%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU528^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 08:26:35 AM UTC 2026
% Result : Theorem 0.11s 0.29s
% Output : CNFRefutation 0.11s
% 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/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.18 % Computer : n016.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Sep 29 13:53:19 UTC 2026
% 0.11/0.19 % CPUTime :
% 0.11/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.23 Running higher-order theorem proving
% 0.11/0.25 Running: /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=300 /export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p
% 0.11/0.29 % Version: 3.5.1-ho
% 0.11/0.29 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.11/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.29 % Starting new_ho_10 with 1500s (5) cores
% 0.11/0.29 % Starting sh5l with 300s (1) cores
% 0.11/0.29 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.29 % Starting new_bool_2 with 300s (1) cores
% 0.11/0.29 % sh5l with pid 382410 completed with status 0
% 0.11/0.29 % Result found by sh5l
% 0.11/0.29 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.11/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.29 % Starting new_ho_10 with 1500s (5) cores
% 0.11/0.29 % Starting sh5l with 300s (1) cores
% 0.11/0.29 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.11/0.29 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.11/0.29 % Search class: HGHSM-FFMS31-SHFSMSBN
% 0.11/0.29 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.29 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.29 % SubtermCWHack with pid 382417 completed with status 0
% 0.11/0.29 % Result found by SubtermCWHack
% 0.11/0.29 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.11/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.29 % Starting new_ho_10 with 1500s (5) cores
% 0.11/0.29 % Starting sh5l with 300s (1) cores
% 0.11/0.29 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.11/0.29 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.11/0.29 % Search class: HGHSM-FFMS31-SHFSMSBN
% 0.11/0.29 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.29 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.29 % Preprocessing time : 0.002 s
% 0.11/0.29
% 0.11/0.29 % Proof found!
% 0.11/0.29 % SZS status Theorem
% 0.11/0.29 % SZS output start CNFRefutation
% 0.11/0.29 thf(decl_23, type, in: $i > $i > $o).
% 0.11/0.29 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.11/0.29 thf(decl_25, type, setextAx: $o).
% 0.11/0.29 thf(decl_26, type, emptyset: $i).
% 0.11/0.29 thf(decl_27, type, emptysetAx: $o).
% 0.11/0.29 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.11/0.29 thf(decl_29, type, setadjoinAx: $o).
% 0.11/0.29 thf(decl_30, type, powerset: $i > $i).
% 0.11/0.29 thf(decl_31, type, powersetAx: $o).
% 0.11/0.29 thf(decl_32, type, setunion: $i > $i).
% 0.11/0.29 thf(decl_33, type, setunionAx: $o).
% 0.11/0.29 thf(decl_34, type, omega: $i).
% 0.11/0.29 thf(decl_35, type, omega0Ax: $o).
% 0.11/0.29 thf(decl_36, type, omegaSAx: $o).
% 0.11/0.29 thf(decl_37, type, omegaIndAx: $o).
% 0.11/0.29 thf(decl_38, type, replAx: $o).
% 0.11/0.29 thf(decl_39, type, foundationAx: $o).
% 0.11/0.29 thf(decl_40, type, wellorderingAx: $o).
% 0.11/0.29 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.11/0.29 thf(decl_42, type, descrp: $o).
% 0.11/0.29 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.11/0.29 thf(decl_44, type, dsetconstrI: $o).
% 0.11/0.29 thf(decl_45, type, dsetconstrEL: $o).
% 0.11/0.29 thf(decl_46, type, dsetconstrER: $o).
% 0.11/0.29 thf(decl_47, type, exuE1: $o).
% 0.11/0.29 thf(decl_48, type, prop2set: $o > $i).
% 0.11/0.29 thf(decl_49, type, prop2setE: $o).
% 0.11/0.29 thf(decl_50, type, emptysetE: $o).
% 0.11/0.29 thf(decl_51, type, emptysetimpfalse: $o).
% 0.11/0.29 thf(decl_52, type, notinemptyset: $o).
% 0.11/0.29 thf(decl_53, type, exuE3e: $o).
% 0.11/0.29 thf(decl_54, type, setext: $o).
% 0.11/0.29 thf(decl_55, type, emptyI: $o).
% 0.11/0.29 thf(decl_56, type, noeltsimpempty: $o).
% 0.11/0.29 thf(decl_57, type, setbeta: $o).
% 0.11/0.29 thf(decl_58, type, nonempty: $i > $o).
% 0.11/0.29 thf(decl_59, type, nonemptyE1: $o).
% 0.11/0.29 thf(decl_60, type, nonemptyI: $o).
% 0.11/0.29 thf(decl_61, type, nonemptyI1: $o).
% 0.11/0.29 thf(decl_62, type, setadjoinIL: $o).
% 0.11/0.29 thf(decl_63, type, emptyinunitempty: $o).
% 0.11/0.29 thf(decl_64, type, setadjoinIR: $o).
% 0.11/0.29 thf(decl_65, type, setadjoinE: $o).
% 0.11/0.29 thf(decl_66, type, setadjoinOr: $o).
% 0.11/0.29 thf(decl_67, type, setoftrueEq: $o).
% 0.11/0.29 thf(decl_68, type, powersetI: $o).
% 0.11/0.29 thf(decl_69, type, emptyinPowerset: $o).
% 0.11/0.29 thf(decl_70, type, emptyInPowerset: $o).
% 0.11/0.29 thf(decl_71, type, powersetE: $o).
% 0.11/0.29 thf(decl_72, type, setunionI: $o).
% 0.11/0.29 thf(decl_73, type, setunionE: $o).
% 0.11/0.29 thf(decl_74, type, subPowSU: $o).
% 0.11/0.29 thf(decl_75, type, exuE2: $o).
% 0.11/0.29 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.11/0.29 thf(decl_77, type, uniqinunit: $o).
% 0.11/0.29 thf(decl_78, type, epred1_0: $o).
% 0.11/0.29 thf(decl_79, type, esk1_2: $i > $i > $i).
% 0.11/0.29 thf(decl_80, type, esk2_2: $i > $i > $i).
% 0.11/0.29 thf(decl_81, type, esk3_2: $i > $i > $i).
% 0.11/0.29 thf(decl_82, type, esk4_1: $i > $i).
% 0.11/0.29 thf(decl_83, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.11/0.29 thf(decl_84, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.11/0.29 thf(decl_85, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.11/0.29 thf(decl_86, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.11/0.29 thf(decl_87, type, esk9_1: $i > $i).
% 0.11/0.29 thf(decl_88, type, esk10_2: ($i > $o) > $i > $i).
% 0.11/0.29 thf(decl_89, type, esk11_2: ($i > $o) > $i > $i).
% 0.11/0.29 thf(decl_90, type, esk12_1: ($i > $o) > $i).
% 0.11/0.29 thf(decl_91, type, esk13_2: ($i > $o) > $i > $i).
% 0.11/0.29 thf(decl_92, type, esk14_1: ($i > $o) > $i).
% 0.11/0.29 thf(decl_93, type, esk15_2: $i > $i > $i).
% 0.11/0.29 thf(decl_94, type, esk16_2: $i > $i > $i).
% 0.11/0.29 thf(decl_95, type, esk17_1: $i > $i).
% 0.11/0.29 thf(decl_96, type, esk18_1: $i > $i).
% 0.11/0.29 thf(decl_97, type, esk19_1: $i > $i).
% 0.11/0.29 thf(decl_98, type, esk20_2: $i > $i > $i).
% 0.11/0.29 thf(decl_99, type, esk21_3: $i > $i > $o > $i).
% 0.11/0.29 thf(decl_100, type, esk22_2: ($i > $o) > $i > $i).
% 0.11/0.29 thf(decl_101, type, esk23_1: ($i > $o) > $i).
% 0.11/0.29 thf(decl_102, type, esk24_1: $i > $i).
% 0.11/0.29 thf(decl_103, type, esk25_0: $i).
% 0.11/0.29 thf(decl_104, type, esk26_0: $i).
% 0.11/0.29 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', exuE2)).
% 0.11/0.29 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', exu)).
% 0.11/0.29 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', nonempty)).
% 0.11/0.29 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', replAx)).
% 0.11/0.29 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', descrp)).
% 0.11/0.29 thf(prop2set, axiom, ((prop2set)=(^[X10:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[X2:$i]:((X10)))))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', prop2set)).
% 0.11/0.29 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', exuE1)).
% 0.11/0.29 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', nonemptyI)).
% 0.11/0.29 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', exuE3e)).
% 0.11/0.29 thf(notinsingleton, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', notinsingleton)).
% 0.11/0.29 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', nonemptyImpWitness)).
% 0.11/0.29 thf(prop2setE, axiom, ((prop2setE)<=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', prop2setE)).
% 0.11/0.29 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', dsetconstrER)).
% 0.11/0.29 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', dsetconstrEL)).
% 0.11/0.29 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', dsetconstrI)).
% 0.11/0.29 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', nonemptyE1)).
% 0.11/0.29 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', setbeta)).
% 0.11/0.29 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', nonemptyI1)).
% 0.11/0.29 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', setoftrueEq)).
% 0.11/0.29 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', setadjoinOr)).
% 0.11/0.29 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X13:$o]:(((((X3)=(X2))=>(X13))=>(((in @ X3 @ X4)=>(X13))=>(X13))))))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', setadjoinE)).
% 0.11/0.29 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', setadjoinIR)).
% 0.11/0.29 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', wellorderingAx)).
% 0.11/0.29 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', emptyinunitempty)).
% 0.11/0.29 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', foundationAx)).
% 0.11/0.29 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', setadjoinIL)).
% 0.11/0.29 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.yUiWx0LOGM/E---3.1_382381.p', omegaIndAx)).
% 0.11/0.29 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', omegaSAx)).
% 0.11/0.29 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', setadjoinAx)).
% 0.11/0.29 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', emptysetimpfalse)).
% 0.11/0.29 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12))))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', emptysetE)).
% 0.11/0.29 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', notinemptyset)).
% 0.11/0.29 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', noeltsimpempty)).
% 0.11/0.29 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', emptyI)).
% 0.11/0.29 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', setext)).
% 0.11/0.29 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X14:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X14))))=>(X14)))))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', setunionE)).
% 0.11/0.29 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', setunionI)).
% 0.11/0.29 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', powersetE)).
% 0.11/0.29 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', emptyInPowerset)).
% 0.11/0.29 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', emptyinPowerset)).
% 0.11/0.29 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', powersetI)).
% 0.11/0.29 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', uniqinunit)).
% 0.11/0.29 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', subPowSU)).
% 0.11/0.29 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', omega0Ax)).
% 0.11/0.29 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', setunionAx)).
% 0.11/0.29 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', powersetAx)).
% 0.11/0.29 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', emptysetAx)).
% 0.11/0.29 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.yUiWx0LOGM/E---3.1_382381.p', setextAx)).
% 0.11/0.29 thf(c_0_48, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.11/0.29 thf(c_0_49, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.11/0.29 thf(c_0_50, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.11/0.29 thf(c_0_51, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.11/0.29 thf(c_0_52, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.11/0.29 thf(c_0_53, plain, ((prop2set)=(^[Z0:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[Z1:$i]:((Z0)))))), inference(fof_simplification,[status(thm)],[prop2set])).
% 0.11/0.29 thf(c_0_54, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.11/0.29 thf(c_0_55, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.11/0.29 thf(c_0_56, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.11/0.29 thf(c_0_57, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[notinsingleton])).
% 0.11/0.29 thf(c_0_58, plain, ((exuE2)=(![X1:$i > $o]:((((?[X147:$i]:(((((X1 @ X147)))&(![X148:$i]:(((((X1 @ X148)))=>(((X147)=(X148))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_48, c_0_49])).
% 0.11/0.29 thf(c_0_59, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_50])).
% 0.11/0.29 thf(c_0_60, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X139:$i]:(((((X6 @ X2 @ X139)))&(![X140:$i]:(((((X6 @ X2 @ X140)))=>(((X139)=(X140)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_51, c_0_49])).
% 0.11/0.29 thf(c_0_61, plain, ((descrp)=(![X1:$i > $o]:((((?[X141:$i]:(((((X1 @ X141)))&(![X142:$i]:(((((X1 @ X142)))=>(((X141)=(X142))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_52, c_0_49])).
% 0.11/0.29 thf(c_0_62, axiom, ((prop2setE)=(![X11:$o, X2:$i]:((((in @ X2 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:(((X11)))))))=>((X11)))))), inference(apply_def,[status(thm)],[prop2setE, c_0_53])).
% 0.11/0.29 thf(c_0_63, plain, ((exuE1)=(![X1:$i > $o]:((((?[X143:$i]:(((((X1 @ X143)))&(![X144:$i]:(((((X1 @ X144)))=>(((X143)=(X144))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_54, c_0_49])).
% 0.11/0.29 thf(c_0_64, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.11/0.29 thf(c_0_65, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.11/0.29 thf(c_0_66, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.11/0.29 thf(c_0_67, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_55, c_0_50])).
% 0.11/0.29 thf(c_0_68, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_50])).
% 0.11/0.29 thf(c_0_69, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.11/0.29 thf(c_0_70, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X145:$i]:(((((X1 @ X145)))&(![X146:$i]:(((((X1 @ X146)))=>(((X145)=(X146))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_56, c_0_49])).
% 0.11/0.29 thf(c_0_71, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_50])).
% 0.11/0.29 thf(c_0_72, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.11/0.29 thf(c_0_73, plain, ((epred1_0)<=>![X178:$i]:(?[X179:$i]:((((![X180:$i]:(((in @ X180 @ X179)=>![X181:$i]:(((in @ X181 @ X180)=>(in @ X181 @ X178)))))&![X182:$i, X183:$i]:((((in @ X182 @ X178)&(in @ X183 @ X178))=>(![X184:$i]:(((in @ X184 @ X179)=>((in @ X182 @ X184)<=>(in @ X183 @ X184))))=>((X182)=(X183))))))&![X185:$i, X186:$i]:((((in @ X185 @ X179)&(in @ X186 @ X179))=>(![X187:$i]:(((in @ X187 @ X185)=>(in @ X187 @ X186)))|![X188:$i]:(((in @ X188 @ X186)=>(in @ X188 @ X185)))))))&![X189:$i]:(((![X190:$i]:(((in @ X190 @ X189)=>(in @ X190 @ X178)))&?[X191:$i]:((in @ X191 @ X189)))=>?[X192:$i, X193:$i]:(((((in @ X192 @ X179)&(in @ X193 @ X189))&~(?[X194:$i]:(((in @ X194 @ X192)&(in @ X194 @ X189)))))&![X195:$i]:(((in @ X195 @ X179)=>(![X196:$i]:(((in @ X196 @ X195)=>(in @ X196 @ X192)))|(in @ X193 @ X195)))))))))))), introduced(definition)).
% 0.11/0.29 thf(c_0_74, negated_conjecture, ~((![X149:$i, X150:$i]:((![X151:$i]:(((in @ X151 @ X149)<=>(in @ X151 @ X150)))=>((X149)=(X150))))=>(![X152:$i]:(~(in @ X152 @ emptyset))=>(![X153:$i, X154:$i, X155:$i]:(((in @ X155 @ (setadjoin @ X153 @ X154))<=>(((X155)=(X153))|(in @ X155 @ X154))))=>(![X156:$i, X157:$i]:(((in @ X157 @ (powerset @ X156))<=>![X158:$i]:(((in @ X158 @ X157)=>(in @ X158 @ X156)))))=>(![X159:$i, X160:$i]:(((in @ X160 @ (setunion @ X159))<=>?[X161:$i]:(((in @ X160 @ X161)&(in @ X161 @ X159)))))=>((in @ emptyset @ omega)=>(![X162:$i]:(((in @ X162 @ omega)=>(in @ (setadjoin @ X162 @ X162) @ omega)))=>(![X163:$i]:((((in @ emptyset @ X163)&![X164:$i]:((((in @ X164 @ omega)&(in @ X164 @ X163))=>(in @ (setadjoin @ X164 @ X164) @ X163))))=>![X165:$i]:(((in @ X165 @ omega)=>(in @ X165 @ X163)))))=>(![X166:$i > $i > $o, X167:$i]:((![X168:$i]:(((in @ X168 @ X167)=>?[X169:$i]:(((X166 @ X168 @ X169)&![X170:$i]:(((X166 @ X168 @ X170)=>((X169)=(X170))))))))=>?[X171:$i]:(![X172:$i]:(((in @ X172 @ X171)<=>?[X173:$i]:(((in @ X173 @ X167)&(X166 @ X173 @ X172))))))))=>(![X174:$i]:((?[X175:$i]:((in @ X175 @ X174))=>?[X176:$i]:(((in @ X176 @ X174)&~(?[X177:$i]:(((in @ X177 @ X176)&(in @ X177 @ X174))))))))=>((epred1_0)=>(![X197:$i > $o]:((?[X198:$i]:(((X197 @ X198)&![X199:$i]:(((X197 @ X199)=>((X198)=(X199))))))=>(X197 @ (descr @ (^[Z0:$i]:(X197 @ Z0))))))=>(![X200:$i, X201:$i > $o, X202:$i]:(((in @ X202 @ X200)=>((X201 @ X202)=>(in @ X202 @ (dsetconstr @ X200 @ X201)))))=>(![X203:$i, X204:$i > $o, X205:$i]:(((in @ X205 @ (dsetconstr @ X203 @ X204))=>(in @ X205 @ X203)))=>(![X206:$i, X207:$i > $o, X208:$i]:(((in @ X208 @ (dsetconstr @ X206 @ X207))=>(X207 @ X208)))=>(![X209:$i > $o]:((?[X210:$i]:(((X209 @ X210)&![X211:$i]:(((X209 @ X211)=>((X210)=(X211))))))=>?[X212:$i]:(((X209 @ X212)&![X213:$i]:(((X209 @ X213)=>((X212)=(X213))))))))=>(![X214:$o, X215:$i]:(((in @ X215 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X214)))))=>(X214)))=>(![X216:$i]:(((in @ X216 @ emptyset)=>![X217:$o]:((X217))))=>(![X218:$i]:(((in @ X218 @ emptyset)=>~($true)))=>(![X219:$i]:(~(in @ X219 @ emptyset))=>(![X220:$i > $o]:((?[X221:$i]:(((X220 @ X221)&![X222:$i]:(((X220 @ X222)=>((X221)=(X222))))))=>?[X223:$i]:((X220 @ X223))))=>(![X224:$i, X225:$i]:((![X226:$i]:(((in @ X226 @ X224)=>(in @ X226 @ X225)))=>(![X227:$i]:(((in @ X227 @ X225)=>(in @ X227 @ X224)))=>((X224)=(X225)))))=>(![X228:$i]:((![X229:$i]:(~(in @ X229 @ X228))=>((X228)=(emptyset))))=>(![X230:$i]:((![X231:$i]:(~(in @ X231 @ X230))=>((X230)=(emptyset))))=>(![X232:$i, X233:$i > $o, X234:$i]:(((in @ X234 @ X232)=>((in @ X234 @ (dsetconstr @ X232 @ X233))<=>(X233 @ X234))))=>(![X235:$i]:((((X235)!=(emptyset))=>?[X236:$i]:((in @ X236 @ X235))))=>(![X237:$i, X238:$i > $o, X239:$i]:(((in @ X239 @ X237)=>((X238 @ X239)=>((dsetconstr @ X237 @ X238)!=(emptyset)))))=>(![X240:$i]:((?[X241:$i]:((in @ X241 @ X240))=>((X240)!=(emptyset))))=>(![X242:$i, X243:$i]:((in @ X242 @ (setadjoin @ X242 @ X243)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X244:$i, X245:$i, X246:$i]:(((in @ X246 @ X245)=>(in @ X246 @ (setadjoin @ X244 @ X245))))=>(![X247:$i, X248:$i, X249:$i]:(((in @ X249 @ (setadjoin @ X247 @ X248))=>![X250:$o]:(((((X249)=(X247))=>(X250))=>(((in @ X249 @ X248)=>(X250))=>(X250))))))=>(![X251:$i, X252:$i, X253:$i]:(((in @ X253 @ (setadjoin @ X251 @ X252))=>(((X253)=(X251))|(in @ X253 @ X252))))=>(![X254:$i]:(((dsetconstr @ X254 @ (^[Z0:$i]:($true)))=(X254)))=>(![X255:$i, X256:$i]:((![X257:$i]:(((in @ X257 @ X256)=>(in @ X257 @ X255)))=>(in @ X256 @ (powerset @ X255))))=>(![X258:$i]:((in @ emptyset @ (powerset @ X258)))=>(![X259:$i]:((in @ emptyset @ (powerset @ X259)))=>(![X260:$i, X261:$i, X262:$i]:(((in @ X261 @ (powerset @ X260))=>((in @ X262 @ X261)=>(in @ X262 @ X260))))=>(![X263:$i, X264:$i, X265:$i]:(((in @ X264 @ X265)=>((in @ X265 @ X263)=>(in @ X264 @ (setunion @ X263)))))=>(![X266:$i, X267:$i]:(((in @ X267 @ (setunion @ X266))=>![X268:$o]:((![X269:$i]:(((in @ X267 @ X269)=>((in @ X269 @ X266)=>(X268))))=>(X268)))))=>(![X270:$i, X271:$i]:(((in @ X271 @ X270)=>(in @ X271 @ (powerset @ (setunion @ X270)))))=>(![X272:$i > $o]:((?[X273:$i]:(((X272 @ X273)&![X274:$i]:(((X272 @ X274)=>((X273)=(X274))))))=>?[X275:$i]:(![X276:$i]:(((X272 @ X276)<=>((X276)=(X275)))))))=>(![X277:$i]:((((X277)!=(emptyset))=>?[X278:$i]:(((in @ X278 @ X277)&$true))))=>(![X279:$i, X280:$i]:(((in @ X279 @ (setadjoin @ X280 @ emptyset))=>((X279)=(X280))))=>![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)],[inference(apply_def,[status(thm)],[c_0_57, setadjoinOr]), c_0_58]), c_0_59]), setadjoinE]), setadjoinIR]), wellorderingAx]), emptyinunitempty]), foundationAx]), setadjoinIL]), c_0_60]), omegaIndAx]), c_0_61]), omegaSAx]), setadjoinAx]), emptysetimpfalse]), emptysetE]), c_0_62]), c_0_63]), c_0_64]), c_0_65]), c_0_66]), notinemptyset]), c_0_67]), c_0_68]), c_0_69]), noeltsimpempty]), emptyI]), setext]), c_0_70]), c_0_71]), setunionE]), setunionI]), powersetE]), emptyInPowerset]), emptyinPowerset]), powersetI]), c_0_72]), uniqinunit]), subPowSU]), omega0Ax]), setunionAx]), powersetAx]), emptysetAx]), setextAx])])]), c_0_73])).
% 0.11/0.29 thf(c_0_75, negated_conjecture, ![X281:$i, X282:$i, X284:$i, X285:$i, X286:$i, X287:$i, X288:$i, X289:$i, X290:$i, X291:$i, X292:$i, X294:$i, X295:$i, X297:$i, X298:$i, X299:$i, X300:$i, X301:$i, X303:$i, X304:$i > $i > $o, X305:$i, X307:$i, X310:$i, X312:$i, X313:$i, X314:$i, X315:$i, X317:$i, X318:$i > $o, X319:$i, X321:$i, X322:$i > $o, X323:$i, X324:$i, X325:$i > $o, X326:$i, X327:$i, X328:$i > $o, X329:$i, X330:$i > $o, X331:$i, X334:$i, X335:$o, X336:$i, X337:$i, X338:$o, X339:$i, X340:$i, X341:$i > $o, X342:$i, X345:$i, X346:$i, X349:$i, X351:$i, X353:$i, X354:$i > $o, X355:$i, X356:$i, X358:$i, X359:$i > $o, X360:$i, X361:$i, X362:$i, X363:$i, X364:$i, X365:$i, X366:$i, X367:$i, X368:$i, X369:$i, X370:$i, X371:$o, X372:$i, X373:$i, X374:$i, X375:$i, X376:$i, X377:$i, X379:$i, X380:$i, X381:$i, X382:$i, X383:$i, X384:$i, X385:$i, X386:$i, X387:$i, X388:$i, X389:$o, X391:$i, X392:$i, X393:$i > $o, X394:$i, X397:$i, X398:$i, X399:$i, X401:$i, X402:$i]:((((~(in @ (esk1_2 @ X281 @ X282) @ X281)|~(in @ (esk1_2 @ X281 @ X282) @ X282)|((X281)=(X282)))&((in @ (esk1_2 @ X281 @ X282) @ X281)|(in @ (esk1_2 @ X281 @ X282) @ X282)|((X281)=(X282))))&(~(in @ X284 @ emptyset)&(((~(in @ X287 @ (setadjoin @ X285 @ X286))|(((X287)=(X285))|(in @ X287 @ X286)))&((((X287)!=(X285))|(in @ X287 @ (setadjoin @ X285 @ X286)))&(~(in @ X287 @ X286)|(in @ X287 @ (setadjoin @ X285 @ X286)))))&(((~(in @ X289 @ (powerset @ X288))|(~(in @ X290 @ X289)|(in @ X290 @ X288)))&(((in @ (esk2_2 @ X291 @ X292) @ X292)|(in @ X292 @ (powerset @ X291)))&(~(in @ (esk2_2 @ X291 @ X292) @ X291)|(in @ X292 @ (powerset @ X291)))))&(((((in @ X295 @ (esk3_2 @ X294 @ X295))|~(in @ X295 @ (setunion @ X294)))&((in @ (esk3_2 @ X294 @ X295) @ X294)|~(in @ X295 @ (setunion @ X294))))&(~(in @ X298 @ X299)|~(in @ X299 @ X297)|(in @ X298 @ (setunion @ X297))))&((in @ emptyset @ omega)&((~(in @ X300 @ omega)|(in @ (setadjoin @ X300 @ X300) @ omega))&(((((in @ (esk4_1 @ X301) @ omega)|~(in @ emptyset @ X301)|(~(in @ X303 @ omega)|(in @ X303 @ X301)))&((in @ (esk4_1 @ X301) @ X301)|~(in @ emptyset @ X301)|(~(in @ X303 @ omega)|(in @ X303 @ X301))))&(~(in @ (setadjoin @ (esk4_1 @ X301) @ (esk4_1 @ X301)) @ X301)|~(in @ emptyset @ X301)|(~(in @ X303 @ omega)|(in @ X303 @ X301))))&((((((in @ (esk8_3 @ X304 @ X305 @ X310) @ X305)|~(in @ X310 @ (esk7_2 @ X304 @ X305))|(in @ (esk5_2 @ X304 @ X305) @ X305))&((X304 @ (esk8_3 @ X304 @ X305 @ X310) @ X310)|~(in @ X310 @ (esk7_2 @ X304 @ X305))|(in @ (esk5_2 @ X304 @ X305) @ X305)))&(~(in @ X313 @ X305)|~(X304 @ X313 @ X312)|(in @ X312 @ (esk7_2 @ X304 @ X305))|(in @ (esk5_2 @ X304 @ X305) @ X305)))&(((((in @ (esk8_3 @ X304 @ X305 @ X310) @ X305)|~(in @ X310 @ (esk7_2 @ X304 @ X305))|((X304 @ (esk5_2 @ X304 @ X305) @ (esk6_3 @ X304 @ X305 @ X307))|~(X304 @ (esk5_2 @ X304 @ X305) @ X307)))&((X304 @ (esk8_3 @ X304 @ X305 @ X310) @ X310)|~(in @ X310 @ (esk7_2 @ X304 @ X305))|((X304 @ (esk5_2 @ X304 @ X305) @ (esk6_3 @ X304 @ X305 @ X307))|~(X304 @ (esk5_2 @ X304 @ X305) @ X307))))&(~(in @ X313 @ X305)|~(X304 @ X313 @ X312)|(in @ X312 @ (esk7_2 @ X304 @ X305))|((X304 @ (esk5_2 @ X304 @ X305) @ (esk6_3 @ X304 @ X305 @ X307))|~(X304 @ (esk5_2 @ X304 @ X305) @ X307))))&((((in @ (esk8_3 @ X304 @ X305 @ X310) @ X305)|~(in @ X310 @ (esk7_2 @ X304 @ X305))|(((X307)!=(esk6_3 @ X304 @ X305 @ X307))|~(X304 @ (esk5_2 @ X304 @ X305) @ X307)))&((X304 @ (esk8_3 @ X304 @ X305 @ X310) @ X310)|~(in @ X310 @ (esk7_2 @ X304 @ X305))|(((X307)!=(esk6_3 @ X304 @ X305 @ X307))|~(X304 @ (esk5_2 @ X304 @ X305) @ X307))))&(~(in @ X313 @ X305)|~(X304 @ X313 @ X312)|(in @ X312 @ (esk7_2 @ X304 @ X305))|(((X307)!=(esk6_3 @ X304 @ X305 @ X307))|~(X304 @ (esk5_2 @ X304 @ X305) @ X307))))))&((((in @ (esk9_1 @ X314) @ X314)|~(in @ X315 @ X314))&(~(in @ X317 @ (esk9_1 @ X314))|~(in @ X317 @ X314)|~(in @ X315 @ X314)))&((epred1_0)&((((X318 @ (esk10_2 @ X318 @ X319))|~(X318 @ X319)|(X318 @ (descr @ X318)))&(((X319)!=(esk10_2 @ X318 @ X319))|~(X318 @ X319)|(X318 @ (descr @ X318))))&((~(in @ X323 @ X321)|(~(X322 @ X323)|(in @ X323 @ (dsetconstr @ X321 @ X322))))&((~(in @ X326 @ (dsetconstr @ X324 @ X325))|(in @ X326 @ X324))&((~(in @ X329 @ (dsetconstr @ X327 @ X328))|(X328 @ X329))&(((((X330 @ (esk12_1 @ X330))|((X330 @ (esk11_2 @ X330 @ X331))|~(X330 @ X331)))&(~(X330 @ X334)|((esk12_1 @ X330)=(X334))|((X330 @ (esk11_2 @ X330 @ X331))|~(X330 @ X331))))&(((X330 @ (esk12_1 @ X330))|(((X331)!=(esk11_2 @ X330 @ X331))|~(X330 @ X331)))&(~(X330 @ X334)|((esk12_1 @ X330)=(X334))|(((X331)!=(esk11_2 @ X330 @ X331))|~(X330 @ X331)))))&((~(in @ X336 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X335)))))|(X335))&((~(in @ X337 @ emptyset)|(X338))&((~(in @ X339 @ emptyset)|~($true))&(~(in @ X340 @ emptyset)&((((X341 @ (esk13_2 @ X341 @ X342))|~(X341 @ X342)|(X341 @ (esk14_1 @ X341)))&(((X342)!=(esk13_2 @ X341 @ X342))|~(X341 @ X342)|(X341 @ (esk14_1 @ X341))))&(((((in @ (esk16_2 @ X345 @ X346) @ X346)|((X345)=(X346))|(in @ (esk15_2 @ X345 @ X346) @ X345))&(~(in @ (esk16_2 @ X345 @ X346) @ X345)|((X345)=(X346))|(in @ (esk15_2 @ X345 @ X346) @ X345)))&(((in @ (esk16_2 @ X345 @ X346) @ X346)|((X345)=(X346))|~(in @ (esk15_2 @ X345 @ X346) @ X346))&(~(in @ (esk16_2 @ X345 @ X346) @ X345)|((X345)=(X346))|~(in @ (esk15_2 @ X345 @ X346) @ X346))))&(((in @ (esk17_1 @ X349) @ X349)|((X349)=(emptyset)))&(((in @ (esk18_1 @ X351) @ X351)|((X351)=(emptyset)))&(((~(in @ X355 @ (dsetconstr @ X353 @ X354))|(X354 @ X355)|~(in @ X355 @ X353))&(~(X354 @ X355)|(in @ X355 @ (dsetconstr @ X353 @ X354))|~(in @ X355 @ X353)))&((((X356)=(emptyset))|(in @ (esk19_1 @ X356) @ X356))&((~(in @ X360 @ X358)|(~(X359 @ X360)|((dsetconstr @ X358 @ X359)!=(emptyset))))&((~(in @ X362 @ X361)|((X361)!=(emptyset)))&((in @ X363 @ (setadjoin @ X363 @ X364))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X367 @ X366)|(in @ X367 @ (setadjoin @ X365 @ X366)))&(((((in @ X370 @ X369)|(X371)|((X370)=(X368))|~(in @ X370 @ (setadjoin @ X368 @ X369)))&(~(X371)|(X371)|((X370)=(X368))|~(in @ X370 @ (setadjoin @ X368 @ X369))))&(((in @ X370 @ X369)|(X371)|~(X371)|~(in @ X370 @ (setadjoin @ X368 @ X369)))&(~(X371)|(X371)|~(X371)|~(in @ X370 @ (setadjoin @ X368 @ X369)))))&((~(in @ X374 @ (setadjoin @ X372 @ X373))|(((X374)=(X372))|(in @ X374 @ X373)))&(((dsetconstr @ X375 @ (^[Z0:$i]:($true)))=(X375))&((((in @ (esk20_2 @ X376 @ X377) @ X377)|(in @ X377 @ (powerset @ X376)))&(~(in @ (esk20_2 @ X376 @ X377) @ X376)|(in @ X377 @ (powerset @ X376))))&((in @ emptyset @ (powerset @ X379))&((in @ emptyset @ (powerset @ X380))&((~(in @ X382 @ (powerset @ X381))|(~(in @ X383 @ X382)|(in @ X383 @ X381)))&((~(in @ X385 @ X386)|(~(in @ X386 @ X384)|(in @ X385 @ (setunion @ X384))))&((((in @ X388 @ (esk21_3 @ X387 @ X388 @ X389))|(X389)|~(in @ X388 @ (setunion @ X387)))&(((in @ (esk21_3 @ X387 @ X388 @ X389) @ X387)|(X389)|~(in @ X388 @ (setunion @ X387)))&(~(X389)|(X389)|~(in @ X388 @ (setunion @ X387)))))&((~(in @ X392 @ X391)|(in @ X392 @ (powerset @ (setunion @ X391))))&((((~(X393 @ X397)|((X397)=(esk23_1 @ X393))|((X393 @ (esk22_2 @ X393 @ X394))|~(X393 @ X394)))&(((X398)!=(esk23_1 @ X393))|(X393 @ X398)|((X393 @ (esk22_2 @ X393 @ X394))|~(X393 @ X394))))&((~(X393 @ X397)|((X397)=(esk23_1 @ X393))|(((X394)!=(esk22_2 @ X393 @ X394))|~(X393 @ X394)))&(((X398)!=(esk23_1 @ X393))|(X393 @ X398)|(((X394)!=(esk22_2 @ X393 @ X394))|~(X393 @ X394)))))&((((in @ (esk24_1 @ X399) @ X399)|((X399)=(emptyset)))&(($true)|((X399)=(emptyset))))&((~(in @ X401 @ (setadjoin @ X402 @ emptyset))|((X401)=(X402)))&(((esk25_0)!=(esk26_0))&(in @ esk26_0 @ (setadjoin @ esk25_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_74])])])])])])])).
% 0.11/0.29 thf(c_0_76, negated_conjecture, ![X2:$i, X3:$i]:((((X2)=(X3))|~((in @ X2 @ (setadjoin @ X3 @ emptyset))))), inference(split_conjunct,[status(thm)],[c_0_75])).
% 0.11/0.29 thf(c_0_77, negated_conjecture, (in @ esk26_0 @ (setadjoin @ esk25_0 @ emptyset)), inference(split_conjunct,[status(thm)],[c_0_75])).
% 0.11/0.29 thf(c_0_78, negated_conjecture, ((esk25_0)!=(esk26_0)), inference(split_conjunct,[status(thm)],[c_0_75])).
% 0.11/0.29 thf(c_0_79, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_76, c_0_77]), c_0_78]), ['proof']).
% 0.11/0.29 % SZS output end CNFRefutation
% 0.11/0.29 % Parsed axioms : 103
% 0.11/0.29 % Removed by relevancy pruning/SinE : 55
% 0.11/0.29 % Initial clauses : 96
% 0.11/0.29 % Removed in clause preprocessing : 5
% 0.11/0.29 % Initial clauses in saturation : 91
% 0.11/0.29 % Processed clauses : 36
% 0.11/0.29 % ...of these trivial : 1
% 0.11/0.29 % ...subsumed : 10
% 0.11/0.29 % ...remaining for further processing : 25
% 0.11/0.29 % Other redundant clauses eliminated : 2
% 0.11/0.29 % Clauses deleted for lack of memory : 0
% 0.11/0.29 % Backward-subsumed : 0
% 0.11/0.29 % Backward-rewritten : 2
% 0.11/0.29 % Generated clauses : 28
% 0.11/0.29 % ...of the previous two non-redundant : 18
% 0.11/0.29 % ...aggressively subsumed : 0
% 0.11/0.29 % Contextual simplify-reflections : 0
% 0.11/0.29 % Paramodulations : 26
% 0.11/0.29 % Factorizations : 0
% 0.11/0.29 % NegExts : 0
% 0.11/0.29 % Equation resolutions : 2
% 0.11/0.29 % Disequality decompositions : 0
% 0.11/0.29 % Total rewrite steps : 8
% 0.11/0.29 % ...of those cached : 1
% 0.11/0.29 % Propositional unsat checks : 0
% 0.11/0.29 % Propositional check models : 0
% 0.11/0.29 % Propositional check unsatisfiable : 0
% 0.11/0.29 % Propositional clauses : 0
% 0.11/0.29 % Propositional clauses after purity: 0
% 0.11/0.29 % Propositional unsat core size : 0
% 0.11/0.29 % Propositional preprocessing time : 0.000
% 0.11/0.29 % Propositional encoding time : 0.000
% 0.11/0.29 % Propositional solver time : 0.000
% 0.11/0.29 % Success case prop preproc time : 0.000
% 0.11/0.29 % Success case prop encoding time : 0.000
% 0.11/0.29 % Success case prop solver time : 0.000
% 0.11/0.29 % Current number of processed clauses : 21
% 0.11/0.29 % Positive orientable unit clauses : 9
% 0.11/0.29 % Positive unorientable unit clauses: 0
% 0.11/0.29 % Negative unit clauses : 2
% 0.11/0.29 % Non-unit-clauses : 10
% 0.11/0.29 % Current number of unprocessed clauses: 73
% 0.11/0.29 % ...number of literals in the above : 246
% 0.11/0.29 % Current number of archived formulas : 0
% 0.11/0.29 % Current number of archived clauses : 2
% 0.11/0.29 % Clause-clause subsumption calls (NU) : 30
% 0.11/0.29 % Rec. Clause-clause subsumption calls : 30
% 0.11/0.29 % Non-unit clause-clause subsumptions : 4
% 0.11/0.29 % Unit Clause-clause subsumption calls : 6
% 0.11/0.29 % Rewrite failures with RHS unbound : 0
% 0.11/0.29 % BW rewrite match attempts : 3
% 0.11/0.29 % BW rewrite match successes : 2
% 0.11/0.29 % Condensation attempts : 0
% 0.11/0.29 % Condensation successes : 0
% 0.11/0.29 % Termbank termtop insertions : 12237
% 0.11/0.29 % Search garbage collected termcells : 4782
% 0.11/0.29
% 0.11/0.29 % -------------------------------------------------
% 0.11/0.29 % User time : 0.010 s
% 0.11/0.29 % System time : 0.003 s
% 0.11/0.29 % Total time : 0.013 s
% 0.11/0.29 % Maximum resident set size: 4760 pages
% 0.11/0.29
% 0.11/0.29 % -------------------------------------------------
% 0.11/0.29 % User time : 0.013 s
% 0.11/0.29 % System time : 0.009 s
% 0.11/0.29 % Total time : 0.022 s
% 0.11/0.29 % Maximum resident set size: 4864 pages
% 0.11/0.29 % E exiting
%------------------------------------------------------------------------------