.12/165.22 ( 164.12/165.22 powersetE1 => 164.12/165.22 ( 164.12/165.22 inPowerset => 164.12/165.22 ( 164.12/165.22 powersetsubset => 164.12/165.22 ( 164.12/165.22 sepInPowerset => 164.12/165.22 ( 164.12/165.22 sepSubset => 164.12/165.22 ( 164.12/165.22 binunionIL => 164.12/165.22 ( 164.12/165.22 upairset2IR => 164.12/165.22 ( 164.12/165.22 binunionIR => 164.12/165.22 ( 164.12/165.22 binunionEcases => 164.12/165.22 ( 164.12/165.22 binunionE => 164.12/165.22 ( 164.12/165.22 binunionLsub => 164.12/165.22 ( 164.12/165.22 binunionRsub => 164.12/165.22 ( 164.12/165.22 binintersectI => 164.12/165.22 ( 164.12/165.22 binintersectSubset5 => 164.12/165.22 ( 164.12/165.22 binintersectEL => 164.12/165.22 ( 164.12/165.22 binintersectLsub => 164.12/165.22 ( 164.12/165.22 binintersectSubset2 => 164.12/165.22 ( 164.12/165.22 binintersectSubset3 => 164.12/165.22 ( 164.12/165.22 binintersectER => 164.12/165.22 ( 164.12/165.22 disjointsetsI1 => 164.12/165.22 ( 164.12/165.22 binintersectRsub => 164.12/165.22 ( 164.12/165.22 binintersectSubset4 => 164.12/165.22 ( 164.12/165.22 binintersectSubset1 => 164.12/165.22 ( 164.12/165.22 bs114d => 164.12/165.22 ( 164.12/165.22 setminusI => 164.12/165.22 ( 164.12/165.22 setminusEL => 164.12/165.22 ( 164.12/165.22 setminusER => 164.12/165.22 ( 164.12/165.22 setminusSubset2 => 164.12/165.22 ( 164.12/165.22 setminusERneg => 164.12/165.22 ( 164.12/165.22 setminusELneg => 164.12/165.22 ( 164.12/165.22 setminusILneg => 164.12/165.22 ( 164.12/165.22 setminusIRneg => 164.12/165.22 ( 164.12/165.22 setminusLsub => 164.12/165.22 ( 164.12/165.22 setminusSubset1 => 164.12/165.22 ( 164.12/165.22 symdiffE => 164.12/165.22 ( 164.12/165.22 symdiffI1 => 164.12/165.22 ( 164.12/165.22 symdiffI2 => 164.12/165.22 ( 164.12/165.22 symdiffIneg1 => 164.12/165.22 ( 164.12/165.22 symdiffIneg2 => 164.12/165.22 ( 164.12/165.22 secondinupair => 164.12/165.22 ( 164.12/165.22 setukpairIL => 164.12/165.22 ( 164.12/165.22 setukpairIR => 164.12/165.22 ( 164.12/165.22 kpairiskpair => 164.12/165.22 ( 164.12/165.22 kpairp => 164.12/165.22 ( 164.12/165.22 singletonsubset => 164.12/165.22 ( 164.12/165.22 singletoninpowerset => 164.12/165.22 ( 164.12/165.22 singletoninpowunion => 164.12/165.22 ( 164.12/165.22 upairset2E => 164.12/165.22 ( 164.12/165.22 upairsubunion => 164.12/165.22 ( 164.12/165.22 upairinpowunion => 164.12/165.22 ( 164.12/165.22 ubforcartprodlem1 => 164.12/165.22 ( 164.12/165.22 ubforcartprodlem2 => 164.12/165.22 ( 164.12/165.22 ubforcartprodlem3 => 164.12/165.22 ( 164.12/165.22 cartprodpairin => 164.12/165.22 ( 164.12/165.22 cartprodmempair1 => 164.12/165.22 ( 164.12/165.22 cartprodmempair => 164.12/165.22 ( 164.12/165.22 setunionE2 => 164.12/165.22 ( 164.12/165.22 setunionsingleton1 => 164.12/165.22 ( 164.12/165.22 setunionsingleton2 => 164.12/165.22 ( 164.12/165.22 setunionsingleton => 164.12/165.22 ( 164.12/165.22 singletonprop => 164.12/165.22 ( 164.12/165.22 ex1E1 => 164.12/165.22 ( 164.12/165.22 ex1I => 164.12/165.22 ( 164.12/165.22 ex1I2 => 164.12/165.22 ( 164.12/165.22 singletonsuniq => 164.12/165.22 ( 164.12/165.22 setukpairinjL1 => 164.12/165.22 ( 164.12/165.22 kfstsingleton => 164.12/165.22 ( 164.12/165.22 theprop => 164.12/165.22 ( 164.12/165.22 kfstpairEq => 164.12/165.22 ( 164.12/165.22 cartprodfstin => 164.12/165.22 ( 164.12/165.22 setukpairinjL2 => 164.12/165.22 ( 164.12/165.22 setukpairinjL => 164.12/165.22 ( 164.12/165.22 setukpairinjR11 => 164.12/165.22 ( 164.12/165.22 setukpairinjR12 => 164.12/165.22 ( 164.12/165.22 setukpairinjR1 => 164.12/165.22 ( 164.12/165.22 upairequniteq => 164.12/165.22 ( 164.12/165.22 setukpairinjR2 => 164.12/165.22 ( 164.12/165.22 setukpairinjR => 164.12/165.22 ( 164.12/165.22 ksndsingleton => 164.12/165.22 ( 164.12/165.22 ksndpairEq => 164.12/165.22 ( 164.12/165.22 kpairsurjEq => 164.12/165.22 ( 164.12/165.22 cartprodsndin => 164.12/165.22 ( 164.12/165.22 cartprodpairmemEL => 164.12/165.22 ( 164.12/165.22 cartprodpairmemER => 164.12/165.22 ( 164.12/165.22 cartprodmempaircEq => 164.12/165.22 ( 164.12/165.22 cartprodfstpairEq => 164.12/165.22 ( 164.12/165.22 cartprodsndpairEq => 164.12/165.22 ( 164.12/165.22 cartprodpairsurjEq => 164.12/165.22 ( 164.12/165.22 dpsetconstrI => 164.12/165.22 ( 164.12/165.22 dpsetconstrSub => 164.12/165.22 ( 164.12/165.22 setOfPairsIsBReln => 164.12/165.22 ( 164.12/165.22 dpsetconstrERa => 164.12/165.22 ( 164.12/165.22 dpsetconstrEL1 => 164.12/165.22 ( 164.12/165.22 dpsetconstrEL2 => 164.12/165.22 ( 164.12/165.22 dpsetconstrER => 164.12/165.22 ( 164.12/165.22 funcImageSingleton => 164.12/165.22 ( 164.12/165.22 apProp => 164.12/165.22 ( 164.12/165.22 app => 164.12/165.22 ( 164.12/165.22 infuncsetfunc => 164.12/165.22 ( 164.12/165.22 ap2p => 164.12/165.22 ( 164.12/165.22 funcinfuncset => 164.12/165.22 ( 164.12/165.22 lamProp => 164.12/165.22 ( 164.12/165.22 lamp => 164.12/165.22 ( 164.12/165.22 lam2p => 164.12/165.22 ( 164.12/165.22 brelnall1 => 164.12/165.22 ( 164.12/165.22 brelnall2 => 164.12/165.22 ( 164.12/165.22 ex1E2 => 164.12/165.22 ( 164.12/165.22 funcGraphProp1 => 164.12/165.22 ( 164.12/165.22 funcGraphProp3 => 164.12/165.22 ( 164.12/165.22 funcGraphProp2 => 164.12/165.22 ( 164.12/165.22 funcextLem => 164.12/165.22 ( 164.12/165.22 funcGraphProp4 => 164.12/165.22 ( 164.12/165.22 subbreln => 164.12/165.22 ( 164.12/165.22 eqbreln => 164.12/165.22 ( 164.12/165.22 funcext => 164.12/165.22 ( 164.12/165.22 funcext2 => 164.12/165.22 ( 164.12/165.22 ap2apEq1 => 164.12/165.22 ( 164.12/165.22 ap2apEq2 => 164.12/165.22 ( 164.12/165.22 beta1 => 164.12/165.22 ( 164.12/165.22 eta1 => 164.12/165.22 ( 164.12/165.22 lam2lamEq => 164.12/165.22 ( 164.12/165.22 beta2 => 164.12/165.22 ( 164.12/165.22 eta2 => 164.12/165.22 ( 164.12/165.22 iffalseProp1 => 164.12/165.22 ( 164.12/165.22 iffalseProp2 => 164.12/165.22 ( 164.12/165.22 iftrueProp1 => 164.12/165.22 ( 164.12/165.22 iftrueProp2 => 164.12/165.22 ( 164.12/165.22 ifSingleton => 164.12/165.22 ( 164.12/165.22 ifp => 164.12/165.22 ( 164.12/165.22 theeq => 164.12/165.22 ( 164.12/165.22 iftrue => 164.12/165.22 ( 164.12/165.22 iffalse => 164.12/165.22 ( 164.12/165.22 iftrueorfalse => 164.12/165.22 ( 164.12/165.22 binintersectT_lem => 164.12/165.22 ( 164.12/165.22 binunionT_lem => 164.12/165.22 ( 164.12/165.22 powersetT_lem => 164.12/165.22 ( 164.12/165.22 setminusT_lem => 164.12/165.22 ( 164.12/165.22 complementT_lem => 164.12/165.22 ( 164.12/165.22 setextT => 164.12/165.22 ( 164.12/165.22 subsetTI => 164.12/165.22 ( 164.12/165.22 powersetTI1 => 164.12/165.22 ( 164.12/165.22 powersetTE1 => 164.12/165.22 ( 164.12/165.22 complementTI1 => 164.12/165.22 ( 164.12/165.22 complementTE1 => 164.12/165.22 ( 164.12/165.22 binintersectTELcontra => 164.12/165.22 ( 164.12/165.22 binintersectTERcontra => 164.12/165.22 ( 164.12/165.22 contrasubsetT => 164.12/165.22 ( 164.12/165.22 contrasubsetT1 => 164.12/165.22 ( 164.12/165.22 contrasubsetT2 => 164.12/165.22 ( 164.12/165.22 contrasubsetT3 => 164.12/165.22 ( 164.12/165.22 doubleComplementI1 => 164.12/165.22 ( 164.12/165.22 doubleComplementE1 => 164.12/165.22 ( 164.12/165.22 doubleComplementSub1 => 164.12/165.22 ( 164.12/165.22 doubleComplementSub2 => 164.12/165.22 ( 164.12/165.22 doubleComplementEq => 164.12/165.22 ( 164.12/165.22 complementTnotintersectT => 164.12/165.22 ( 164.12/165.22 complementImpComplementIntersect => 164.12/165.22 ( 164.12/165.22 complementSubsetComplementIntersect => 164.12/165.22 ( 164.12/165.22 complementInPowersetComplementIntersect => 164.12/165.22 ( 164.12/165.22 contraSubsetComplement => 164.12/165.22 ( 164.12/165.22 complementTcontraSubset => 164.12/165.22 ( 164.12/165.22 binunionTILcontra => 164.12/165.22 ( 164.12/165.22 binunionTIRcontra => 164.12/165.22 ( 164.12/165.22 inIntersectImpInUnion => 164.12/165.22 ( 164.12/165.22 inIntersectImpInUnion2 => 164.12/165.22 ( 164.12/165.22 inIntersectImpInIntersectUnions => 164.12/165.22 ( 164.12/165.22 intersectInPowersetIntersectUnions => 164.12/165.22 ( 164.12/165.22 inComplementUnionImpNotIn1 => 164.12/165.22 ( 164.12/165.22 inComplementUnionImpInComplement1 => 164.12/165.22 ( 164.12/165.22 binunionTE => 164.12/165.22 ( 164.12/165.22 binunionTEcontra => 164.12/165.22 ( 164.12/165.22 demorgan2a1 => 164.12/165.22 ( 164.12/165.22 complementUnionInPowersetComplement => 164.12/165.22 ( 164.12/165.22 demorgan2a2 => 164.12/165.22 ( 164.12/165.22 demorgan1a => 164.12/165.22 ( 164.12/165.22 demorgan1b => 164.12/165.22 ( 164.12/165.22 demorgan1 => 164.12/165.22 ( 164.12/165.22 demorgan2a => 164.12/165.22 ( 164.12/165.22 demorgan2b2 => 164.12/165.22 ( 164.12/165.22 demorgan2b => 164.12/165.22 ( 164.12/165.22 demorgan2 => 164.12/165.22 ( 164.12/165.22 woz13rule0 => 164.12/165.22 ( 164.12/165.22 woz13rule1 => 164.12/165.22 ( 164.12/165.22 woz13rule2 => 164.12/165.22 ( 164.12/165.22 woz13rule3 => 164.12/165.22 ( 164.12/165.22 woz13rule4 => 164.12/165.22 ( 164.12/165.22 woz1_1 => 164.12/165.22 ( 164.12/165.22 woz1_2 => 164.12/165.22 ( 164.12/165.22 woz1_3 => 164.12/165.22 ( 164.12/165.22 woz1_4 => 164.12/165.22 ( 164.12/165.22 woz1_5 => 164.12/165.22 ( 164.12/165.22 breln1all2 => 164.12/165.22 ( 164.12/165.22 breln1SetBreln1 => 164.12/165.22 ( 164.12/165.22 choice2fnsingleton => 164.12/165.22 ( 164.12/165.22 setOfPairsIsBReln1 => 164.12/165.22 ( 164.12/165.22 breln1all1 => 164.12/165.22 ( 164.12/165.22 subbreln1 => 164.12/165.22 ( 164.12/165.22 eqbreln1 => 164.12/165.22 ( 164.12/165.22 breln1invprop => 164.12/165.22 ( 164.12/165.22 breln1invI => 164.12/165.22 ( 164.12/165.22 breln1invE => 164.12/165.22 ( 164.12/165.22 breln1compprop => 164.12/165.22 ( 164.12/165.22 breln1compI => 164.12/165.22 ( 164.12/165.22 breln1compE => 164.12/165.22 ( 164.12/165.22 breln1compEex => 164.12/165.22 ( 164.12/165.22 breln1unionprop => 164.12/165.22 ( 164.12/165.22 breln1unionIL => 164.12/165.22 ( 164.12/165.22 breln1unionIR => 164.12/165.22 ( 164.12/165.22 breln1unionI => 164.12/165.22 ( 164.12/165.22 breln1unionE => 164.12/165.22 ( 164.12/165.22 breln1unionEcases => 164.12/165.22 ( 164.12/165.22 breln1unionCommutes => 164.12/165.22 ( 164.12/165.22 woz2Ex => 164.12/165.22 ( 164.12/165.22 woz2W => 164.12/165.22 ( 164.12/165.22 woz2A => 164.12/165.22 ( 164.12/165.22 woz2B => 164.12/165.22 ( 164.12/165.22 image1Ex => 164.12/165.22 ( 164.12/165.22 image1Ex1 => 164.12/165.22 ( 164.12/165.22 image1Equiv => 164.12/165.22 ( 164.12/165.22 image1E => 164.12/165.22 ( 164.12/165.22 image1I => 164.12/165.22 ( 164.12/165.22 injFuncInInjFuncSet => 164.12/165.22 ( 164.12/165.22 injFuncSetFuncIn => 164.12/165.22 ( 164.12/165.22 injFuncSetFuncInj => 164.12/165.22 ( 164.12/165.22 surjFuncSetFuncIn => 164.12/165.22 ( 164.12/165.22 surjFuncSetFuncSurj => 164.12/165.22 ( 164.12/165.22 leftInvIsSurj => 164.12/165.22 ( 164.12/165.22 surjCantorThm => 164.12/165.22 ( 164.12/165.22 foundation2 => 164.12/165.22 ( 164.12/165.22 notinself => 164.12/165.22 ( 164.12/165.22 notinself2 => 164.12/165.22 ( 164.12/165.22 omegaSp => 164.12/165.22 ( 164.12/165.22 omegaSclos => 164.12/165.22 ( 164.12/165.22 peano0notS => 164.12/165.22 ( 164.12/165.22 peanoSinj => 164.12/165.22 ( 164.12/165.22 transitivesetOp1 => 164.12/165.22 ( 164.12/165.22 binintTransitive => 164.12/165.22 ( 164.12/165.22 transitivesetOp2 => 164.12/165.22 ( 164.12/165.22 ![X]: 164.12/165.22 (( 164.12/165.22 ![Xx]: 164.12/165.22 (in(Xx,X) => 164.12/165.22 transitiveset( 164.12/165.22 Xx))) => 164.12/165.22 transitiveset( 164.12/165.22 setunion( 164.12/165.22 X))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 164.12/165.22 tff('0', plain, ~ transitiveset(setunion(sk_X_65)), 164.12/165.22 inference('cnf', [status(esa)], [zf_stmt_0])). 164.12/165.22 tff(transitiveset, axiom, 164.12/165.22 (transitiveset = (^[A]: (![X]: (in(X,A) => subset(X,A)))))). 164.12/165.22 tff(zf_stmt_1, axiom, 164.12/165.22 (transitiveset = 164.12/165.22 (^[Y0 : $i]: (!! (^[Y1 : $i]: (in(Y1, Y0) => subset(Y1, Y0))))))). 164.12/165.22 tff('1', plain, 164.12/165.22 transitiveset = (^[V_1]: (![X2]: (in(X2,V_1) => subset(X2,V_1)))), 164.12/165.22 define([status(thm)])). 164.12/165.22 tff('2', plain, 164.12/165.22 ~ (!! 164.12/165.22 (^[Y0 : $i]: 164.12/165.22 (in(Y0, setunion(sk_X_65)) => subset(Y0, setunion(sk_X_65))))), 164.12/165.22 inference('rw', [status(thm)], ['0', '1'])). 164.12/165.22 tff('3', plain, in(sk_X2_, setunion(sk_X_65)), 164.12/165.22 inference('cnf_otf', [status(thm)], ['2'])). 164.12/165.22 tff(setunionAx, axiom, 164.12/165.22 (setunionAx <=> 164.12/165.22 (![A,Xx]: (in(Xx,setunion(A)) <=> (?[B]: (in(B,A) & in(Xx,B))))))). 164.12/165.22 tff('4', plain, 164.12/165.22 ![X15, X17]: 164.12/165.22 (~ in(X17, setunion(X15)) | in(X17, sk_B_3(X17, X15)) | ~ setunionAx), 164.12/165.22 inference('cnf', [status(esa)], [setunionAx])). 164.12/165.22 tff('5', plain, setunionAx, inference('cnf', [status(esa)], [zf_stmt_0])). 164.12/165.22 tff('6', plain, 164.12/165.22 ![X15, X17]: (~ in(X17, setunion(X15)) | in(X17, sk_B_3(X17, X15))), 164.12/165.22 inference('demod', [status(thm)], ['4', '5'])). 164.12/165.22 tff('7', plain, in(sk_X2_, sk_B_3(sk_X2_, sk_X_65)), 164.12/165.22 inference('sup-', [status(thm)], ['3', '6'])). 164.12/165.22 tff('8', plain, 164.12/165.22 ![X15, X17]: 164.12/165.22 (~ in(X17, setunion(X15)) | in(sk_B_3(X17, X15), X15) | ~ setunionAx), 164.12/165.22 inference('cnf', [status(esa)], [setunionAx])). 164.12/165.22 tff('9', plain, 164.12/165.22 ![X15, X17]: (~ in(X17, setunion(X15)) | in(sk_B_3(X17, X15), X15)), 164.12/165.22 inference('demod', [status(thm)], ['8', '5'])). 164.12/165.22 tff('10', plain, in(sk_B_3(sk_X2_, sk_X_65), sk_X_65), 164.12/165.22 inference('sup-', [status(thm)], ['3', '9'])). 164.12/165.22 tff('11', plain, transitivesetOp1, 164.12/165.22 inference('cnf', [status(esa)], [zf_stmt_0])). 164.12/165.22 tff('12', plain, bs114d, inference('cnf', [status(esa)], [zf_stmt_0])). 164.12/165.22 tff('13', plain, ![X1140]: (transitiveset(X1140) | ~ in(X1140, sk_X_65)), 164.12/165.22 inference('cnf', [status(esa)], [zf_stmt_0])). 164.12/165.22 tff(transitivesetOp1, axiom, 164.12/165.22 (transitivesetOp1 <=> 164.12/165.22 (![X]: (transitiveset(X) => (![A]: (in(A,X) => subset(A,X))))))). 164.12/165.22 tff('14', plain, 164.12/165.22 ![X1133, X1134]: 164.12/165.22 (~ transitiveset(X1133) 164.12/165.22 | subset(X1134, X1133) 164.12/165.22 | ~ in(X1134, X1133) 164.12/165.22 | ~ transitivesetOp1), 164.12/165.22 inference('cnf', [status(esa)], [transitivesetOp1])). 164.12/165.22 tff('15', plain, binintersectSubset2, 164.12/165.22 inference('cnf', [status(esa)], [zf_stmt_0])). 164.12/165.22 tff('16', plain, subsetRefl, inference('cnf', [status(esa)], [zf_stmt_0])). 164.12/165.22 tff('17', plain, binintersectSubset4, 164.12/165.22 inference('cnf', [status(esa)], [zf_stmt_0])). 164.12/165.22 tff(bs114d, axiom, 164.12/165.22 (bs114d <=> 164.12/165.22 (![A,B,C]: 164.12/165.22 (binintersect(A,binunion(B,C)) = 164.12/165.22 binunion(binintersect(A,B),binintersect(A,C)))))). 164.12/165.22 tff('18', plain, 164.12/165.22 ![X342, X343, X344]: 164.12/165.22 (binintersect(X342, binunion(X343, X344)) 164.12/165.22 = binunion(binintersect(X342, X343), binintersect(X342, X344)) 164.12/165.22 | ~ bs114d), 164.12/165.22 inference('cnf', [status(esa)], [bs114d])). 164.12/165.22 tff(binintersectSubset2, axiom, 164.12/165.22 (binintersectSubset2 <=> (![A,B]: (subset(A,B) => (binintersect(A,B) = A))))). 164.12/165.22 tff('19', plain, 164.12/165.22 ![X326, X327]: 164.12/165.22 (~ subset(X326, X327) 164.12/165.22 | binintersect(X326, X327) = X326 164.12/165.22 | ~ binintersectSubset2), 164.12/165.22 inference('cnf', [status(esa)], [binintersectSubset2])). 164.12/165.22 tff(subsetRefl, axiom, (subsetRefl <=> (![A]: subset(A,A)))). 164.12/165.22 tff('20', plain, ![X271]: (subset(X271, X271) | ~ subsetRefl), 164.12/165.22 inference('cnf', [status(esa)], [subsetRefl])). 164.12/165.23 tff(binintersectSubset4, axiom, 164.12/165.23 (binintersectSubset4 <=> (![A,B]: (subset(B,A) => (binintersect(A,B) = B))))). 164.12/165.23 tff('21', plain, 164.12/165.23 ![X338, X339]: 164.12/165.23 (~ subset(X338, X339) 164.12/165.23 | binintersect(X339, X338) = X338 164.12/165.23 | ~ binintersectSubset4), 164.12/165.23 inference('cnf', [status(esa)], [binintersectSubset4])). 164.12/165.23 tff('22', plain, subPowSU, inference('cnf', [status(esa)], [zf_stmt_0])). 164.12/165.23 tff('23', plain, powersetE1, inference('cnf', [status(esa)], [zf_stmt_0])). 164.12/165.23 tff(subPowSU, axiom, 164.12/165.23 (subPowSU <=> (![A,Xx]: (in(Xx,A) => in(Xx,powerset(setunion(A))))))). 164.12/165.23 tff('24', plain, 164.12/165.23 ![X141, X142]: 164.12/165.23 (~ in(X141, X142) | in(X141, powerset(setunion(X142))) | ~ subPowSU), 164.12/165.23 inference('cnf', [status(esa)], [subPowSU])). 164.12/165.23 tff(powersetE1, axiom, 164.12/165.23 (powersetE1 <=> (![A,B]: (in(B,powerset(A)) => subset(B,A))))). 164.12/165.23 tff('25', plain, 164.12/165.23 ![X287, X288]: 164.12/165.23 (~ in(X287, powerset(X288)) | subset(X287, X288) | ~ powersetE1), 164.12/165.23 inference('cnf', [status(esa)], [powersetE1])). 164.12/165.23 tff('26', plain, binunionLsub, inference('cnf', [status(esa)], [zf_stmt_0])). 164.12/165.23 tff(binunionLsub, axiom, 164.12/165.23 (binunionLsub <=> (![A,B]: subset(A,binunion(A,B))))). 164.12/165.23 tff('27', plain, 164.12/165.23 ![X311, X312]: (subset(X311, binunion(X311, X312)) | ~ binunionLsub), 164.12/165.23 inference('cnf', [status(esa)], [binunionLsub])). 164.12/165.23 tff('28', plain, subsetTrans, inference('cnf', [status(esa)], [zf_stmt_0])). 164.12/165.23 tff('29', plain, ~ subset(sk_X2_, setunion(sk_X_65)), 164.12/165.23 inference('cnf_otf', [status(thm)], ['2'])). 164.12/165.23 tff(subsetTrans, axiom, 164.12/165.23 (subsetTrans <=> (![A,B,C]: (subset(A,B) => (subset(B,C) => subset(A,C)))))). 164.12/165.23 tff('30', plain, 164.12/165.23 ![X272, X273, X274]: 164.12/165.23 (~ subset(X272, X273) 164.12/165.23 | subset(X274, X273) 164.12/165.23 | ~ subset(X274, X272) 164.12/165.23 | ~ subsetTrans), 164.12/165.23 inference('cnf', [status(esa)], [subsetTrans])). 164.12/165.23 tff('31', plain, $false, 164.12/165.23 inference('eprover', [status(thm)], 164.12/165.23 ['7', '10', '11', '12', '13', '14', '15', '16', '17', '18', 164.12/165.23 '19', '20', '21', '22', '23', '24', '25', '26', '27', '28', 164.12/165.23 '29', '30'])). 164.12/165.23 164.12/165.23 % SZS output end Refutation 164.12/165.23 % Zipperpin 1.5 exiting 164.12/165.23 EOF