0.05/0.10 % Problem : Vampire---4.8_23338 : TPTP v0.0.0. Released v0.0.0. 0.05/0.11 % Command : run_E %s %d THM 0.10/0.31 % Computer : n005.cluster.edu 0.10/0.31 % Model : x86_64 x86_64 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.31 % Memory : 8042.1875MB 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.31 % CPULimit : 1440 0.10/0.31 % WCLimit : 180 0.10/0.31 % DateTime : Mon Jul 3 13:04:00 EDT 2023 0.10/0.31 % CPUTime : 0.15/0.41 Running higher-order theorem provingRunning: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=180 /export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338 0.15/0.42 # Version: 3.1pre001-ho 0.15/0.44 # Preprocessing class: HSMSSLSSMLLCHSA. 0.15/0.44 # Scheduled 4 strats onto 8 cores with 180 seconds (1440 total) 0.15/0.44 # Starting new_ho_10 with 900s (5) cores 0.15/0.44 # Starting sh5l with 180s (1) cores 0.15/0.44 # Starting new_bool_1 with 180s (1) cores 0.15/0.44 # Starting new_bool_2 with 180s (1) cores 0.15/0.44 # new_bool_1 with pid 23518 completed with status 0 0.15/0.44 # Result found by new_bool_1 0.15/0.44 # Preprocessing class: HSMSSLSSMLLCHSA. 0.15/0.44 # Scheduled 4 strats onto 8 cores with 180 seconds (1440 total) 0.15/0.44 # Starting new_ho_10 with 900s (5) cores 0.15/0.44 # Starting sh5l with 180s (1) cores 0.15/0.44 # Starting new_bool_1 with 180s (1) cores 0.15/0.44 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0) 0.15/0.44 # Search class: HGHSM-FFMS31-SHSSMSBN 0.15/0.44 # Scheduled 5 strats onto 1 cores with 180 seconds (180 total) 0.15/0.44 # Starting new_ho_10 with 109s (1) cores 0.15/0.44 # new_ho_10 with pid 23520 completed with status 0 0.15/0.44 # Result found by new_ho_10 0.15/0.44 # Preprocessing class: HSMSSLSSMLLCHSA. 0.15/0.44 # Scheduled 4 strats onto 8 cores with 180 seconds (1440 total) 0.15/0.44 # Starting new_ho_10 with 900s (5) cores 0.15/0.44 # Starting sh5l with 180s (1) cores 0.15/0.44 # Starting new_bool_1 with 180s (1) cores 0.15/0.44 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0) 0.15/0.44 # Search class: HGHSM-FFMS31-SHSSMSBN 0.15/0.44 # Scheduled 5 strats onto 1 cores with 180 seconds (180 total) 0.15/0.44 # Starting new_ho_10 with 109s (1) cores 0.15/0.44 # Preprocessing time : 0.004 s 0.15/0.44 # Presaturation interreduction done 0.15/0.44 0.15/0.44 # Proof found! 0.15/0.44 # SZS status Theorem 0.15/0.44 # SZS output start CNFRefutation 0.15/0.44 thf(decl_22, type, in: $i > $i > $o). 0.15/0.44 thf(decl_23, type, exu: ($i > $o) > $o). 0.15/0.44 thf(decl_24, type, setextAx: $o). 0.15/0.44 thf(decl_25, type, emptyset: $i). 0.15/0.44 thf(decl_26, type, emptysetAx: $o). 0.15/0.44 thf(decl_27, type, setadjoin: $i > $i > $i). 0.15/0.44 thf(decl_28, type, setadjoinAx: $o). 0.15/0.44 thf(decl_29, type, powerset: $i > $i). 0.15/0.44 thf(decl_30, type, powersetAx: $o). 0.15/0.44 thf(decl_31, type, setunion: $i > $i). 0.15/0.44 thf(decl_32, type, setunionAx: $o). 0.15/0.44 thf(decl_33, type, omega: $i). 0.15/0.44 thf(decl_34, type, omega0Ax: $o). 0.15/0.44 thf(decl_35, type, omegaSAx: $o). 0.15/0.44 thf(decl_36, type, omegaIndAx: $o). 0.15/0.44 thf(decl_37, type, replAx: $o). 0.15/0.44 thf(decl_38, type, foundationAx: $o). 0.15/0.44 thf(decl_39, type, wellorderingAx: $o). 0.15/0.44 thf(decl_41, type, descrp: $o). 0.15/0.44 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 0.15/0.44 thf(decl_43, type, dsetconstrI: $o). 0.15/0.44 thf(decl_44, type, dsetconstrEL: $o). 0.15/0.44 thf(decl_45, type, dsetconstrER: $o). 0.15/0.44 thf(decl_46, type, exuE1: $o). 0.15/0.44 thf(decl_47, type, prop2set: $o > $i). 0.15/0.44 thf(decl_48, type, prop2setE: $o). 0.15/0.44 thf(decl_49, type, emptysetE: $o). 0.15/0.44 thf(decl_50, type, emptysetimpfalse: $o). 0.15/0.44 thf(decl_51, type, notinemptyset: $o). 0.15/0.44 thf(decl_52, type, exuE3e: $o). 0.15/0.44 thf(decl_53, type, setext: $o). 0.15/0.44 thf(decl_54, type, emptyI: $o). 0.15/0.44 thf(decl_55, type, noeltsimpempty: $o). 0.15/0.44 thf(decl_56, type, setbeta: $o). 0.15/0.44 thf(decl_57, type, nonempty: $i > $o). 0.15/0.44 thf(decl_58, type, nonemptyE1: $o). 0.15/0.44 thf(decl_59, type, nonemptyI: $o). 0.15/0.44 thf(decl_60, type, nonemptyI1: $o). 0.15/0.44 thf(decl_61, type, setadjoinIL: $o). 0.15/0.44 thf(decl_62, type, emptyinunitempty: $o). 0.15/0.44 thf(decl_63, type, setadjoinIR: $o). 0.15/0.44 thf(decl_64, type, setadjoinE: $o). 0.15/0.44 thf(decl_65, type, setadjoinOr: $o). 0.15/0.44 thf(decl_66, type, setoftrueEq: $o). 0.15/0.44 thf(decl_67, type, powersetI: $o). 0.15/0.44 thf(decl_68, type, emptyinPowerset: $o). 0.15/0.44 thf(decl_69, type, emptyInPowerset: $o). 0.15/0.44 thf(decl_70, type, powersetE: $o). 0.15/0.44 thf(decl_71, type, setunionI: $o). 0.15/0.44 thf(decl_72, type, setunionE: $o). 0.15/0.44 thf(decl_73, type, subPowSU: $o). 0.15/0.44 thf(decl_74, type, exuE2: $o). 0.15/0.44 thf(decl_75, type, nonemptyImpWitness: $o). 0.15/0.44 thf(decl_76, type, uniqinunit: $o). 0.15/0.44 thf(decl_77, type, notinsingleton: $o). 0.15/0.44 thf(decl_78, type, eqinunit: $o). 0.15/0.44 thf(decl_79, type, singletonsswitch: $o). 0.15/0.44 thf(decl_80, type, upairsetE: $o). 0.15/0.44 thf(decl_81, type, upairsetIL: $o). 0.15/0.44 thf(decl_82, type, upairsetIR: $o). 0.15/0.44 thf(decl_83, type, emptyE1: $o). 0.15/0.44 thf(decl_84, type, epred1_0: $o). 0.15/0.44 thf(decl_85, type, esk1_2: $i > $i > $i). 0.15/0.44 thf(decl_86, type, esk2_2: $i > $i > $i). 0.15/0.44 thf(decl_87, type, esk3_2: $i > $i > $i). 0.15/0.44 thf(decl_88, type, esk4_1: $i > $i). 0.15/0.44 thf(decl_89, type, esk5_2: ($i > $i > $o) > $i > $i). 0.15/0.44 thf(decl_90, type, esk6_3: ($i > $i > $o) > $i > $i > $i). 0.15/0.44 thf(decl_91, type, esk7_2: ($i > $i > $o) > $i > $i). 0.15/0.44 thf(decl_92, type, esk8_3: ($i > $i > $o) > $i > $i > $i). 0.15/0.44 thf(decl_93, type, esk9_1: $i > $i). 0.15/0.44 thf(decl_94, type, esk10_2: ($i > $o) > $i > $i). 0.15/0.44 thf(decl_95, type, esk11_1: ($i > $o) > $i). 0.15/0.44 thf(decl_96, type, esk12_2: ($i > $o) > $i > $i). 0.15/0.44 thf(decl_97, type, esk13_1: ($i > $o) > $i). 0.15/0.44 thf(decl_98, type, esk14_2: $i > $i > $i). 0.15/0.44 thf(decl_99, type, esk15_2: $i > $i > $i). 0.15/0.44 thf(decl_100, type, esk16_1: $i > $i). 0.15/0.44 thf(decl_101, type, esk17_1: $i > $i). 0.15/0.44 thf(decl_102, type, esk18_1: $i > $i). 0.15/0.44 thf(decl_103, type, esk19_2: $i > $i > $i). 0.15/0.44 thf(decl_104, type, esk20_3: $i > $i > $o > $i). 0.15/0.44 thf(decl_105, type, esk21_2: ($i > $o) > $i > $i). 0.15/0.44 thf(decl_106, type, esk22_1: ($i > $o) > $i). 0.15/0.44 thf(decl_107, type, esk23_1: $i > $i). 0.15/0.44 thf(decl_108, type, epred2_0: $i > $o). 0.15/0.44 thf(decl_109, type, esk24_0: $i). 0.15/0.44 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', exuE3e)). 0.15/0.44 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', exu)). 0.15/0.44 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', nonemptyI)). 0.15/0.44 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', nonempty)). 0.15/0.44 thf(prop2set, axiom, ((prop2set)=(^[X10:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[X2:$i]:((X10)))))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', prop2set)). 0.15/0.44 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/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', exuE1)). 0.15/0.44 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', exuE2)). 0.15/0.44 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', replAx)). 0.15/0.44 thf(prop2setE, axiom, ((prop2setE)<=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', prop2setE)). 0.15/0.44 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', dsetconstrER)). 0.15/0.44 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', dsetconstrEL)). 0.15/0.44 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', dsetconstrI)). 0.15/0.44 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', emptyE1)). 0.15/0.44 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', nonemptyImpWitness)). 0.15/0.44 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', setbeta)). 0.15/0.44 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', setoftrueEq)). 0.15/0.44 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', nonemptyI1)). 0.15/0.44 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', nonemptyE1)). 0.15/0.44 thf(vacuousDall, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>(((setunionAx)=>((((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((((((((emptysetimpfalse)=>(((exuE3e)=>((((noeltsimpempty)=>((setbeta)=>(((nonemptyI)=>(((((((setadjoinOr)=>((((emptyinPowerset)=>(((((setunionE)=>((((((notinsingleton)=>((eqinunit)=>((((upairsetIL)=>(((emptyE1)=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2))))<=(upairsetIR)))<=(upairsetE))<=(singletonsswitch))))<=(uniqinunit))<=(nonemptyImpWitness))<=(exuE2))<=(subPowSU)))<=(setunionI))<=(powersetE))<=(emptyInPowerset)))<=(powersetI))<=(setoftrueEq)))<=(setadjoinE))<=(setadjoinIR))<=(emptyinunitempty))<=(setadjoinIL))<=(nonemptyI1)))<=(nonemptyE1))))<=(emptyI))<=(setext)))<=(notinemptyset)))<=(emptysetE))<=(prop2setE))<=(exuE1))<=(dsetconstrER))<=(dsetconstrEL))<=(dsetconstrI)))))))<=(omegaSAx))<=(omega0Ax)))<=(powersetAx))))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', vacuousDall)). 0.15/0.44 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', noeltsimpempty)). 0.15/0.44 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', powersetAx)). 0.15/0.44 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', setext)). 0.15/0.44 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', notinemptyset)). 0.15/0.44 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12))))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', emptysetE)). 0.15/0.44 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', setadjoinOr)). 0.15/0.44 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', emptyinPowerset)). 0.15/0.44 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', omegaSAx)). 0.15/0.44 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', omega0Ax)). 0.15/0.44 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X14:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X14))))=>(X14)))))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', setunionE)). 0.15/0.44 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', notinsingleton)). 0.15/0.44 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', eqinunit)). 0.15/0.44 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', upairsetIL)). 0.15/0.44 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', upairsetIR)). 0.15/0.44 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X15:$i]:(((in @ X15 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X15)=(X2))|((X15)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', upairsetE)). 0.15/0.44 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', singletonsswitch)). 0.15/0.44 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', uniqinunit)). 0.15/0.44 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', subPowSU)). 0.15/0.44 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', setunionI)). 0.15/0.44 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', powersetE)). 0.15/0.44 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', emptyInPowerset)). 0.15/0.44 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', powersetI)). 0.15/0.44 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X13:$o]:(((((X3)=(X2))=>(X13))=>(((in @ X3 @ X4)=>(X13))=>(X13))))))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', setadjoinE)). 0.15/0.44 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', setadjoinIR)). 0.15/0.44 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', emptyinunitempty)). 0.15/0.44 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', setadjoinIL)). 0.15/0.44 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', emptyI)). 0.15/0.44 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', emptysetimpfalse)). 0.15/0.44 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', wellorderingAx)). 0.15/0.44 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/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', foundationAx)). 0.15/0.44 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', omegaIndAx)). 0.15/0.44 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', setunionAx)). 0.15/0.44 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', setadjoinAx)). 0.15/0.44 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', emptysetAx)). 0.15/0.44 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.k5cmQRetwo/Vampire---4.8_23338', setextAx)). 0.15/0.44 thf(c_0_54, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 0.15/0.44 thf(c_0_55, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])). 0.15/0.44 thf(c_0_56, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 0.15/0.44 thf(c_0_57, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 0.15/0.44 thf(c_0_58, plain, ((prop2set)=(^[Z0/* 42 */:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[Z1/* 3 */:$i]:((Z0)))))), inference(fof_simplification,[status(thm)],[prop2set])). 0.15/0.44 thf(c_0_59, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 0.15/0.44 thf(c_0_60, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 0.15/0.44 thf(c_0_61, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0/* 3 */:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 0.15/0.44 thf(c_0_62, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X159:$i]:((((X1 @ X159))&![X160:$i]:((((X1 @ X160))=>((X159)=(X160)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_54, c_0_55])). 0.15/0.44 thf(c_0_63, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_56, c_0_57])). 0.15/0.44 thf(c_0_64, axiom, ((prop2setE)=(![X11:$o, X2:$i]:(((in @ X2 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0/* 3 */:$i]:(((X11))))))=>(X11))))), inference(apply_def,[status(thm)],[prop2setE, c_0_58])). 0.15/0.44 thf(c_0_65, plain, ((exuE1)=(![X1:$i > $o]:(((?[X157:$i]:((((X1 @ X157))&![X158:$i]:((((X1 @ X158))=>((X157)=(X158)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_59, c_0_55])). 0.15/0.44 thf(c_0_66, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 0.15/0.44 thf(c_0_67, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 0.15/0.44 thf(c_0_68, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 0.15/0.44 thf(c_0_69, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])). 0.15/0.44 thf(c_0_70, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_57])). 0.15/0.44 thf(c_0_71, plain, ((exuE2)=(![X1:$i > $o]:(((?[X161:$i]:((((X1 @ X161))&![X162:$i]:((((X1 @ X162))=>((X161)=(X162)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_60, c_0_55])). 0.15/0.44 thf(c_0_72, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 0.15/0.44 thf(c_0_73, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 0.15/0.44 thf(c_0_74, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_57])). 0.15/0.44 thf(c_0_75, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_57])). 0.15/0.44 thf(c_0_76, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X155:$i]:((((X6 @ X2 @ X155))&![X156:$i]:((((X6 @ X2 @ X156))=>((X155)=(X156)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_61, c_0_55])). 0.15/0.44 thf(c_0_77, plain, ((epred1_0)<=>![X188:$i]:(?[X189:$i]:((((![X190:$i]:(((in @ X190 @ X189)=>![X191:$i]:(((in @ X191 @ X190)=>(in @ X191 @ X188)))))&![X192:$i, X193:$i]:((((in @ X192 @ X188)&(in @ X193 @ X188))=>(![X194:$i]:(((in @ X194 @ X189)=>((in @ X192 @ X194)<=>(in @ X193 @ X194))))=>((X192)=(X193))))))&![X195:$i, X196:$i]:((((in @ X195 @ X189)&(in @ X196 @ X189))=>(![X197:$i]:(((in @ X197 @ X195)=>(in @ X197 @ X196)))|![X198:$i]:(((in @ X198 @ X196)=>(in @ X198 @ X195)))))))&![X199:$i]:(((![X200:$i]:(((in @ X200 @ X199)=>(in @ X200 @ X188)))&?[X201:$i]:((in @ X201 @ X199)))=>?[X202:$i, X203:$i]:(((((in @ X202 @ X189)&(in @ X203 @ X199))&~(?[X204:$i]:(((in @ X204 @ X202)&(in @ X204 @ X199)))))&![X205:$i]:(((in @ X205 @ X189)=>(![X206:$i]:(((in @ X206 @ X205)=>(in @ X206 @ X202)))|(in @ X203 @ X205)))))))))))), introduced(definition)). 0.15/0.44 thf(c_0_78, negated_conjecture, ~((![X163:$i, X164:$i]:((![X165:$i]:(((in @ X165 @ X163)<=>(in @ X165 @ X164)))=>((X163)=(X164))))=>(![X166:$i]:(~(in @ X166 @ emptyset))=>(![X167:$i, X168:$i, X169:$i]:(((in @ X169 @ (setadjoin @ X167 @ X168))<=>(((X169)=(X167))|(in @ X169 @ X168))))=>(![X305:$i, X306:$i]:(((in @ X306 @ (powerset @ X305))<=>![X307:$i]:(((in @ X307 @ X306)=>(in @ X307 @ X305)))))=>(![X170:$i, X171:$i]:(((in @ X171 @ (setunion @ X170))<=>?[X172:$i]:(((in @ X171 @ X172)&(in @ X172 @ X170)))))=>((in @ emptyset @ omega)=>(![X304:$i]:(((in @ X304 @ omega)=>(in @ (setadjoin @ X304 @ X304) @ omega)))=>(![X173:$i]:((((in @ emptyset @ X173)&![X174:$i]:((((in @ X174 @ omega)&(in @ X174 @ X173))=>(in @ (setadjoin @ X174 @ X174) @ X173))))=>![X175:$i]:(((in @ X175 @ omega)=>(in @ X175 @ X173)))))=>(![X176:$i > $i > $o, X177:$i]:((![X178:$i]:(((in @ X178 @ X177)=>?[X179:$i]:(((X176 @ X178 @ X179)&![X180:$i]:(((X176 @ X178 @ X180)=>((X179)=(X180))))))))=>?[X181:$i]:(![X182:$i]:(((in @ X182 @ X181)<=>?[X183:$i]:(((in @ X183 @ X177)&(X176 @ X183 @ X182))))))))=>(![X184:$i]:((?[X185:$i]:((in @ X185 @ X184))=>?[X186:$i]:(((in @ X186 @ X184)&~(?[X187:$i]:(((in @ X187 @ X186)&(in @ X187 @ X184))))))))=>((epred1_0)=>((descrp)=>(![X301:$i, X302:$i > $o, X303:$i]:(((in @ X303 @ X301)=>((X302 @ X303)=>(in @ X303 @ (dsetconstr @ X301 @ (^[Z0/* 3 */:$i]:((X302 @ Z0))))))))=>(![X298:$i, X299:$i > $o, X300:$i]:(((in @ X300 @ (dsetconstr @ X298 @ (^[Z0/* 3 */:$i]:((X299 @ Z0)))))=>(in @ X300 @ X298)))=>(![X295:$i, X296:$i > $o, X297:$i]:(((in @ X297 @ (dsetconstr @ X295 @ (^[Z0/* 3 */:$i]:((X296 @ Z0)))))=>(X296 @ X297)))=>(![X290:$i > $o]:((?[X291:$i]:(((X290 @ X291)&![X292:$i]:(((X290 @ X292)=>((X291)=(X292))))))=>?[X293:$i]:(((X290 @ X293)&![X294:$i]:(((X290 @ X294)=>((X293)=(X294))))))))=>(![X288:$o, X289:$i]:(((in @ X289 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0/* 3 */:$i]:((X288)))))=>(X288)))=>(![X286:$i]:(((in @ X286 @ emptyset)=>![X287:$o]:((X287))))=>(![X207:$i]:(~(in @ X207 @ emptyset))=>(![X285:$i]:(~(in @ X285 @ emptyset))=>(![X208:$i > $o]:((?[X209:$i]:(((X208 @ X209)&![X210:$i]:(((X208 @ X210)=>((X209)=(X210))))))=>?[X211:$i]:((X208 @ X211))))=>(![X281:$i, X282:$i]:((![X283:$i]:(((in @ X283 @ X281)=>(in @ X283 @ X282)))=>(![X284:$i]:(((in @ X284 @ X282)=>(in @ X284 @ X281)))=>((X281)=(X282)))))=>(![X279:$i]:((![X280:$i]:(~(in @ X280 @ X279))=>((X279)=(emptyset))))=>(![X212:$i]:((![X213:$i]:(~(in @ X213 @ X212))=>((X212)=(emptyset))))=>(![X214:$i, X215:$i > $o, X216:$i]:(((in @ X216 @ X214)=>((in @ X216 @ (dsetconstr @ X214 @ (^[Z0/* 3 */:$i]:((X215 @ Z0)))))<=>(X215 @ X216))))=>(![X277:$i]:((((X277)!=(emptyset))=>?[X278:$i]:((in @ X278 @ X277))))=>(![X217:$i, X218:$i > $o, X219:$i]:(((in @ X219 @ X217)=>((X218 @ X219)=>((dsetconstr @ X217 @ (^[Z0/* 3 */:$i]:((X218 @ Z0))))!=(emptyset)))))=>(![X275:$i]:((?[X276:$i]:((in @ X276 @ X275))=>((X275)!=(emptyset))))=>(![X273:$i, X274:$i]:((in @ X273 @ (setadjoin @ X273 @ X274)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X270:$i, X271:$i, X272:$i]:(((in @ X272 @ X271)=>(in @ X272 @ (setadjoin @ X270 @ X271))))=>(![X266:$i, X267:$i, X268:$i]:(((in @ X268 @ (setadjoin @ X266 @ X267))=>![X269:$o]:(((((X268)=(X266))=>(X269))=>(((in @ X268 @ X267)=>(X269))=>(X269))))))=>(![X220:$i, X221:$i, X222:$i]:(((in @ X222 @ (setadjoin @ X220 @ X221))=>(((X222)=(X220))|(in @ X222 @ X221))))=>(![X265:$i]:(((dsetconstr @ X265 @ (^[Z0/* 3 */:$i]:(($true))))=(X265)))=>(![X262:$i, X263:$i]:((![X264:$i]:(((in @ X264 @ X263)=>(in @ X264 @ X262)))=>(in @ X263 @ (powerset @ X262))))=>(![X223:$i]:((in @ emptyset @ (powerset @ X223)))=>(![X261:$i]:((in @ emptyset @ (powerset @ X261)))=>(![X258:$i, X259:$i, X260:$i]:(((in @ X259 @ (powerset @ X258))=>((in @ X260 @ X259)=>(in @ X260 @ X258))))=>(![X255:$i, X256:$i, X257:$i]:(((in @ X256 @ X257)=>((in @ X257 @ X255)=>(in @ X256 @ (setunion @ X255)))))=>(![X224:$i, X225:$i]:(((in @ X225 @ (setunion @ X224))=>![X226:$o]:((![X227:$i]:(((in @ X225 @ X227)=>((in @ X227 @ X224)=>(X226))))=>(X226)))))=>(![X253:$i, X254:$i]:(((in @ X254 @ X253)=>(in @ X254 @ (powerset @ (setunion @ X253)))))=>(![X248:$i > $o]:((?[X249:$i]:(((X248 @ X249)&![X250:$i]:(((X248 @ X250)=>((X249)=(X250))))))=>?[X251:$i]:(![X252:$i]:(((X248 @ X252)<=>((X252)=(X251)))))))=>(![X246:$i]:((((X246)!=(emptyset))=>?[X247:$i]:((in @ X247 @ X246))))=>(![X244:$i, X245:$i]:(((in @ X244 @ (setadjoin @ X245 @ emptyset))=>((X244)=(X245))))=>(![X228:$i, X229:$i]:((((X228)!=(X229))=>~(in @ X229 @ (setadjoin @ X228 @ emptyset))))=>(![X230:$i, X231:$i]:((((X230)=(X231))=>(in @ X230 @ (setadjoin @ X231 @ emptyset))))=>(![X242:$i, X243:$i]:(((in @ X242 @ (setadjoin @ X243 @ emptyset))=>(in @ X243 @ (setadjoin @ X242 @ emptyset))))=>(![X239:$i, X240:$i, X241:$i]:(((in @ X241 @ (setadjoin @ X239 @ (setadjoin @ X240 @ emptyset)))=>(((X241)=(X239))|((X241)=(X240)))))=>(![X232:$i, X233:$i]:((in @ X232 @ (setadjoin @ X232 @ (setadjoin @ X233 @ emptyset))))=>(![X237:$i, X238:$i]:((in @ X238 @ (setadjoin @ X237 @ (setadjoin @ X238 @ emptyset))))=>(![X234:$i, X235:$i > $o]:((?[X236:$i]:(((in @ X236 @ X234)&(X235 @ X236)))=>((dsetconstr @ X234 @ (^[Z0/* 3 */:$i]:((X235 @ Z0))))!=(emptyset))))=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[vacuousDall]), noeltsimpempty]), powersetAx]), setext]), c_0_62]), notinemptyset]), emptysetE]), c_0_63]), c_0_64]), c_0_65]), setadjoinOr]), c_0_66]), c_0_67]), c_0_68]), emptyinPowerset]), omegaSAx]), omega0Ax]), setunionE]), notinsingleton]), eqinunit]), upairsetIL]), c_0_69]), upairsetIR]), upairsetE]), singletonsswitch]), uniqinunit]), c_0_70]), c_0_71]), subPowSU]), c_0_72]), setunionI]), powersetE]), emptyInPowerset]), powersetI]), c_0_73]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), c_0_74]), c_0_75]), emptyI]), emptysetimpfalse]), wellorderingAx]), foundationAx]), c_0_76]), omegaIndAx]), setunionAx]), setadjoinAx]), emptysetAx]), setextAx])]), c_0_77])). 0.15/0.44 thf(c_0_79, negated_conjecture, ![X308:$i, X309:$i, X311:$i, X312:$i, X313:$i, X314:$i, X315:$i, X316:$i, X317:$i, X318:$i, X319:$i, X321:$i, X322:$i, X324:$i, X325:$i, X326:$i, X327:$i, X328:$i, X330:$i, X331:$i > $i > $o, X332:$i, X334:$i, X337:$i, X339:$i, X340:$i, X341:$i, X342:$i, X344:$i, X345:$i, X346:$i > $o, X347:$i, X348:$i, X349:$i > $o, X350:$i, X351:$i, X352:$i > $o, X353:$i, X354:$i > $o, X355:$i, X358:$i, X359:$o, X360:$i, X361:$i, X362:$o, X363:$i, X364:$i, X365:$i > $o, X366:$i, X369:$i, X370:$i, X373:$i, X375:$i, X377:$i, X378:$i > $o, X379:$i, X380:$i, X382:$i, X383:$i > $o, X384:$i, X385:$i, X386:$i, X387:$i, X388:$i, X389:$i, X390:$i, X391:$i, X392:$i, X393:$i, X394:$i, X395:$o, X396:$i, X397:$i, X398:$i, X399:$i, X400:$i, X401:$i, X403:$i, X404:$i, X405:$i, X406:$i, X407:$i, X408:$i, X409:$i, X410:$i, X411:$i, X412:$i, X413:$o, X415:$i, X416:$i, X417:$i > $o, X418:$i, X421:$i, X422:$i, X423:$i, X425:$i, X426:$i, X427:$i, X428:$i, X429:$i, X430:$i, X431:$i, X432:$i, X433:$i, X434:$i, X435:$i, X436:$i, X437:$i, X438:$i, X439:$i, X440:$i, X441:$i > $o, X442:$i]:((((~(in @ (esk1_2 @ X308 @ X309) @ X308)|~(in @ (esk1_2 @ X308 @ X309) @ X309)|((X308)=(X309)))&((in @ (esk1_2 @ X308 @ X309) @ X308)|(in @ (esk1_2 @ X308 @ X309) @ X309)|((X308)=(X309))))&(~(in @ X311 @ emptyset)&(((~(in @ X314 @ (setadjoin @ X312 @ X313))|(((X314)=(X312))|(in @ X314 @ X313)))&((((X314)!=(X312))|(in @ X314 @ (setadjoin @ X312 @ X313)))&(~(in @ X314 @ X313)|(in @ X314 @ (setadjoin @ X312 @ X313)))))&(((~(in @ X316 @ (powerset @ X315))|(~(in @ X317 @ X316)|(in @ X317 @ X315)))&(((in @ (esk2_2 @ X318 @ X319) @ X319)|(in @ X319 @ (powerset @ X318)))&(~(in @ (esk2_2 @ X318 @ X319) @ X318)|(in @ X319 @ (powerset @ X318)))))&(((((in @ X322 @ (esk3_2 @ X321 @ X322))|~(in @ X322 @ (setunion @ X321)))&((in @ (esk3_2 @ X321 @ X322) @ X321)|~(in @ X322 @ (setunion @ X321))))&(~(in @ X325 @ X326)|~(in @ X326 @ X324)|(in @ X325 @ (setunion @ X324))))&((in @ emptyset @ omega)&((~(in @ X327 @ omega)|(in @ (setadjoin @ X327 @ X327) @ omega))&(((((in @ (esk4_1 @ X328) @ omega)|~(in @ emptyset @ X328)|(~(in @ X330 @ omega)|(in @ X330 @ X328)))&((in @ (esk4_1 @ X328) @ X328)|~(in @ emptyset @ X328)|(~(in @ X330 @ omega)|(in @ X330 @ X328))))&(~(in @ (setadjoin @ (esk4_1 @ X328) @ (esk4_1 @ X328)) @ X328)|~(in @ emptyset @ X328)|(~(in @ X330 @ omega)|(in @ X330 @ X328))))&((((((in @ (esk8_3 @ X331 @ X332 @ X337) @ X332)|~(in @ X337 @ (esk7_2 @ X331 @ X332))|(in @ (esk5_2 @ X331 @ X332) @ X332))&((X331 @ (esk8_3 @ X331 @ X332 @ X337) @ X337)|~(in @ X337 @ (esk7_2 @ X331 @ X332))|(in @ (esk5_2 @ X331 @ X332) @ X332)))&(~(in @ X340 @ X332)|~(X331 @ X340 @ X339)|(in @ X339 @ (esk7_2 @ X331 @ X332))|(in @ (esk5_2 @ X331 @ X332) @ X332)))&(((((in @ (esk8_3 @ X331 @ X332 @ X337) @ X332)|~(in @ X337 @ (esk7_2 @ X331 @ X332))|((X331 @ (esk5_2 @ X331 @ X332) @ (esk6_3 @ X331 @ X332 @ X334))|~(X331 @ (esk5_2 @ X331 @ X332) @ X334)))&((X331 @ (esk8_3 @ X331 @ X332 @ X337) @ X337)|~(in @ X337 @ (esk7_2 @ X331 @ X332))|((X331 @ (esk5_2 @ X331 @ X332) @ (esk6_3 @ X331 @ X332 @ X334))|~(X331 @ (esk5_2 @ X331 @ X332) @ X334))))&(~(in @ X340 @ X332)|~(X331 @ X340 @ X339)|(in @ X339 @ (esk7_2 @ X331 @ X332))|((X331 @ (esk5_2 @ X331 @ X332) @ (esk6_3 @ X331 @ X332 @ X334))|~(X331 @ (esk5_2 @ X331 @ X332) @ X334))))&((((in @ (esk8_3 @ X331 @ X332 @ X337) @ X332)|~(in @ X337 @ (esk7_2 @ X331 @ X332))|(((X334)!=(esk6_3 @ X331 @ X332 @ X334))|~(X331 @ (esk5_2 @ X331 @ X332) @ X334)))&((X331 @ (esk8_3 @ X331 @ X332 @ X337) @ X337)|~(in @ X337 @ (esk7_2 @ X331 @ X332))|(((X334)!=(esk6_3 @ X331 @ X332 @ X334))|~(X331 @ (esk5_2 @ X331 @ X332) @ X334))))&(~(in @ X340 @ X332)|~(X331 @ X340 @ X339)|(in @ X339 @ (esk7_2 @ X331 @ X332))|(((X334)!=(esk6_3 @ X331 @ X332 @ X334))|~(X331 @ (esk5_2 @ X331 @ X332) @ X334))))))&((((in @ (esk9_1 @ X341) @ X341)|~(in @ X342 @ X341))&(~(in @ X344 @ (esk9_1 @ X341))|~(in @ X344 @ X341)|~(in @ X342 @ X341)))&((epred1_0)&((descrp)&((~(in @ X347 @ X345)|(~(X346 @ X347)|(in @ X347 @ (dsetconstr @ X345 @ (^[Z0/* 3 */:$i]:((X346 @ Z0)))))))&((~(in @ X350 @ (dsetconstr @ X348 @ (^[Z0/* 3 */:$i]:((X349 @ Z0)))))|(in @ X350 @ X348))&((~(in @ X353 @ (dsetconstr @ X351 @ (^[Z0/* 3 */:$i]:((X352 @ Z0)))))|(X352 @ X353))&(((((X354 @ (esk11_1 @ X354))|((X354 @ (esk10_2 @ X354 @ X355))|~(X354 @ X355)))&(~(X354 @ X358)|((esk11_1 @ X354)=(X358))|((X354 @ (esk10_2 @ X354 @ X355))|~(X354 @ X355))))&(((X354 @ (esk11_1 @ X354))|(((X355)!=(esk10_2 @ X354 @ X355))|~(X354 @ X355)))&(~(X354 @ X358)|((esk11_1 @ X354)=(X358))|(((X355)!=(esk10_2 @ X354 @ X355))|~(X354 @ X355)))))&((~(in @ X360 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0/* 3 */:$i]:((X359)))))|(X359))&((~(in @ X361 @ emptyset)|(X362))&(~(in @ X363 @ emptyset)&(~(in @ X364 @ emptyset)&((((X365 @ (esk12_2 @ X365 @ X366))|~(X365 @ X366)|(X365 @ (esk13_1 @ X365)))&(((X366)!=(esk12_2 @ X365 @ X366))|~(X365 @ X366)|(X365 @ (esk13_1 @ X365))))&(((((in @ (esk15_2 @ X369 @ X370) @ X370)|((X369)=(X370))|(in @ (esk14_2 @ X369 @ X370) @ X369))&(~(in @ (esk15_2 @ X369 @ X370) @ X369)|((X369)=(X370))|(in @ (esk14_2 @ X369 @ X370) @ X369)))&(((in @ (esk15_2 @ X369 @ X370) @ X370)|((X369)=(X370))|~(in @ (esk14_2 @ X369 @ X370) @ X370))&(~(in @ (esk15_2 @ X369 @ X370) @ X369)|((X369)=(X370))|~(in @ (esk14_2 @ X369 @ X370) @ X370))))&(((in @ (esk16_1 @ X373) @ X373)|((X373)=(emptyset)))&(((in @ (esk17_1 @ X375) @ X375)|((X375)=(emptyset)))&(((~(in @ X379 @ (dsetconstr @ X377 @ (^[Z0/* 3 */:$i]:((X378 @ Z0)))))|(X378 @ X379)|~(in @ X379 @ X377))&(~(X378 @ X379)|(in @ X379 @ (dsetconstr @ X377 @ (^[Z0/* 3 */:$i]:((X378 @ Z0)))))|~(in @ X379 @ X377)))&((((X380)=(emptyset))|(in @ (esk18_1 @ X380) @ X380))&((~(in @ X384 @ X382)|(~(X383 @ X384)|((dsetconstr @ X382 @ (^[Z0/* 3 */:$i]:((X383 @ Z0))))!=(emptyset))))&((~(in @ X386 @ X385)|((X385)!=(emptyset)))&((in @ X387 @ (setadjoin @ X387 @ X388))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X391 @ X390)|(in @ X391 @ (setadjoin @ X389 @ X390)))&(((((in @ X394 @ X393)|(X395)|((X394)=(X392))|~(in @ X394 @ (setadjoin @ X392 @ X393)))&(~(X395)|(X395)|((X394)=(X392))|~(in @ X394 @ (setadjoin @ X392 @ X393))))&(((in @ X394 @ X393)|(X395)|~(X395)|~(in @ X394 @ (setadjoin @ X392 @ X393)))&(~(X395)|(X395)|~(X395)|~(in @ X394 @ (setadjoin @ X392 @ X393)))))&((~(in @ X398 @ (setadjoin @ X396 @ X397))|(((X398)=(X396))|(in @ X398 @ X397)))&(((dsetconstr @ X399 @ (^[Z0/* 3 */:$i]:(($true))))=(X399))&((((in @ (esk19_2 @ X400 @ X401) @ X401)|(in @ X401 @ (powerset @ X400)))&(~(in @ (esk19_2 @ X400 @ X401) @ X400)|(in @ X401 @ (powerset @ X400))))&((in @ emptyset @ (powerset @ X403))&((in @ emptyset @ (powerset @ X404))&((~(in @ X406 @ (powerset @ X405))|(~(in @ X407 @ X406)|(in @ X407 @ X405)))&((~(in @ X409 @ X410)|(~(in @ X410 @ X408)|(in @ X409 @ (setunion @ X408))))&((((in @ X412 @ (esk20_3 @ X411 @ X412 @ X413))|(X413)|~(in @ X412 @ (setunion @ X411)))&(((in @ (esk20_3 @ X411 @ X412 @ X413) @ X411)|(X413)|~(in @ X412 @ (setunion @ X411)))&(~(X413)|(X413)|~(in @ X412 @ (setunion @ X411)))))&((~(in @ X416 @ X415)|(in @ X416 @ (powerset @ (setunion @ X415))))&((((~(X417 @ X421)|((X421)=(esk22_1 @ X417))|((X417 @ (esk21_2 @ X417 @ X418))|~(X417 @ X418)))&(((X422)!=(esk22_1 @ X417))|(X417 @ X422)|((X417 @ (esk21_2 @ X417 @ X418))|~(X417 @ X418))))&((~(X417 @ X421)|((X421)=(esk22_1 @ X417))|(((X418)!=(esk21_2 @ X417 @ X418))|~(X417 @ X418)))&(((X422)!=(esk22_1 @ X417))|(X417 @ X422)|(((X418)!=(esk21_2 @ X417 @ X418))|~(X417 @ X418)))))&((((X423)=(emptyset))|(in @ (esk23_1 @ X423) @ X423))&((~(in @ X425 @ (setadjoin @ X426 @ emptyset))|((X425)=(X426)))&((((X427)=(X428))|~(in @ X428 @ (setadjoin @ X427 @ emptyset)))&((((X429)!=(X430))|(in @ X429 @ (setadjoin @ X430 @ emptyset)))&((~(in @ X431 @ (setadjoin @ X432 @ emptyset))|(in @ X432 @ (setadjoin @ X431 @ emptyset)))&((~(in @ X435 @ (setadjoin @ X433 @ (setadjoin @ X434 @ emptyset)))|(((X435)=(X433))|((X435)=(X434))))&((in @ X436 @ (setadjoin @ X436 @ (setadjoin @ X437 @ emptyset)))&((in @ X439 @ (setadjoin @ X438 @ (setadjoin @ X439 @ emptyset)))&((~(in @ X442 @ X440)|~(X441 @ X442)|((dsetconstr @ X440 @ (^[Z0/* 3 */:$i]:((X441 @ Z0))))!=(emptyset)))&((in @ esk24_0 @ emptyset)&~(epred2_0 @ esk24_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_78])])])])])])). 0.15/0.44 thf(c_0_80, negated_conjecture, (in @ esk24_0 @ emptyset), inference(split_conjunct,[status(thm)],[c_0_79])). 0.15/0.44 thf(c_0_81, negated_conjecture, ![X2:$i]:(~((in @ X2 @ emptyset))), inference(split_conjunct,[status(thm)],[c_0_79])). 0.15/0.44 thf(c_0_82, negated_conjecture, ($false), inference(sr,[status(thm)],[c_0_80, c_0_81]), ['proof']). 0.15/0.44 # SZS output end CNFRefutation 0.15/0.44 # Parsed axioms : 117 0.15/0.44 # Removed by relevancy pruning/SinE : 63 0.15/0.44 # Initial clauses : 101 0.15/0.44 # Removed in clause preprocessing : 4 0.15/0.44 # Initial clauses in saturation : 97 0.15/0.44 # Processed clauses : 7 0.15/0.44 # ...of these trivial : 0 0.15/0.44 # ...subsumed : 0 0.15/0.44 # ...remaining for further processing : 7 0.15/0.44 # Other redundant clauses eliminated : 0 0.15/0.44 # Clauses deleted for lack of memory : 0 0.15/0.44 # Backward-subsumed : 0 0.15/0.44 # Backward-rewritten : 0 0.15/0.44 # Generated clauses : 1 0.15/0.44 # ...of the previous two non-redundant : 0 0.15/0.44 # ...aggressively subsumed : 0 0.15/0.44 # Contextual simplify-reflections : 0 0.15/0.44 # Paramodulations : 0 0.15/0.44 # Factorizations : 0 0.15/0.44 # NegExts : 0 0.15/0.44 # Equation resolutions : 0 0.15/0.44 # Total rewrite steps : 0 0.15/0.44 # Propositional unsat checks : 0 0.15/0.44 # Propositional check models : 0 0.15/0.44 # Propositional check unsatisfiable : 0 0.15/0.44 # Propositional clauses : 0 0.15/0.44 # Propositional clauses after purity: 0 0.15/0.44 # Propositional unsat core size : 0 0.15/0.44 # Propositional preprocessing time : 0.000 0.15/0.44 # Propositional encoding time : 0.000 0.15/0.44 # Propositional solver time : 0.000 0.15/0.44 # Success case prop preproc time : 0.000 0.15/0.44 # Success case prop encoding time : 0.000 0.15/0.44 # Success case prop solver time : 0.000 0.15/0.44 # Current number of processed clauses : 6 0.15/0.44 # Positive orientable unit clauses : 4 0.15/0.44 # Positive unorientable unit clauses: 0 0.15/0.44 # Negative unit clauses : 2 0.15/0.44 # Non-unit-clauses : 0 0.15/0.44 # Current number of unprocessed clauses: 90 0.15/0.44 # ...number of literals in the above : 272 0.15/0.44 # Current number of archived formulas : 0 0.15/0.44 # Current number of archived clauses : 1 0.15/0.44 # Clause-clause subsumption calls (NU) : 0 0.15/0.44 # Rec. Clause-clause subsumption calls : 0 0.15/0.44 # Non-unit clause-clause subsumptions : 0 0.15/0.44 # Unit Clause-clause subsumption calls : 0 0.15/0.44 # Rewrite failures with RHS unbound : 0 0.15/0.44 # BW rewrite match attempts : 0 0.15/0.44 # BW rewrite match successes : 0 0.15/0.44 # Condensation attempts : 7 0.15/0.44 # Condensation successes : 0 0.15/0.44 # Termbank termtop insertions : 11133 0.15/0.44 0.15/0.44 # ------------------------------------------------- 0.15/0.44 # User time : 0.011 s 0.15/0.44 # System time : 0.005 s 0.15/0.44 # Total time : 0.016 s 0.15/0.44 # Maximum resident set size: 3036 pages 0.15/0.44 0.15/0.44 # ------------------------------------------------- 0.15/0.44 # User time : 0.014 s 0.15/0.44 # System time : 0.007 s 0.15/0.44 # Total time : 0.021 s 0.15/0.44 # Maximum resident set size: 2080 pages 0.15/0.44 % E---3.1 exiting 0.15/0.44 EOF