0.11/0.13 % Problem : Vampire---4.8_3786 : TPTP v0.0.0. Released v0.0.0. 0.11/0.14 % Command : run_E %s %d THM 0.13/0.35 % Computer : n027.cluster.edu 0.13/0.35 % Model : x86_64 x86_64 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.35 % Memory : 8042.1875MB 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.35 % CPULimit : 1440 0.13/0.35 % WCLimit : 180 0.13/0.35 % DateTime : Mon Jul 3 13:18:47 EDT 2023 0.13/0.35 % CPUTime : 0.20/0.49 Running higher-order theorem provingRunning: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786 0.20/0.49 # Version: 3.1pre001-ho 0.20/0.53 # Preprocessing class: HSMSSLSSMLLCHFA. 0.20/0.53 # Scheduled 4 strats onto 8 cores with 180 seconds (1440 total) 0.20/0.53 # Starting new_ho_10 with 900s (5) cores 0.20/0.53 # Starting sh5l with 180s (1) cores 0.20/0.53 # Starting new_bool_1 with 180s (1) cores 0.20/0.53 # Starting new_bool_2 with 180s (1) cores 0.20/0.53 # new_bool_1 with pid 4128 completed with status 0 0.20/0.53 # Result found by new_bool_1 0.20/0.53 # Preprocessing class: HSMSSLSSMLLCHFA. 0.20/0.53 # Scheduled 4 strats onto 8 cores with 180 seconds (1440 total) 0.20/0.53 # Starting new_ho_10 with 900s (5) cores 0.20/0.53 # Starting sh5l with 180s (1) cores 0.20/0.53 # Starting new_bool_1 with 180s (1) cores 0.20/0.53 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0) 0.20/0.53 # Search class: HGHSM-FFMS31-SHFSMSBN 0.20/0.53 # Scheduled 5 strats onto 1 cores with 180 seconds (180 total) 0.20/0.53 # Starting new_ho_10 with 109s (1) cores 0.20/0.53 # new_ho_10 with pid 4130 completed with status 0 0.20/0.53 # Result found by new_ho_10 0.20/0.53 # Preprocessing class: HSMSSLSSMLLCHFA. 0.20/0.53 # Scheduled 4 strats onto 8 cores with 180 seconds (1440 total) 0.20/0.53 # Starting new_ho_10 with 900s (5) cores 0.20/0.53 # Starting sh5l with 180s (1) cores 0.20/0.53 # Starting new_bool_1 with 180s (1) cores 0.20/0.53 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0) 0.20/0.53 # Search class: HGHSM-FFMS31-SHFSMSBN 0.20/0.53 # Scheduled 5 strats onto 1 cores with 180 seconds (180 total) 0.20/0.53 # Starting new_ho_10 with 109s (1) cores 0.20/0.53 # Preprocessing time : 0.003 s 0.20/0.53 # Presaturation interreduction done 0.20/0.53 0.20/0.53 # Proof found! 0.20/0.53 # SZS status Theorem 0.20/0.53 # SZS output start CNFRefutation 0.20/0.53 thf(decl_22, type, in: $i > $i > $o). 0.20/0.53 thf(decl_23, type, exu: ($i > $o) > $o). 0.20/0.53 thf(decl_24, type, setextAx: $o). 0.20/0.53 thf(decl_25, type, emptyset: $i). 0.20/0.53 thf(decl_26, type, emptysetAx: $o). 0.20/0.53 thf(decl_27, type, setadjoin: $i > $i > $i). 0.20/0.53 thf(decl_28, type, setadjoinAx: $o). 0.20/0.53 thf(decl_29, type, powerset: $i > $i). 0.20/0.53 thf(decl_30, type, powersetAx: $o). 0.20/0.53 thf(decl_31, type, setunion: $i > $i). 0.20/0.53 thf(decl_32, type, setunionAx: $o). 0.20/0.53 thf(decl_33, type, omega: $i). 0.20/0.53 thf(decl_34, type, omega0Ax: $o). 0.20/0.53 thf(decl_35, type, omegaSAx: $o). 0.20/0.53 thf(decl_36, type, omegaIndAx: $o). 0.20/0.53 thf(decl_37, type, replAx: $o). 0.20/0.53 thf(decl_38, type, foundationAx: $o). 0.20/0.53 thf(decl_39, type, wellorderingAx: $o). 0.20/0.53 thf(decl_41, type, descrp: $o). 0.20/0.53 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 0.20/0.53 thf(decl_43, type, dsetconstrI: $o). 0.20/0.53 thf(decl_44, type, dsetconstrEL: $o). 0.20/0.53 thf(decl_45, type, dsetconstrER: $o). 0.20/0.53 thf(decl_46, type, exuE1: $o). 0.20/0.53 thf(decl_47, type, prop2set: $o > $i). 0.20/0.53 thf(decl_48, type, prop2setE: $o). 0.20/0.53 thf(decl_49, type, emptysetE: $o). 0.20/0.53 thf(decl_50, type, emptysetimpfalse: $o). 0.20/0.53 thf(decl_51, type, notinemptyset: $o). 0.20/0.53 thf(decl_52, type, exuE3e: $o). 0.20/0.53 thf(decl_53, type, setext: $o). 0.20/0.53 thf(decl_54, type, emptyI: $o). 0.20/0.53 thf(decl_55, type, noeltsimpempty: $o). 0.20/0.53 thf(decl_56, type, setbeta: $o). 0.20/0.53 thf(decl_57, type, nonempty: $i > $o). 0.20/0.53 thf(decl_58, type, nonemptyE1: $o). 0.20/0.53 thf(decl_59, type, nonemptyI: $o). 0.20/0.53 thf(decl_60, type, nonemptyI1: $o). 0.20/0.53 thf(decl_61, type, setadjoinIL: $o). 0.20/0.53 thf(decl_62, type, emptyinunitempty: $o). 0.20/0.53 thf(decl_63, type, setadjoinIR: $o). 0.20/0.53 thf(decl_64, type, setadjoinE: $o). 0.20/0.53 thf(decl_65, type, setadjoinOr: $o). 0.20/0.53 thf(decl_66, type, setoftrueEq: $o). 0.20/0.53 thf(decl_67, type, powersetI: $o). 0.20/0.53 thf(decl_68, type, emptyinPowerset: $o). 0.20/0.53 thf(decl_69, type, emptyInPowerset: $o). 0.20/0.53 thf(decl_70, type, powersetE: $o). 0.20/0.53 thf(decl_71, type, setunionI: $o). 0.20/0.53 thf(decl_72, type, setunionE: $o). 0.20/0.53 thf(decl_73, type, subPowSU: $o). 0.20/0.53 thf(decl_74, type, exuE2: $o). 0.20/0.53 thf(decl_75, type, nonemptyImpWitness: $o). 0.20/0.53 thf(decl_76, type, uniqinunit: $o). 0.20/0.53 thf(decl_77, type, notinsingleton: $o). 0.20/0.53 thf(decl_78, type, eqinunit: $o). 0.20/0.53 thf(decl_79, type, singletonsswitch: $o). 0.20/0.53 thf(decl_80, type, epred1_0: $o). 0.20/0.53 thf(decl_81, type, esk1_2: $i > $i > $i). 0.20/0.53 thf(decl_82, type, esk2_2: $i > $i > $i). 0.20/0.53 thf(decl_83, type, esk3_2: $i > $i > $i). 0.20/0.53 thf(decl_84, type, esk4_1: $i > $i). 0.20/0.53 thf(decl_85, type, esk5_2: ($i > $i > $o) > $i > $i). 0.20/0.53 thf(decl_86, type, esk6_3: ($i > $i > $o) > $i > $i > $i). 0.20/0.53 thf(decl_87, type, esk7_2: ($i > $i > $o) > $i > $i). 0.20/0.53 thf(decl_88, type, esk8_3: ($i > $i > $o) > $i > $i > $i). 0.20/0.53 thf(decl_89, type, esk9_1: $i > $i). 0.20/0.53 thf(decl_90, type, esk10_2: ($i > $o) > $i > $i). 0.20/0.53 thf(decl_91, type, esk11_1: ($i > $o) > $i). 0.20/0.53 thf(decl_92, type, esk12_2: ($i > $o) > $i > $i). 0.20/0.53 thf(decl_93, type, esk13_1: ($i > $o) > $i). 0.20/0.53 thf(decl_94, type, esk14_2: $i > $i > $i). 0.20/0.53 thf(decl_95, type, esk15_2: $i > $i > $i). 0.20/0.53 thf(decl_96, type, esk16_1: $i > $i). 0.20/0.53 thf(decl_97, type, esk17_1: $i > $i). 0.20/0.53 thf(decl_98, type, esk18_1: $i > $i). 0.20/0.53 thf(decl_99, type, esk19_2: $i > $i > $i). 0.20/0.53 thf(decl_100, type, esk20_3: $i > $i > $o > $i). 0.20/0.53 thf(decl_101, type, esk21_2: ($i > $o) > $i > $i). 0.20/0.53 thf(decl_102, type, esk22_1: ($i > $o) > $i). 0.20/0.53 thf(decl_103, type, esk23_1: $i > $i). 0.20/0.53 thf(decl_104, type, esk24_0: $i). 0.20/0.53 thf(decl_105, type, esk25_0: $i). 0.20/0.53 thf(decl_106, type, esk26_0: $i). 0.20/0.53 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', exuE1)). 0.20/0.53 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', exu)). 0.20/0.53 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', exuE3e)). 0.20/0.53 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', nonemptyI)). 0.20/0.53 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', nonempty)). 0.20/0.53 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', replAx)). 0.20/0.53 thf(prop2set, axiom, ((prop2set)=(^[X10:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[X2:$i]:((X10)))))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', prop2set)). 0.20/0.53 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', exuE2)). 0.20/0.53 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', dsetconstrER)). 0.20/0.53 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', dsetconstrEL)). 0.20/0.53 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', dsetconstrI)). 0.20/0.53 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', nonemptyI1)). 0.20/0.53 thf(prop2setE, axiom, ((prop2setE)<=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', prop2setE)). 0.20/0.53 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', setoftrueEq)). 0.20/0.53 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', nonemptyImpWitness)). 0.20/0.53 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', nonemptyE1)). 0.20/0.53 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', setbeta)). 0.20/0.53 thf(upairsetE, conjecture, (((emptysetAx)=>(((powersetAx)=>((setunionAx)=>(((omegaSAx)=>((omegaIndAx)=>(((foundationAx)=>((wellorderingAx)=>((((((exuE1)=>((prop2setE)=>((((notinemptyset)=>(((setext)=>(((noeltsimpempty)=>((((nonemptyI)=>((nonemptyI1)=>((((setadjoinIR)=>(((setadjoinOr)=>((setoftrueEq)=>((((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>(((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>(((![X2:$i, X3:$i, X15:$i]:(((in @ X15 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X15)=(X2))|((X15)=(X3)))))<=(singletonsswitch))<=(eqinunit))<=(notinsingleton)))))<=(subPowSU))))))<=(emptyinPowerset))<=(powersetI))))<=(setadjoinE)))<=(emptyinunitempty))<=(setadjoinIL))))<=(nonemptyE1))<=(setbeta)))<=(emptyI)))<=(exuE3e)))<=(emptysetimpfalse))<=(emptysetE))))<=(dsetconstrER))<=(dsetconstrEL))<=(dsetconstrI))<=(descrp))))<=(replAx))))<=(omega0Ax))))<=(setadjoinAx)))<=(setextAx)), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', upairsetE)). 0.20/0.53 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', emptyInPowerset)). 0.20/0.53 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', setextAx)). 0.20/0.53 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', emptyI)). 0.20/0.53 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', setext)). 0.20/0.53 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', emptysetimpfalse)). 0.20/0.53 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12))))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', emptysetE)). 0.20/0.53 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', noeltsimpempty)). 0.20/0.53 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', omega0Ax)). 0.20/0.53 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', setadjoinAx)). 0.20/0.53 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', setadjoinIR)). 0.20/0.53 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', setadjoinOr)). 0.20/0.53 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', notinemptyset)). 0.20/0.53 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', powersetE)). 0.20/0.53 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', setunionI)). 0.20/0.53 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/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', setunionE)). 0.20/0.53 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', uniqinunit)). 0.20/0.53 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', singletonsswitch)). 0.20/0.53 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', eqinunit)). 0.20/0.53 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', notinsingleton)). 0.20/0.53 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', subPowSU)). 0.20/0.53 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', emptyinPowerset)). 0.20/0.53 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', powersetI)). 0.20/0.53 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/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', setadjoinE)). 0.20/0.53 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', emptyinunitempty)). 0.20/0.53 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', setadjoinIL)). 0.20/0.53 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', wellorderingAx)). 0.20/0.53 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', foundationAx)). 0.20/0.53 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', omegaIndAx)). 0.20/0.53 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', omegaSAx)). 0.20/0.53 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', setunionAx)). 0.20/0.53 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', powersetAx)). 0.20/0.53 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.0zh5d9kLHB/Vampire---4.8_3786', emptysetAx)). 0.20/0.53 thf(c_0_50, 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])). 0.20/0.53 thf(c_0_51, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])). 0.20/0.53 thf(c_0_52, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 0.20/0.53 thf(c_0_53, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 0.20/0.53 thf(c_0_54, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 0.20/0.53 thf(c_0_55, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 0.20/0.53 thf(c_0_56, plain, ((prop2set)=(^[Z0/* 42 */:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[Z1/* 3 */:$i]:((Z0)))))), inference(fof_simplification,[status(thm)],[prop2set])). 0.20/0.53 thf(c_0_57, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 0.20/0.53 thf(c_0_58, plain, ((exuE1)=(![X1:$i > $o]:(((?[X148:$i]:((((X1 @ X148))&![X149:$i]:((((X1 @ X149))=>((X148)=(X149)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_50, c_0_51])). 0.20/0.53 thf(c_0_59, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X150:$i]:((((X1 @ X150))&![X151:$i]:((((X1 @ X151))=>((X150)=(X151)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_52, c_0_51])). 0.20/0.53 thf(c_0_60, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 0.20/0.53 thf(c_0_61, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 0.20/0.53 thf(c_0_62, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 0.20/0.53 thf(c_0_63, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_53, c_0_54])). 0.20/0.53 thf(c_0_64, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X146:$i]:((((X6 @ X2 @ X146))&![X147:$i]:((((X6 @ X2 @ X147))=>((X146)=(X147)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_55, c_0_51])). 0.20/0.53 thf(c_0_65, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_54])). 0.20/0.53 thf(c_0_66, axiom, ((prop2setE)=(![X11:$o, X2:$i]:(((in @ X2 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0/* 3 */:$i]:(((X11))))))=>(X11))))), inference(apply_def,[status(thm)],[prop2setE, c_0_56])). 0.20/0.53 thf(c_0_67, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 0.20/0.53 thf(c_0_68, plain, ((exuE2)=(![X1:$i > $o]:(((?[X152:$i]:((((X1 @ X152))&![X153:$i]:((((X1 @ X153))=>((X152)=(X153)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_57, c_0_51])). 0.20/0.53 thf(c_0_69, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_54])). 0.20/0.53 thf(c_0_70, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_54])). 0.20/0.53 thf(c_0_71, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 0.20/0.53 thf(c_0_72, plain, ((epred1_0)<=>![X169:$i]:(?[X170:$i]:((((![X171:$i]:(((in @ X171 @ X170)=>![X172:$i]:(((in @ X172 @ X171)=>(in @ X172 @ X169)))))&![X173:$i, X174:$i]:((((in @ X173 @ X169)&(in @ X174 @ X169))=>(![X175:$i]:(((in @ X175 @ X170)=>((in @ X173 @ X175)<=>(in @ X174 @ X175))))=>((X173)=(X174))))))&![X176:$i, X177:$i]:((((in @ X176 @ X170)&(in @ X177 @ X170))=>(![X178:$i]:(((in @ X178 @ X176)=>(in @ X178 @ X177)))|![X179:$i]:(((in @ X179 @ X177)=>(in @ X179 @ X176)))))))&![X180:$i]:(((![X181:$i]:(((in @ X181 @ X180)=>(in @ X181 @ X169)))&?[X182:$i]:((in @ X182 @ X180)))=>?[X183:$i, X184:$i]:(((((in @ X183 @ X170)&(in @ X184 @ X180))&~(?[X185:$i]:(((in @ X185 @ X183)&(in @ X185 @ X180)))))&![X186:$i]:(((in @ X186 @ X170)=>(![X187:$i]:(((in @ X187 @ X186)=>(in @ X187 @ X183)))|(in @ X184 @ X186)))))))))))), introduced(definition)). 0.20/0.53 thf(c_0_73, negated_conjecture, ~((![X286:$i, X287:$i]:((![X288:$i]:(((in @ X288 @ X286)<=>(in @ X288 @ X287)))=>((X286)=(X287))))=>(![X154:$i]:(~(in @ X154 @ emptyset))=>(![X283:$i, X284:$i, X285:$i]:(((in @ X285 @ (setadjoin @ X283 @ X284))<=>(((X285)=(X283))|(in @ X285 @ X284))))=>(![X155:$i, X156:$i]:(((in @ X156 @ (powerset @ X155))<=>![X157:$i]:(((in @ X157 @ X156)=>(in @ X157 @ X155)))))=>(![X158:$i, X159:$i]:(((in @ X159 @ (setunion @ X158))<=>?[X160:$i]:(((in @ X159 @ X160)&(in @ X160 @ X158)))))=>((in @ emptyset @ omega)=>(![X161:$i]:(((in @ X161 @ omega)=>(in @ (setadjoin @ X161 @ X161) @ omega)))=>(![X162:$i]:((((in @ emptyset @ X162)&![X163:$i]:((((in @ X163 @ omega)&(in @ X163 @ X162))=>(in @ (setadjoin @ X163 @ X163) @ X162))))=>![X164:$i]:(((in @ X164 @ omega)=>(in @ X164 @ X162)))))=>(![X275:$i > $i > $o, X276:$i]:((![X277:$i]:(((in @ X277 @ X276)=>?[X278:$i]:(((X275 @ X277 @ X278)&![X279:$i]:(((X275 @ X277 @ X279)=>((X278)=(X279))))))))=>?[X280:$i]:(![X281:$i]:(((in @ X281 @ X280)<=>?[X282:$i]:(((in @ X282 @ X276)&(X275 @ X282 @ X281))))))))=>(![X165:$i]:((?[X166:$i]:((in @ X166 @ X165))=>?[X167:$i]:(((in @ X167 @ X165)&~(?[X168:$i]:(((in @ X168 @ X167)&(in @ X168 @ X165))))))))=>((epred1_0)=>((descrp)=>(![X272:$i, X273:$i > $o, X274:$i]:(((in @ X274 @ X272)=>((X273 @ X274)=>(in @ X274 @ (dsetconstr @ X272 @ (^[Z0/* 3 */:$i]:((X273 @ Z0))))))))=>(![X269:$i, X270:$i > $o, X271:$i]:(((in @ X271 @ (dsetconstr @ X269 @ (^[Z0/* 3 */:$i]:((X270 @ Z0)))))=>(in @ X271 @ X269)))=>(![X266:$i, X267:$i > $o, X268:$i]:(((in @ X268 @ (dsetconstr @ X266 @ (^[Z0/* 3 */:$i]:((X267 @ Z0)))))=>(X267 @ X268)))=>(![X188:$i > $o]:((?[X189:$i]:(((X188 @ X189)&![X190:$i]:(((X188 @ X190)=>((X189)=(X190))))))=>?[X191:$i]:(((X188 @ X191)&![X192:$i]:(((X188 @ X192)=>((X191)=(X192))))))))=>(![X193:$o, X194:$i]:(((in @ X194 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0/* 3 */:$i]:((X193)))))=>(X193)))=>(![X264:$i]:(((in @ X264 @ emptyset)=>![X265:$o]:((X265))))=>(![X263:$i]:(~(in @ X263 @ emptyset))=>(![X195:$i]:(~(in @ X195 @ emptyset))=>(![X259:$i > $o]:((?[X260:$i]:(((X259 @ X260)&![X261:$i]:(((X259 @ X261)=>((X260)=(X261))))))=>?[X262:$i]:((X259 @ X262))))=>(![X196:$i, X197:$i]:((![X198:$i]:(((in @ X198 @ X196)=>(in @ X198 @ X197)))=>(![X199:$i]:(((in @ X199 @ X197)=>(in @ X199 @ X196)))=>((X196)=(X197)))))=>(![X257:$i]:((![X258:$i]:(~(in @ X258 @ X257))=>((X257)=(emptyset))))=>(![X200:$i]:((![X201:$i]:(~(in @ X201 @ X200))=>((X200)=(emptyset))))=>(![X254:$i, X255:$i > $o, X256:$i]:(((in @ X256 @ X254)=>((in @ X256 @ (dsetconstr @ X254 @ (^[Z0/* 3 */:$i]:((X255 @ Z0)))))<=>(X255 @ X256))))=>(![X252:$i]:((((X252)!=(emptyset))=>?[X253:$i]:((in @ X253 @ X252))))=>(![X202:$i, X203:$i > $o, X204:$i]:(((in @ X204 @ X202)=>((X203 @ X204)=>((dsetconstr @ X202 @ (^[Z0/* 3 */:$i]:((X203 @ Z0))))!=(emptyset)))))=>(![X205:$i]:((?[X206:$i]:((in @ X206 @ X205))=>((X205)!=(emptyset))))=>(![X250:$i, X251:$i]:((in @ X250 @ (setadjoin @ X250 @ X251)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X207:$i, X208:$i, X209:$i]:(((in @ X209 @ X208)=>(in @ X209 @ (setadjoin @ X207 @ X208))))=>(![X246:$i, X247:$i, X248:$i]:(((in @ X248 @ (setadjoin @ X246 @ X247))=>![X249:$o]:(((((X248)=(X246))=>(X249))=>(((in @ X248 @ X247)=>(X249))=>(X249))))))=>(![X210:$i, X211:$i, X212:$i]:(((in @ X212 @ (setadjoin @ X210 @ X211))=>(((X212)=(X210))|(in @ X212 @ X211))))=>(![X213:$i]:(((dsetconstr @ X213 @ (^[Z0/* 3 */:$i]:(($true))))=(X213)))=>(![X243:$i, X244:$i]:((![X245:$i]:(((in @ X245 @ X244)=>(in @ X245 @ X243)))=>(in @ X244 @ (powerset @ X243))))=>(![X242:$i]:((in @ emptyset @ (powerset @ X242)))=>(![X214:$i]:((in @ emptyset @ (powerset @ X214)))=>(![X215:$i, X216:$i, X217:$i]:(((in @ X216 @ (powerset @ X215))=>((in @ X217 @ X216)=>(in @ X217 @ X215))))=>(![X218:$i, X219:$i, X220:$i]:(((in @ X219 @ X220)=>((in @ X220 @ X218)=>(in @ X219 @ (setunion @ X218)))))=>(![X221:$i, X222:$i]:(((in @ X222 @ (setunion @ X221))=>![X223:$o]:((![X224:$i]:(((in @ X222 @ X224)=>((in @ X224 @ X221)=>(X223))))=>(X223)))))=>(![X240:$i, X241:$i]:(((in @ X241 @ X240)=>(in @ X241 @ (powerset @ (setunion @ X240)))))=>(![X225:$i > $o]:((?[X226:$i]:(((X225 @ X226)&![X227:$i]:(((X225 @ X227)=>((X226)=(X227))))))=>?[X228:$i]:(![X229:$i]:(((X225 @ X229)<=>((X229)=(X228)))))))=>(![X230:$i]:((((X230)!=(emptyset))=>?[X231:$i]:((in @ X231 @ X230))))=>(![X232:$i, X233:$i]:(((in @ X232 @ (setadjoin @ X233 @ emptyset))=>((X232)=(X233))))=>(![X238:$i, X239:$i]:((((X238)!=(X239))=>~(in @ X239 @ (setadjoin @ X238 @ emptyset))))=>(![X236:$i, X237:$i]:((((X236)=(X237))=>(in @ X236 @ (setadjoin @ X237 @ emptyset))))=>(![X234:$i, X235:$i]:(((in @ X234 @ (setadjoin @ X235 @ emptyset))=>(in @ X235 @ (setadjoin @ X234 @ emptyset))))=>![X2:$i, X3:$i, X15:$i]:(((in @ X15 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X15)=(X2))|((X15)=(X3))))))))))))))))))))))))))))))))))))))))))))))))))))), 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(assume_negation,[status(cth)],[upairsetE]), emptyInPowerset]), setextAx]), emptyI]), c_0_58]), c_0_59]), setext]), emptysetimpfalse]), emptysetE]), noeltsimpempty]), c_0_60]), c_0_61]), c_0_62]), c_0_63]), c_0_64]), omega0Ax]), c_0_65]), setadjoinAx]), setadjoinIR]), c_0_66]), setadjoinOr]), c_0_67]), notinemptyset]), powersetE]), setunionI]), setunionE]), c_0_68]), c_0_69]), uniqinunit]), singletonsswitch]), eqinunit]), notinsingleton]), subPowSU]), emptyinPowerset]), powersetI]), setadjoinE]), emptyinunitempty]), setadjoinIL]), c_0_70]), c_0_71]), wellorderingAx]), foundationAx]), omegaIndAx]), omegaSAx]), setunionAx]), powersetAx]), emptysetAx])]), c_0_72])). 0.20/0.53 thf(c_0_74, negated_conjecture, ![X289:$i, X290:$i, X292:$i, X293:$i, X294:$i, X295:$i, X296:$i, X297:$i, X298:$i, X299:$i, X300:$i, X302:$i, X303:$i, X305:$i, X306:$i, X307:$i, X308:$i, X309:$i, X311:$i, X312:$i > $i > $o, X313:$i, X315:$i, X318:$i, X320:$i, X321:$i, X322:$i, X323:$i, X325:$i, X326:$i, X327:$i > $o, X328:$i, X329:$i, X330:$i > $o, X331:$i, X332:$i, X333:$i > $o, X334:$i, X335:$i > $o, X336:$i, X339:$i, X340:$o, X341:$i, X342:$i, X343:$o, X344:$i, X345:$i, X346:$i > $o, X347:$i, X350:$i, X351:$i, X354:$i, X356:$i, X358:$i, X359:$i > $o, X360:$i, X361:$i, X363:$i, X364:$i > $o, X365:$i, X366:$i, X367:$i, X368:$i, X369:$i, X370:$i, X371:$i, X372:$i, X373:$i, X374:$i, X375:$i, X376:$o, X377:$i, X378:$i, X379:$i, X380:$i, X381:$i, X382:$i, X384:$i, X385:$i, X386:$i, X387:$i, X388:$i, X389:$i, X390:$i, X391:$i, X392:$i, X393:$i, X394:$o, X396:$i, X397:$i, X398:$i > $o, X399:$i, X402:$i, X403:$i, X404:$i, X406:$i, X407:$i, X408:$i, X409:$i, X410:$i, X411:$i, X412:$i, X413:$i]:((((~(in @ (esk1_2 @ X289 @ X290) @ X289)|~(in @ (esk1_2 @ X289 @ X290) @ X290)|((X289)=(X290)))&((in @ (esk1_2 @ X289 @ X290) @ X289)|(in @ (esk1_2 @ X289 @ X290) @ X290)|((X289)=(X290))))&(~(in @ X292 @ emptyset)&(((~(in @ X295 @ (setadjoin @ X293 @ X294))|(((X295)=(X293))|(in @ X295 @ X294)))&((((X295)!=(X293))|(in @ X295 @ (setadjoin @ X293 @ X294)))&(~(in @ X295 @ X294)|(in @ X295 @ (setadjoin @ X293 @ X294)))))&(((~(in @ X297 @ (powerset @ X296))|(~(in @ X298 @ X297)|(in @ X298 @ X296)))&(((in @ (esk2_2 @ X299 @ X300) @ X300)|(in @ X300 @ (powerset @ X299)))&(~(in @ (esk2_2 @ X299 @ X300) @ X299)|(in @ X300 @ (powerset @ X299)))))&(((((in @ X303 @ (esk3_2 @ X302 @ X303))|~(in @ X303 @ (setunion @ X302)))&((in @ (esk3_2 @ X302 @ X303) @ X302)|~(in @ X303 @ (setunion @ X302))))&(~(in @ X306 @ X307)|~(in @ X307 @ X305)|(in @ X306 @ (setunion @ X305))))&((in @ emptyset @ omega)&((~(in @ X308 @ omega)|(in @ (setadjoin @ X308 @ X308) @ omega))&(((((in @ (esk4_1 @ X309) @ omega)|~(in @ emptyset @ X309)|(~(in @ X311 @ omega)|(in @ X311 @ X309)))&((in @ (esk4_1 @ X309) @ X309)|~(in @ emptyset @ X309)|(~(in @ X311 @ omega)|(in @ X311 @ X309))))&(~(in @ (setadjoin @ (esk4_1 @ X309) @ (esk4_1 @ X309)) @ X309)|~(in @ emptyset @ X309)|(~(in @ X311 @ omega)|(in @ X311 @ X309))))&((((((in @ (esk8_3 @ X312 @ X313 @ X318) @ X313)|~(in @ X318 @ (esk7_2 @ X312 @ X313))|(in @ (esk5_2 @ X312 @ X313) @ X313))&((X312 @ (esk8_3 @ X312 @ X313 @ X318) @ X318)|~(in @ X318 @ (esk7_2 @ X312 @ X313))|(in @ (esk5_2 @ X312 @ X313) @ X313)))&(~(in @ X321 @ X313)|~(X312 @ X321 @ X320)|(in @ X320 @ (esk7_2 @ X312 @ X313))|(in @ (esk5_2 @ X312 @ X313) @ X313)))&(((((in @ (esk8_3 @ X312 @ X313 @ X318) @ X313)|~(in @ X318 @ (esk7_2 @ X312 @ X313))|((X312 @ (esk5_2 @ X312 @ X313) @ (esk6_3 @ X312 @ X313 @ X315))|~(X312 @ (esk5_2 @ X312 @ X313) @ X315)))&((X312 @ (esk8_3 @ X312 @ X313 @ X318) @ X318)|~(in @ X318 @ (esk7_2 @ X312 @ X313))|((X312 @ (esk5_2 @ X312 @ X313) @ (esk6_3 @ X312 @ X313 @ X315))|~(X312 @ (esk5_2 @ X312 @ X313) @ X315))))&(~(in @ X321 @ X313)|~(X312 @ X321 @ X320)|(in @ X320 @ (esk7_2 @ X312 @ X313))|((X312 @ (esk5_2 @ X312 @ X313) @ (esk6_3 @ X312 @ X313 @ X315))|~(X312 @ (esk5_2 @ X312 @ X313) @ X315))))&((((in @ (esk8_3 @ X312 @ X313 @ X318) @ X313)|~(in @ X318 @ (esk7_2 @ X312 @ X313))|(((X315)!=(esk6_3 @ X312 @ X313 @ X315))|~(X312 @ (esk5_2 @ X312 @ X313) @ X315)))&((X312 @ (esk8_3 @ X312 @ X313 @ X318) @ X318)|~(in @ X318 @ (esk7_2 @ X312 @ X313))|(((X315)!=(esk6_3 @ X312 @ X313 @ X315))|~(X312 @ (esk5_2 @ X312 @ X313) @ X315))))&(~(in @ X321 @ X313)|~(X312 @ X321 @ X320)|(in @ X320 @ (esk7_2 @ X312 @ X313))|(((X315)!=(esk6_3 @ X312 @ X313 @ X315))|~(X312 @ (esk5_2 @ X312 @ X313) @ X315))))))&((((in @ (esk9_1 @ X322) @ X322)|~(in @ X323 @ X322))&(~(in @ X325 @ (esk9_1 @ X322))|~(in @ X325 @ X322)|~(in @ X323 @ X322)))&((epred1_0)&((descrp)&((~(in @ X328 @ X326)|(~(X327 @ X328)|(in @ X328 @ (dsetconstr @ X326 @ (^[Z0/* 3 */:$i]:((X327 @ Z0)))))))&((~(in @ X331 @ (dsetconstr @ X329 @ (^[Z0/* 3 */:$i]:((X330 @ Z0)))))|(in @ X331 @ X329))&((~(in @ X334 @ (dsetconstr @ X332 @ (^[Z0/* 3 */:$i]:((X333 @ Z0)))))|(X333 @ X334))&(((((X335 @ (esk11_1 @ X335))|((X335 @ (esk10_2 @ X335 @ X336))|~(X335 @ X336)))&(~(X335 @ X339)|((esk11_1 @ X335)=(X339))|((X335 @ (esk10_2 @ X335 @ X336))|~(X335 @ X336))))&(((X335 @ (esk11_1 @ X335))|(((X336)!=(esk10_2 @ X335 @ X336))|~(X335 @ X336)))&(~(X335 @ X339)|((esk11_1 @ X335)=(X339))|(((X336)!=(esk10_2 @ X335 @ X336))|~(X335 @ X336)))))&((~(in @ X341 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0/* 3 */:$i]:((X340)))))|(X340))&((~(in @ X342 @ emptyset)|(X343))&(~(in @ X344 @ emptyset)&(~(in @ X345 @ emptyset)&((((X346 @ (esk12_2 @ X346 @ X347))|~(X346 @ X347)|(X346 @ (esk13_1 @ X346)))&(((X347)!=(esk12_2 @ X346 @ X347))|~(X346 @ X347)|(X346 @ (esk13_1 @ X346))))&(((((in @ (esk15_2 @ X350 @ X351) @ X351)|((X350)=(X351))|(in @ (esk14_2 @ X350 @ X351) @ X350))&(~(in @ (esk15_2 @ X350 @ X351) @ X350)|((X350)=(X351))|(in @ (esk14_2 @ X350 @ X351) @ X350)))&(((in @ (esk15_2 @ X350 @ X351) @ X351)|((X350)=(X351))|~(in @ (esk14_2 @ X350 @ X351) @ X351))&(~(in @ (esk15_2 @ X350 @ X351) @ X350)|((X350)=(X351))|~(in @ (esk14_2 @ X350 @ X351) @ X351))))&(((in @ (esk16_1 @ X354) @ X354)|((X354)=(emptyset)))&(((in @ (esk17_1 @ X356) @ X356)|((X356)=(emptyset)))&(((~(in @ X360 @ (dsetconstr @ X358 @ (^[Z0/* 3 */:$i]:((X359 @ Z0)))))|(X359 @ X360)|~(in @ X360 @ X358))&(~(X359 @ X360)|(in @ X360 @ (dsetconstr @ X358 @ (^[Z0/* 3 */:$i]:((X359 @ Z0)))))|~(in @ X360 @ X358)))&((((X361)=(emptyset))|(in @ (esk18_1 @ X361) @ X361))&((~(in @ X365 @ X363)|(~(X364 @ X365)|((dsetconstr @ X363 @ (^[Z0/* 3 */:$i]:((X364 @ Z0))))!=(emptyset))))&((~(in @ X367 @ X366)|((X366)!=(emptyset)))&((in @ X368 @ (setadjoin @ X368 @ X369))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X372 @ X371)|(in @ X372 @ (setadjoin @ X370 @ X371)))&(((((in @ X375 @ X374)|(X376)|((X375)=(X373))|~(in @ X375 @ (setadjoin @ X373 @ X374)))&(~(X376)|(X376)|((X375)=(X373))|~(in @ X375 @ (setadjoin @ X373 @ X374))))&(((in @ X375 @ X374)|(X376)|~(X376)|~(in @ X375 @ (setadjoin @ X373 @ X374)))&(~(X376)|(X376)|~(X376)|~(in @ X375 @ (setadjoin @ X373 @ X374)))))&((~(in @ X379 @ (setadjoin @ X377 @ X378))|(((X379)=(X377))|(in @ X379 @ X378)))&(((dsetconstr @ X380 @ (^[Z0/* 3 */:$i]:(($true))))=(X380))&((((in @ (esk19_2 @ X381 @ X382) @ X382)|(in @ X382 @ (powerset @ X381)))&(~(in @ (esk19_2 @ X381 @ X382) @ X381)|(in @ X382 @ (powerset @ X381))))&((in @ emptyset @ (powerset @ X384))&((in @ emptyset @ (powerset @ X385))&((~(in @ X387 @ (powerset @ X386))|(~(in @ X388 @ X387)|(in @ X388 @ X386)))&((~(in @ X390 @ X391)|(~(in @ X391 @ X389)|(in @ X390 @ (setunion @ X389))))&((((in @ X393 @ (esk20_3 @ X392 @ X393 @ X394))|(X394)|~(in @ X393 @ (setunion @ X392)))&(((in @ (esk20_3 @ X392 @ X393 @ X394) @ X392)|(X394)|~(in @ X393 @ (setunion @ X392)))&(~(X394)|(X394)|~(in @ X393 @ (setunion @ X392)))))&((~(in @ X397 @ X396)|(in @ X397 @ (powerset @ (setunion @ X396))))&((((~(X398 @ X402)|((X402)=(esk22_1 @ X398))|((X398 @ (esk21_2 @ X398 @ X399))|~(X398 @ X399)))&(((X403)!=(esk22_1 @ X398))|(X398 @ X403)|((X398 @ (esk21_2 @ X398 @ X399))|~(X398 @ X399))))&((~(X398 @ X402)|((X402)=(esk22_1 @ X398))|(((X399)!=(esk21_2 @ X398 @ X399))|~(X398 @ X399)))&(((X403)!=(esk22_1 @ X398))|(X398 @ X403)|(((X399)!=(esk21_2 @ X398 @ X399))|~(X398 @ X399)))))&((((X404)=(emptyset))|(in @ (esk23_1 @ X404) @ X404))&((~(in @ X406 @ (setadjoin @ X407 @ emptyset))|((X406)=(X407)))&((((X408)=(X409))|~(in @ X409 @ (setadjoin @ X408 @ emptyset)))&((((X410)!=(X411))|(in @ X410 @ (setadjoin @ X411 @ emptyset)))&((~(in @ X412 @ (setadjoin @ X413 @ emptyset))|(in @ X413 @ (setadjoin @ X412 @ emptyset)))&((in @ esk26_0 @ (setadjoin @ esk24_0 @ (setadjoin @ esk25_0 @ emptyset)))&(((esk26_0)!=(esk24_0))&((esk26_0)!=(esk25_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_73])])])])])])). 0.20/0.53 thf(c_0_75, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ X3)|((X2)=(X4))|~((in @ X2 @ (setadjoin @ X4 @ X3))))), inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_74])])])). 0.20/0.53 thf(c_0_76, negated_conjecture, (in @ esk26_0 @ (setadjoin @ esk24_0 @ (setadjoin @ esk25_0 @ emptyset))), inference(split_conjunct,[status(thm)],[c_0_74])). 0.20/0.53 thf(c_0_77, negated_conjecture, ((esk26_0)!=(esk24_0)), inference(split_conjunct,[status(thm)],[c_0_74])). 0.20/0.53 thf(c_0_78, negated_conjecture, (in @ esk26_0 @ (setadjoin @ esk25_0 @ emptyset)), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_75, c_0_76]), c_0_77])). 0.20/0.53 thf(c_0_79, negated_conjecture, ((esk26_0)!=(esk25_0)), inference(split_conjunct,[status(thm)],[c_0_74])). 0.20/0.53 thf(c_0_80, negated_conjecture, ![X2:$i]:(~((in @ X2 @ emptyset))), inference(split_conjunct,[status(thm)],[c_0_74])). 0.20/0.53 thf(c_0_81, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_75, c_0_78]), c_0_79]), c_0_80]), ['proof']). 0.20/0.53 # SZS output end CNFRefutation 0.20/0.53 # Parsed axioms : 109 0.20/0.53 # Removed by relevancy pruning/SinE : 59 0.20/0.53 # Initial clauses : 98 0.20/0.53 # Removed in clause preprocessing : 4 0.20/0.53 # Initial clauses in saturation : 94 0.20/0.53 # Processed clauses : 154 0.20/0.53 # ...of these trivial : 3 0.20/0.53 # ...subsumed : 17 0.20/0.53 # ...remaining for further processing : 134 0.20/0.53 # Other redundant clauses eliminated : 6 0.20/0.53 # Clauses deleted for lack of memory : 0 0.20/0.53 # Backward-subsumed : 0 0.20/0.53 # Backward-rewritten : 3 0.20/0.53 # Generated clauses : 145 0.20/0.53 # ...of the previous two non-redundant : 130 0.20/0.53 # ...aggressively subsumed : 0 0.20/0.53 # Contextual simplify-reflections : 0 0.20/0.53 # Paramodulations : 139 0.20/0.53 # Factorizations : 0 0.20/0.53 # NegExts : 0 0.20/0.53 # Equation resolutions : 6 0.20/0.53 # Total rewrite steps : 28 0.20/0.53 # Propositional unsat checks : 0 0.20/0.53 # Propositional check models : 0 0.20/0.53 # Propositional check unsatisfiable : 0 0.20/0.53 # Propositional clauses : 0 0.20/0.53 # Propositional clauses after purity: 0 0.20/0.53 # Propositional unsat core size : 0 0.20/0.53 # Propositional preprocessing time : 0.000 0.20/0.53 # Propositional encoding time : 0.000 0.20/0.53 # Propositional solver time : 0.000 0.20/0.53 # Success case prop preproc time : 0.000 0.20/0.53 # Success case prop encoding time : 0.000 0.20/0.53 # Success case prop solver time : 0.000 0.20/0.53 # Current number of processed clauses : 48 0.20/0.53 # Positive orientable unit clauses : 13 0.20/0.53 # Positive unorientable unit clauses: 0 0.20/0.53 # Negative unit clauses : 3 0.20/0.53 # Non-unit-clauses : 32 0.20/0.53 # Current number of unprocessed clauses: 141 0.20/0.53 # ...number of literals in the above : 388 0.20/0.53 # Current number of archived formulas : 0 0.20/0.53 # Current number of archived clauses : 81 0.20/0.53 # Clause-clause subsumption calls (NU) : 2387 0.20/0.53 # Rec. Clause-clause subsumption calls : 1158 0.20/0.53 # Non-unit clause-clause subsumptions : 11 0.20/0.53 # Unit Clause-clause subsumption calls : 30 0.20/0.53 # Rewrite failures with RHS unbound : 0 0.20/0.53 # BW rewrite match attempts : 11 0.20/0.53 # BW rewrite match successes : 3 0.20/0.53 # Condensation attempts : 154 0.20/0.53 # Condensation successes : 3 0.20/0.53 # Termbank termtop insertions : 13948 0.20/0.53 0.20/0.53 # ------------------------------------------------- 0.20/0.53 # User time : 0.022 s 0.20/0.53 # System time : 0.007 s 0.20/0.53 # Total time : 0.029 s 0.20/0.53 # Maximum resident set size: 3084 pages 0.20/0.53 0.20/0.53 # ------------------------------------------------- 0.20/0.53 # User time : 0.025 s 0.20/0.53 # System time : 0.010 s 0.20/0.53 # Total time : 0.035 s 0.20/0.53 # Maximum resident set size: 1836 pages 0.20/0.53 % E---3.1 exiting 0.20/0.53 EOF