%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU530^1 : 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 : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:24:23 AM UTC 2026
% Result : Theorem 0.11s 0.26s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU530^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.16 % Computer : n007.cluster.edu
% 0.11/0.16 % Model : x86_64 x86_64
% 0.11/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.16 % Memory : 8046.5625MB
% 0.11/0.16 % OS : Linux 6.8.0-71-generic
% 0.11/0.16 % CPULimit : 300
% 0.11/0.16 % WCLimit : 300
% 0.11/0.16 % DateTime : Tue Sep 29 13:46:26 UTC 2026
% 0.11/0.16 % CPUTime :
% 0.11/0.16 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.21 Running higher-order theorem proving
% 0.11/0.23 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.r1n9Z5iX7m/E---3.1_3386413.p
% 0.11/0.26 % Version: 3.5.1-ho
% 0.11/0.26 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.11/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.11/0.26 % Starting sh5l with 300s (1) cores
% 0.11/0.26 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.26 % Starting new_bool_2 with 300s (1) cores
% 0.11/0.26 % sh5l with pid 3386427 completed with status 0
% 0.11/0.26 % Result found by sh5l
% 0.11/0.26 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.11/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.11/0.26 % Starting sh5l with 300s (1) cores
% 0.11/0.26 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.11/0.26 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.11/0.26 % Search class: HGHSM-FFMS31-SHFSMSBN
% 0.11/0.26 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.26 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.26 % SubtermCWHack with pid 3386432 completed with status 0
% 0.11/0.26 % Result found by SubtermCWHack
% 0.11/0.26 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.11/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.11/0.26 % Starting sh5l with 300s (1) cores
% 0.11/0.26 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.11/0.26 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.11/0.26 % Search class: HGHSM-FFMS31-SHFSMSBN
% 0.11/0.26 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.26 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.26 % Preprocessing time : 0.002 s
% 0.11/0.26
% 0.11/0.26 % Proof found!
% 0.11/0.26 % SZS status Theorem
% 0.11/0.26 % SZS output start CNFRefutation
% 0.11/0.26 thf(decl_23, type, in: $i > $i > $o).
% 0.11/0.26 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.11/0.26 thf(decl_25, type, setextAx: $o).
% 0.11/0.26 thf(decl_26, type, emptyset: $i).
% 0.11/0.26 thf(decl_27, type, emptysetAx: $o).
% 0.11/0.26 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.11/0.26 thf(decl_29, type, setadjoinAx: $o).
% 0.11/0.26 thf(decl_30, type, powerset: $i > $i).
% 0.11/0.26 thf(decl_31, type, powersetAx: $o).
% 0.11/0.26 thf(decl_32, type, setunion: $i > $i).
% 0.11/0.26 thf(decl_33, type, setunionAx: $o).
% 0.11/0.26 thf(decl_34, type, omega: $i).
% 0.11/0.26 thf(decl_35, type, omega0Ax: $o).
% 0.11/0.26 thf(decl_36, type, omegaSAx: $o).
% 0.11/0.26 thf(decl_37, type, omegaIndAx: $o).
% 0.11/0.26 thf(decl_38, type, replAx: $o).
% 0.11/0.26 thf(decl_39, type, foundationAx: $o).
% 0.11/0.26 thf(decl_40, type, wellorderingAx: $o).
% 0.11/0.26 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.11/0.26 thf(decl_42, type, descrp: $o).
% 0.11/0.26 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.11/0.26 thf(decl_44, type, dsetconstrI: $o).
% 0.11/0.26 thf(decl_45, type, dsetconstrEL: $o).
% 0.11/0.26 thf(decl_46, type, dsetconstrER: $o).
% 0.11/0.26 thf(decl_47, type, exuE1: $o).
% 0.11/0.26 thf(decl_48, type, prop2set: $o > $i).
% 0.11/0.26 thf(decl_49, type, prop2setE: $o).
% 0.11/0.26 thf(decl_50, type, emptysetE: $o).
% 0.11/0.26 thf(decl_51, type, emptysetimpfalse: $o).
% 0.11/0.26 thf(decl_52, type, notinemptyset: $o).
% 0.11/0.26 thf(decl_53, type, exuE3e: $o).
% 0.11/0.26 thf(decl_54, type, setext: $o).
% 0.11/0.26 thf(decl_55, type, emptyI: $o).
% 0.11/0.26 thf(decl_56, type, noeltsimpempty: $o).
% 0.11/0.26 thf(decl_57, type, setbeta: $o).
% 0.11/0.26 thf(decl_58, type, nonempty: $i > $o).
% 0.11/0.26 thf(decl_59, type, nonemptyE1: $o).
% 0.11/0.26 thf(decl_60, type, nonemptyI: $o).
% 0.11/0.26 thf(decl_61, type, nonemptyI1: $o).
% 0.11/0.26 thf(decl_62, type, setadjoinIL: $o).
% 0.11/0.26 thf(decl_63, type, emptyinunitempty: $o).
% 0.11/0.26 thf(decl_64, type, setadjoinIR: $o).
% 0.11/0.26 thf(decl_65, type, setadjoinE: $o).
% 0.11/0.26 thf(decl_66, type, setadjoinOr: $o).
% 0.11/0.26 thf(decl_67, type, setoftrueEq: $o).
% 0.11/0.26 thf(decl_68, type, powersetI: $o).
% 0.11/0.26 thf(decl_69, type, emptyinPowerset: $o).
% 0.11/0.26 thf(decl_70, type, emptyInPowerset: $o).
% 0.11/0.26 thf(decl_71, type, powersetE: $o).
% 0.11/0.26 thf(decl_72, type, setunionI: $o).
% 0.11/0.26 thf(decl_73, type, setunionE: $o).
% 0.11/0.26 thf(decl_74, type, subPowSU: $o).
% 0.11/0.26 thf(decl_75, type, exuE2: $o).
% 0.11/0.26 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.11/0.26 thf(decl_77, type, uniqinunit: $o).
% 0.11/0.26 thf(decl_78, type, notinsingleton: $o).
% 0.11/0.26 thf(decl_79, type, eqinunit: $o).
% 0.11/0.26 thf(decl_80, type, epred1_0: $o).
% 0.11/0.26 thf(decl_81, type, esk1_2: $i > $i > $i).
% 0.11/0.26 thf(decl_82, type, esk2_2: $i > $i > $i).
% 0.11/0.26 thf(decl_83, type, esk3_2: $i > $i > $i).
% 0.11/0.26 thf(decl_84, type, esk4_1: $i > $i).
% 0.11/0.26 thf(decl_85, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.11/0.26 thf(decl_86, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.11/0.26 thf(decl_87, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.11/0.26 thf(decl_88, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.11/0.26 thf(decl_89, type, esk9_1: $i > $i).
% 0.11/0.26 thf(decl_90, type, esk10_2: ($i > $o) > $i > $i).
% 0.11/0.26 thf(decl_91, type, esk11_2: ($i > $o) > $i > $i).
% 0.11/0.26 thf(decl_92, type, esk12_1: ($i > $o) > $i).
% 0.11/0.26 thf(decl_93, type, esk13_2: ($i > $o) > $i > $i).
% 0.11/0.26 thf(decl_94, type, esk14_1: ($i > $o) > $i).
% 0.11/0.26 thf(decl_95, type, esk15_2: $i > $i > $i).
% 0.11/0.26 thf(decl_96, type, esk16_2: $i > $i > $i).
% 0.11/0.26 thf(decl_97, type, esk17_1: $i > $i).
% 0.11/0.26 thf(decl_98, type, esk18_1: $i > $i).
% 0.11/0.26 thf(decl_99, type, esk19_1: $i > $i).
% 0.11/0.26 thf(decl_100, type, esk20_2: $i > $i > $i).
% 0.11/0.26 thf(decl_101, type, esk21_3: $i > $i > $o > $i).
% 0.11/0.26 thf(decl_102, type, esk22_2: ($i > $o) > $i > $i).
% 0.11/0.26 thf(decl_103, type, esk23_1: ($i > $o) > $i).
% 0.11/0.26 thf(decl_104, type, esk24_1: $i > $i).
% 0.11/0.26 thf(decl_105, type, esk25_0: $i).
% 0.11/0.26 thf(decl_106, type, esk26_0: $i).
% 0.11/0.26 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', exuE2)).
% 0.11/0.26 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', exu)).
% 0.11/0.26 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', nonempty)).
% 0.11/0.26 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', replAx)).
% 0.11/0.26 thf(prop2set, axiom, ((prop2set)=(^[X10:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[X2:$i]:((X10)))))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', prop2set)).
% 0.11/0.26 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', exuE1)).
% 0.11/0.26 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', descrp)).
% 0.11/0.26 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', exuE3e)).
% 0.11/0.26 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', nonemptyI)).
% 0.11/0.26 thf(singletonsswitch, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset)))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', singletonsswitch)).
% 0.11/0.26 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', nonemptyImpWitness)).
% 0.11/0.26 thf(prop2setE, axiom, ((prop2setE)<=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', prop2setE)).
% 0.11/0.26 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', dsetconstrER)).
% 0.11/0.26 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', dsetconstrEL)).
% 0.11/0.26 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', dsetconstrI)).
% 0.11/0.26 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', nonemptyE1)).
% 0.11/0.26 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', setbeta)).
% 0.11/0.26 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', setoftrueEq)).
% 0.11/0.26 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', nonemptyI1)).
% 0.11/0.26 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X14:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X14))))=>(X14)))))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', setunionE)).
% 0.11/0.26 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', emptyinPowerset)).
% 0.11/0.26 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', powersetE)).
% 0.11/0.26 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', emptyInPowerset)).
% 0.11/0.26 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', subPowSU)).
% 0.11/0.26 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', uniqinunit)).
% 0.11/0.26 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', notinsingleton)).
% 0.11/0.26 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', eqinunit)).
% 0.11/0.26 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', foundationAx)).
% 0.11/0.26 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', omegaIndAx)).
% 0.11/0.26 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', omegaSAx)).
% 0.11/0.26 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', omega0Ax)).
% 0.11/0.26 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', setunionAx)).
% 0.11/0.26 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', powersetAx)).
% 0.11/0.26 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', wellorderingAx)).
% 0.11/0.26 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12))))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', emptysetE)).
% 0.11/0.26 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', emptysetimpfalse)).
% 0.11/0.26 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', noeltsimpempty)).
% 0.11/0.26 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', emptyI)).
% 0.11/0.26 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', setext)).
% 0.11/0.26 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', notinemptyset)).
% 0.11/0.26 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', setadjoinOr)).
% 0.11/0.26 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X13:$o]:(((((X3)=(X2))=>(X13))=>(((in @ X3 @ X4)=>(X13))=>(X13))))))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', setadjoinE)).
% 0.11/0.26 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', setadjoinIR)).
% 0.11/0.26 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', emptyinunitempty)).
% 0.11/0.26 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', setadjoinIL)).
% 0.11/0.26 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', setunionI)).
% 0.11/0.26 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', powersetI)).
% 0.11/0.26 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', setadjoinAx)).
% 0.11/0.26 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', emptysetAx)).
% 0.11/0.26 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.r1n9Z5iX7m/E---3.1_3386413.p', setextAx)).
% 0.11/0.26 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])).
% 0.11/0.26 thf(c_0_51, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.11/0.26 thf(c_0_52, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.11/0.26 thf(c_0_53, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.11/0.26 thf(c_0_54, plain, ((prop2set)=(^[Z0:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[Z1:$i]:((Z0)))))), inference(fof_simplification,[status(thm)],[prop2set])).
% 0.11/0.26 thf(c_0_55, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.11/0.26 thf(c_0_56, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.11/0.26 thf(c_0_57, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.11/0.26 thf(c_0_58, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.11/0.26 thf(c_0_59, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[singletonsswitch])).
% 0.11/0.26 thf(c_0_60, plain, ((exuE2)=(![X1:$i > $o]:((((?[X151:$i]:(((((X1 @ X151)))&(![X152:$i]:(((((X1 @ X152)))=>(((X151)=(X152))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_50, c_0_51])).
% 0.11/0.26 thf(c_0_61, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_52])).
% 0.11/0.26 thf(c_0_62, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X143:$i]:(((((X6 @ X2 @ X143)))&(![X144:$i]:(((((X6 @ X2 @ X144)))=>(((X143)=(X144)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_53, c_0_51])).
% 0.11/0.26 thf(c_0_63, axiom, ((prop2setE)=(![X11:$o, X2:$i]:((((in @ X2 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:(((X11)))))))=>((X11)))))), inference(apply_def,[status(thm)],[prop2setE, c_0_54])).
% 0.11/0.26 thf(c_0_64, plain, ((exuE1)=(![X1:$i > $o]:((((?[X147:$i]:(((((X1 @ X147)))&(![X148:$i]:(((((X1 @ X148)))=>(((X147)=(X148))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_55, c_0_51])).
% 0.11/0.26 thf(c_0_65, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.11/0.26 thf(c_0_66, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.11/0.26 thf(c_0_67, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.11/0.26 thf(c_0_68, plain, ((descrp)=(![X1:$i > $o]:((((?[X145:$i]:(((((X1 @ X145)))&(![X146:$i]:(((((X1 @ X146)))=>(((X145)=(X146))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_56, c_0_51])).
% 0.11/0.26 thf(c_0_69, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_52])).
% 0.11/0.26 thf(c_0_70, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.11/0.26 thf(c_0_71, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X149:$i]:(((((X1 @ X149)))&(![X150:$i]:(((((X1 @ X150)))=>(((X149)=(X150))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_57, c_0_51])).
% 0.11/0.26 thf(c_0_72, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_58, c_0_52])).
% 0.11/0.26 thf(c_0_73, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.11/0.26 thf(c_0_74, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_52])).
% 0.11/0.26 thf(c_0_75, plain, ((epred1_0)<=>![X182:$i]:(?[X183:$i]:((((![X184:$i]:(((in @ X184 @ X183)=>![X185:$i]:(((in @ X185 @ X184)=>(in @ X185 @ X182)))))&![X186:$i, X187:$i]:((((in @ X186 @ X182)&(in @ X187 @ X182))=>(![X188:$i]:(((in @ X188 @ X183)=>((in @ X186 @ X188)<=>(in @ X187 @ X188))))=>((X186)=(X187))))))&![X189:$i, X190:$i]:((((in @ X189 @ X183)&(in @ X190 @ X183))=>(![X191:$i]:(((in @ X191 @ X189)=>(in @ X191 @ X190)))|![X192:$i]:(((in @ X192 @ X190)=>(in @ X192 @ X189)))))))&![X193:$i]:(((![X194:$i]:(((in @ X194 @ X193)=>(in @ X194 @ X182)))&?[X195:$i]:((in @ X195 @ X193)))=>?[X196:$i, X197:$i]:(((((in @ X196 @ X183)&(in @ X197 @ X193))&~(?[X198:$i]:(((in @ X198 @ X196)&(in @ X198 @ X193)))))&![X199:$i]:(((in @ X199 @ X183)=>(![X200:$i]:(((in @ X200 @ X199)=>(in @ X200 @ X196)))|(in @ X197 @ X199)))))))))))), introduced(definition)).
% 0.11/0.26 thf(c_0_76, negated_conjecture, ~((![X153:$i, X154:$i]:((![X155:$i]:(((in @ X155 @ X153)<=>(in @ X155 @ X154)))=>((X153)=(X154))))=>(![X156:$i]:(~(in @ X156 @ emptyset))=>(![X157:$i, X158:$i, X159:$i]:(((in @ X159 @ (setadjoin @ X157 @ X158))<=>(((X159)=(X157))|(in @ X159 @ X158))))=>(![X160:$i, X161:$i]:(((in @ X161 @ (powerset @ X160))<=>![X162:$i]:(((in @ X162 @ X161)=>(in @ X162 @ X160)))))=>(![X163:$i, X164:$i]:(((in @ X164 @ (setunion @ X163))<=>?[X165:$i]:(((in @ X164 @ X165)&(in @ X165 @ X163)))))=>((in @ emptyset @ omega)=>(![X166:$i]:(((in @ X166 @ omega)=>(in @ (setadjoin @ X166 @ X166) @ omega)))=>(![X167:$i]:((((in @ emptyset @ X167)&![X168:$i]:((((in @ X168 @ omega)&(in @ X168 @ X167))=>(in @ (setadjoin @ X168 @ X168) @ X167))))=>![X169:$i]:(((in @ X169 @ omega)=>(in @ X169 @ X167)))))=>(![X170:$i > $i > $o, X171:$i]:((![X172:$i]:(((in @ X172 @ X171)=>?[X173:$i]:(((X170 @ X172 @ X173)&![X174:$i]:(((X170 @ X172 @ X174)=>((X173)=(X174))))))))=>?[X175:$i]:(![X176:$i]:(((in @ X176 @ X175)<=>?[X177:$i]:(((in @ X177 @ X171)&(X170 @ X177 @ X176))))))))=>(![X178:$i]:((?[X179:$i]:((in @ X179 @ X178))=>?[X180:$i]:(((in @ X180 @ X178)&~(?[X181:$i]:(((in @ X181 @ X180)&(in @ X181 @ X178))))))))=>((epred1_0)=>(![X201:$i > $o]:((?[X202:$i]:(((X201 @ X202)&![X203:$i]:(((X201 @ X203)=>((X202)=(X203))))))=>(X201 @ (descr @ (^[Z0:$i]:(X201 @ Z0))))))=>(![X204:$i, X205:$i > $o, X206:$i]:(((in @ X206 @ X204)=>((X205 @ X206)=>(in @ X206 @ (dsetconstr @ X204 @ X205)))))=>(![X207:$i, X208:$i > $o, X209:$i]:(((in @ X209 @ (dsetconstr @ X207 @ X208))=>(in @ X209 @ X207)))=>(![X210:$i, X211:$i > $o, X212:$i]:(((in @ X212 @ (dsetconstr @ X210 @ X211))=>(X211 @ X212)))=>(![X213:$i > $o]:((?[X214:$i]:(((X213 @ X214)&![X215:$i]:(((X213 @ X215)=>((X214)=(X215))))))=>?[X216:$i]:(((X213 @ X216)&![X217:$i]:(((X213 @ X217)=>((X216)=(X217))))))))=>(![X218:$o, X219:$i]:(((in @ X219 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X218)))))=>(X218)))=>(![X220:$i]:(((in @ X220 @ emptyset)=>![X221:$o]:((X221))))=>(![X222:$i]:(((in @ X222 @ emptyset)=>~($true)))=>(![X223:$i]:(~(in @ X223 @ emptyset))=>(![X224:$i > $o]:((?[X225:$i]:(((X224 @ X225)&![X226:$i]:(((X224 @ X226)=>((X225)=(X226))))))=>?[X227:$i]:((X224 @ X227))))=>(![X228:$i, X229:$i]:((![X230:$i]:(((in @ X230 @ X228)=>(in @ X230 @ X229)))=>(![X231:$i]:(((in @ X231 @ X229)=>(in @ X231 @ X228)))=>((X228)=(X229)))))=>(![X232:$i]:((![X233:$i]:(~(in @ X233 @ X232))=>((X232)=(emptyset))))=>(![X234:$i]:((![X235:$i]:(~(in @ X235 @ X234))=>((X234)=(emptyset))))=>(![X236:$i, X237:$i > $o, X238:$i]:(((in @ X238 @ X236)=>((in @ X238 @ (dsetconstr @ X236 @ X237))<=>(X237 @ X238))))=>(![X239:$i]:((((X239)!=(emptyset))=>?[X240:$i]:((in @ X240 @ X239))))=>(![X241:$i, X242:$i > $o, X243:$i]:(((in @ X243 @ X241)=>((X242 @ X243)=>((dsetconstr @ X241 @ X242)!=(emptyset)))))=>(![X244:$i]:((?[X245:$i]:((in @ X245 @ X244))=>((X244)!=(emptyset))))=>(![X246:$i, X247:$i]:((in @ X246 @ (setadjoin @ X246 @ X247)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X248:$i, X249:$i, X250:$i]:(((in @ X250 @ X249)=>(in @ X250 @ (setadjoin @ X248 @ X249))))=>(![X251:$i, X252:$i, X253:$i]:(((in @ X253 @ (setadjoin @ X251 @ X252))=>![X254:$o]:(((((X253)=(X251))=>(X254))=>(((in @ X253 @ X252)=>(X254))=>(X254))))))=>(![X255:$i, X256:$i, X257:$i]:(((in @ X257 @ (setadjoin @ X255 @ X256))=>(((X257)=(X255))|(in @ X257 @ X256))))=>(![X258:$i]:(((dsetconstr @ X258 @ (^[Z0:$i]:($true)))=(X258)))=>(![X259:$i, X260:$i]:((![X261:$i]:(((in @ X261 @ X260)=>(in @ X261 @ X259)))=>(in @ X260 @ (powerset @ X259))))=>(![X262:$i]:((in @ emptyset @ (powerset @ X262)))=>(![X263:$i]:((in @ emptyset @ (powerset @ X263)))=>(![X264:$i, X265:$i, X266:$i]:(((in @ X265 @ (powerset @ X264))=>((in @ X266 @ X265)=>(in @ X266 @ X264))))=>(![X267:$i, X268:$i, X269:$i]:(((in @ X268 @ X269)=>((in @ X269 @ X267)=>(in @ X268 @ (setunion @ X267)))))=>(![X270:$i, X271:$i]:(((in @ X271 @ (setunion @ X270))=>![X272:$o]:((![X273:$i]:(((in @ X271 @ X273)=>((in @ X273 @ X270)=>(X272))))=>(X272)))))=>(![X274:$i, X275:$i]:(((in @ X275 @ X274)=>(in @ X275 @ (powerset @ (setunion @ X274)))))=>(![X276:$i > $o]:((?[X277:$i]:(((X276 @ X277)&![X278:$i]:(((X276 @ X278)=>((X277)=(X278))))))=>?[X279:$i]:(![X280:$i]:(((X276 @ X280)<=>((X280)=(X279)))))))=>(![X281:$i]:((((X281)!=(emptyset))=>?[X282:$i]:(((in @ X282 @ X281)&$true))))=>(![X283:$i, X284:$i]:(((in @ X283 @ (setadjoin @ X284 @ emptyset))=>((X283)=(X284))))=>(![X285:$i, X286:$i]:((((X285)!=(X286))=>~(in @ X286 @ (setadjoin @ X285 @ emptyset))))=>(![X287:$i, X288:$i]:((((X287)=(X288))=>(in @ X287 @ (setadjoin @ X288 @ 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(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_59, setunionE]), emptyinPowerset]), powersetE]), emptyInPowerset]), subPowSU]), c_0_60]), c_0_61]), uniqinunit]), notinsingleton]), eqinunit]), foundationAx]), c_0_62]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), wellorderingAx]), emptysetE]), c_0_63]), c_0_64]), c_0_65]), c_0_66]), c_0_67]), c_0_68]), emptysetimpfalse]), c_0_69]), c_0_70]), noeltsimpempty]), emptyI]), setext]), c_0_71]), notinemptyset]), c_0_72]), c_0_73]), setadjoinOr]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), setunionI]), c_0_74]), powersetI]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_75])).
% 0.11/0.26 thf(c_0_77, 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 > $o, X327:$i, X329:$i, X330:$i > $o, X331:$i, X332:$i, X333:$i > $o, X334:$i, X335:$i, X336:$i > $o, X337:$i, X338:$i > $o, X339:$i, X342:$i, X343:$o, X344:$i, X345:$i, X346:$o, X347:$i, X348:$i, X349:$i > $o, X350:$i, X353:$i, X354:$i, X357:$i, X359:$i, X361:$i, X362:$i > $o, X363:$i, X364:$i, X366:$i, X367:$i > $o, X368:$i, X369:$i, X370:$i, X371:$i, X372:$i, X373:$i, X374:$i, X375:$i, X376:$i, X377:$i, X378:$i, X379:$o, X380:$i, X381:$i, X382:$i, X383:$i, X384:$i, X385:$i, X387:$i, X388:$i, X389:$i, X390:$i, X391:$i, X392:$i, X393:$i, X394:$i, X395:$i, X396:$i, X397:$o, X399:$i, X400:$i, X401:$i > $o, X402:$i, X405:$i, X406:$i, X407:$i, X409:$i, X410:$i, X411:$i, X412:$i, X413:$i, X414:$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)&((((X326 @ (esk10_2 @ X326 @ X327))|~(X326 @ X327)|(X326 @ (descr @ X326)))&(((X327)!=(esk10_2 @ X326 @ X327))|~(X326 @ X327)|(X326 @ (descr @ X326))))&((~(in @ X331 @ X329)|(~(X330 @ X331)|(in @ X331 @ (dsetconstr @ X329 @ X330))))&((~(in @ X334 @ (dsetconstr @ X332 @ X333))|(in @ X334 @ X332))&((~(in @ X337 @ (dsetconstr @ X335 @ X336))|(X336 @ X337))&(((((X338 @ (esk12_1 @ X338))|((X338 @ (esk11_2 @ X338 @ X339))|~(X338 @ X339)))&(~(X338 @ X342)|((esk12_1 @ X338)=(X342))|((X338 @ (esk11_2 @ X338 @ X339))|~(X338 @ X339))))&(((X338 @ (esk12_1 @ X338))|(((X339)!=(esk11_2 @ X338 @ X339))|~(X338 @ X339)))&(~(X338 @ X342)|((esk12_1 @ X338)=(X342))|(((X339)!=(esk11_2 @ X338 @ X339))|~(X338 @ X339)))))&((~(in @ X344 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X343)))))|(X343))&((~(in @ X345 @ emptyset)|(X346))&((~(in @ X347 @ emptyset)|~($true))&(~(in @ X348 @ emptyset)&((((X349 @ (esk13_2 @ X349 @ X350))|~(X349 @ X350)|(X349 @ (esk14_1 @ X349)))&(((X350)!=(esk13_2 @ X349 @ X350))|~(X349 @ X350)|(X349 @ (esk14_1 @ X349))))&(((((in @ (esk16_2 @ X353 @ X354) @ X354)|((X353)=(X354))|(in @ (esk15_2 @ X353 @ X354) @ X353))&(~(in @ (esk16_2 @ X353 @ X354) @ X353)|((X353)=(X354))|(in @ (esk15_2 @ X353 @ X354) @ X353)))&(((in @ (esk16_2 @ X353 @ X354) @ X354)|((X353)=(X354))|~(in @ (esk15_2 @ X353 @ X354) @ X354))&(~(in @ (esk16_2 @ X353 @ X354) @ X353)|((X353)=(X354))|~(in @ (esk15_2 @ X353 @ X354) @ X354))))&(((in @ (esk17_1 @ X357) @ X357)|((X357)=(emptyset)))&(((in @ (esk18_1 @ X359) @ X359)|((X359)=(emptyset)))&(((~(in @ X363 @ (dsetconstr @ X361 @ X362))|(X362 @ X363)|~(in @ X363 @ X361))&(~(X362 @ X363)|(in @ X363 @ (dsetconstr @ X361 @ X362))|~(in @ X363 @ X361)))&((((X364)=(emptyset))|(in @ (esk19_1 @ X364) @ X364))&((~(in @ X368 @ X366)|(~(X367 @ X368)|((dsetconstr @ X366 @ X367)!=(emptyset))))&((~(in @ X370 @ X369)|((X369)!=(emptyset)))&((in @ X371 @ (setadjoin @ X371 @ X372))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X375 @ X374)|(in @ X375 @ (setadjoin @ X373 @ X374)))&(((((in @ X378 @ X377)|(X379)|((X378)=(X376))|~(in @ X378 @ (setadjoin @ X376 @ X377)))&(~(X379)|(X379)|((X378)=(X376))|~(in @ X378 @ (setadjoin @ X376 @ X377))))&(((in @ X378 @ X377)|(X379)|~(X379)|~(in @ X378 @ (setadjoin @ X376 @ X377)))&(~(X379)|(X379)|~(X379)|~(in @ X378 @ (setadjoin @ X376 @ X377)))))&((~(in @ X382 @ (setadjoin @ X380 @ X381))|(((X382)=(X380))|(in @ X382 @ X381)))&(((dsetconstr @ X383 @ (^[Z0:$i]:($true)))=(X383))&((((in @ (esk20_2 @ X384 @ X385) @ X385)|(in @ X385 @ (powerset @ X384)))&(~(in @ (esk20_2 @ X384 @ X385) @ X384)|(in @ X385 @ (powerset @ X384))))&((in @ emptyset @ (powerset @ X387))&((in @ emptyset @ (powerset @ X388))&((~(in @ X390 @ (powerset @ X389))|(~(in @ X391 @ X390)|(in @ X391 @ X389)))&((~(in @ X393 @ X394)|(~(in @ X394 @ X392)|(in @ X393 @ (setunion @ X392))))&((((in @ X396 @ (esk21_3 @ X395 @ X396 @ X397))|(X397)|~(in @ X396 @ (setunion @ X395)))&(((in @ (esk21_3 @ X395 @ X396 @ X397) @ X395)|(X397)|~(in @ X396 @ (setunion @ X395)))&(~(X397)|(X397)|~(in @ X396 @ (setunion @ X395)))))&((~(in @ X400 @ X399)|(in @ X400 @ (powerset @ (setunion @ X399))))&((((~(X401 @ X405)|((X405)=(esk23_1 @ X401))|((X401 @ (esk22_2 @ X401 @ X402))|~(X401 @ X402)))&(((X406)!=(esk23_1 @ X401))|(X401 @ X406)|((X401 @ (esk22_2 @ X401 @ X402))|~(X401 @ X402))))&((~(X401 @ X405)|((X405)=(esk23_1 @ X401))|(((X402)!=(esk22_2 @ X401 @ X402))|~(X401 @ X402)))&(((X406)!=(esk23_1 @ X401))|(X401 @ X406)|(((X402)!=(esk22_2 @ X401 @ X402))|~(X401 @ X402)))))&((((in @ (esk24_1 @ X407) @ X407)|((X407)=(emptyset)))&(($true)|((X407)=(emptyset))))&((~(in @ X409 @ (setadjoin @ X410 @ emptyset))|((X409)=(X410)))&((((X411)=(X412))|~(in @ X412 @ (setadjoin @ X411 @ emptyset)))&((((X413)!=(X414))|(in @ X413 @ (setadjoin @ X414 @ emptyset)))&((in @ esk25_0 @ (setadjoin @ esk26_0 @ emptyset))&~(in @ esk26_0 @ (setadjoin @ esk25_0 @ emptyset)))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_76])])])])])])])).
% 0.11/0.26 thf(c_0_78, negated_conjecture, ![X3:$i, X2:$i]:((((X2)=(X3))|~((in @ X3 @ (setadjoin @ X2 @ emptyset))))), inference(split_conjunct,[status(thm)],[c_0_77])).
% 0.11/0.26 thf(c_0_79, negated_conjecture, (in @ esk25_0 @ (setadjoin @ esk26_0 @ emptyset)), inference(split_conjunct,[status(thm)],[c_0_77])).
% 0.11/0.26 thf(c_0_80, negated_conjecture, ~((in @ esk26_0 @ (setadjoin @ esk25_0 @ emptyset))), inference(split_conjunct,[status(thm)],[c_0_77])).
% 0.11/0.26 thf(c_0_81, negated_conjecture, ((esk26_0)=(esk25_0)), inference(spm,[status(thm)],[c_0_78, c_0_79])).
% 0.11/0.26 thf(c_0_82, negated_conjecture, ![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_77])).
% 0.11/0.26 thf(c_0_83, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_80, c_0_81]), c_0_82])]), ['proof']).
% 0.11/0.26 % SZS output end CNFRefutation
% 0.11/0.26 % Parsed axioms : 107
% 0.11/0.26 % Removed by relevancy pruning/SinE : 57
% 0.11/0.26 % Initial clauses : 98
% 0.11/0.26 % Removed in clause preprocessing : 5
% 0.11/0.26 % Initial clauses in saturation : 93
% 0.11/0.26 % Processed clauses : 38
% 0.11/0.26 % ...of these trivial : 1
% 0.11/0.26 % ...subsumed : 10
% 0.11/0.26 % ...remaining for further processing : 27
% 0.11/0.26 % Other redundant clauses eliminated : 3
% 0.11/0.26 % Clauses deleted for lack of memory : 0
% 0.11/0.26 % Backward-subsumed : 0
% 0.11/0.26 % Backward-rewritten : 3
% 0.11/0.26 % Generated clauses : 30
% 0.11/0.26 % ...of the previous two non-redundant : 24
% 0.11/0.26 % ...aggressively subsumed : 0
% 0.11/0.26 % Contextual simplify-reflections : 0
% 0.11/0.26 % Paramodulations : 27
% 0.11/0.26 % Factorizations : 0
% 0.11/0.26 % NegExts : 0
% 0.11/0.26 % Equation resolutions : 3
% 0.11/0.26 % Disequality decompositions : 0
% 0.11/0.26 % Total rewrite steps : 11
% 0.11/0.26 % ...of those cached : 1
% 0.11/0.26 % Propositional unsat checks : 0
% 0.11/0.26 % Propositional check models : 0
% 0.11/0.26 % Propositional check unsatisfiable : 0
% 0.11/0.26 % Propositional clauses : 0
% 0.11/0.26 % Propositional clauses after purity: 0
% 0.11/0.26 % Propositional unsat core size : 0
% 0.11/0.26 % Propositional preprocessing time : 0.000
% 0.11/0.26 % Propositional encoding time : 0.000
% 0.11/0.26 % Propositional solver time : 0.000
% 0.11/0.26 % Success case prop preproc time : 0.000
% 0.11/0.26 % Success case prop encoding time : 0.000
% 0.11/0.26 % Success case prop solver time : 0.000
% 0.11/0.26 % Current number of processed clauses : 21
% 0.11/0.26 % Positive orientable unit clauses : 10
% 0.11/0.26 % Positive unorientable unit clauses: 0
% 0.11/0.26 % Negative unit clauses : 1
% 0.11/0.26 % Non-unit-clauses : 10
% 0.11/0.26 % Current number of unprocessed clauses: 79
% 0.11/0.26 % ...number of literals in the above : 258
% 0.11/0.26 % Current number of archived formulas : 0
% 0.11/0.26 % Current number of archived clauses : 3
% 0.11/0.26 % Clause-clause subsumption calls (NU) : 34
% 0.11/0.26 % Rec. Clause-clause subsumption calls : 34
% 0.11/0.26 % Non-unit clause-clause subsumptions : 4
% 0.11/0.26 % Unit Clause-clause subsumption calls : 13
% 0.11/0.26 % Rewrite failures with RHS unbound : 0
% 0.11/0.26 % BW rewrite match attempts : 4
% 0.11/0.26 % BW rewrite match successes : 3
% 0.11/0.26 % Condensation attempts : 0
% 0.11/0.26 % Condensation successes : 0
% 0.11/0.26 % Termbank termtop insertions : 12551
% 0.11/0.26 % Search garbage collected termcells : 4903
% 0.11/0.26
% 0.11/0.26 % -------------------------------------------------
% 0.11/0.26 % User time : 0.014 s
% 0.11/0.26 % System time : 0.004 s
% 0.11/0.26 % Total time : 0.018 s
% 0.11/0.26 % Maximum resident set size: 4764 pages
% 0.11/0.26
% 0.11/0.26 % -------------------------------------------------
% 0.11/0.26 % User time : 0.016 s
% 0.11/0.26 % System time : 0.006 s
% 0.11/0.26 % Total time : 0.023 s
% 0.11/0.26 % Maximum resident set size: 4864 pages
% 0.11/0.26 % E exiting
%------------------------------------------------------------------------------