%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU527^1 : 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 : n004.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 0.34s 0.26s
% Output : CNFRefutation 0.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU527^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n004.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Sep 29 13:48:07 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running higher-order theorem proving
% 0.09/0.22 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.0CdHSHc1dF/E---3.1_1312910.p
% 0.34/0.26 % Version: 3.5.1-ho
% 0.34/0.26 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.34/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.34/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.34/0.26 % Starting sh5l with 300s (1) cores
% 0.34/0.26 % Starting new_bool_1 with 300s (1) cores
% 0.34/0.26 % Starting new_bool_2 with 300s (1) cores
% 0.34/0.26 % sh5l with pid 1312924 completed with status 0
% 0.34/0.26 % Result found by sh5l
% 0.34/0.26 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.34/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.34/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.34/0.26 % Starting sh5l with 300s (1) cores
% 0.34/0.26 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.34/0.26 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.34/0.26 % Search class: HGHSM-FFMS31-SHFSMSBN
% 0.34/0.26 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.34/0.26 % Starting SubtermCWHack with 31s (1) cores
% 0.34/0.26 % SubtermCWHack with pid 1312929 completed with status 0
% 0.34/0.26 % Result found by SubtermCWHack
% 0.34/0.26 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.34/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.34/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.34/0.26 % Starting sh5l with 300s (1) cores
% 0.34/0.26 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.34/0.26 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.34/0.26 % Search class: HGHSM-FFMS31-SHFSMSBN
% 0.34/0.26 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.34/0.26 % Starting SubtermCWHack with 31s (1) cores
% 0.34/0.26 % Preprocessing time : 0.002 s
% 0.34/0.26
% 0.34/0.26 % Proof found!
% 0.34/0.26 % SZS status Theorem
% 0.34/0.26 % SZS output start CNFRefutation
% 0.34/0.26 thf(decl_23, type, in: $i > $i > $o).
% 0.34/0.26 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.34/0.26 thf(decl_25, type, setextAx: $o).
% 0.34/0.26 thf(decl_26, type, emptyset: $i).
% 0.34/0.26 thf(decl_27, type, emptysetAx: $o).
% 0.34/0.26 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.34/0.26 thf(decl_29, type, setadjoinAx: $o).
% 0.34/0.26 thf(decl_30, type, powerset: $i > $i).
% 0.34/0.26 thf(decl_31, type, powersetAx: $o).
% 0.34/0.26 thf(decl_32, type, setunion: $i > $i).
% 0.34/0.26 thf(decl_33, type, setunionAx: $o).
% 0.34/0.26 thf(decl_34, type, omega: $i).
% 0.34/0.26 thf(decl_35, type, omega0Ax: $o).
% 0.34/0.26 thf(decl_36, type, omegaSAx: $o).
% 0.34/0.26 thf(decl_37, type, omegaIndAx: $o).
% 0.34/0.26 thf(decl_38, type, replAx: $o).
% 0.34/0.26 thf(decl_39, type, foundationAx: $o).
% 0.34/0.26 thf(decl_40, type, wellorderingAx: $o).
% 0.34/0.26 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.34/0.26 thf(decl_42, type, descrp: $o).
% 0.34/0.26 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.34/0.26 thf(decl_44, type, dsetconstrI: $o).
% 0.34/0.26 thf(decl_45, type, dsetconstrEL: $o).
% 0.34/0.26 thf(decl_46, type, dsetconstrER: $o).
% 0.34/0.26 thf(decl_47, type, exuE1: $o).
% 0.34/0.26 thf(decl_48, type, prop2set: $o > $i).
% 0.34/0.26 thf(decl_49, type, prop2setE: $o).
% 0.34/0.26 thf(decl_50, type, emptysetE: $o).
% 0.34/0.26 thf(decl_51, type, emptysetimpfalse: $o).
% 0.34/0.26 thf(decl_52, type, notinemptyset: $o).
% 0.34/0.26 thf(decl_53, type, exuE3e: $o).
% 0.34/0.26 thf(decl_54, type, setext: $o).
% 0.34/0.26 thf(decl_55, type, emptyI: $o).
% 0.34/0.26 thf(decl_56, type, noeltsimpempty: $o).
% 0.34/0.26 thf(decl_57, type, setbeta: $o).
% 0.34/0.26 thf(decl_58, type, nonempty: $i > $o).
% 0.34/0.26 thf(decl_59, type, nonemptyE1: $o).
% 0.34/0.26 thf(decl_60, type, nonemptyI: $o).
% 0.34/0.26 thf(decl_61, type, nonemptyI1: $o).
% 0.34/0.26 thf(decl_62, type, setadjoinIL: $o).
% 0.34/0.26 thf(decl_63, type, emptyinunitempty: $o).
% 0.34/0.26 thf(decl_64, type, setadjoinIR: $o).
% 0.34/0.26 thf(decl_65, type, setadjoinE: $o).
% 0.34/0.26 thf(decl_66, type, setadjoinOr: $o).
% 0.34/0.26 thf(decl_67, type, setoftrueEq: $o).
% 0.34/0.26 thf(decl_68, type, powersetI: $o).
% 0.34/0.26 thf(decl_69, type, emptyinPowerset: $o).
% 0.34/0.26 thf(decl_70, type, emptyInPowerset: $o).
% 0.34/0.26 thf(decl_71, type, powersetE: $o).
% 0.34/0.26 thf(decl_72, type, setunionI: $o).
% 0.34/0.26 thf(decl_73, type, setunionE: $o).
% 0.34/0.26 thf(decl_74, type, subPowSU: $o).
% 0.34/0.26 thf(decl_75, type, exuE2: $o).
% 0.34/0.26 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.34/0.26 thf(decl_77, type, epred1_0: $o).
% 0.34/0.26 thf(decl_78, type, esk1_2: $i > $i > $i).
% 0.34/0.26 thf(decl_79, type, esk2_2: $i > $i > $i).
% 0.34/0.26 thf(decl_80, type, esk3_2: $i > $i > $i).
% 0.34/0.26 thf(decl_81, type, esk4_1: $i > $i).
% 0.34/0.26 thf(decl_82, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.34/0.26 thf(decl_83, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.34/0.26 thf(decl_84, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.34/0.26 thf(decl_85, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.34/0.26 thf(decl_86, type, esk9_1: $i > $i).
% 0.34/0.26 thf(decl_87, type, esk10_2: ($i > $o) > $i > $i).
% 0.34/0.26 thf(decl_88, type, esk11_2: ($i > $o) > $i > $i).
% 0.34/0.26 thf(decl_89, type, esk12_1: ($i > $o) > $i).
% 0.34/0.26 thf(decl_90, type, esk13_2: ($i > $o) > $i > $i).
% 0.34/0.26 thf(decl_91, type, esk14_1: ($i > $o) > $i).
% 0.34/0.26 thf(decl_92, type, esk15_2: $i > $i > $i).
% 0.34/0.26 thf(decl_93, type, esk16_2: $i > $i > $i).
% 0.34/0.26 thf(decl_94, type, esk17_1: $i > $i).
% 0.34/0.26 thf(decl_95, type, esk18_1: $i > $i).
% 0.34/0.26 thf(decl_96, type, esk19_1: $i > $i).
% 0.34/0.26 thf(decl_97, type, esk20_2: $i > $i > $i).
% 0.34/0.26 thf(decl_98, type, esk21_3: $i > $i > $o > $i).
% 0.34/0.26 thf(decl_99, type, esk22_2: ($i > $o) > $i > $i).
% 0.34/0.26 thf(decl_100, type, esk23_1: ($i > $o) > $i).
% 0.34/0.26 thf(decl_101, type, esk24_1: $i > $i).
% 0.34/0.26 thf(decl_102, type, esk25_0: $i).
% 0.34/0.26 thf(decl_103, type, esk26_0: $i).
% 0.34/0.26 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', nonempty)).
% 0.34/0.26 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.0CdHSHc1dF/E---3.1_1312910.p', exuE2)).
% 0.34/0.26 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', exu)).
% 0.34/0.26 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', replAx)).
% 0.34/0.26 thf(prop2set, axiom, ((prop2set)=(^[X10:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[X2:$i]:((X10)))))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', prop2set)).
% 0.34/0.26 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', exuE1)).
% 0.34/0.26 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', descrp)).
% 0.34/0.26 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', exuE3e)).
% 0.34/0.26 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', nonemptyI)).
% 0.34/0.26 thf(uniqinunit, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', uniqinunit)).
% 0.34/0.26 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', nonemptyImpWitness)).
% 0.34/0.26 thf(prop2setE, axiom, ((prop2setE)<=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', prop2setE)).
% 0.34/0.26 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', dsetconstrER)).
% 0.34/0.26 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', dsetconstrEL)).
% 0.34/0.26 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', dsetconstrI)).
% 0.34/0.26 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', nonemptyE1)).
% 0.34/0.26 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', setbeta)).
% 0.34/0.26 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', setoftrueEq)).
% 0.34/0.26 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', nonemptyI1)).
% 0.34/0.26 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12))))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', emptysetE)).
% 0.34/0.26 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', setadjoinOr)).
% 0.34/0.26 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', subPowSU)).
% 0.34/0.26 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X13:$o]:(((((X3)=(X2))=>(X13))=>(((in @ X3 @ X4)=>(X13))=>(X13))))))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', setadjoinE)).
% 0.34/0.26 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', setadjoinIR)).
% 0.34/0.26 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.0CdHSHc1dF/E---3.1_1312910.p', foundationAx)).
% 0.34/0.26 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', emptyinunitempty)).
% 0.34/0.26 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', setadjoinIL)).
% 0.34/0.26 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', wellorderingAx)).
% 0.34/0.26 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.0CdHSHc1dF/E---3.1_1312910.p', omegaIndAx)).
% 0.34/0.26 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', omegaSAx)).
% 0.34/0.26 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', setadjoinAx)).
% 0.34/0.26 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', emptysetimpfalse)).
% 0.34/0.26 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', noeltsimpempty)).
% 0.34/0.26 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', emptyI)).
% 0.34/0.26 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.0CdHSHc1dF/E---3.1_1312910.p', setext)).
% 0.34/0.26 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', notinemptyset)).
% 0.34/0.26 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', setunionI)).
% 0.34/0.26 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', powersetE)).
% 0.34/0.26 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', emptyInPowerset)).
% 0.34/0.26 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', emptyinPowerset)).
% 0.34/0.26 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', powersetI)).
% 0.34/0.26 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.0CdHSHc1dF/E---3.1_1312910.p', setunionE)).
% 0.34/0.26 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', omega0Ax)).
% 0.34/0.26 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', setunionAx)).
% 0.34/0.26 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', powersetAx)).
% 0.34/0.26 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', emptysetAx)).
% 0.34/0.26 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.0CdHSHc1dF/E---3.1_1312910.p', setextAx)).
% 0.34/0.26 thf(c_0_47, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.34/0.26 thf(c_0_48, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.34/0.26 thf(c_0_49, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.34/0.26 thf(c_0_50, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.34/0.26 thf(c_0_51, plain, ((prop2set)=(^[Z0:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[Z1:$i]:((Z0)))))), inference(fof_simplification,[status(thm)],[prop2set])).
% 0.34/0.26 thf(c_0_52, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.34/0.26 thf(c_0_53, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.34/0.26 thf(c_0_54, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.34/0.26 thf(c_0_55, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.34/0.26 thf(c_0_56, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3)))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[uniqinunit])).
% 0.34/0.26 thf(c_0_57, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_47])).
% 0.34/0.26 thf(c_0_58, plain, ((exuE2)=(![X1:$i > $o]:((((?[X145:$i]:(((((X1 @ X145)))&(![X146:$i]:(((((X1 @ X146)))=>(((X145)=(X146))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_48, c_0_49])).
% 0.34/0.26 thf(c_0_59, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X137:$i]:(((((X6 @ X2 @ X137)))&(![X138:$i]:(((((X6 @ X2 @ X138)))=>(((X137)=(X138)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_50, c_0_49])).
% 0.34/0.26 thf(c_0_60, axiom, ((prop2setE)=(![X11:$o, X2:$i]:((((in @ X2 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:(((X11)))))))=>((X11)))))), inference(apply_def,[status(thm)],[prop2setE, c_0_51])).
% 0.34/0.26 thf(c_0_61, plain, ((exuE1)=(![X1:$i > $o]:((((?[X141:$i]:(((((X1 @ X141)))&(![X142:$i]:(((((X1 @ X142)))=>(((X141)=(X142))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_52, c_0_49])).
% 0.34/0.26 thf(c_0_62, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.34/0.26 thf(c_0_63, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.34/0.26 thf(c_0_64, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.34/0.26 thf(c_0_65, plain, ((descrp)=(![X1:$i > $o]:((((?[X139:$i]:(((((X1 @ X139)))&(![X140:$i]:(((((X1 @ X140)))=>(((X139)=(X140))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_53, c_0_49])).
% 0.34/0.26 thf(c_0_66, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_47])).
% 0.34/0.26 thf(c_0_67, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.34/0.26 thf(c_0_68, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X143:$i]:(((((X1 @ X143)))&(![X144:$i]:(((((X1 @ X144)))=>(((X143)=(X144))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_54, c_0_49])).
% 0.34/0.26 thf(c_0_69, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_55, c_0_47])).
% 0.34/0.26 thf(c_0_70, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.34/0.26 thf(c_0_71, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_47])).
% 0.34/0.26 thf(c_0_72, plain, ((epred1_0)<=>![X176:$i]:(?[X177:$i]:((((![X178:$i]:(((in @ X178 @ X177)=>![X179:$i]:(((in @ X179 @ X178)=>(in @ X179 @ X176)))))&![X180:$i, X181:$i]:((((in @ X180 @ X176)&(in @ X181 @ X176))=>(![X182:$i]:(((in @ X182 @ X177)=>((in @ X180 @ X182)<=>(in @ X181 @ X182))))=>((X180)=(X181))))))&![X183:$i, X184:$i]:((((in @ X183 @ X177)&(in @ X184 @ X177))=>(![X185:$i]:(((in @ X185 @ X183)=>(in @ X185 @ X184)))|![X186:$i]:(((in @ X186 @ X184)=>(in @ X186 @ X183)))))))&![X187:$i]:(((![X188:$i]:(((in @ X188 @ X187)=>(in @ X188 @ X176)))&?[X189:$i]:((in @ X189 @ X187)))=>?[X190:$i, X191:$i]:(((((in @ X190 @ X177)&(in @ X191 @ X187))&~(?[X192:$i]:(((in @ X192 @ X190)&(in @ X192 @ X187)))))&![X193:$i]:(((in @ X193 @ X177)=>(![X194:$i]:(((in @ X194 @ X193)=>(in @ X194 @ X190)))|(in @ X191 @ X193)))))))))))), introduced(definition)).
% 0.34/0.26 thf(c_0_73, negated_conjecture, ~((![X147:$i, X148:$i]:((![X149:$i]:(((in @ X149 @ X147)<=>(in @ X149 @ X148)))=>((X147)=(X148))))=>(![X150:$i]:(~(in @ X150 @ emptyset))=>(![X151:$i, X152:$i, X153:$i]:(((in @ X153 @ (setadjoin @ X151 @ X152))<=>(((X153)=(X151))|(in @ X153 @ X152))))=>(![X154:$i, X155:$i]:(((in @ X155 @ (powerset @ X154))<=>![X156:$i]:(((in @ X156 @ X155)=>(in @ X156 @ X154)))))=>(![X157:$i, X158:$i]:(((in @ X158 @ (setunion @ X157))<=>?[X159:$i]:(((in @ X158 @ X159)&(in @ X159 @ X157)))))=>((in @ emptyset @ omega)=>(![X160:$i]:(((in @ X160 @ omega)=>(in @ (setadjoin @ X160 @ X160) @ omega)))=>(![X161:$i]:((((in @ emptyset @ X161)&![X162:$i]:((((in @ X162 @ omega)&(in @ X162 @ X161))=>(in @ (setadjoin @ X162 @ X162) @ X161))))=>![X163:$i]:(((in @ X163 @ omega)=>(in @ X163 @ X161)))))=>(![X164:$i > $i > $o, X165:$i]:((![X166:$i]:(((in @ X166 @ X165)=>?[X167:$i]:(((X164 @ X166 @ X167)&![X168:$i]:(((X164 @ X166 @ X168)=>((X167)=(X168))))))))=>?[X169:$i]:(![X170:$i]:(((in @ X170 @ X169)<=>?[X171:$i]:(((in @ X171 @ X165)&(X164 @ X171 @ X170))))))))=>(![X172:$i]:((?[X173:$i]:((in @ X173 @ X172))=>?[X174:$i]:(((in @ X174 @ X172)&~(?[X175:$i]:(((in @ X175 @ X174)&(in @ X175 @ X172))))))))=>((epred1_0)=>(![X195:$i > $o]:((?[X196:$i]:(((X195 @ X196)&![X197:$i]:(((X195 @ X197)=>((X196)=(X197))))))=>(X195 @ (descr @ (^[Z0:$i]:(X195 @ Z0))))))=>(![X198:$i, X199:$i > $o, X200:$i]:(((in @ X200 @ X198)=>((X199 @ X200)=>(in @ X200 @ (dsetconstr @ X198 @ X199)))))=>(![X201:$i, X202:$i > $o, X203:$i]:(((in @ X203 @ (dsetconstr @ X201 @ X202))=>(in @ X203 @ X201)))=>(![X204:$i, X205:$i > $o, X206:$i]:(((in @ X206 @ (dsetconstr @ X204 @ X205))=>(X205 @ X206)))=>(![X207:$i > $o]:((?[X208:$i]:(((X207 @ X208)&![X209:$i]:(((X207 @ X209)=>((X208)=(X209))))))=>?[X210:$i]:(((X207 @ X210)&![X211:$i]:(((X207 @ X211)=>((X210)=(X211))))))))=>(![X212:$o, X213:$i]:(((in @ X213 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X212)))))=>(X212)))=>(![X214:$i]:(((in @ X214 @ emptyset)=>![X215:$o]:((X215))))=>(![X216:$i]:(((in @ X216 @ emptyset)=>~($true)))=>(![X217:$i]:(~(in @ X217 @ emptyset))=>(![X218:$i > $o]:((?[X219:$i]:(((X218 @ X219)&![X220:$i]:(((X218 @ X220)=>((X219)=(X220))))))=>?[X221:$i]:((X218 @ X221))))=>(![X222:$i, X223:$i]:((![X224:$i]:(((in @ X224 @ X222)=>(in @ X224 @ X223)))=>(![X225:$i]:(((in @ X225 @ X223)=>(in @ X225 @ X222)))=>((X222)=(X223)))))=>(![X226:$i]:((![X227:$i]:(~(in @ X227 @ X226))=>((X226)=(emptyset))))=>(![X228:$i]:((![X229:$i]:(~(in @ X229 @ X228))=>((X228)=(emptyset))))=>(![X230:$i, X231:$i > $o, X232:$i]:(((in @ X232 @ X230)=>((in @ X232 @ (dsetconstr @ X230 @ X231))<=>(X231 @ X232))))=>(![X233:$i]:((((X233)!=(emptyset))=>?[X234:$i]:((in @ X234 @ X233))))=>(![X235:$i, X236:$i > $o, X237:$i]:(((in @ X237 @ X235)=>((X236 @ X237)=>((dsetconstr @ X235 @ X236)!=(emptyset)))))=>(![X238:$i]:((?[X239:$i]:((in @ X239 @ X238))=>((X238)!=(emptyset))))=>(![X240:$i, X241:$i]:((in @ X240 @ (setadjoin @ X240 @ X241)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X242:$i, X243:$i, X244:$i]:(((in @ X244 @ X243)=>(in @ X244 @ (setadjoin @ X242 @ X243))))=>(![X245:$i, X246:$i, X247:$i]:(((in @ X247 @ (setadjoin @ X245 @ X246))=>![X248:$o]:(((((X247)=(X245))=>(X248))=>(((in @ X247 @ X246)=>(X248))=>(X248))))))=>(![X249:$i, X250:$i, X251:$i]:(((in @ X251 @ (setadjoin @ X249 @ X250))=>(((X251)=(X249))|(in @ X251 @ X250))))=>(![X252:$i]:(((dsetconstr @ X252 @ (^[Z0:$i]:($true)))=(X252)))=>(![X253:$i, X254:$i]:((![X255:$i]:(((in @ X255 @ X254)=>(in @ X255 @ X253)))=>(in @ X254 @ (powerset @ X253))))=>(![X256:$i]:((in @ emptyset @ (powerset @ X256)))=>(![X257:$i]:((in @ emptyset @ (powerset @ X257)))=>(![X258:$i, X259:$i, X260:$i]:(((in @ X259 @ (powerset @ X258))=>((in @ X260 @ X259)=>(in @ X260 @ X258))))=>(![X261:$i, X262:$i, X263:$i]:(((in @ X262 @ X263)=>((in @ X263 @ X261)=>(in @ X262 @ (setunion @ X261)))))=>(![X264:$i, X265:$i]:(((in @ X265 @ (setunion @ X264))=>![X266:$o]:((![X267:$i]:(((in @ X265 @ X267)=>((in @ X267 @ X264)=>(X266))))=>(X266)))))=>(![X268:$i, X269:$i]:(((in @ X269 @ X268)=>(in @ X269 @ (powerset @ (setunion @ X268)))))=>(![X270:$i > $o]:((?[X271:$i]:(((X270 @ X271)&![X272:$i]:(((X270 @ X272)=>((X271)=(X272))))))=>?[X273:$i]:(![X274:$i]:(((X270 @ X274)<=>((X274)=(X273)))))))=>(![X275:$i]:((((X275)!=(emptyset))=>?[X276:$i]:(((in @ X276 @ X275)&$true))))=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3)))))))))))))))))))))))))))))))))))))))))))))))), 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_56, emptysetE]), setadjoinOr]), subPowSU]), c_0_57]), c_0_58]), setadjoinE]), setadjoinIR]), foundationAx]), emptyinunitempty]), c_0_59]), setadjoinIL]), wellorderingAx]), omegaIndAx]), omegaSAx]), setadjoinAx]), c_0_60]), c_0_61]), c_0_62]), c_0_63]), c_0_64]), c_0_65]), emptysetimpfalse]), c_0_66]), c_0_67]), noeltsimpempty]), emptyI]), setext]), c_0_68]), notinemptyset]), c_0_69]), setunionI]), powersetE]), emptyInPowerset]), emptyinPowerset]), powersetI]), c_0_70]), c_0_71]), setunionE]), omega0Ax]), setunionAx]), powersetAx]), emptysetAx]), setextAx])])]), c_0_72])).
% 0.34/0.26 thf(c_0_74, negated_conjecture, ![X277:$i, X278:$i, X280:$i, X281:$i, X282:$i, X283:$i, X284:$i, X285:$i, X286:$i, X287:$i, X288:$i, X290:$i, X291:$i, X293:$i, X294:$i, X295:$i, X296:$i, X297:$i, X299:$i, X300:$i > $i > $o, X301:$i, X303:$i, X306:$i, X308:$i, X309:$i, X310:$i, X311:$i, X313:$i, X314:$i > $o, X315:$i, X317:$i, X318:$i > $o, X319:$i, X320:$i, X321:$i > $o, X322:$i, X323:$i, X324:$i > $o, X325:$i, X326:$i > $o, X327:$i, X330:$i, X331:$o, X332:$i, X333:$i, X334:$o, X335:$i, X336:$i, X337:$i > $o, X338:$i, X341:$i, X342:$i, X345:$i, X347:$i, X349:$i, X350:$i > $o, X351:$i, X352:$i, X354:$i, X355:$i > $o, X356:$i, X357:$i, X358:$i, X359:$i, X360:$i, X361:$i, X362:$i, X363:$i, X364:$i, X365:$i, X366:$i, X367:$o, X368:$i, X369:$i, X370:$i, X371:$i, X372:$i, X373:$i, X375:$i, X376:$i, X377:$i, X378:$i, X379:$i, X380:$i, X381:$i, X382:$i, X383:$i, X384:$i, X385:$o, X387:$i, X388:$i, X389:$i > $o, X390:$i, X393:$i, X394:$i, X395:$i]:((((~(in @ (esk1_2 @ X277 @ X278) @ X277)|~(in @ (esk1_2 @ X277 @ X278) @ X278)|((X277)=(X278)))&((in @ (esk1_2 @ X277 @ X278) @ X277)|(in @ (esk1_2 @ X277 @ X278) @ X278)|((X277)=(X278))))&(~(in @ X280 @ emptyset)&(((~(in @ X283 @ (setadjoin @ X281 @ X282))|(((X283)=(X281))|(in @ X283 @ X282)))&((((X283)!=(X281))|(in @ X283 @ (setadjoin @ X281 @ X282)))&(~(in @ X283 @ X282)|(in @ X283 @ (setadjoin @ X281 @ X282)))))&(((~(in @ X285 @ (powerset @ X284))|(~(in @ X286 @ X285)|(in @ X286 @ X284)))&(((in @ (esk2_2 @ X287 @ X288) @ X288)|(in @ X288 @ (powerset @ X287)))&(~(in @ (esk2_2 @ X287 @ X288) @ X287)|(in @ X288 @ (powerset @ X287)))))&(((((in @ X291 @ (esk3_2 @ X290 @ X291))|~(in @ X291 @ (setunion @ X290)))&((in @ (esk3_2 @ X290 @ X291) @ X290)|~(in @ X291 @ (setunion @ X290))))&(~(in @ X294 @ X295)|~(in @ X295 @ X293)|(in @ X294 @ (setunion @ X293))))&((in @ emptyset @ omega)&((~(in @ X296 @ omega)|(in @ (setadjoin @ X296 @ X296) @ omega))&(((((in @ (esk4_1 @ X297) @ omega)|~(in @ emptyset @ X297)|(~(in @ X299 @ omega)|(in @ X299 @ X297)))&((in @ (esk4_1 @ X297) @ X297)|~(in @ emptyset @ X297)|(~(in @ X299 @ omega)|(in @ X299 @ X297))))&(~(in @ (setadjoin @ (esk4_1 @ X297) @ (esk4_1 @ X297)) @ X297)|~(in @ emptyset @ X297)|(~(in @ X299 @ omega)|(in @ X299 @ X297))))&((((((in @ (esk8_3 @ X300 @ X301 @ X306) @ X301)|~(in @ X306 @ (esk7_2 @ X300 @ X301))|(in @ (esk5_2 @ X300 @ X301) @ X301))&((X300 @ (esk8_3 @ X300 @ X301 @ X306) @ X306)|~(in @ X306 @ (esk7_2 @ X300 @ X301))|(in @ (esk5_2 @ X300 @ X301) @ X301)))&(~(in @ X309 @ X301)|~(X300 @ X309 @ X308)|(in @ X308 @ (esk7_2 @ X300 @ X301))|(in @ (esk5_2 @ X300 @ X301) @ X301)))&(((((in @ (esk8_3 @ X300 @ X301 @ X306) @ X301)|~(in @ X306 @ (esk7_2 @ X300 @ X301))|((X300 @ (esk5_2 @ X300 @ X301) @ (esk6_3 @ X300 @ X301 @ X303))|~(X300 @ (esk5_2 @ X300 @ X301) @ X303)))&((X300 @ (esk8_3 @ X300 @ X301 @ X306) @ X306)|~(in @ X306 @ (esk7_2 @ X300 @ X301))|((X300 @ (esk5_2 @ X300 @ X301) @ (esk6_3 @ X300 @ X301 @ X303))|~(X300 @ (esk5_2 @ X300 @ X301) @ X303))))&(~(in @ X309 @ X301)|~(X300 @ X309 @ X308)|(in @ X308 @ (esk7_2 @ X300 @ X301))|((X300 @ (esk5_2 @ X300 @ X301) @ (esk6_3 @ X300 @ X301 @ X303))|~(X300 @ (esk5_2 @ X300 @ X301) @ X303))))&((((in @ (esk8_3 @ X300 @ X301 @ X306) @ X301)|~(in @ X306 @ (esk7_2 @ X300 @ X301))|(((X303)!=(esk6_3 @ X300 @ X301 @ X303))|~(X300 @ (esk5_2 @ X300 @ X301) @ X303)))&((X300 @ (esk8_3 @ X300 @ X301 @ X306) @ X306)|~(in @ X306 @ (esk7_2 @ X300 @ X301))|(((X303)!=(esk6_3 @ X300 @ X301 @ X303))|~(X300 @ (esk5_2 @ X300 @ X301) @ X303))))&(~(in @ X309 @ X301)|~(X300 @ X309 @ X308)|(in @ X308 @ (esk7_2 @ X300 @ X301))|(((X303)!=(esk6_3 @ X300 @ X301 @ X303))|~(X300 @ (esk5_2 @ X300 @ X301) @ X303))))))&((((in @ (esk9_1 @ X310) @ X310)|~(in @ X311 @ X310))&(~(in @ X313 @ (esk9_1 @ X310))|~(in @ X313 @ X310)|~(in @ X311 @ X310)))&((epred1_0)&((((X314 @ (esk10_2 @ X314 @ X315))|~(X314 @ X315)|(X314 @ (descr @ X314)))&(((X315)!=(esk10_2 @ X314 @ X315))|~(X314 @ X315)|(X314 @ (descr @ X314))))&((~(in @ X319 @ X317)|(~(X318 @ X319)|(in @ X319 @ (dsetconstr @ X317 @ X318))))&((~(in @ X322 @ (dsetconstr @ X320 @ X321))|(in @ X322 @ X320))&((~(in @ X325 @ (dsetconstr @ X323 @ X324))|(X324 @ X325))&(((((X326 @ (esk12_1 @ X326))|((X326 @ (esk11_2 @ X326 @ X327))|~(X326 @ X327)))&(~(X326 @ X330)|((esk12_1 @ X326)=(X330))|((X326 @ (esk11_2 @ X326 @ X327))|~(X326 @ X327))))&(((X326 @ (esk12_1 @ X326))|(((X327)!=(esk11_2 @ X326 @ X327))|~(X326 @ X327)))&(~(X326 @ X330)|((esk12_1 @ X326)=(X330))|(((X327)!=(esk11_2 @ X326 @ X327))|~(X326 @ X327)))))&((~(in @ X332 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X331)))))|(X331))&((~(in @ X333 @ emptyset)|(X334))&((~(in @ X335 @ emptyset)|~($true))&(~(in @ X336 @ emptyset)&((((X337 @ (esk13_2 @ X337 @ X338))|~(X337 @ X338)|(X337 @ (esk14_1 @ X337)))&(((X338)!=(esk13_2 @ X337 @ X338))|~(X337 @ X338)|(X337 @ (esk14_1 @ X337))))&(((((in @ (esk16_2 @ X341 @ X342) @ X342)|((X341)=(X342))|(in @ (esk15_2 @ X341 @ X342) @ X341))&(~(in @ (esk16_2 @ X341 @ X342) @ X341)|((X341)=(X342))|(in @ (esk15_2 @ X341 @ X342) @ X341)))&(((in @ (esk16_2 @ X341 @ X342) @ X342)|((X341)=(X342))|~(in @ (esk15_2 @ X341 @ X342) @ X342))&(~(in @ (esk16_2 @ X341 @ X342) @ X341)|((X341)=(X342))|~(in @ (esk15_2 @ X341 @ X342) @ X342))))&(((in @ (esk17_1 @ X345) @ X345)|((X345)=(emptyset)))&(((in @ (esk18_1 @ X347) @ X347)|((X347)=(emptyset)))&(((~(in @ X351 @ (dsetconstr @ X349 @ X350))|(X350 @ X351)|~(in @ X351 @ X349))&(~(X350 @ X351)|(in @ X351 @ (dsetconstr @ X349 @ X350))|~(in @ X351 @ X349)))&((((X352)=(emptyset))|(in @ (esk19_1 @ X352) @ X352))&((~(in @ X356 @ X354)|(~(X355 @ X356)|((dsetconstr @ X354 @ X355)!=(emptyset))))&((~(in @ X358 @ X357)|((X357)!=(emptyset)))&((in @ X359 @ (setadjoin @ X359 @ X360))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X363 @ X362)|(in @ X363 @ (setadjoin @ X361 @ X362)))&(((((in @ X366 @ X365)|(X367)|((X366)=(X364))|~(in @ X366 @ (setadjoin @ X364 @ X365)))&(~(X367)|(X367)|((X366)=(X364))|~(in @ X366 @ (setadjoin @ X364 @ X365))))&(((in @ X366 @ X365)|(X367)|~(X367)|~(in @ X366 @ (setadjoin @ X364 @ X365)))&(~(X367)|(X367)|~(X367)|~(in @ X366 @ (setadjoin @ X364 @ X365)))))&((~(in @ X370 @ (setadjoin @ X368 @ X369))|(((X370)=(X368))|(in @ X370 @ X369)))&(((dsetconstr @ X371 @ (^[Z0:$i]:($true)))=(X371))&((((in @ (esk20_2 @ X372 @ X373) @ X373)|(in @ X373 @ (powerset @ X372)))&(~(in @ (esk20_2 @ X372 @ X373) @ X372)|(in @ X373 @ (powerset @ X372))))&((in @ emptyset @ (powerset @ X375))&((in @ emptyset @ (powerset @ X376))&((~(in @ X378 @ (powerset @ X377))|(~(in @ X379 @ X378)|(in @ X379 @ X377)))&((~(in @ X381 @ X382)|(~(in @ X382 @ X380)|(in @ X381 @ (setunion @ X380))))&((((in @ X384 @ (esk21_3 @ X383 @ X384 @ X385))|(X385)|~(in @ X384 @ (setunion @ X383)))&(((in @ (esk21_3 @ X383 @ X384 @ X385) @ X383)|(X385)|~(in @ X384 @ (setunion @ X383)))&(~(X385)|(X385)|~(in @ X384 @ (setunion @ X383)))))&((~(in @ X388 @ X387)|(in @ X388 @ (powerset @ (setunion @ X387))))&((((~(X389 @ X393)|((X393)=(esk23_1 @ X389))|((X389 @ (esk22_2 @ X389 @ X390))|~(X389 @ X390)))&(((X394)!=(esk23_1 @ X389))|(X389 @ X394)|((X389 @ (esk22_2 @ X389 @ X390))|~(X389 @ X390))))&((~(X389 @ X393)|((X393)=(esk23_1 @ X389))|(((X390)!=(esk22_2 @ X389 @ X390))|~(X389 @ X390)))&(((X394)!=(esk23_1 @ X389))|(X389 @ X394)|(((X390)!=(esk22_2 @ X389 @ X390))|~(X389 @ X390)))))&((((in @ (esk24_1 @ X395) @ X395)|((X395)=(emptyset)))&(($true)|((X395)=(emptyset))))&((in @ esk25_0 @ (setadjoin @ esk26_0 @ emptyset))&((esk25_0)!=(esk26_0))))))))))))))))))))))))))))))))))))))))))))))), 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_73])])])])])])])).
% 0.34/0.26 thf(c_0_75, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ X3)|((X2)=(X4))|~((in @ X2 @ (setadjoin @ X4 @ X3))))), inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_74])])])).
% 0.34/0.26 thf(c_0_76, negated_conjecture, (in @ esk25_0 @ (setadjoin @ esk26_0 @ emptyset)), inference(split_conjunct,[status(thm)],[c_0_74])).
% 0.34/0.26 thf(c_0_77, negated_conjecture, ((esk25_0)!=(esk26_0)), inference(split_conjunct,[status(thm)],[c_0_74])).
% 0.34/0.26 thf(c_0_78, negated_conjecture, ![X2:$i]:(~((in @ X2 @ emptyset))), inference(split_conjunct,[status(thm)],[c_0_74])).
% 0.34/0.26 thf(c_0_79, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_75, c_0_76]), c_0_77]), c_0_78]), ['proof']).
% 0.34/0.26 % SZS output end CNFRefutation
% 0.34/0.26 % Parsed axioms : 101
% 0.34/0.26 % Removed by relevancy pruning/SinE : 54
% 0.34/0.26 % Initial clauses : 95
% 0.34/0.26 % Removed in clause preprocessing : 5
% 0.34/0.26 % Initial clauses in saturation : 90
% 0.34/0.26 % Processed clauses : 150
% 0.34/0.26 % ...of these trivial : 1
% 0.34/0.26 % ...subsumed : 66
% 0.34/0.26 % ...remaining for further processing : 83
% 0.34/0.26 % Other redundant clauses eliminated : 4
% 0.34/0.26 % Clauses deleted for lack of memory : 0
% 0.34/0.26 % Backward-subsumed : 0
% 0.34/0.26 % Backward-rewritten : 4
% 0.34/0.26 % Generated clauses : 384
% 0.34/0.26 % ...of the previous two non-redundant : 323
% 0.34/0.26 % ...aggressively subsumed : 0
% 0.34/0.26 % Contextual simplify-reflections : 0
% 0.34/0.26 % Paramodulations : 380
% 0.34/0.26 % Factorizations : 0
% 0.34/0.26 % NegExts : 0
% 0.34/0.26 % Equation resolutions : 4
% 0.34/0.26 % Disequality decompositions : 0
% 0.34/0.26 % Total rewrite steps : 61
% 0.34/0.26 % ...of those cached : 47
% 0.34/0.26 % Propositional unsat checks : 0
% 0.34/0.26 % Propositional check models : 0
% 0.34/0.26 % Propositional check unsatisfiable : 0
% 0.34/0.26 % Propositional clauses : 0
% 0.34/0.26 % Propositional clauses after purity: 0
% 0.34/0.26 % Propositional unsat core size : 0
% 0.34/0.26 % Propositional preprocessing time : 0.000
% 0.34/0.26 % Propositional encoding time : 0.000
% 0.34/0.26 % Propositional solver time : 0.000
% 0.34/0.26 % Success case prop preproc time : 0.000
% 0.34/0.26 % Success case prop encoding time : 0.000
% 0.34/0.26 % Success case prop solver time : 0.000
% 0.34/0.26 % Current number of processed clauses : 76
% 0.34/0.26 % Positive orientable unit clauses : 12
% 0.34/0.26 % Positive unorientable unit clauses: 0
% 0.34/0.26 % Negative unit clauses : 2
% 0.34/0.26 % Non-unit-clauses : 62
% 0.34/0.26 % Current number of unprocessed clauses: 255
% 0.34/0.26 % ...number of literals in the above : 720
% 0.34/0.26 % Current number of archived formulas : 0
% 0.34/0.26 % Current number of archived clauses : 4
% 0.34/0.26 % Clause-clause subsumption calls (NU) : 543
% 0.34/0.26 % Rec. Clause-clause subsumption calls : 430
% 0.34/0.26 % Non-unit clause-clause subsumptions : 46
% 0.34/0.26 % Unit Clause-clause subsumption calls : 10
% 0.34/0.26 % Rewrite failures with RHS unbound : 0
% 0.34/0.26 % BW rewrite match attempts : 10
% 0.34/0.26 % BW rewrite match successes : 4
% 0.34/0.26 % Condensation attempts : 0
% 0.34/0.26 % Condensation successes : 0
% 0.34/0.26 % Termbank termtop insertions : 16429
% 0.34/0.26 % Search garbage collected termcells : 4723
% 0.34/0.26
% 0.34/0.26 % -------------------------------------------------
% 0.34/0.26 % User time : 0.015 s
% 0.34/0.26 % System time : 0.006 s
% 0.34/0.26 % Total time : 0.021 s
% 0.34/0.26 % Maximum resident set size: 4760 pages
% 0.34/0.26
% 0.34/0.26 % -------------------------------------------------
% 0.34/0.26 % User time : 0.016 s
% 0.34/0.26 % System time : 0.009 s
% 0.34/0.26 % Total time : 0.025 s
% 0.34/0.26 % Maximum resident set size: 4864 pages
% 0.34/0.26 % E exiting
%------------------------------------------------------------------------------