%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU528^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:24:23 AM UTC 2026
% Result : Theorem 0.12s 0.28s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU528^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.18 % Computer : n016.cluster.edu
% 0.12/0.18 % Model : x86_64 x86_64
% 0.12/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.18 % Memory : 8046.5625MB
% 0.12/0.18 % OS : Linux 6.8.0-71-generic
% 0.12/0.18 % CPULimit : 300
% 0.12/0.18 % WCLimit : 300
% 0.12/0.18 % DateTime : Tue Sep 29 13:53:19 UTC 2026
% 0.12/0.18 % CPUTime :
% 0.12/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.22 Running higher-order theorem proving
% 0.12/0.24 Running: /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=300 /export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p
% 0.12/0.28 % Version: 3.5.1-ho
% 0.12/0.28 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.12/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.12/0.28 % Starting sh5l with 300s (1) cores
% 0.12/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.28 % Starting new_bool_2 with 300s (1) cores
% 0.12/0.28 % new_bool_1 with pid 382415 completed with status 0
% 0.12/0.28 % Result found by new_bool_1
% 0.12/0.28 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.12/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.12/0.28 % Starting sh5l with 300s (1) cores
% 0.12/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.28 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.12/0.28 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.12/0.28 % Search class: HGHSM-FFMS31-SHFSMSBN
% 0.12/0.28 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.28 % Starting SubtermCWHack with 31s (1) cores
% 0.12/0.28 % SubtermCWHack with pid 382425 completed with status 0
% 0.12/0.28 % Result found by SubtermCWHack
% 0.12/0.28 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.12/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.12/0.28 % Starting sh5l with 300s (1) cores
% 0.12/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.28 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.12/0.28 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.12/0.28 % Search class: HGHSM-FFMS31-SHFSMSBN
% 0.12/0.28 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.28 % Starting SubtermCWHack with 31s (1) cores
% 0.12/0.28 % Preprocessing time : 0.002 s
% 0.12/0.28
% 0.12/0.28 % Proof found!
% 0.12/0.28 % SZS status Theorem
% 0.12/0.28 % SZS output start CNFRefutation
% 0.12/0.28 thf(decl_23, type, in: $i > $i > $o).
% 0.12/0.28 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.12/0.28 thf(decl_25, type, setextAx: $o).
% 0.12/0.28 thf(decl_26, type, emptyset: $i).
% 0.12/0.28 thf(decl_27, type, emptysetAx: $o).
% 0.12/0.28 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.12/0.28 thf(decl_29, type, setadjoinAx: $o).
% 0.12/0.28 thf(decl_30, type, powerset: $i > $i).
% 0.12/0.28 thf(decl_31, type, powersetAx: $o).
% 0.12/0.28 thf(decl_32, type, setunion: $i > $i).
% 0.12/0.28 thf(decl_33, type, setunionAx: $o).
% 0.12/0.28 thf(decl_34, type, omega: $i).
% 0.12/0.28 thf(decl_35, type, omega0Ax: $o).
% 0.12/0.28 thf(decl_36, type, omegaSAx: $o).
% 0.12/0.28 thf(decl_37, type, omegaIndAx: $o).
% 0.12/0.28 thf(decl_38, type, replAx: $o).
% 0.12/0.28 thf(decl_39, type, foundationAx: $o).
% 0.12/0.28 thf(decl_40, type, wellorderingAx: $o).
% 0.12/0.28 thf(decl_42, type, descrp: $o).
% 0.12/0.28 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.12/0.28 thf(decl_44, type, dsetconstrI: $o).
% 0.12/0.28 thf(decl_45, type, dsetconstrEL: $o).
% 0.12/0.28 thf(decl_46, type, dsetconstrER: $o).
% 0.12/0.28 thf(decl_47, type, exuE1: $o).
% 0.12/0.28 thf(decl_48, type, prop2set: $o > $i).
% 0.12/0.28 thf(decl_49, type, prop2setE: $o).
% 0.12/0.28 thf(decl_50, type, emptysetE: $o).
% 0.12/0.28 thf(decl_51, type, emptysetimpfalse: $o).
% 0.12/0.28 thf(decl_52, type, notinemptyset: $o).
% 0.12/0.28 thf(decl_53, type, exuE3e: $o).
% 0.12/0.28 thf(decl_54, type, setext: $o).
% 0.12/0.28 thf(decl_55, type, emptyI: $o).
% 0.12/0.28 thf(decl_56, type, noeltsimpempty: $o).
% 0.12/0.28 thf(decl_57, type, setbeta: $o).
% 0.12/0.28 thf(decl_58, type, nonempty: $i > $o).
% 0.12/0.28 thf(decl_59, type, nonemptyE1: $o).
% 0.12/0.28 thf(decl_60, type, nonemptyI: $o).
% 0.12/0.28 thf(decl_61, type, nonemptyI1: $o).
% 0.12/0.28 thf(decl_62, type, setadjoinIL: $o).
% 0.12/0.28 thf(decl_63, type, emptyinunitempty: $o).
% 0.12/0.28 thf(decl_64, type, setadjoinIR: $o).
% 0.12/0.28 thf(decl_65, type, setadjoinE: $o).
% 0.12/0.28 thf(decl_66, type, setadjoinOr: $o).
% 0.12/0.28 thf(decl_67, type, setoftrueEq: $o).
% 0.12/0.28 thf(decl_68, type, powersetI: $o).
% 0.12/0.28 thf(decl_69, type, emptyinPowerset: $o).
% 0.12/0.28 thf(decl_70, type, emptyInPowerset: $o).
% 0.12/0.28 thf(decl_71, type, powersetE: $o).
% 0.12/0.28 thf(decl_72, type, setunionI: $o).
% 0.12/0.28 thf(decl_73, type, setunionE: $o).
% 0.12/0.28 thf(decl_74, type, subPowSU: $o).
% 0.12/0.28 thf(decl_75, type, exuE2: $o).
% 0.12/0.28 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.12/0.28 thf(decl_77, type, uniqinunit: $o).
% 0.12/0.28 thf(decl_78, type, epred1_0: $o).
% 0.12/0.28 thf(decl_79, type, esk1_2: $i > $i > $i).
% 0.12/0.28 thf(decl_80, type, esk2_2: $i > $i > $i).
% 0.12/0.28 thf(decl_81, type, esk3_2: $i > $i > $i).
% 0.12/0.28 thf(decl_82, type, esk4_1: $i > $i).
% 0.12/0.28 thf(decl_83, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.12/0.28 thf(decl_84, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.12/0.28 thf(decl_85, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.12/0.28 thf(decl_86, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.12/0.28 thf(decl_87, type, esk9_1: $i > $i).
% 0.12/0.28 thf(decl_88, type, esk10_2: ($i > $o) > $i > $i).
% 0.12/0.28 thf(decl_89, type, esk11_1: ($i > $o) > $i).
% 0.12/0.28 thf(decl_90, type, esk12_2: ($i > $o) > $i > $i).
% 0.12/0.28 thf(decl_91, type, esk13_1: ($i > $o) > $i).
% 0.12/0.28 thf(decl_92, type, esk14_2: $i > $i > $i).
% 0.12/0.28 thf(decl_93, type, esk15_2: $i > $i > $i).
% 0.12/0.28 thf(decl_94, type, esk16_1: $i > $i).
% 0.12/0.28 thf(decl_95, type, esk17_1: $i > $i).
% 0.12/0.28 thf(decl_96, type, esk18_1: $i > $i).
% 0.12/0.28 thf(decl_97, type, esk19_2: $i > $i > $i).
% 0.12/0.28 thf(decl_98, type, esk20_3: $i > $i > $o > $i).
% 0.12/0.28 thf(decl_99, type, esk21_2: ($i > $o) > $i > $i).
% 0.12/0.28 thf(decl_100, type, esk22_1: ($i > $o) > $i).
% 0.12/0.28 thf(decl_101, type, esk23_1: $i > $i).
% 0.12/0.28 thf(decl_102, type, esk24_0: $i).
% 0.12/0.28 thf(decl_103, type, esk25_0: $i).
% 0.12/0.28 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', exuE2)).
% 0.12/0.28 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', exu)).
% 0.12/0.28 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', nonempty)).
% 0.12/0.28 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', replAx)).
% 0.12/0.28 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', exuE3e)).
% 0.12/0.28 thf(prop2set, axiom, ((prop2set)=(^[X10:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[X2:$i]:((X10)))))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', prop2set)).
% 0.12/0.28 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', exuE1)).
% 0.12/0.28 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', nonemptyI)).
% 0.12/0.28 thf(notinsingleton, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', notinsingleton)).
% 0.12/0.28 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', nonemptyImpWitness)).
% 0.12/0.28 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', dsetconstrI)).
% 0.12/0.28 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', dsetconstrEL)).
% 0.12/0.28 thf(prop2setE, axiom, ((prop2setE)<=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', prop2setE)).
% 0.12/0.28 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', dsetconstrER)).
% 0.12/0.28 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', nonemptyI1)).
% 0.12/0.28 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', nonemptyE1)).
% 0.12/0.28 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', setbeta)).
% 0.12/0.28 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', setoftrueEq)).
% 0.12/0.28 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', powersetI)).
% 0.12/0.28 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', emptyinPowerset)).
% 0.12/0.28 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', emptyInPowerset)).
% 0.12/0.28 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', powersetAx)).
% 0.12/0.28 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', powersetE)).
% 0.12/0.28 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', setadjoinAx)).
% 0.12/0.28 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', setunionI)).
% 0.12/0.28 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', emptysetAx)).
% 0.12/0.28 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.lJjo22q9Uq/E---3.1_382386.p', setunionE)).
% 0.12/0.28 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', setextAx)).
% 0.12/0.28 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', subPowSU)).
% 0.12/0.28 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', setunionAx)).
% 0.12/0.28 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', uniqinunit)).
% 0.12/0.28 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', wellorderingAx)).
% 0.12/0.28 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', foundationAx)).
% 0.12/0.28 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.lJjo22q9Uq/E---3.1_382386.p', omegaIndAx)).
% 0.12/0.28 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', omegaSAx)).
% 0.12/0.28 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', omega0Ax)).
% 0.12/0.28 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', notinemptyset)).
% 0.12/0.28 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', emptysetimpfalse)).
% 0.12/0.28 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12))))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', emptysetE)).
% 0.12/0.28 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.lJjo22q9Uq/E---3.1_382386.p', setext)).
% 0.12/0.28 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', setadjoinIL)).
% 0.12/0.28 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', noeltsimpempty)).
% 0.12/0.28 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', emptyI)).
% 0.12/0.28 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', setadjoinIR)).
% 0.12/0.28 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X13:$o]:(((((X3)=(X2))=>(X13))=>(((in @ X3 @ X4)=>(X13))=>(X13))))))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', setadjoinE)).
% 0.12/0.28 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', setadjoinOr)).
% 0.12/0.28 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.lJjo22q9Uq/E---3.1_382386.p', emptyinunitempty)).
% 0.12/0.28 thf(c_0_47, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.12/0.28 thf(c_0_48, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.12/0.28 thf(c_0_49, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.12/0.28 thf(c_0_50, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.12/0.28 thf(c_0_51, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.12/0.28 thf(c_0_52, plain, ((prop2set)=(^[Z0:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[Z1:$i]:((Z0)))))), inference(fof_simplification,[status(thm)],[prop2set])).
% 0.12/0.28 thf(c_0_53, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.12/0.28 thf(c_0_54, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.12/0.28 thf(c_0_55, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[notinsingleton])).
% 0.12/0.28 thf(c_0_56, plain, ((exuE2)=(![X1:$i > $o]:((((?[X144:$i]:(((((X1 @ X144)))&(![X145:$i]:(((((X1 @ X145)))=>(((X144)=(X145))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_47, c_0_48])).
% 0.12/0.28 thf(c_0_57, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_49])).
% 0.12/0.28 thf(c_0_58, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.12/0.28 thf(c_0_59, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X138:$i]:(((((X6 @ X2 @ X138)))&(![X139:$i]:(((((X6 @ X2 @ X139)))=>(((X138)=(X139)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_50, c_0_48])).
% 0.12/0.28 thf(c_0_60, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.12/0.28 thf(c_0_61, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X142:$i]:(((((X1 @ X142)))&(![X143:$i]:(((((X1 @ X143)))=>(((X142)=(X143))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_51, c_0_48])).
% 0.12/0.28 thf(c_0_62, axiom, ((prop2setE)=(![X11:$o, X2:$i]:((((in @ X2 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:(((X11)))))))=>((X11)))))), inference(apply_def,[status(thm)],[prop2setE, c_0_52])).
% 0.12/0.28 thf(c_0_63, plain, ((exuE1)=(![X1:$i > $o]:((((?[X140:$i]:(((((X1 @ X140)))&(![X141:$i]:(((((X1 @ X141)))=>(((X140)=(X141))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_53, c_0_48])).
% 0.12/0.28 thf(c_0_64, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.12/0.28 thf(c_0_65, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_49])).
% 0.12/0.28 thf(c_0_66, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_54, c_0_49])).
% 0.12/0.28 thf(c_0_67, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_49])).
% 0.12/0.28 thf(c_0_68, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.12/0.28 thf(c_0_69, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.12/0.28 thf(c_0_70, plain, ((epred1_0)<=>![X175:$i]:(?[X176:$i]:((((![X177:$i]:(((in @ X177 @ X176)=>![X178:$i]:(((in @ X178 @ X177)=>(in @ X178 @ X175)))))&![X179:$i, X180:$i]:((((in @ X179 @ X175)&(in @ X180 @ X175))=>(![X181:$i]:(((in @ X181 @ X176)=>((in @ X179 @ X181)<=>(in @ X180 @ X181))))=>((X179)=(X180))))))&![X182:$i, X183:$i]:((((in @ X182 @ X176)&(in @ X183 @ X176))=>(![X184:$i]:(((in @ X184 @ X182)=>(in @ X184 @ X183)))|![X185:$i]:(((in @ X185 @ X183)=>(in @ X185 @ X182)))))))&![X186:$i]:(((![X187:$i]:(((in @ X187 @ X186)=>(in @ X187 @ X175)))&?[X188:$i]:((in @ X188 @ X186)))=>?[X189:$i, X190:$i]:(((((in @ X189 @ X176)&(in @ X190 @ X186))&~(?[X191:$i]:(((in @ X191 @ X189)&(in @ X191 @ X186)))))&![X192:$i]:(((in @ X192 @ X176)=>(![X193:$i]:(((in @ X193 @ X192)=>(in @ X193 @ X189)))|(in @ X190 @ X192)))))))))))), introduced(definition)).
% 0.12/0.28 thf(c_0_71, negated_conjecture, ~((![X146:$i, X147:$i]:((![X148:$i]:(((in @ X148 @ X146)<=>(in @ X148 @ X147)))=>((X146)=(X147))))=>(![X149:$i]:(~(in @ X149 @ emptyset))=>(![X150:$i, X151:$i, X152:$i]:(((in @ X152 @ (setadjoin @ X150 @ X151))<=>(((X152)=(X150))|(in @ X152 @ X151))))=>(![X153:$i, X154:$i]:(((in @ X154 @ (powerset @ X153))<=>![X155:$i]:(((in @ X155 @ X154)=>(in @ X155 @ X153)))))=>(![X156:$i, X157:$i]:(((in @ X157 @ (setunion @ X156))<=>?[X158:$i]:(((in @ X157 @ X158)&(in @ X158 @ X156)))))=>((in @ emptyset @ omega)=>(![X159:$i]:(((in @ X159 @ omega)=>(in @ (setadjoin @ X159 @ X159) @ omega)))=>(![X160:$i]:((((in @ emptyset @ X160)&![X161:$i]:((((in @ X161 @ omega)&(in @ X161 @ X160))=>(in @ (setadjoin @ X161 @ X161) @ X160))))=>![X162:$i]:(((in @ X162 @ omega)=>(in @ X162 @ X160)))))=>(![X163:$i > $i > $o, X164:$i]:((![X165:$i]:(((in @ X165 @ X164)=>?[X166:$i]:(((X163 @ X165 @ X166)&![X167:$i]:(((X163 @ X165 @ X167)=>((X166)=(X167))))))))=>?[X168:$i]:(![X169:$i]:(((in @ X169 @ X168)<=>?[X170:$i]:(((in @ X170 @ X164)&(X163 @ X170 @ X169))))))))=>(![X171:$i]:((?[X172:$i]:((in @ X172 @ X171))=>?[X173:$i]:(((in @ X173 @ X171)&~(?[X174:$i]:(((in @ X174 @ X173)&(in @ X174 @ X171))))))))=>((epred1_0)=>((descrp)=>(![X194:$i, X195:$i > $o, X196:$i]:(((in @ X196 @ X194)=>((X195 @ X196)=>(in @ X196 @ (dsetconstr @ X194 @ X195)))))=>(![X197:$i, X198:$i > $o, X199:$i]:(((in @ X199 @ (dsetconstr @ X197 @ X198))=>(in @ X199 @ X197)))=>(![X200:$i, X201:$i > $o, X202:$i]:(((in @ X202 @ (dsetconstr @ X200 @ X201))=>(X201 @ X202)))=>(![X203:$i > $o]:((?[X204:$i]:(((X203 @ X204)&![X205:$i]:(((X203 @ X205)=>((X204)=(X205))))))=>?[X206:$i]:(((X203 @ X206)&![X207:$i]:(((X203 @ X207)=>((X206)=(X207))))))))=>(![X208:$o, X209:$i]:(((in @ X209 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X208)))))=>(X208)))=>(![X210:$i]:(((in @ X210 @ emptyset)=>![X211:$o]:((X211))))=>(![X212:$i]:(((in @ X212 @ emptyset)=>~($true)))=>(![X213:$i]:(~(in @ X213 @ emptyset))=>(![X214:$i > $o]:((?[X215:$i]:(((X214 @ X215)&![X216:$i]:(((X214 @ X216)=>((X215)=(X216))))))=>?[X217:$i]:((X214 @ X217))))=>(![X218:$i, X219:$i]:((![X220:$i]:(((in @ X220 @ X218)=>(in @ X220 @ X219)))=>(![X221:$i]:(((in @ X221 @ X219)=>(in @ X221 @ X218)))=>((X218)=(X219)))))=>(![X222:$i]:((![X223:$i]:(~(in @ X223 @ X222))=>((X222)=(emptyset))))=>(![X224:$i]:((![X225:$i]:(~(in @ X225 @ X224))=>((X224)=(emptyset))))=>(![X226:$i, X227:$i > $o, X228:$i]:(((in @ X228 @ X226)=>((in @ X228 @ (dsetconstr @ X226 @ X227))<=>(X227 @ X228))))=>(![X229:$i]:((((X229)!=(emptyset))=>?[X230:$i]:((in @ X230 @ X229))))=>(![X231:$i, X232:$i > $o, X233:$i]:(((in @ X233 @ X231)=>((X232 @ X233)=>((dsetconstr @ X231 @ X232)!=(emptyset)))))=>(![X234:$i]:((?[X235:$i]:((in @ X235 @ X234))=>((X234)!=(emptyset))))=>(![X236:$i, X237:$i]:((in @ X236 @ (setadjoin @ X236 @ X237)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X238:$i, X239:$i, X240:$i]:(((in @ X240 @ X239)=>(in @ X240 @ (setadjoin @ X238 @ X239))))=>(![X241:$i, X242:$i, X243:$i]:(((in @ X243 @ (setadjoin @ X241 @ X242))=>![X244:$o]:(((((X243)=(X241))=>(X244))=>(((in @ X243 @ X242)=>(X244))=>(X244))))))=>(![X245:$i, X246:$i, X247:$i]:(((in @ X247 @ (setadjoin @ X245 @ X246))=>(((X247)=(X245))|(in @ X247 @ X246))))=>(![X248:$i]:(((dsetconstr @ X248 @ (^[Z0:$i]:($true)))=(X248)))=>(![X249:$i, X250:$i]:((![X251:$i]:(((in @ X251 @ X250)=>(in @ X251 @ X249)))=>(in @ X250 @ (powerset @ X249))))=>(![X252:$i]:((in @ emptyset @ (powerset @ X252)))=>(![X253:$i]:((in @ emptyset @ (powerset @ X253)))=>(![X254:$i, X255:$i, X256:$i]:(((in @ X255 @ (powerset @ X254))=>((in @ X256 @ X255)=>(in @ X256 @ X254))))=>(![X257:$i, X258:$i, X259:$i]:(((in @ X258 @ X259)=>((in @ X259 @ X257)=>(in @ X258 @ (setunion @ X257)))))=>(![X260:$i, X261:$i]:(((in @ X261 @ (setunion @ X260))=>![X262:$o]:((![X263:$i]:(((in @ X261 @ X263)=>((in @ X263 @ X260)=>(X262))))=>(X262)))))=>(![X264:$i, X265:$i]:(((in @ X265 @ X264)=>(in @ X265 @ (powerset @ (setunion @ X264)))))=>(![X266:$i > $o]:((?[X267:$i]:(((X266 @ X267)&![X268:$i]:(((X266 @ X268)=>((X267)=(X268))))))=>?[X269:$i]:(![X270:$i]:(((X266 @ X270)<=>((X270)=(X269)))))))=>(![X271:$i]:((((X271)!=(emptyset))=>?[X272:$i]:(((in @ X272 @ X271)&$true))))=>(![X273:$i, X274:$i]:(((in @ X273 @ (setadjoin @ X274 @ emptyset))=>((X273)=(X274))))=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~(in @ X3 @ (setadjoin @ X2 @ emptyset))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[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)],[c_0_55, powersetI]), emptyinPowerset]), emptyInPowerset]), powersetAx]), powersetE]), setadjoinAx]), setunionI]), emptysetAx]), setunionE]), setextAx]), subPowSU]), setunionAx]), c_0_56]), c_0_57]), uniqinunit]), c_0_58]), wellorderingAx]), foundationAx]), c_0_59]), omegaIndAx]), omegaSAx]), omega0Ax]), c_0_60]), c_0_61]), notinemptyset]), emptysetimpfalse]), emptysetE]), c_0_62]), c_0_63]), c_0_64]), setext]), setadjoinIL]), c_0_65]), c_0_66]), c_0_67]), c_0_68]), noeltsimpempty]), emptyI]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_69]), emptyinunitempty])])]), c_0_70])).
% 0.12/0.28 thf(c_0_72, negated_conjecture, ![X275:$i, X276:$i, X278:$i, X279:$i, X280:$i, X281:$i, X282:$i, X283:$i, X284:$i, X285:$i, X286:$i, X288:$i, X289:$i, X291:$i, X292:$i, X293:$i, X294:$i, X295:$i, X297:$i, X298:$i > $i > $o, X299:$i, X301:$i, X304:$i, X306:$i, X307:$i, X308:$i, X309:$i, X311:$i, X312:$i, X313:$i > $o, X314:$i, X315:$i, X316:$i > $o, X317:$i, X318:$i, X319:$i > $o, X320:$i, X321:$i > $o, X322:$i, X325:$i, X326:$o, X327:$i, X328:$i, X329:$o, X330:$i, X331:$i, X332:$i > $o, X333:$i, X336:$i, X337:$i, X340:$i, X342:$i, X344:$i, X345:$i > $o, X346:$i, X347:$i, X349:$i, X350:$i > $o, X351:$i, X352:$i, X353:$i, X354:$i, X355:$i, X356:$i, X357:$i, X358:$i, X359:$i, X360:$i, X361:$i, X362:$o, X363:$i, X364:$i, X365:$i, X366:$i, X367:$i, X368:$i, X370:$i, X371:$i, X372:$i, X373:$i, X374:$i, X375:$i, X376:$i, X377:$i, X378:$i, X379:$i, X380:$o, X382:$i, X383:$i, X384:$i > $o, X385:$i, X388:$i, X389:$i, X390:$i, X392:$i, X393:$i]:((((~(in @ (esk1_2 @ X275 @ X276) @ X275)|~(in @ (esk1_2 @ X275 @ X276) @ X276)|((X275)=(X276)))&((in @ (esk1_2 @ X275 @ X276) @ X275)|(in @ (esk1_2 @ X275 @ X276) @ X276)|((X275)=(X276))))&(~(in @ X278 @ emptyset)&(((~(in @ X281 @ (setadjoin @ X279 @ X280))|(((X281)=(X279))|(in @ X281 @ X280)))&((((X281)!=(X279))|(in @ X281 @ (setadjoin @ X279 @ X280)))&(~(in @ X281 @ X280)|(in @ X281 @ (setadjoin @ X279 @ X280)))))&(((~(in @ X283 @ (powerset @ X282))|(~(in @ X284 @ X283)|(in @ X284 @ X282)))&(((in @ (esk2_2 @ X285 @ X286) @ X286)|(in @ X286 @ (powerset @ X285)))&(~(in @ (esk2_2 @ X285 @ X286) @ X285)|(in @ X286 @ (powerset @ X285)))))&(((((in @ X289 @ (esk3_2 @ X288 @ X289))|~(in @ X289 @ (setunion @ X288)))&((in @ (esk3_2 @ X288 @ X289) @ X288)|~(in @ X289 @ (setunion @ X288))))&(~(in @ X292 @ X293)|~(in @ X293 @ X291)|(in @ X292 @ (setunion @ X291))))&((in @ emptyset @ omega)&((~(in @ X294 @ omega)|(in @ (setadjoin @ X294 @ X294) @ omega))&(((((in @ (esk4_1 @ X295) @ omega)|~(in @ emptyset @ X295)|(~(in @ X297 @ omega)|(in @ X297 @ X295)))&((in @ (esk4_1 @ X295) @ X295)|~(in @ emptyset @ X295)|(~(in @ X297 @ omega)|(in @ X297 @ X295))))&(~(in @ (setadjoin @ (esk4_1 @ X295) @ (esk4_1 @ X295)) @ X295)|~(in @ emptyset @ X295)|(~(in @ X297 @ omega)|(in @ X297 @ X295))))&((((((in @ (esk8_3 @ X298 @ X299 @ X304) @ X299)|~(in @ X304 @ (esk7_2 @ X298 @ X299))|(in @ (esk5_2 @ X298 @ X299) @ X299))&((X298 @ (esk8_3 @ X298 @ X299 @ X304) @ X304)|~(in @ X304 @ (esk7_2 @ X298 @ X299))|(in @ (esk5_2 @ X298 @ X299) @ X299)))&(~(in @ X307 @ X299)|~(X298 @ X307 @ X306)|(in @ X306 @ (esk7_2 @ X298 @ X299))|(in @ (esk5_2 @ X298 @ X299) @ X299)))&(((((in @ (esk8_3 @ X298 @ X299 @ X304) @ X299)|~(in @ X304 @ (esk7_2 @ X298 @ X299))|((X298 @ (esk5_2 @ X298 @ X299) @ (esk6_3 @ X298 @ X299 @ X301))|~(X298 @ (esk5_2 @ X298 @ X299) @ X301)))&((X298 @ (esk8_3 @ X298 @ X299 @ X304) @ X304)|~(in @ X304 @ (esk7_2 @ X298 @ X299))|((X298 @ (esk5_2 @ X298 @ X299) @ (esk6_3 @ X298 @ X299 @ X301))|~(X298 @ (esk5_2 @ X298 @ X299) @ X301))))&(~(in @ X307 @ X299)|~(X298 @ X307 @ X306)|(in @ X306 @ (esk7_2 @ X298 @ X299))|((X298 @ (esk5_2 @ X298 @ X299) @ (esk6_3 @ X298 @ X299 @ X301))|~(X298 @ (esk5_2 @ X298 @ X299) @ X301))))&((((in @ (esk8_3 @ X298 @ X299 @ X304) @ X299)|~(in @ X304 @ (esk7_2 @ X298 @ X299))|(((X301)!=(esk6_3 @ X298 @ X299 @ X301))|~(X298 @ (esk5_2 @ X298 @ X299) @ X301)))&((X298 @ (esk8_3 @ X298 @ X299 @ X304) @ X304)|~(in @ X304 @ (esk7_2 @ X298 @ X299))|(((X301)!=(esk6_3 @ X298 @ X299 @ X301))|~(X298 @ (esk5_2 @ X298 @ X299) @ X301))))&(~(in @ X307 @ X299)|~(X298 @ X307 @ X306)|(in @ X306 @ (esk7_2 @ X298 @ X299))|(((X301)!=(esk6_3 @ X298 @ X299 @ X301))|~(X298 @ (esk5_2 @ X298 @ X299) @ X301))))))&((((in @ (esk9_1 @ X308) @ X308)|~(in @ X309 @ X308))&(~(in @ X311 @ (esk9_1 @ X308))|~(in @ X311 @ X308)|~(in @ X309 @ X308)))&((epred1_0)&((descrp)&((~(in @ X314 @ X312)|(~(X313 @ X314)|(in @ X314 @ (dsetconstr @ X312 @ X313))))&((~(in @ X317 @ (dsetconstr @ X315 @ X316))|(in @ X317 @ X315))&((~(in @ X320 @ (dsetconstr @ X318 @ X319))|(X319 @ X320))&(((((X321 @ (esk11_1 @ X321))|((X321 @ (esk10_2 @ X321 @ X322))|~(X321 @ X322)))&(~(X321 @ X325)|((esk11_1 @ X321)=(X325))|((X321 @ (esk10_2 @ X321 @ X322))|~(X321 @ X322))))&(((X321 @ (esk11_1 @ X321))|(((X322)!=(esk10_2 @ X321 @ X322))|~(X321 @ X322)))&(~(X321 @ X325)|((esk11_1 @ X321)=(X325))|(((X322)!=(esk10_2 @ X321 @ X322))|~(X321 @ X322)))))&((~(in @ X327 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X326)))))|(X326))&((~(in @ X328 @ emptyset)|(X329))&((~(in @ X330 @ emptyset)|~($true))&(~(in @ X331 @ emptyset)&((((X332 @ (esk12_2 @ X332 @ X333))|~(X332 @ X333)|(X332 @ (esk13_1 @ X332)))&(((X333)!=(esk12_2 @ X332 @ X333))|~(X332 @ X333)|(X332 @ (esk13_1 @ X332))))&(((((in @ (esk15_2 @ X336 @ X337) @ X337)|((X336)=(X337))|(in @ (esk14_2 @ X336 @ X337) @ X336))&(~(in @ (esk15_2 @ X336 @ X337) @ X336)|((X336)=(X337))|(in @ (esk14_2 @ X336 @ X337) @ X336)))&(((in @ (esk15_2 @ X336 @ X337) @ X337)|((X336)=(X337))|~(in @ (esk14_2 @ X336 @ X337) @ X337))&(~(in @ (esk15_2 @ X336 @ X337) @ X336)|((X336)=(X337))|~(in @ (esk14_2 @ X336 @ X337) @ X337))))&(((in @ (esk16_1 @ X340) @ X340)|((X340)=(emptyset)))&(((in @ (esk17_1 @ X342) @ X342)|((X342)=(emptyset)))&(((~(in @ X346 @ (dsetconstr @ X344 @ X345))|(X345 @ X346)|~(in @ X346 @ X344))&(~(X345 @ X346)|(in @ X346 @ (dsetconstr @ X344 @ X345))|~(in @ X346 @ X344)))&((((X347)=(emptyset))|(in @ (esk18_1 @ X347) @ X347))&((~(in @ X351 @ X349)|(~(X350 @ X351)|((dsetconstr @ X349 @ X350)!=(emptyset))))&((~(in @ X353 @ X352)|((X352)!=(emptyset)))&((in @ X354 @ (setadjoin @ X354 @ X355))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X358 @ X357)|(in @ X358 @ (setadjoin @ X356 @ X357)))&(((((in @ X361 @ X360)|(X362)|((X361)=(X359))|~(in @ X361 @ (setadjoin @ X359 @ X360)))&(~(X362)|(X362)|((X361)=(X359))|~(in @ X361 @ (setadjoin @ X359 @ X360))))&(((in @ X361 @ X360)|(X362)|~(X362)|~(in @ X361 @ (setadjoin @ X359 @ X360)))&(~(X362)|(X362)|~(X362)|~(in @ X361 @ (setadjoin @ X359 @ X360)))))&((~(in @ X365 @ (setadjoin @ X363 @ X364))|(((X365)=(X363))|(in @ X365 @ X364)))&(((dsetconstr @ X366 @ (^[Z0:$i]:($true)))=(X366))&((((in @ (esk19_2 @ X367 @ X368) @ X368)|(in @ X368 @ (powerset @ X367)))&(~(in @ (esk19_2 @ X367 @ X368) @ X367)|(in @ X368 @ (powerset @ X367))))&((in @ emptyset @ (powerset @ X370))&((in @ emptyset @ (powerset @ X371))&((~(in @ X373 @ (powerset @ X372))|(~(in @ X374 @ X373)|(in @ X374 @ X372)))&((~(in @ X376 @ X377)|(~(in @ X377 @ X375)|(in @ X376 @ (setunion @ X375))))&((((in @ X379 @ (esk20_3 @ X378 @ X379 @ X380))|(X380)|~(in @ X379 @ (setunion @ X378)))&(((in @ (esk20_3 @ X378 @ X379 @ X380) @ X378)|(X380)|~(in @ X379 @ (setunion @ X378)))&(~(X380)|(X380)|~(in @ X379 @ (setunion @ X378)))))&((~(in @ X383 @ X382)|(in @ X383 @ (powerset @ (setunion @ X382))))&((((~(X384 @ X388)|((X388)=(esk22_1 @ X384))|((X384 @ (esk21_2 @ X384 @ X385))|~(X384 @ X385)))&(((X389)!=(esk22_1 @ X384))|(X384 @ X389)|((X384 @ (esk21_2 @ X384 @ X385))|~(X384 @ X385))))&((~(X384 @ X388)|((X388)=(esk22_1 @ X384))|(((X385)!=(esk21_2 @ X384 @ X385))|~(X384 @ X385)))&(((X389)!=(esk22_1 @ X384))|(X384 @ X389)|(((X385)!=(esk21_2 @ X384 @ X385))|~(X384 @ X385)))))&((((in @ (esk23_1 @ X390) @ X390)|((X390)=(emptyset)))&(($true)|((X390)=(emptyset))))&((~(in @ X392 @ (setadjoin @ X393 @ emptyset))|((X392)=(X393)))&(((esk24_0)!=(esk25_0))&(in @ esk25_0 @ (setadjoin @ esk24_0 @ emptyset)))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[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_71])])])])])])])).
% 0.12/0.28 thf(c_0_73, negated_conjecture, ![X2:$i, X3:$i]:((((X2)=(X3))|~((in @ X2 @ (setadjoin @ X3 @ emptyset))))), inference(split_conjunct,[status(thm)],[c_0_72])).
% 0.12/0.28 thf(c_0_74, negated_conjecture, (in @ esk25_0 @ (setadjoin @ esk24_0 @ emptyset)), inference(split_conjunct,[status(thm)],[c_0_72])).
% 0.12/0.28 thf(c_0_75, negated_conjecture, ((esk24_0)!=(esk25_0)), inference(split_conjunct,[status(thm)],[c_0_72])).
% 0.12/0.28 thf(c_0_76, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_73, c_0_74]), c_0_75]), ['proof']).
% 0.12/0.28 % SZS output end CNFRefutation
% 0.12/0.28 % Parsed axioms : 103
% 0.12/0.28 % Removed by relevancy pruning/SinE : 56
% 0.12/0.28 % Initial clauses : 95
% 0.12/0.28 % Removed in clause preprocessing : 5
% 0.12/0.28 % Initial clauses in saturation : 90
% 0.12/0.28 % Processed clauses : 37
% 0.12/0.28 % ...of these trivial : 1
% 0.12/0.28 % ...subsumed : 10
% 0.12/0.28 % ...remaining for further processing : 26
% 0.12/0.28 % Other redundant clauses eliminated : 2
% 0.12/0.28 % Clauses deleted for lack of memory : 0
% 0.12/0.28 % Backward-subsumed : 0
% 0.12/0.28 % Backward-rewritten : 2
% 0.12/0.28 % Generated clauses : 28
% 0.12/0.28 % ...of the previous two non-redundant : 18
% 0.12/0.28 % ...aggressively subsumed : 0
% 0.12/0.28 % Contextual simplify-reflections : 0
% 0.12/0.28 % Paramodulations : 26
% 0.12/0.28 % Factorizations : 0
% 0.12/0.28 % NegExts : 0
% 0.12/0.28 % Equation resolutions : 2
% 0.12/0.28 % Disequality decompositions : 0
% 0.12/0.28 % Total rewrite steps : 8
% 0.12/0.28 % ...of those cached : 1
% 0.12/0.28 % Propositional unsat checks : 0
% 0.12/0.28 % Propositional check models : 0
% 0.12/0.28 % Propositional check unsatisfiable : 0
% 0.12/0.28 % Propositional clauses : 0
% 0.12/0.28 % Propositional clauses after purity: 0
% 0.12/0.28 % Propositional unsat core size : 0
% 0.12/0.28 % Propositional preprocessing time : 0.000
% 0.12/0.28 % Propositional encoding time : 0.000
% 0.12/0.28 % Propositional solver time : 0.000
% 0.12/0.28 % Success case prop preproc time : 0.000
% 0.12/0.28 % Success case prop encoding time : 0.000
% 0.12/0.28 % Success case prop solver time : 0.000
% 0.12/0.28 % Current number of processed clauses : 22
% 0.12/0.28 % Positive orientable unit clauses : 10
% 0.12/0.28 % Positive unorientable unit clauses: 0
% 0.12/0.28 % Negative unit clauses : 2
% 0.12/0.28 % Non-unit-clauses : 10
% 0.12/0.28 % Current number of unprocessed clauses: 71
% 0.12/0.28 % ...number of literals in the above : 240
% 0.12/0.28 % Current number of archived formulas : 0
% 0.12/0.28 % Current number of archived clauses : 2
% 0.12/0.28 % Clause-clause subsumption calls (NU) : 24
% 0.12/0.28 % Rec. Clause-clause subsumption calls : 24
% 0.12/0.28 % Non-unit clause-clause subsumptions : 4
% 0.12/0.28 % Unit Clause-clause subsumption calls : 6
% 0.12/0.28 % Rewrite failures with RHS unbound : 0
% 0.12/0.28 % BW rewrite match attempts : 3
% 0.12/0.28 % BW rewrite match successes : 2
% 0.12/0.28 % Condensation attempts : 0
% 0.12/0.28 % Condensation successes : 0
% 0.12/0.28 % Termbank termtop insertions : 11916
% 0.12/0.28 % Search garbage collected termcells : 4626
% 0.12/0.28
% 0.12/0.28 % -------------------------------------------------
% 0.12/0.28 % User time : 0.009 s
% 0.12/0.28 % System time : 0.006 s
% 0.12/0.28 % Total time : 0.015 s
% 0.12/0.28 % Maximum resident set size: 4452 pages
% 0.12/0.28
% 0.12/0.28 % -------------------------------------------------
% 0.12/0.28 % User time : 0.012 s
% 0.12/0.28 % System time : 0.011 s
% 0.12/0.28 % Total time : 0.023 s
% 0.12/0.28 % Maximum resident set size: 4608 pages
% 0.12/0.28 % E exiting
%------------------------------------------------------------------------------