%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU530^1 : 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 : n012.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 08:26:36 AM UTC 2026
% Result : Theorem 0.09s 0.16s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU530^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 13:48:03 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.12 Running higher-order theorem proving
% 0.09/0.13 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.5FUHNDqpGy/E---3.1_129301.p
% 0.09/0.16 % Version: 3.5.1-ho
% 0.09/0.16 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.09/0.16 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.16 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.16 % Starting sh5l with 300s (1) cores
% 0.09/0.16 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.16 % Starting new_bool_2 with 300s (1) cores
% 0.09/0.16 % new_bool_2 with pid 129336 completed with status 0
% 0.09/0.16 % Result found by new_bool_2
% 0.09/0.16 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.09/0.16 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.16 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.16 % Starting sh5l with 300s (1) cores
% 0.09/0.16 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.16 % Starting new_bool_2 with 300s (1) cores
% 0.09/0.16 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.09/0.16 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.09/0.16 % Search class: HGHSM-FFMS31-SHFSMSBN
% 0.09/0.16 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.16 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.16 % SubtermCWHack with pid 129341 completed with status 0
% 0.09/0.16 % Result found by SubtermCWHack
% 0.09/0.16 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.09/0.16 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.16 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.16 % Starting sh5l with 300s (1) cores
% 0.09/0.16 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.16 % Starting new_bool_2 with 300s (1) cores
% 0.09/0.16 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.09/0.16 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.09/0.16 % Search class: HGHSM-FFMS31-SHFSMSBN
% 0.09/0.16 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.16 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.16 % Preprocessing time : 0.002 s
% 0.09/0.16
% 0.09/0.16 % Proof found!
% 0.09/0.16 % SZS status Theorem
% 0.09/0.16 % SZS output start CNFRefutation
% 0.09/0.16 thf(decl_23, type, in: $i > $i > $o).
% 0.09/0.16 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.09/0.16 thf(decl_25, type, setextAx: $o).
% 0.09/0.16 thf(decl_26, type, emptyset: $i).
% 0.09/0.16 thf(decl_27, type, emptysetAx: $o).
% 0.09/0.16 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.09/0.16 thf(decl_29, type, setadjoinAx: $o).
% 0.09/0.16 thf(decl_30, type, powerset: $i > $i).
% 0.09/0.16 thf(decl_31, type, powersetAx: $o).
% 0.09/0.16 thf(decl_32, type, setunion: $i > $i).
% 0.09/0.16 thf(decl_33, type, setunionAx: $o).
% 0.09/0.16 thf(decl_34, type, omega: $i).
% 0.09/0.16 thf(decl_35, type, omega0Ax: $o).
% 0.09/0.16 thf(decl_36, type, omegaSAx: $o).
% 0.09/0.16 thf(decl_37, type, omegaIndAx: $o).
% 0.09/0.16 thf(decl_38, type, replAx: $o).
% 0.09/0.16 thf(decl_39, type, foundationAx: $o).
% 0.09/0.16 thf(decl_40, type, wellorderingAx: $o).
% 0.09/0.16 thf(decl_42, type, descrp: $o).
% 0.09/0.16 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.09/0.16 thf(decl_44, type, dsetconstrI: $o).
% 0.09/0.16 thf(decl_45, type, dsetconstrEL: $o).
% 0.09/0.16 thf(decl_46, type, dsetconstrER: $o).
% 0.09/0.16 thf(decl_47, type, exuE1: $o).
% 0.09/0.16 thf(decl_48, type, prop2set: $o > $i).
% 0.09/0.16 thf(decl_49, type, prop2setE: $o).
% 0.09/0.16 thf(decl_50, type, emptysetE: $o).
% 0.09/0.16 thf(decl_51, type, emptysetimpfalse: $o).
% 0.09/0.16 thf(decl_52, type, notinemptyset: $o).
% 0.09/0.16 thf(decl_53, type, exuE3e: $o).
% 0.09/0.16 thf(decl_54, type, setext: $o).
% 0.09/0.16 thf(decl_55, type, emptyI: $o).
% 0.09/0.16 thf(decl_56, type, noeltsimpempty: $o).
% 0.09/0.16 thf(decl_57, type, setbeta: $o).
% 0.09/0.16 thf(decl_58, type, nonempty: $i > $o).
% 0.09/0.16 thf(decl_59, type, nonemptyE1: $o).
% 0.09/0.16 thf(decl_60, type, nonemptyI: $o).
% 0.09/0.16 thf(decl_61, type, nonemptyI1: $o).
% 0.09/0.16 thf(decl_62, type, setadjoinIL: $o).
% 0.09/0.16 thf(decl_63, type, emptyinunitempty: $o).
% 0.09/0.16 thf(decl_64, type, setadjoinIR: $o).
% 0.09/0.16 thf(decl_65, type, setadjoinE: $o).
% 0.09/0.16 thf(decl_66, type, setadjoinOr: $o).
% 0.09/0.16 thf(decl_67, type, setoftrueEq: $o).
% 0.09/0.16 thf(decl_68, type, powersetI: $o).
% 0.09/0.16 thf(decl_69, type, emptyinPowerset: $o).
% 0.09/0.16 thf(decl_70, type, emptyInPowerset: $o).
% 0.09/0.16 thf(decl_71, type, powersetE: $o).
% 0.09/0.16 thf(decl_72, type, setunionI: $o).
% 0.09/0.16 thf(decl_73, type, setunionE: $o).
% 0.09/0.16 thf(decl_74, type, subPowSU: $o).
% 0.09/0.16 thf(decl_75, type, exuE2: $o).
% 0.09/0.16 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.09/0.16 thf(decl_77, type, uniqinunit: $o).
% 0.09/0.16 thf(decl_78, type, notinsingleton: $o).
% 0.09/0.16 thf(decl_79, type, eqinunit: $o).
% 0.09/0.16 thf(decl_80, type, epred1_0: $o).
% 0.09/0.16 thf(decl_81, type, esk1_2: $i > $i > $i).
% 0.09/0.16 thf(decl_82, type, esk2_2: $i > $i > $i).
% 0.09/0.16 thf(decl_83, type, esk3_2: $i > $i > $i).
% 0.09/0.16 thf(decl_84, type, esk4_1: $i > $i).
% 0.09/0.16 thf(decl_85, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.09/0.16 thf(decl_86, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.09/0.16 thf(decl_87, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.09/0.16 thf(decl_88, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.09/0.16 thf(decl_89, type, esk9_1: $i > $i).
% 0.09/0.16 thf(decl_90, type, esk10_2: ($i > $o) > $i > $i).
% 0.09/0.16 thf(decl_91, type, esk11_1: ($i > $o) > $i).
% 0.09/0.16 thf(decl_92, type, esk12_2: ($i > $o) > $i > $i).
% 0.09/0.16 thf(decl_93, type, esk13_1: ($i > $o) > $i).
% 0.09/0.16 thf(decl_94, type, esk14_2: $i > $i > $i).
% 0.09/0.16 thf(decl_95, type, esk15_2: $i > $i > $i).
% 0.09/0.16 thf(decl_96, type, esk16_1: $i > $i).
% 0.09/0.16 thf(decl_97, type, esk17_1: $i > $i).
% 0.09/0.16 thf(decl_98, type, esk18_1: $i > $i).
% 0.09/0.16 thf(decl_99, type, esk19_2: $i > $i > $i).
% 0.09/0.16 thf(decl_100, type, esk20_3: $i > $i > $o > $i).
% 0.09/0.16 thf(decl_101, type, esk21_2: ($i > $o) > $i > $i).
% 0.09/0.16 thf(decl_102, type, esk22_1: ($i > $o) > $i).
% 0.09/0.16 thf(decl_103, type, esk23_1: $i > $i).
% 0.09/0.16 thf(decl_104, type, esk24_0: $i).
% 0.09/0.16 thf(decl_105, type, esk25_0: $i).
% 0.09/0.16 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', exuE2)).
% 0.09/0.16 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', exu)).
% 0.09/0.16 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', nonempty)).
% 0.09/0.16 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', replAx)).
% 0.09/0.16 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', exuE1)).
% 0.09/0.16 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', exuE3e)).
% 0.09/0.16 thf(prop2set, axiom, ((prop2set)=(^[X10:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[X2:$i]:((X10)))))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', prop2set)).
% 0.09/0.16 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', nonemptyI)).
% 0.09/0.16 thf(singletonsswitch, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset)))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', singletonsswitch)).
% 0.09/0.16 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', nonemptyImpWitness)).
% 0.09/0.16 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', dsetconstrER)).
% 0.09/0.16 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', dsetconstrEL)).
% 0.09/0.16 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', dsetconstrI)).
% 0.09/0.16 thf(prop2setE, axiom, ((prop2setE)<=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', prop2setE)).
% 0.09/0.16 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', nonemptyI1)).
% 0.09/0.16 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', nonemptyE1)).
% 0.09/0.16 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', setoftrueEq)).
% 0.09/0.16 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', setbeta)).
% 0.09/0.16 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', emptyInPowerset)).
% 0.09/0.16 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', powersetE)).
% 0.09/0.16 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', setunionI)).
% 0.09/0.16 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', omega0Ax)).
% 0.09/0.16 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.5FUHNDqpGy/E---3.1_129301.p', setunionE)).
% 0.09/0.16 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', setunionAx)).
% 0.09/0.16 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', subPowSU)).
% 0.09/0.16 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', powersetAx)).
% 0.09/0.16 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', setadjoinAx)).
% 0.09/0.16 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', emptysetAx)).
% 0.09/0.16 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', uniqinunit)).
% 0.09/0.16 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', setextAx)).
% 0.09/0.16 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', notinsingleton)).
% 0.09/0.16 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', eqinunit)).
% 0.09/0.16 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', omegaSAx)).
% 0.09/0.16 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', wellorderingAx)).
% 0.09/0.16 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', foundationAx)).
% 0.09/0.16 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.5FUHNDqpGy/E---3.1_129301.p', omegaIndAx)).
% 0.09/0.16 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', emptyI)).
% 0.09/0.16 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.5FUHNDqpGy/E---3.1_129301.p', setext)).
% 0.09/0.16 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', notinemptyset)).
% 0.09/0.16 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', emptysetimpfalse)).
% 0.09/0.16 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12))))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', emptysetE)).
% 0.09/0.16 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', noeltsimpempty)).
% 0.09/0.16 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', setadjoinIR)).
% 0.09/0.16 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', emptyinunitempty)).
% 0.09/0.16 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', setadjoinIL)).
% 0.09/0.16 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', setadjoinOr)).
% 0.09/0.16 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', powersetI)).
% 0.09/0.16 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', emptyinPowerset)).
% 0.09/0.16 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X13:$o]:(((((X3)=(X2))=>(X13))=>(((in @ X3 @ X4)=>(X13))=>(X13))))))), file('/export/starexec/sandbox/tmp/tmp.5FUHNDqpGy/E---3.1_129301.p', setadjoinE)).
% 0.09/0.16 thf(c_0_49, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.09/0.16 thf(c_0_50, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.09/0.16 thf(c_0_51, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.09/0.16 thf(c_0_52, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.09/0.16 thf(c_0_53, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.09/0.16 thf(c_0_54, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.09/0.16 thf(c_0_55, plain, ((prop2set)=(^[Z0:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[Z1:$i]:((Z0)))))), inference(fof_simplification,[status(thm)],[prop2set])).
% 0.09/0.16 thf(c_0_56, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.09/0.16 thf(c_0_57, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[singletonsswitch])).
% 0.09/0.16 thf(c_0_58, plain, ((exuE2)=(![X1:$i > $o]:((((?[X148:$i]:(((((X1 @ X148)))&(![X149:$i]:(((((X1 @ X149)))=>(((X148)=(X149))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_49, c_0_50])).
% 0.09/0.16 thf(c_0_59, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_51])).
% 0.09/0.16 thf(c_0_60, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.09/0.16 thf(c_0_61, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.09/0.16 thf(c_0_62, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.09/0.16 thf(c_0_63, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X142:$i]:(((((X6 @ X2 @ X142)))&(![X143:$i]:(((((X6 @ X2 @ X143)))=>(((X142)=(X143)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_52, c_0_50])).
% 0.09/0.16 thf(c_0_64, plain, ((exuE1)=(![X1:$i > $o]:((((?[X144:$i]:(((((X1 @ X144)))&(![X145:$i]:(((((X1 @ X145)))=>(((X144)=(X145))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_53, c_0_50])).
% 0.09/0.16 thf(c_0_65, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X146:$i]:(((((X1 @ X146)))&(![X147:$i]:(((((X1 @ X147)))=>(((X146)=(X147))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_54, c_0_50])).
% 0.09/0.16 thf(c_0_66, axiom, ((prop2setE)=(![X11:$o, X2:$i]:((((in @ X2 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:(((X11)))))))=>((X11)))))), inference(apply_def,[status(thm)],[prop2setE, c_0_55])).
% 0.09/0.16 thf(c_0_67, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_51])).
% 0.09/0.16 thf(c_0_68, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_56, c_0_51])).
% 0.09/0.16 thf(c_0_69, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_51])).
% 0.09/0.16 thf(c_0_70, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.09/0.16 thf(c_0_71, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.09/0.16 thf(c_0_72, plain, ((epred1_0)<=>![X179:$i]:(?[X180:$i]:((((![X181:$i]:(((in @ X181 @ X180)=>![X182:$i]:(((in @ X182 @ X181)=>(in @ X182 @ X179)))))&![X183:$i, X184:$i]:((((in @ X183 @ X179)&(in @ X184 @ X179))=>(![X185:$i]:(((in @ X185 @ X180)=>((in @ X183 @ X185)<=>(in @ X184 @ X185))))=>((X183)=(X184))))))&![X186:$i, X187:$i]:((((in @ X186 @ X180)&(in @ X187 @ X180))=>(![X188:$i]:(((in @ X188 @ X186)=>(in @ X188 @ X187)))|![X189:$i]:(((in @ X189 @ X187)=>(in @ X189 @ X186)))))))&![X190:$i]:(((![X191:$i]:(((in @ X191 @ X190)=>(in @ X191 @ X179)))&?[X192:$i]:((in @ X192 @ X190)))=>?[X193:$i, X194:$i]:(((((in @ X193 @ X180)&(in @ X194 @ X190))&~(?[X195:$i]:(((in @ X195 @ X193)&(in @ X195 @ X190)))))&![X196:$i]:(((in @ X196 @ X180)=>(![X197:$i]:(((in @ X197 @ X196)=>(in @ X197 @ X193)))|(in @ X194 @ X196)))))))))))), introduced(definition)).
% 0.09/0.16 thf(c_0_73, negated_conjecture, ~((![X150:$i, X151:$i]:((![X152:$i]:(((in @ X152 @ X150)<=>(in @ X152 @ X151)))=>((X150)=(X151))))=>(![X153:$i]:(~(in @ X153 @ emptyset))=>(![X154:$i, X155:$i, X156:$i]:(((in @ X156 @ (setadjoin @ X154 @ X155))<=>(((X156)=(X154))|(in @ X156 @ X155))))=>(![X157:$i, X158:$i]:(((in @ X158 @ (powerset @ X157))<=>![X159:$i]:(((in @ X159 @ X158)=>(in @ X159 @ X157)))))=>(![X160:$i, X161:$i]:(((in @ X161 @ (setunion @ X160))<=>?[X162:$i]:(((in @ X161 @ X162)&(in @ X162 @ X160)))))=>((in @ emptyset @ omega)=>(![X163:$i]:(((in @ X163 @ omega)=>(in @ (setadjoin @ X163 @ X163) @ omega)))=>(![X164:$i]:((((in @ emptyset @ X164)&![X165:$i]:((((in @ X165 @ omega)&(in @ X165 @ X164))=>(in @ (setadjoin @ X165 @ X165) @ X164))))=>![X166:$i]:(((in @ X166 @ omega)=>(in @ X166 @ X164)))))=>(![X167:$i > $i > $o, X168:$i]:((![X169:$i]:(((in @ X169 @ X168)=>?[X170:$i]:(((X167 @ X169 @ X170)&![X171:$i]:(((X167 @ X169 @ X171)=>((X170)=(X171))))))))=>?[X172:$i]:(![X173:$i]:(((in @ X173 @ X172)<=>?[X174:$i]:(((in @ X174 @ X168)&(X167 @ X174 @ X173))))))))=>(![X175:$i]:((?[X176:$i]:((in @ X176 @ X175))=>?[X177:$i]:(((in @ X177 @ X175)&~(?[X178:$i]:(((in @ X178 @ X177)&(in @ X178 @ X175))))))))=>((epred1_0)=>((descrp)=>(![X198:$i, X199:$i > $o, X200:$i]:(((in @ X200 @ X198)=>((X199 @ X200)=>(in @ X200 @ (dsetconstr @ X198 @ (^[Z0:$i]:((X199 @ Z0))))))))=>(![X201:$i, X202:$i > $o, X203:$i]:(((in @ X203 @ (dsetconstr @ X201 @ (^[Z0:$i]:((X202 @ Z0)))))=>(in @ X203 @ X201)))=>(![X204:$i, X205:$i > $o, X206:$i]:(((in @ X206 @ (dsetconstr @ X204 @ (^[Z0:$i]:((X205 @ Z0)))))=>(X205 @ X206)))=>(![X207:$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:$i]:(~(in @ X216 @ emptyset))=>(![X217:$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 @ (^[Z0:$i]:((X231 @ Z0)))))<=>(X231 @ X232))))=>(![X233:$i]:((((X233)!=(emptyset))=>?[X234:$i]:((in @ X234 @ X233))))=>(![X235:$i, X236:$i > $o, X237:$i]:(((in @ X237 @ X235)=>((X236 @ X237)=>((dsetconstr @ X235 @ (^[Z0:$i]:((X236 @ Z0))))!=(emptyset)))))=>(![X238:$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:$i]:((in @ X276 @ X275))))=>(![X277:$i, X278:$i]:(((in @ X277 @ (setadjoin @ X278 @ emptyset))=>((X277)=(X278))))=>(![X279:$i, X280:$i]:((((X279)!=(X280))=>~(in @ X280 @ (setadjoin @ X279 @ emptyset))))=>(![X281:$i, X282:$i]:((((X281)=(X282))=>(in @ X281 @ (setadjoin @ X282 @ emptyset))))=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_57, emptyInPowerset]), powersetE]), setunionI]), omega0Ax]), setunionE]), setunionAx]), subPowSU]), powersetAx]), c_0_58]), setadjoinAx]), c_0_59]), emptysetAx]), uniqinunit]), setextAx]), notinsingleton]), eqinunit]), omegaSAx]), c_0_60]), c_0_61]), c_0_62]), wellorderingAx]), foundationAx]), c_0_63]), omegaIndAx]), c_0_64]), emptyI]), setext]), c_0_65]), notinemptyset]), emptysetimpfalse]), emptysetE]), c_0_66]), noeltsimpempty]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), c_0_67]), c_0_68]), c_0_69]), setadjoinOr]), c_0_70]), powersetI]), emptyinPowerset]), c_0_71]), setadjoinE])]), c_0_72])).
% 0.09/0.16 thf(c_0_74, negated_conjecture, ![X283:$i, X284:$i, X286:$i, X287:$i, X288:$i, X289:$i, X290:$i, X291:$i, X292:$i, X293:$i, X294:$i, X296:$i, X297:$i, X299:$i, X300:$i, X301:$i, X302:$i, X303:$i, X305:$i, X306:$i > $i > $o, X307:$i, X309:$i, X312:$i, X314:$i, X315:$i, X316:$i, X317:$i, X319:$i, X320:$i, X321:$i > $o, X322:$i, X323:$i, X324:$i > $o, X325:$i, X326:$i, X327:$i > $o, X328:$i, X329:$i > $o, X330:$i, X333:$i, X334:$o, X335:$i, X336:$i, X337:$o, X338:$i, X339:$i, X340:$i > $o, X341:$i, X344:$i, X345:$i, X348:$i, X350:$i, X352:$i, X353:$i > $o, X354:$i, X355:$i, X357:$i, X358:$i > $o, X359:$i, X360:$i, X361:$i, X362:$i, X363:$i, X364:$i, X365:$i, X366:$i, X367:$i, X368:$i, X369:$i, X370:$o, X371:$i, X372:$i, X373:$i, X374:$i, X375:$i, X376:$i, X378:$i, X379:$i, X380:$i, X381:$i, X382:$i, X383:$i, X384:$i, X385:$i, X386:$i, X387:$i, X388:$o, X390:$i, X391:$i, X392:$i > $o, X393:$i, X396:$i, X397:$i, X398:$i, X400:$i, X401:$i, X402:$i, X403:$i, X404:$i, X405:$i]:((((~(in @ (esk1_2 @ X283 @ X284) @ X283)|~(in @ (esk1_2 @ X283 @ X284) @ X284)|((X283)=(X284)))&((in @ (esk1_2 @ X283 @ X284) @ X283)|(in @ (esk1_2 @ X283 @ X284) @ X284)|((X283)=(X284))))&(~(in @ X286 @ emptyset)&(((~(in @ X289 @ (setadjoin @ X287 @ X288))|(((X289)=(X287))|(in @ X289 @ X288)))&((((X289)!=(X287))|(in @ X289 @ (setadjoin @ X287 @ X288)))&(~(in @ X289 @ X288)|(in @ X289 @ (setadjoin @ X287 @ X288)))))&(((~(in @ X291 @ (powerset @ X290))|(~(in @ X292 @ X291)|(in @ X292 @ X290)))&(((in @ (esk2_2 @ X293 @ X294) @ X294)|(in @ X294 @ (powerset @ X293)))&(~(in @ (esk2_2 @ X293 @ X294) @ X293)|(in @ X294 @ (powerset @ X293)))))&(((((in @ X297 @ (esk3_2 @ X296 @ X297))|~(in @ X297 @ (setunion @ X296)))&((in @ (esk3_2 @ X296 @ X297) @ X296)|~(in @ X297 @ (setunion @ X296))))&(~(in @ X300 @ X301)|~(in @ X301 @ X299)|(in @ X300 @ (setunion @ X299))))&((in @ emptyset @ omega)&((~(in @ X302 @ omega)|(in @ (setadjoin @ X302 @ X302) @ omega))&(((((in @ (esk4_1 @ X303) @ omega)|~(in @ emptyset @ X303)|(~(in @ X305 @ omega)|(in @ X305 @ X303)))&((in @ (esk4_1 @ X303) @ X303)|~(in @ emptyset @ X303)|(~(in @ X305 @ omega)|(in @ X305 @ X303))))&(~(in @ (setadjoin @ (esk4_1 @ X303) @ (esk4_1 @ X303)) @ X303)|~(in @ emptyset @ X303)|(~(in @ X305 @ omega)|(in @ X305 @ X303))))&((((((in @ (esk8_3 @ X306 @ X307 @ X312) @ X307)|~(in @ X312 @ (esk7_2 @ X306 @ X307))|(in @ (esk5_2 @ X306 @ X307) @ X307))&((X306 @ (esk8_3 @ X306 @ X307 @ X312) @ X312)|~(in @ X312 @ (esk7_2 @ X306 @ X307))|(in @ (esk5_2 @ X306 @ X307) @ X307)))&(~(in @ X315 @ X307)|~(X306 @ X315 @ X314)|(in @ X314 @ (esk7_2 @ X306 @ X307))|(in @ (esk5_2 @ X306 @ X307) @ X307)))&(((((in @ (esk8_3 @ X306 @ X307 @ X312) @ X307)|~(in @ X312 @ (esk7_2 @ X306 @ X307))|((X306 @ (esk5_2 @ X306 @ X307) @ (esk6_3 @ X306 @ X307 @ X309))|~(X306 @ (esk5_2 @ X306 @ X307) @ X309)))&((X306 @ (esk8_3 @ X306 @ X307 @ X312) @ X312)|~(in @ X312 @ (esk7_2 @ X306 @ X307))|((X306 @ (esk5_2 @ X306 @ X307) @ (esk6_3 @ X306 @ X307 @ X309))|~(X306 @ (esk5_2 @ X306 @ X307) @ X309))))&(~(in @ X315 @ X307)|~(X306 @ X315 @ X314)|(in @ X314 @ (esk7_2 @ X306 @ X307))|((X306 @ (esk5_2 @ X306 @ X307) @ (esk6_3 @ X306 @ X307 @ X309))|~(X306 @ (esk5_2 @ X306 @ X307) @ X309))))&((((in @ (esk8_3 @ X306 @ X307 @ X312) @ X307)|~(in @ X312 @ (esk7_2 @ X306 @ X307))|(((X309)!=(esk6_3 @ X306 @ X307 @ X309))|~(X306 @ (esk5_2 @ X306 @ X307) @ X309)))&((X306 @ (esk8_3 @ X306 @ X307 @ X312) @ X312)|~(in @ X312 @ (esk7_2 @ X306 @ X307))|(((X309)!=(esk6_3 @ X306 @ X307 @ X309))|~(X306 @ (esk5_2 @ X306 @ X307) @ X309))))&(~(in @ X315 @ X307)|~(X306 @ X315 @ X314)|(in @ X314 @ (esk7_2 @ X306 @ X307))|(((X309)!=(esk6_3 @ X306 @ X307 @ X309))|~(X306 @ (esk5_2 @ X306 @ X307) @ X309))))))&((((in @ (esk9_1 @ X316) @ X316)|~(in @ X317 @ X316))&(~(in @ X319 @ (esk9_1 @ X316))|~(in @ X319 @ X316)|~(in @ X317 @ X316)))&((epred1_0)&((descrp)&((~(in @ X322 @ X320)|(~(X321 @ X322)|(in @ X322 @ (dsetconstr @ X320 @ (^[Z0:$i]:((X321 @ Z0)))))))&((~(in @ X325 @ (dsetconstr @ X323 @ (^[Z0:$i]:((X324 @ Z0)))))|(in @ X325 @ X323))&((~(in @ X328 @ (dsetconstr @ X326 @ (^[Z0:$i]:((X327 @ Z0)))))|(X327 @ X328))&(((((X329 @ (esk11_1 @ X329))|((X329 @ (esk10_2 @ X329 @ X330))|~(X329 @ X330)))&(~(X329 @ X333)|((esk11_1 @ X329)=(X333))|((X329 @ (esk10_2 @ X329 @ X330))|~(X329 @ X330))))&(((X329 @ (esk11_1 @ X329))|(((X330)!=(esk10_2 @ X329 @ X330))|~(X329 @ X330)))&(~(X329 @ X333)|((esk11_1 @ X329)=(X333))|(((X330)!=(esk10_2 @ X329 @ X330))|~(X329 @ X330)))))&((~(in @ X335 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X334)))))|(X334))&((~(in @ X336 @ emptyset)|(X337))&(~(in @ X338 @ emptyset)&(~(in @ X339 @ emptyset)&((((X340 @ (esk12_2 @ X340 @ X341))|~(X340 @ X341)|(X340 @ (esk13_1 @ X340)))&(((X341)!=(esk12_2 @ X340 @ X341))|~(X340 @ X341)|(X340 @ (esk13_1 @ X340))))&(((((in @ (esk15_2 @ X344 @ X345) @ X345)|((X344)=(X345))|(in @ (esk14_2 @ X344 @ X345) @ X344))&(~(in @ (esk15_2 @ X344 @ X345) @ X344)|((X344)=(X345))|(in @ (esk14_2 @ X344 @ X345) @ X344)))&(((in @ (esk15_2 @ X344 @ X345) @ X345)|((X344)=(X345))|~(in @ (esk14_2 @ X344 @ X345) @ X345))&(~(in @ (esk15_2 @ X344 @ X345) @ X344)|((X344)=(X345))|~(in @ (esk14_2 @ X344 @ X345) @ X345))))&(((in @ (esk16_1 @ X348) @ X348)|((X348)=(emptyset)))&(((in @ (esk17_1 @ X350) @ X350)|((X350)=(emptyset)))&(((~(in @ X354 @ (dsetconstr @ X352 @ (^[Z0:$i]:((X353 @ Z0)))))|(X353 @ X354)|~(in @ X354 @ X352))&(~(X353 @ X354)|(in @ X354 @ (dsetconstr @ X352 @ (^[Z0:$i]:((X353 @ Z0)))))|~(in @ X354 @ X352)))&((((X355)=(emptyset))|(in @ (esk18_1 @ X355) @ X355))&((~(in @ X359 @ X357)|(~(X358 @ X359)|((dsetconstr @ X357 @ (^[Z0:$i]:((X358 @ Z0))))!=(emptyset))))&((~(in @ X361 @ X360)|((X360)!=(emptyset)))&((in @ X362 @ (setadjoin @ X362 @ X363))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X366 @ X365)|(in @ X366 @ (setadjoin @ X364 @ X365)))&(((((in @ X369 @ X368)|(X370)|((X369)=(X367))|~(in @ X369 @ (setadjoin @ X367 @ X368)))&(~(X370)|(X370)|((X369)=(X367))|~(in @ X369 @ (setadjoin @ X367 @ X368))))&(((in @ X369 @ X368)|(X370)|~(X370)|~(in @ X369 @ (setadjoin @ X367 @ X368)))&(~(X370)|(X370)|~(X370)|~(in @ X369 @ (setadjoin @ X367 @ X368)))))&((~(in @ X373 @ (setadjoin @ X371 @ X372))|(((X373)=(X371))|(in @ X373 @ X372)))&(((dsetconstr @ X374 @ (^[Z0:$i]:(($true))))=(X374))&((((in @ (esk19_2 @ X375 @ X376) @ X376)|(in @ X376 @ (powerset @ X375)))&(~(in @ (esk19_2 @ X375 @ X376) @ X375)|(in @ X376 @ (powerset @ X375))))&((in @ emptyset @ (powerset @ X378))&((in @ emptyset @ (powerset @ X379))&((~(in @ X381 @ (powerset @ X380))|(~(in @ X382 @ X381)|(in @ X382 @ X380)))&((~(in @ X384 @ X385)|(~(in @ X385 @ X383)|(in @ X384 @ (setunion @ X383))))&((((in @ X387 @ (esk20_3 @ X386 @ X387 @ X388))|(X388)|~(in @ X387 @ (setunion @ X386)))&(((in @ (esk20_3 @ X386 @ X387 @ X388) @ X386)|(X388)|~(in @ X387 @ (setunion @ X386)))&(~(X388)|(X388)|~(in @ X387 @ (setunion @ X386)))))&((~(in @ X391 @ X390)|(in @ X391 @ (powerset @ (setunion @ X390))))&((((~(X392 @ X396)|((X396)=(esk22_1 @ X392))|((X392 @ (esk21_2 @ X392 @ X393))|~(X392 @ X393)))&(((X397)!=(esk22_1 @ X392))|(X392 @ X397)|((X392 @ (esk21_2 @ X392 @ X393))|~(X392 @ X393))))&((~(X392 @ X396)|((X396)=(esk22_1 @ X392))|(((X393)!=(esk21_2 @ X392 @ X393))|~(X392 @ X393)))&(((X397)!=(esk22_1 @ X392))|(X392 @ X397)|(((X393)!=(esk21_2 @ X392 @ X393))|~(X392 @ X393)))))&((((X398)=(emptyset))|(in @ (esk23_1 @ X398) @ X398))&((~(in @ X400 @ (setadjoin @ X401 @ emptyset))|((X400)=(X401)))&((((X402)=(X403))|~(in @ X403 @ (setadjoin @ X402 @ emptyset)))&((((X404)!=(X405))|(in @ X404 @ (setadjoin @ X405 @ emptyset)))&((in @ esk24_0 @ (setadjoin @ esk25_0 @ emptyset))&~(in @ esk25_0 @ (setadjoin @ esk24_0 @ emptyset)))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_73])])])])])])).
% 0.09/0.16 thf(c_0_75, negated_conjecture, ![X3:$i, X2:$i]:((((X2)=(X3))|~((in @ X3 @ (setadjoin @ X2 @ emptyset))))), inference(split_conjunct,[status(thm)],[c_0_74])).
% 0.09/0.16 thf(c_0_76, negated_conjecture, (in @ esk24_0 @ (setadjoin @ esk25_0 @ emptyset)), inference(split_conjunct,[status(thm)],[c_0_74])).
% 0.09/0.16 thf(c_0_77, negated_conjecture, ~((in @ esk25_0 @ (setadjoin @ esk24_0 @ emptyset))), inference(split_conjunct,[status(thm)],[c_0_74])).
% 0.09/0.16 thf(c_0_78, negated_conjecture, ((esk25_0)=(esk24_0)), inference(spm,[status(thm)],[c_0_75, c_0_76])).
% 0.09/0.16 thf(c_0_79, negated_conjecture, ![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_74])).
% 0.09/0.16 thf(c_0_80, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_77, c_0_78]), c_0_79])]), ['proof']).
% 0.09/0.16 % SZS output end CNFRefutation
% 0.09/0.16 % Parsed axioms : 107
% 0.09/0.16 % Removed by relevancy pruning/SinE : 58
% 0.09/0.16 % Initial clauses : 96
% 0.09/0.16 % Removed in clause preprocessing : 4
% 0.09/0.16 % Initial clauses in saturation : 92
% 0.09/0.16 % Processed clauses : 39
% 0.09/0.16 % ...of these trivial : 1
% 0.09/0.16 % ...subsumed : 10
% 0.09/0.16 % ...remaining for further processing : 28
% 0.09/0.16 % Other redundant clauses eliminated : 3
% 0.09/0.16 % Clauses deleted for lack of memory : 0
% 0.09/0.16 % Backward-subsumed : 0
% 0.09/0.16 % Backward-rewritten : 3
% 0.09/0.16 % Generated clauses : 30
% 0.09/0.16 % ...of the previous two non-redundant : 24
% 0.09/0.16 % ...aggressively subsumed : 0
% 0.09/0.16 % Contextual simplify-reflections : 0
% 0.09/0.16 % Paramodulations : 27
% 0.09/0.16 % Factorizations : 0
% 0.09/0.16 % NegExts : 0
% 0.09/0.16 % Equation resolutions : 3
% 0.09/0.16 % Disequality decompositions : 0
% 0.09/0.16 % Total rewrite steps : 11
% 0.09/0.16 % ...of those cached : 1
% 0.09/0.16 % Propositional unsat checks : 0
% 0.09/0.16 % Propositional check models : 0
% 0.09/0.16 % Propositional check unsatisfiable : 0
% 0.09/0.16 % Propositional clauses : 0
% 0.09/0.16 % Propositional clauses after purity: 0
% 0.09/0.16 % Propositional unsat core size : 0
% 0.09/0.16 % Propositional preprocessing time : 0.000
% 0.09/0.16 % Propositional encoding time : 0.000
% 0.09/0.16 % Propositional solver time : 0.000
% 0.09/0.16 % Success case prop preproc time : 0.000
% 0.09/0.16 % Success case prop encoding time : 0.000
% 0.09/0.16 % Success case prop solver time : 0.000
% 0.09/0.16 % Current number of processed clauses : 22
% 0.09/0.16 % Positive orientable unit clauses : 11
% 0.09/0.16 % Positive unorientable unit clauses: 0
% 0.09/0.16 % Negative unit clauses : 1
% 0.09/0.16 % Non-unit-clauses : 10
% 0.09/0.16 % Current number of unprocessed clauses: 77
% 0.09/0.16 % ...number of literals in the above : 252
% 0.09/0.16 % Current number of archived formulas : 0
% 0.09/0.16 % Current number of archived clauses : 3
% 0.09/0.16 % Clause-clause subsumption calls (NU) : 28
% 0.09/0.16 % Rec. Clause-clause subsumption calls : 28
% 0.09/0.16 % Non-unit clause-clause subsumptions : 4
% 0.09/0.16 % Unit Clause-clause subsumption calls : 18
% 0.09/0.16 % Rewrite failures with RHS unbound : 0
% 0.09/0.16 % BW rewrite match attempts : 4
% 0.09/0.16 % BW rewrite match successes : 3
% 0.09/0.16 % Condensation attempts : 0
% 0.09/0.16 % Condensation successes : 0
% 0.09/0.16 % Termbank termtop insertions : 10702
% 0.09/0.16 % Search garbage collected termcells : 3995
% 0.09/0.16
% 0.09/0.16 % -------------------------------------------------
% 0.09/0.16 % User time : 0.004 s
% 0.09/0.16 % System time : 0.006 s
% 0.09/0.16 % Total time : 0.011 s
% 0.09/0.16 % Maximum resident set size: 4764 pages
% 0.09/0.16
% 0.09/0.16 % -------------------------------------------------
% 0.09/0.16 % User time : 0.007 s
% 0.09/0.16 % System time : 0.008 s
% 0.09/0.16 % Total time : 0.015 s
% 0.09/0.16 % Maximum resident set size: 4864 pages
% 0.09/0.16 % E exiting
%------------------------------------------------------------------------------