%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU531^1 : 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 : n001.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 08:24:24 AM UTC 2026
% Result : Theorem 0.20s 0.30s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU531^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n001.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 13:54:20 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.25 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.6h5OELkb3N/E---3.1_1273953.p
% 0.20/0.30 % Version: 3.5.1-ho
% 0.20/0.30 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.20/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.30 % Starting new_ho_10 with 1500s (5) cores
% 0.20/0.30 % Starting sh5l with 300s (1) cores
% 0.20/0.30 % Starting new_bool_1 with 300s (1) cores
% 0.20/0.30 % Starting new_bool_2 with 300s (1) cores
% 0.20/0.30 % new_bool_1 with pid 1273987 completed with status 0
% 0.20/0.30 % Result found by new_bool_1
% 0.20/0.30 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.20/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.30 % Starting new_ho_10 with 1500s (5) cores
% 0.20/0.30 % Starting sh5l with 300s (1) cores
% 0.20/0.30 % Starting new_bool_1 with 300s (1) cores
% 0.20/0.30 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.20/0.30 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.30 % Search class: HGHSM-FFMS31-SHFSMSBN
% 0.20/0.30 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.30 % Starting SubtermCWHack with 31s (1) cores
% 0.20/0.30 % SubtermCWHack with pid 1273996 completed with status 0
% 0.20/0.30 % Result found by SubtermCWHack
% 0.20/0.30 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.20/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.30 % Starting new_ho_10 with 1500s (5) cores
% 0.20/0.30 % Starting sh5l with 300s (1) cores
% 0.20/0.30 % Starting new_bool_1 with 300s (1) cores
% 0.20/0.30 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.20/0.30 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.30 % Search class: HGHSM-FFMS31-SHFSMSBN
% 0.20/0.30 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.30 % Starting SubtermCWHack with 31s (1) cores
% 0.20/0.30 % Preprocessing time : 0.002 s
% 0.20/0.30
% 0.20/0.30 % Proof found!
% 0.20/0.30 % SZS status Theorem
% 0.20/0.30 % SZS output start CNFRefutation
% 0.20/0.30 thf(decl_23, type, in: $i > $i > $o).
% 0.20/0.30 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.20/0.30 thf(decl_25, type, setextAx: $o).
% 0.20/0.30 thf(decl_26, type, emptyset: $i).
% 0.20/0.30 thf(decl_27, type, emptysetAx: $o).
% 0.20/0.30 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.20/0.30 thf(decl_29, type, setadjoinAx: $o).
% 0.20/0.30 thf(decl_30, type, powerset: $i > $i).
% 0.20/0.30 thf(decl_31, type, powersetAx: $o).
% 0.20/0.30 thf(decl_32, type, setunion: $i > $i).
% 0.20/0.30 thf(decl_33, type, setunionAx: $o).
% 0.20/0.30 thf(decl_34, type, omega: $i).
% 0.20/0.30 thf(decl_35, type, omega0Ax: $o).
% 0.20/0.30 thf(decl_36, type, omegaSAx: $o).
% 0.20/0.30 thf(decl_37, type, omegaIndAx: $o).
% 0.20/0.30 thf(decl_38, type, replAx: $o).
% 0.20/0.30 thf(decl_39, type, foundationAx: $o).
% 0.20/0.30 thf(decl_40, type, wellorderingAx: $o).
% 0.20/0.30 thf(decl_42, type, descrp: $o).
% 0.20/0.30 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.20/0.30 thf(decl_44, type, dsetconstrI: $o).
% 0.20/0.30 thf(decl_45, type, dsetconstrEL: $o).
% 0.20/0.30 thf(decl_46, type, dsetconstrER: $o).
% 0.20/0.30 thf(decl_47, type, exuE1: $o).
% 0.20/0.30 thf(decl_48, type, prop2set: $o > $i).
% 0.20/0.30 thf(decl_49, type, prop2setE: $o).
% 0.20/0.30 thf(decl_50, type, emptysetE: $o).
% 0.20/0.30 thf(decl_51, type, emptysetimpfalse: $o).
% 0.20/0.30 thf(decl_52, type, notinemptyset: $o).
% 0.20/0.30 thf(decl_53, type, exuE3e: $o).
% 0.20/0.30 thf(decl_54, type, setext: $o).
% 0.20/0.30 thf(decl_55, type, emptyI: $o).
% 0.20/0.30 thf(decl_56, type, noeltsimpempty: $o).
% 0.20/0.30 thf(decl_57, type, setbeta: $o).
% 0.20/0.30 thf(decl_58, type, nonempty: $i > $o).
% 0.20/0.30 thf(decl_59, type, nonemptyE1: $o).
% 0.20/0.30 thf(decl_60, type, nonemptyI: $o).
% 0.20/0.30 thf(decl_61, type, nonemptyI1: $o).
% 0.20/0.30 thf(decl_62, type, setadjoinIL: $o).
% 0.20/0.30 thf(decl_63, type, emptyinunitempty: $o).
% 0.20/0.30 thf(decl_64, type, setadjoinIR: $o).
% 0.20/0.30 thf(decl_65, type, setadjoinE: $o).
% 0.20/0.30 thf(decl_66, type, setadjoinOr: $o).
% 0.20/0.30 thf(decl_67, type, setoftrueEq: $o).
% 0.20/0.30 thf(decl_68, type, powersetI: $o).
% 0.20/0.30 thf(decl_69, type, emptyinPowerset: $o).
% 0.20/0.30 thf(decl_70, type, emptyInPowerset: $o).
% 0.20/0.30 thf(decl_71, type, powersetE: $o).
% 0.20/0.30 thf(decl_72, type, setunionI: $o).
% 0.20/0.30 thf(decl_73, type, setunionE: $o).
% 0.20/0.30 thf(decl_74, type, subPowSU: $o).
% 0.20/0.30 thf(decl_75, type, exuE2: $o).
% 0.20/0.30 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.20/0.30 thf(decl_77, type, uniqinunit: $o).
% 0.20/0.30 thf(decl_78, type, notinsingleton: $o).
% 0.20/0.30 thf(decl_79, type, eqinunit: $o).
% 0.20/0.30 thf(decl_80, type, singletonsswitch: $o).
% 0.20/0.30 thf(decl_81, type, epred1_0: $o).
% 0.20/0.30 thf(decl_82, type, esk1_2: $i > $i > $i).
% 0.20/0.30 thf(decl_83, type, esk2_2: $i > $i > $i).
% 0.20/0.30 thf(decl_84, type, esk3_2: $i > $i > $i).
% 0.20/0.30 thf(decl_85, type, esk4_1: $i > $i).
% 0.20/0.30 thf(decl_86, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.20/0.30 thf(decl_87, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.20/0.30 thf(decl_88, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.20/0.30 thf(decl_89, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.20/0.30 thf(decl_90, type, esk9_1: $i > $i).
% 0.20/0.30 thf(decl_91, type, esk10_2: ($i > $o) > $i > $i).
% 0.20/0.30 thf(decl_92, type, esk11_1: ($i > $o) > $i).
% 0.20/0.30 thf(decl_93, type, esk12_2: ($i > $o) > $i > $i).
% 0.20/0.30 thf(decl_94, type, esk13_1: ($i > $o) > $i).
% 0.20/0.30 thf(decl_95, type, esk14_2: $i > $i > $i).
% 0.20/0.30 thf(decl_96, type, esk15_2: $i > $i > $i).
% 0.20/0.30 thf(decl_97, type, esk16_1: $i > $i).
% 0.20/0.30 thf(decl_98, type, esk17_1: $i > $i).
% 0.20/0.30 thf(decl_99, type, esk18_1: $i > $i).
% 0.20/0.30 thf(decl_100, type, esk19_2: $i > $i > $i).
% 0.20/0.30 thf(decl_101, type, esk20_3: $i > $i > $o > $i).
% 0.20/0.30 thf(decl_102, type, esk21_2: ($i > $o) > $i > $i).
% 0.20/0.30 thf(decl_103, type, esk22_1: ($i > $o) > $i).
% 0.20/0.30 thf(decl_104, type, esk23_1: $i > $i).
% 0.20/0.30 thf(decl_105, type, esk24_0: $i).
% 0.20/0.30 thf(decl_106, type, esk25_0: $i).
% 0.20/0.30 thf(decl_107, type, esk26_0: $i).
% 0.20/0.30 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', exuE2)).
% 0.20/0.30 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', exu)).
% 0.20/0.30 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', nonempty)).
% 0.20/0.30 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.6h5OELkb3N/E---3.1_1273953.p', exuE1)).
% 0.20/0.30 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', replAx)).
% 0.20/0.30 thf(prop2set, axiom, ((prop2set)=(^[X10:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[X2:$i]:((X10)))))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', prop2set)).
% 0.20/0.30 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', exuE3e)).
% 0.20/0.30 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', nonemptyI)).
% 0.20/0.30 thf(upairsetE, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>![X2:$i, X3:$i, X15:$i]:(((in @ X15 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X15)=(X2))|((X15)=(X3)))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', upairsetE)).
% 0.20/0.30 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', nonemptyImpWitness)).
% 0.20/0.30 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', dsetconstrER)).
% 0.20/0.30 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', dsetconstrEL)).
% 0.20/0.30 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', dsetconstrI)).
% 0.20/0.30 thf(prop2setE, axiom, ((prop2setE)<=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', prop2setE)).
% 0.20/0.30 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', setbeta)).
% 0.20/0.30 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', nonemptyI1)).
% 0.20/0.30 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', nonemptyE1)).
% 0.20/0.30 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', setoftrueEq)).
% 0.20/0.30 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', powersetE)).
% 0.20/0.30 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', setunionI)).
% 0.20/0.30 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.6h5OELkb3N/E---3.1_1273953.p', setunionE)).
% 0.20/0.30 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', subPowSU)).
% 0.20/0.30 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', omegaSAx)).
% 0.20/0.30 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', omega0Ax)).
% 0.20/0.30 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', setunionAx)).
% 0.20/0.30 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', uniqinunit)).
% 0.20/0.30 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', powersetAx)).
% 0.20/0.30 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', notinsingleton)).
% 0.20/0.30 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', setadjoinAx)).
% 0.20/0.30 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', eqinunit)).
% 0.20/0.30 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', emptysetAx)).
% 0.20/0.30 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', singletonsswitch)).
% 0.20/0.30 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', setextAx)).
% 0.20/0.30 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', omegaIndAx)).
% 0.20/0.30 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.6h5OELkb3N/E---3.1_1273953.p', wellorderingAx)).
% 0.20/0.30 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.6h5OELkb3N/E---3.1_1273953.p', foundationAx)).
% 0.20/0.30 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', noeltsimpempty)).
% 0.20/0.30 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', emptyI)).
% 0.20/0.30 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.6h5OELkb3N/E---3.1_1273953.p', setext)).
% 0.20/0.30 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', notinemptyset)).
% 0.20/0.30 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', emptysetimpfalse)).
% 0.20/0.30 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12))))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', emptysetE)).
% 0.20/0.30 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X13:$o]:(((((X3)=(X2))=>(X13))=>(((in @ X3 @ X4)=>(X13))=>(X13))))))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', setadjoinE)).
% 0.20/0.30 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', setadjoinIR)).
% 0.20/0.30 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', emptyinunitempty)).
% 0.20/0.30 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', setadjoinIL)).
% 0.20/0.30 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', setadjoinOr)).
% 0.20/0.30 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', powersetI)).
% 0.20/0.30 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', emptyinPowerset)).
% 0.20/0.30 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.6h5OELkb3N/E---3.1_1273953.p', emptyInPowerset)).
% 0.20/0.30 thf(c_0_50, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.20/0.30 thf(c_0_51, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.20/0.30 thf(c_0_52, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.20/0.30 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])).
% 0.20/0.30 thf(c_0_54, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.20/0.30 thf(c_0_55, plain, ((prop2set)=(^[Z0:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[Z1:$i]:((Z0)))))), inference(fof_simplification,[status(thm)],[prop2set])).
% 0.20/0.30 thf(c_0_56, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.20/0.30 thf(c_0_57, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.20/0.30 thf(c_0_58, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>![X2:$i, X3:$i, X15:$i]:(((in @ X15 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X15)=(X2))|((X15)=(X3))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[upairsetE])).
% 0.20/0.30 thf(c_0_59, plain, ((exuE2)=(![X1:$i > $o]:((((?[X152:$i]:(((((X1 @ X152)))&(![X153:$i]:(((((X1 @ X153)))=>(((X152)=(X153))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_50, c_0_51])).
% 0.20/0.30 thf(c_0_60, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_52])).
% 0.20/0.30 thf(c_0_61, plain, ((exuE1)=(![X1:$i > $o]:((((?[X148:$i]:(((((X1 @ X148)))&(![X149:$i]:(((((X1 @ X149)))=>(((X148)=(X149))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_53, c_0_51])).
% 0.20/0.30 thf(c_0_62, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.20/0.30 thf(c_0_63, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.20/0.30 thf(c_0_64, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.20/0.30 thf(c_0_65, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X146:$i]:(((((X6 @ X2 @ X146)))&(![X147:$i]:(((((X6 @ X2 @ X147)))=>(((X146)=(X147)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_54, c_0_51])).
% 0.20/0.30 thf(c_0_66, axiom, ((prop2setE)=(![X11:$o, X2:$i]:((((in @ X2 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:(((X11)))))))=>((X11)))))), inference(apply_def,[status(thm)],[prop2setE, c_0_55])).
% 0.20/0.30 thf(c_0_67, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X150:$i]:(((((X1 @ X150)))&(![X151:$i]:(((((X1 @ X151)))=>(((X150)=(X151))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_56, c_0_51])).
% 0.20/0.30 thf(c_0_68, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.20/0.30 thf(c_0_69, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_52])).
% 0.20/0.30 thf(c_0_70, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_57, c_0_52])).
% 0.20/0.30 thf(c_0_71, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_52])).
% 0.20/0.30 thf(c_0_72, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.20/0.30 thf(c_0_73, plain, ((epred1_0)<=>![X183:$i]:(?[X184:$i]:((((![X185:$i]:(((in @ X185 @ X184)=>![X186:$i]:(((in @ X186 @ X185)=>(in @ X186 @ X183)))))&![X187:$i, X188:$i]:((((in @ X187 @ X183)&(in @ X188 @ X183))=>(![X189:$i]:(((in @ X189 @ X184)=>((in @ X187 @ X189)<=>(in @ X188 @ X189))))=>((X187)=(X188))))))&![X190:$i, X191:$i]:((((in @ X190 @ X184)&(in @ X191 @ X184))=>(![X192:$i]:(((in @ X192 @ X190)=>(in @ X192 @ X191)))|![X193:$i]:(((in @ X193 @ X191)=>(in @ X193 @ X190)))))))&![X194:$i]:(((![X195:$i]:(((in @ X195 @ X194)=>(in @ X195 @ X183)))&?[X196:$i]:((in @ X196 @ X194)))=>?[X197:$i, X198:$i]:(((((in @ X197 @ X184)&(in @ X198 @ X194))&~(?[X199:$i]:(((in @ X199 @ X197)&(in @ X199 @ X194)))))&![X200:$i]:(((in @ X200 @ X184)=>(![X201:$i]:(((in @ X201 @ X200)=>(in @ X201 @ X197)))|(in @ X198 @ X200)))))))))))), introduced(definition)).
% 0.20/0.30 thf(c_0_74, negated_conjecture, ~((![X154:$i, X155:$i]:((![X156:$i]:(((in @ X156 @ X154)<=>(in @ X156 @ X155)))=>((X154)=(X155))))=>(![X157:$i]:(~(in @ X157 @ emptyset))=>(![X158:$i, X159:$i, X160:$i]:(((in @ X160 @ (setadjoin @ X158 @ X159))<=>(((X160)=(X158))|(in @ X160 @ X159))))=>(![X161:$i, X162:$i]:(((in @ X162 @ (powerset @ X161))<=>![X163:$i]:(((in @ X163 @ X162)=>(in @ X163 @ X161)))))=>(![X164:$i, X165:$i]:(((in @ X165 @ (setunion @ X164))<=>?[X166:$i]:(((in @ X165 @ X166)&(in @ X166 @ X164)))))=>((in @ emptyset @ omega)=>(![X167:$i]:(((in @ X167 @ omega)=>(in @ (setadjoin @ X167 @ X167) @ omega)))=>(![X168:$i]:((((in @ emptyset @ X168)&![X169:$i]:((((in @ X169 @ omega)&(in @ X169 @ X168))=>(in @ (setadjoin @ X169 @ X169) @ X168))))=>![X170:$i]:(((in @ X170 @ omega)=>(in @ X170 @ X168)))))=>(![X171:$i > $i > $o, X172:$i]:((![X173:$i]:(((in @ X173 @ X172)=>?[X174:$i]:(((X171 @ X173 @ X174)&![X175:$i]:(((X171 @ X173 @ X175)=>((X174)=(X175))))))))=>?[X176:$i]:(![X177:$i]:(((in @ X177 @ X176)<=>?[X178:$i]:(((in @ X178 @ X172)&(X171 @ X178 @ X177))))))))=>(![X179:$i]:((?[X180:$i]:((in @ X180 @ X179))=>?[X181:$i]:(((in @ X181 @ X179)&~(?[X182:$i]:(((in @ X182 @ X181)&(in @ X182 @ X179))))))))=>((epred1_0)=>((descrp)=>(![X202:$i, X203:$i > $o, X204:$i]:(((in @ X204 @ X202)=>((X203 @ X204)=>(in @ X204 @ (dsetconstr @ X202 @ X203)))))=>(![X205:$i, X206:$i > $o, X207:$i]:(((in @ X207 @ (dsetconstr @ X205 @ X206))=>(in @ X207 @ X205)))=>(![X208:$i, X209:$i > $o, X210:$i]:(((in @ X210 @ (dsetconstr @ X208 @ X209))=>(X209 @ X210)))=>(![X211:$i > $o]:((?[X212:$i]:(((X211 @ X212)&![X213:$i]:(((X211 @ X213)=>((X212)=(X213))))))=>?[X214:$i]:(((X211 @ X214)&![X215:$i]:(((X211 @ X215)=>((X214)=(X215))))))))=>(![X216:$o, X217:$i]:(((in @ X217 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X216)))))=>(X216)))=>(![X218:$i]:(((in @ X218 @ emptyset)=>![X219:$o]:((X219))))=>(![X220:$i]:(((in @ X220 @ emptyset)=>~($true)))=>(![X221:$i]:(~(in @ X221 @ emptyset))=>(![X222:$i > $o]:((?[X223:$i]:(((X222 @ X223)&![X224:$i]:(((X222 @ X224)=>((X223)=(X224))))))=>?[X225:$i]:((X222 @ X225))))=>(![X226:$i, X227:$i]:((![X228:$i]:(((in @ X228 @ X226)=>(in @ X228 @ X227)))=>(![X229:$i]:(((in @ X229 @ X227)=>(in @ X229 @ X226)))=>((X226)=(X227)))))=>(![X230:$i]:((![X231:$i]:(~(in @ X231 @ X230))=>((X230)=(emptyset))))=>(![X232:$i]:((![X233:$i]:(~(in @ X233 @ X232))=>((X232)=(emptyset))))=>(![X234:$i, X235:$i > $o, X236:$i]:(((in @ X236 @ X234)=>((in @ X236 @ (dsetconstr @ X234 @ X235))<=>(X235 @ X236))))=>(![X237:$i]:((((X237)!=(emptyset))=>?[X238:$i]:((in @ X238 @ X237))))=>(![X239:$i, X240:$i > $o, X241:$i]:(((in @ X241 @ X239)=>((X240 @ X241)=>((dsetconstr @ X239 @ X240)!=(emptyset)))))=>(![X242:$i]:((?[X243:$i]:((in @ X243 @ X242))=>((X242)!=(emptyset))))=>(![X244:$i, X245:$i]:((in @ X244 @ (setadjoin @ X244 @ X245)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X246:$i, X247:$i, X248:$i]:(((in @ X248 @ X247)=>(in @ X248 @ (setadjoin @ X246 @ X247))))=>(![X249:$i, X250:$i, X251:$i]:(((in @ X251 @ (setadjoin @ X249 @ X250))=>![X252:$o]:(((((X251)=(X249))=>(X252))=>(((in @ X251 @ X250)=>(X252))=>(X252))))))=>(![X253:$i, X254:$i, X255:$i]:(((in @ X255 @ (setadjoin @ X253 @ X254))=>(((X255)=(X253))|(in @ X255 @ X254))))=>(![X256:$i]:(((dsetconstr @ X256 @ (^[Z0:$i]:($true)))=(X256)))=>(![X257:$i, X258:$i]:((![X259:$i]:(((in @ X259 @ X258)=>(in @ X259 @ X257)))=>(in @ X258 @ (powerset @ X257))))=>(![X260:$i]:((in @ emptyset @ (powerset @ X260)))=>(![X261:$i]:((in @ emptyset @ (powerset @ X261)))=>(![X262:$i, X263:$i, X264:$i]:(((in @ X263 @ (powerset @ X262))=>((in @ X264 @ X263)=>(in @ X264 @ X262))))=>(![X265:$i, X266:$i, X267:$i]:(((in @ X266 @ X267)=>((in @ X267 @ X265)=>(in @ X266 @ (setunion @ X265)))))=>(![X268:$i, X269:$i]:(((in @ X269 @ (setunion @ X268))=>![X270:$o]:((![X271:$i]:(((in @ X269 @ X271)=>((in @ X271 @ X268)=>(X270))))=>(X270)))))=>(![X272:$i, X273:$i]:(((in @ X273 @ X272)=>(in @ X273 @ (powerset @ (setunion @ X272)))))=>(![X274:$i > $o]:((?[X275:$i]:(((X274 @ X275)&![X276:$i]:(((X274 @ X276)=>((X275)=(X276))))))=>?[X277:$i]:(![X278:$i]:(((X274 @ X278)<=>((X278)=(X277)))))))=>(![X279:$i]:((((X279)!=(emptyset))=>?[X280:$i]:(((in @ X280 @ X279)&$true))))=>(![X281:$i, X282:$i]:(((in @ X281 @ (setadjoin @ X282 @ emptyset))=>((X281)=(X282))))=>(![X283:$i, X284:$i]:((((X283)!=(X284))=>~(in @ X284 @ (setadjoin @ X283 @ emptyset))))=>(![X285:$i, X286:$i]:((((X285)=(X286))=>(in @ X285 @ (setadjoin @ X286 @ emptyset))))=>(![X287:$i, X288:$i]:(((in @ X287 @ (setadjoin @ X288 @ emptyset))=>(in @ X288 @ (setadjoin @ X287 @ emptyset))))=>![X2:$i, X3:$i, X15:$i]:(((in @ X15 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X15)=(X2))|((X15)=(X3))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(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)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_58, powersetE]), setunionI]), setunionE]), subPowSU]), omegaSAx]), c_0_59]), omega0Ax]), c_0_60]), setunionAx]), uniqinunit]), powersetAx]), notinsingleton]), setadjoinAx]), eqinunit]), emptysetAx]), singletonsswitch]), setextAx]), omegaIndAx]), c_0_61]), c_0_62]), c_0_63]), c_0_64]), wellorderingAx]), foundationAx]), c_0_65]), c_0_66]), noeltsimpempty]), emptyI]), setext]), c_0_67]), notinemptyset]), emptysetimpfalse]), emptysetE]), c_0_68]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), c_0_69]), c_0_70]), c_0_71]), setadjoinOr]), c_0_72]), powersetI]), emptyinPowerset]), emptyInPowerset])])]), c_0_73])).
% 0.20/0.30 thf(c_0_75, negated_conjecture, ![X289:$i, X290:$i, X292:$i, X293:$i, X294:$i, X295:$i, X296:$i, X297:$i, X298:$i, X299:$i, X300:$i, X302:$i, X303:$i, X305:$i, X306:$i, X307:$i, X308:$i, X309:$i, X311:$i, X312:$i > $i > $o, X313:$i, X315:$i, X318:$i, X320:$i, X321:$i, X322:$i, X323:$i, X325:$i, X326:$i, X327:$i > $o, X328:$i, X329:$i, X330:$i > $o, X331:$i, X332:$i, X333:$i > $o, X334:$i, X335:$i > $o, X336:$i, X339:$i, X340:$o, X341:$i, X342:$i, X343:$o, X344:$i, X345:$i, X346:$i > $o, X347:$i, X350:$i, X351:$i, X354:$i, X356:$i, X358:$i, X359:$i > $o, X360:$i, X361:$i, X363:$i, X364:$i > $o, X365:$i, X366:$i, X367:$i, X368:$i, X369:$i, X370:$i, X371:$i, X372:$i, X373:$i, X374:$i, X375:$i, X376:$o, X377:$i, X378:$i, X379:$i, X380:$i, X381:$i, X382:$i, X384:$i, X385:$i, X386:$i, X387:$i, X388:$i, X389:$i, X390:$i, X391:$i, X392:$i, X393:$i, X394:$o, X396:$i, X397:$i, X398:$i > $o, X399:$i, X402:$i, X403:$i, X404:$i, X406:$i, X407:$i, X408:$i, X409:$i, X410:$i, X411:$i, X412:$i, X413:$i]:((((~(in @ (esk1_2 @ X289 @ X290) @ X289)|~(in @ (esk1_2 @ X289 @ X290) @ X290)|((X289)=(X290)))&((in @ (esk1_2 @ X289 @ X290) @ X289)|(in @ (esk1_2 @ X289 @ X290) @ X290)|((X289)=(X290))))&(~(in @ X292 @ emptyset)&(((~(in @ X295 @ (setadjoin @ X293 @ X294))|(((X295)=(X293))|(in @ X295 @ X294)))&((((X295)!=(X293))|(in @ X295 @ (setadjoin @ X293 @ X294)))&(~(in @ X295 @ X294)|(in @ X295 @ (setadjoin @ X293 @ X294)))))&(((~(in @ X297 @ (powerset @ X296))|(~(in @ X298 @ X297)|(in @ X298 @ X296)))&(((in @ (esk2_2 @ X299 @ X300) @ X300)|(in @ X300 @ (powerset @ X299)))&(~(in @ (esk2_2 @ X299 @ X300) @ X299)|(in @ X300 @ (powerset @ X299)))))&(((((in @ X303 @ (esk3_2 @ X302 @ X303))|~(in @ X303 @ (setunion @ X302)))&((in @ (esk3_2 @ X302 @ X303) @ X302)|~(in @ X303 @ (setunion @ X302))))&(~(in @ X306 @ X307)|~(in @ X307 @ X305)|(in @ X306 @ (setunion @ X305))))&((in @ emptyset @ omega)&((~(in @ X308 @ omega)|(in @ (setadjoin @ X308 @ X308) @ omega))&(((((in @ (esk4_1 @ X309) @ omega)|~(in @ emptyset @ X309)|(~(in @ X311 @ omega)|(in @ X311 @ X309)))&((in @ (esk4_1 @ X309) @ X309)|~(in @ emptyset @ X309)|(~(in @ X311 @ omega)|(in @ X311 @ X309))))&(~(in @ (setadjoin @ (esk4_1 @ X309) @ (esk4_1 @ X309)) @ X309)|~(in @ emptyset @ X309)|(~(in @ X311 @ omega)|(in @ X311 @ X309))))&((((((in @ (esk8_3 @ X312 @ X313 @ X318) @ X313)|~(in @ X318 @ (esk7_2 @ X312 @ X313))|(in @ (esk5_2 @ X312 @ X313) @ X313))&((X312 @ (esk8_3 @ X312 @ X313 @ X318) @ X318)|~(in @ X318 @ (esk7_2 @ X312 @ X313))|(in @ (esk5_2 @ X312 @ X313) @ X313)))&(~(in @ X321 @ X313)|~(X312 @ X321 @ X320)|(in @ X320 @ (esk7_2 @ X312 @ X313))|(in @ (esk5_2 @ X312 @ X313) @ X313)))&(((((in @ (esk8_3 @ X312 @ X313 @ X318) @ X313)|~(in @ X318 @ (esk7_2 @ X312 @ X313))|((X312 @ (esk5_2 @ X312 @ X313) @ (esk6_3 @ X312 @ X313 @ X315))|~(X312 @ (esk5_2 @ X312 @ X313) @ X315)))&((X312 @ (esk8_3 @ X312 @ X313 @ X318) @ X318)|~(in @ X318 @ (esk7_2 @ X312 @ X313))|((X312 @ (esk5_2 @ X312 @ X313) @ (esk6_3 @ X312 @ X313 @ X315))|~(X312 @ (esk5_2 @ X312 @ X313) @ X315))))&(~(in @ X321 @ X313)|~(X312 @ X321 @ X320)|(in @ X320 @ (esk7_2 @ X312 @ X313))|((X312 @ (esk5_2 @ X312 @ X313) @ (esk6_3 @ X312 @ X313 @ X315))|~(X312 @ (esk5_2 @ X312 @ X313) @ X315))))&((((in @ (esk8_3 @ X312 @ X313 @ X318) @ X313)|~(in @ X318 @ (esk7_2 @ X312 @ X313))|(((X315)!=(esk6_3 @ X312 @ X313 @ X315))|~(X312 @ (esk5_2 @ X312 @ X313) @ X315)))&((X312 @ (esk8_3 @ X312 @ X313 @ X318) @ X318)|~(in @ X318 @ (esk7_2 @ X312 @ X313))|(((X315)!=(esk6_3 @ X312 @ X313 @ X315))|~(X312 @ (esk5_2 @ X312 @ X313) @ X315))))&(~(in @ X321 @ X313)|~(X312 @ X321 @ X320)|(in @ X320 @ (esk7_2 @ X312 @ X313))|(((X315)!=(esk6_3 @ X312 @ X313 @ X315))|~(X312 @ (esk5_2 @ X312 @ X313) @ X315))))))&((((in @ (esk9_1 @ X322) @ X322)|~(in @ X323 @ X322))&(~(in @ X325 @ (esk9_1 @ X322))|~(in @ X325 @ X322)|~(in @ X323 @ X322)))&((epred1_0)&((descrp)&((~(in @ X328 @ X326)|(~(X327 @ X328)|(in @ X328 @ (dsetconstr @ X326 @ X327))))&((~(in @ X331 @ (dsetconstr @ X329 @ X330))|(in @ X331 @ X329))&((~(in @ X334 @ (dsetconstr @ X332 @ X333))|(X333 @ X334))&(((((X335 @ (esk11_1 @ X335))|((X335 @ (esk10_2 @ X335 @ X336))|~(X335 @ X336)))&(~(X335 @ X339)|((esk11_1 @ X335)=(X339))|((X335 @ (esk10_2 @ X335 @ X336))|~(X335 @ X336))))&(((X335 @ (esk11_1 @ X335))|(((X336)!=(esk10_2 @ X335 @ X336))|~(X335 @ X336)))&(~(X335 @ X339)|((esk11_1 @ X335)=(X339))|(((X336)!=(esk10_2 @ X335 @ X336))|~(X335 @ X336)))))&((~(in @ X341 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X340)))))|(X340))&((~(in @ X342 @ emptyset)|(X343))&((~(in @ X344 @ emptyset)|~($true))&(~(in @ X345 @ emptyset)&((((X346 @ (esk12_2 @ X346 @ X347))|~(X346 @ X347)|(X346 @ (esk13_1 @ X346)))&(((X347)!=(esk12_2 @ X346 @ X347))|~(X346 @ X347)|(X346 @ (esk13_1 @ X346))))&(((((in @ (esk15_2 @ X350 @ X351) @ X351)|((X350)=(X351))|(in @ (esk14_2 @ X350 @ X351) @ X350))&(~(in @ (esk15_2 @ X350 @ X351) @ X350)|((X350)=(X351))|(in @ (esk14_2 @ X350 @ X351) @ X350)))&(((in @ (esk15_2 @ X350 @ X351) @ X351)|((X350)=(X351))|~(in @ (esk14_2 @ X350 @ X351) @ X351))&(~(in @ (esk15_2 @ X350 @ X351) @ X350)|((X350)=(X351))|~(in @ (esk14_2 @ X350 @ X351) @ X351))))&(((in @ (esk16_1 @ X354) @ X354)|((X354)=(emptyset)))&(((in @ (esk17_1 @ X356) @ X356)|((X356)=(emptyset)))&(((~(in @ X360 @ (dsetconstr @ X358 @ X359))|(X359 @ X360)|~(in @ X360 @ X358))&(~(X359 @ X360)|(in @ X360 @ (dsetconstr @ X358 @ X359))|~(in @ X360 @ X358)))&((((X361)=(emptyset))|(in @ (esk18_1 @ X361) @ X361))&((~(in @ X365 @ X363)|(~(X364 @ X365)|((dsetconstr @ X363 @ X364)!=(emptyset))))&((~(in @ X367 @ X366)|((X366)!=(emptyset)))&((in @ X368 @ (setadjoin @ X368 @ X369))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X372 @ X371)|(in @ X372 @ (setadjoin @ X370 @ X371)))&(((((in @ X375 @ X374)|(X376)|((X375)=(X373))|~(in @ X375 @ (setadjoin @ X373 @ X374)))&(~(X376)|(X376)|((X375)=(X373))|~(in @ X375 @ (setadjoin @ X373 @ X374))))&(((in @ X375 @ X374)|(X376)|~(X376)|~(in @ X375 @ (setadjoin @ X373 @ X374)))&(~(X376)|(X376)|~(X376)|~(in @ X375 @ (setadjoin @ X373 @ X374)))))&((~(in @ X379 @ (setadjoin @ X377 @ X378))|(((X379)=(X377))|(in @ X379 @ X378)))&(((dsetconstr @ X380 @ (^[Z0:$i]:($true)))=(X380))&((((in @ (esk19_2 @ X381 @ X382) @ X382)|(in @ X382 @ (powerset @ X381)))&(~(in @ (esk19_2 @ X381 @ X382) @ X381)|(in @ X382 @ (powerset @ X381))))&((in @ emptyset @ (powerset @ X384))&((in @ emptyset @ (powerset @ X385))&((~(in @ X387 @ (powerset @ X386))|(~(in @ X388 @ X387)|(in @ X388 @ X386)))&((~(in @ X390 @ X391)|(~(in @ X391 @ X389)|(in @ X390 @ (setunion @ X389))))&((((in @ X393 @ (esk20_3 @ X392 @ X393 @ X394))|(X394)|~(in @ X393 @ (setunion @ X392)))&(((in @ (esk20_3 @ X392 @ X393 @ X394) @ X392)|(X394)|~(in @ X393 @ (setunion @ X392)))&(~(X394)|(X394)|~(in @ X393 @ (setunion @ X392)))))&((~(in @ X397 @ X396)|(in @ X397 @ (powerset @ (setunion @ X396))))&((((~(X398 @ X402)|((X402)=(esk22_1 @ X398))|((X398 @ (esk21_2 @ X398 @ X399))|~(X398 @ X399)))&(((X403)!=(esk22_1 @ X398))|(X398 @ X403)|((X398 @ (esk21_2 @ X398 @ X399))|~(X398 @ X399))))&((~(X398 @ X402)|((X402)=(esk22_1 @ X398))|(((X399)!=(esk21_2 @ X398 @ X399))|~(X398 @ X399)))&(((X403)!=(esk22_1 @ X398))|(X398 @ X403)|(((X399)!=(esk21_2 @ X398 @ X399))|~(X398 @ X399)))))&((((in @ (esk23_1 @ X404) @ X404)|((X404)=(emptyset)))&(($true)|((X404)=(emptyset))))&((~(in @ X406 @ (setadjoin @ X407 @ emptyset))|((X406)=(X407)))&((((X408)=(X409))|~(in @ X409 @ (setadjoin @ X408 @ emptyset)))&((((X410)!=(X411))|(in @ X410 @ (setadjoin @ X411 @ emptyset)))&((~(in @ X412 @ (setadjoin @ X413 @ emptyset))|(in @ X413 @ (setadjoin @ X412 @ emptyset)))&((in @ esk26_0 @ (setadjoin @ esk24_0 @ (setadjoin @ esk25_0 @ emptyset)))&(((esk26_0)!=(esk24_0))&((esk26_0)!=(esk25_0)))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(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])])])])])])])).
% 0.20/0.30 thf(c_0_76, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ X3)|((X2)=(X4))|~((in @ X2 @ (setadjoin @ X4 @ X3))))), inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_75])])])).
% 0.20/0.30 thf(c_0_77, negated_conjecture, (in @ esk26_0 @ (setadjoin @ esk24_0 @ (setadjoin @ esk25_0 @ emptyset))), inference(split_conjunct,[status(thm)],[c_0_75])).
% 0.20/0.30 thf(c_0_78, negated_conjecture, ((esk26_0)!=(esk24_0)), inference(split_conjunct,[status(thm)],[c_0_75])).
% 0.20/0.30 thf(c_0_79, negated_conjecture, (in @ esk26_0 @ (setadjoin @ esk25_0 @ emptyset)), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_76, c_0_77]), c_0_78])).
% 0.20/0.30 thf(c_0_80, negated_conjecture, ((esk26_0)!=(esk25_0)), inference(split_conjunct,[status(thm)],[c_0_75])).
% 0.20/0.30 thf(c_0_81, negated_conjecture, ![X2:$i]:(~((in @ X2 @ emptyset))), inference(split_conjunct,[status(thm)],[c_0_75])).
% 0.20/0.30 thf(c_0_82, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_76, c_0_79]), c_0_80]), c_0_81]), ['proof']).
% 0.20/0.30 % SZS output end CNFRefutation
% 0.20/0.30 % Parsed axioms : 109
% 0.20/0.30 % Removed by relevancy pruning/SinE : 59
% 0.20/0.30 % Initial clauses : 99
% 0.20/0.30 % Removed in clause preprocessing : 5
% 0.20/0.30 % Initial clauses in saturation : 94
% 0.20/0.30 % Processed clauses : 156
% 0.20/0.30 % ...of these trivial : 1
% 0.20/0.30 % ...subsumed : 69
% 0.20/0.30 % ...remaining for further processing : 86
% 0.20/0.30 % Other redundant clauses eliminated : 5
% 0.20/0.30 % Clauses deleted for lack of memory : 0
% 0.20/0.30 % Backward-subsumed : 0
% 0.20/0.30 % Backward-rewritten : 3
% 0.20/0.30 % Generated clauses : 426
% 0.20/0.30 % ...of the previous two non-redundant : 356
% 0.20/0.30 % ...aggressively subsumed : 0
% 0.20/0.30 % Contextual simplify-reflections : 0
% 0.20/0.30 % Paramodulations : 421
% 0.20/0.30 % Factorizations : 0
% 0.20/0.30 % NegExts : 0
% 0.20/0.30 % Equation resolutions : 5
% 0.20/0.30 % Disequality decompositions : 0
% 0.20/0.30 % Total rewrite steps : 92
% 0.20/0.30 % ...of those cached : 76
% 0.20/0.30 % Propositional unsat checks : 0
% 0.20/0.30 % Propositional check models : 0
% 0.20/0.30 % Propositional check unsatisfiable : 0
% 0.20/0.30 % Propositional clauses : 0
% 0.20/0.30 % Propositional clauses after purity: 0
% 0.20/0.30 % Propositional unsat core size : 0
% 0.20/0.30 % Propositional preprocessing time : 0.000
% 0.20/0.30 % Propositional encoding time : 0.000
% 0.20/0.30 % Propositional solver time : 0.000
% 0.20/0.30 % Success case prop preproc time : 0.000
% 0.20/0.30 % Success case prop encoding time : 0.000
% 0.20/0.30 % Success case prop solver time : 0.000
% 0.20/0.30 % Current number of processed clauses : 79
% 0.20/0.30 % Positive orientable unit clauses : 15
% 0.20/0.30 % Positive unorientable unit clauses: 0
% 0.20/0.30 % Negative unit clauses : 3
% 0.20/0.30 % Non-unit-clauses : 61
% 0.20/0.30 % Current number of unprocessed clauses: 285
% 0.20/0.30 % ...number of literals in the above : 791
% 0.20/0.30 % Current number of archived formulas : 0
% 0.20/0.30 % Current number of archived clauses : 3
% 0.20/0.30 % Clause-clause subsumption calls (NU) : 991
% 0.20/0.30 % Rec. Clause-clause subsumption calls : 747
% 0.20/0.30 % Non-unit clause-clause subsumptions : 47
% 0.20/0.30 % Unit Clause-clause subsumption calls : 32
% 0.20/0.30 % Rewrite failures with RHS unbound : 0
% 0.20/0.30 % BW rewrite match attempts : 8
% 0.20/0.30 % BW rewrite match successes : 3
% 0.20/0.30 % Condensation attempts : 0
% 0.20/0.30 % Condensation successes : 0
% 0.20/0.30 % Termbank termtop insertions : 17050
% 0.20/0.30 % Search garbage collected termcells : 4820
% 0.20/0.30
% 0.20/0.30 % -------------------------------------------------
% 0.20/0.30 % User time : 0.017 s
% 0.20/0.30 % System time : 0.007 s
% 0.20/0.30 % Total time : 0.024 s
% 0.20/0.30 % Maximum resident set size: 4768 pages
% 0.20/0.30
% 0.20/0.30 % -------------------------------------------------
% 0.20/0.30 % User time : 0.022 s
% 0.20/0.30 % System time : 0.010 s
% 0.20/0.30 % Total time : 0.032 s
% 0.20/0.30 % Maximum resident set size: 4864 pages
% 0.20/0.30 % E exiting
%------------------------------------------------------------------------------