%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU548^1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/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 08:24:28 AM UTC 2026
% Result : Theorem 0.08s 0.28s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU548^1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n001.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 13:55:20 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p
% 0.08/0.28 % Version: 3.5.1-ho
% 0.08/0.28 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.08/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.28 % Starting sh5l with 300s (1) cores
% 0.08/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.28 % Starting new_bool_2 with 300s (1) cores
% 0.08/0.28 % sh5l with pid 1277359 completed with status 0
% 0.08/0.28 % Result found by sh5l
% 0.08/0.28 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.08/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.28 % Starting sh5l with 300s (1) cores
% 0.08/0.28 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.08/0.28 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.08/0.28 % Search class: HGHSM-FFMM31-SHFMMSBN
% 0.08/0.28 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.28 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.28 % SubtermCWHack with pid 1277364 completed with status 0
% 0.08/0.28 % Result found by SubtermCWHack
% 0.08/0.28 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.08/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.28 % Starting sh5l with 300s (1) cores
% 0.08/0.28 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.08/0.28 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.08/0.28 % Search class: HGHSM-FFMM31-SHFMMSBN
% 0.08/0.28 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.28 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.28 % Preprocessing time : 0.004 s
% 0.08/0.28
% 0.08/0.28 % Proof found!
% 0.08/0.28 % SZS status Theorem
% 0.08/0.28 % SZS output start CNFRefutation
% 0.08/0.28 thf(decl_23, type, in: $i > $i > $o).
% 0.08/0.28 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.08/0.28 thf(decl_25, type, setextAx: $o).
% 0.08/0.28 thf(decl_26, type, emptyset: $i).
% 0.08/0.28 thf(decl_27, type, emptysetAx: $o).
% 0.08/0.28 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.08/0.28 thf(decl_29, type, setadjoinAx: $o).
% 0.08/0.28 thf(decl_30, type, powerset: $i > $i).
% 0.08/0.28 thf(decl_31, type, powersetAx: $o).
% 0.08/0.28 thf(decl_32, type, setunion: $i > $i).
% 0.08/0.28 thf(decl_33, type, setunionAx: $o).
% 0.08/0.28 thf(decl_34, type, omega: $i).
% 0.08/0.28 thf(decl_35, type, omega0Ax: $o).
% 0.08/0.28 thf(decl_36, type, omegaSAx: $o).
% 0.08/0.28 thf(decl_37, type, omegaIndAx: $o).
% 0.08/0.28 thf(decl_38, type, replAx: $o).
% 0.08/0.28 thf(decl_39, type, foundationAx: $o).
% 0.08/0.28 thf(decl_40, type, wellorderingAx: $o).
% 0.08/0.28 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.08/0.28 thf(decl_42, type, descrp: $o).
% 0.08/0.28 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.08/0.28 thf(decl_44, type, dsetconstrI: $o).
% 0.08/0.28 thf(decl_45, type, dsetconstrEL: $o).
% 0.08/0.28 thf(decl_46, type, dsetconstrER: $o).
% 0.08/0.28 thf(decl_47, type, exuE1: $o).
% 0.08/0.28 thf(decl_48, type, prop2set: $o > $i).
% 0.08/0.28 thf(decl_49, type, prop2setE: $o).
% 0.08/0.28 thf(decl_50, type, emptysetE: $o).
% 0.08/0.28 thf(decl_51, type, emptysetimpfalse: $o).
% 0.08/0.28 thf(decl_52, type, notinemptyset: $o).
% 0.08/0.28 thf(decl_53, type, exuE3e: $o).
% 0.08/0.28 thf(decl_54, type, setext: $o).
% 0.08/0.28 thf(decl_55, type, emptyI: $o).
% 0.08/0.28 thf(decl_56, type, noeltsimpempty: $o).
% 0.08/0.28 thf(decl_57, type, setbeta: $o).
% 0.08/0.28 thf(decl_58, type, nonempty: $i > $o).
% 0.08/0.28 thf(decl_59, type, nonemptyE1: $o).
% 0.08/0.28 thf(decl_60, type, nonemptyI: $o).
% 0.08/0.28 thf(decl_61, type, nonemptyI1: $o).
% 0.08/0.28 thf(decl_62, type, setadjoinIL: $o).
% 0.08/0.28 thf(decl_63, type, emptyinunitempty: $o).
% 0.08/0.28 thf(decl_64, type, setadjoinIR: $o).
% 0.08/0.28 thf(decl_65, type, setadjoinE: $o).
% 0.08/0.28 thf(decl_66, type, setadjoinOr: $o).
% 0.08/0.28 thf(decl_67, type, setoftrueEq: $o).
% 0.08/0.28 thf(decl_68, type, powersetI: $o).
% 0.08/0.28 thf(decl_69, type, emptyinPowerset: $o).
% 0.08/0.28 thf(decl_70, type, emptyInPowerset: $o).
% 0.08/0.28 thf(decl_71, type, powersetE: $o).
% 0.08/0.28 thf(decl_72, type, setunionI: $o).
% 0.08/0.28 thf(decl_73, type, setunionE: $o).
% 0.08/0.28 thf(decl_74, type, subPowSU: $o).
% 0.08/0.28 thf(decl_75, type, exuE2: $o).
% 0.08/0.28 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.08/0.28 thf(decl_77, type, uniqinunit: $o).
% 0.08/0.28 thf(decl_78, type, notinsingleton: $o).
% 0.08/0.28 thf(decl_79, type, eqinunit: $o).
% 0.08/0.28 thf(decl_80, type, singletonsswitch: $o).
% 0.08/0.28 thf(decl_81, type, upairsetE: $o).
% 0.08/0.28 thf(decl_82, type, upairsetIL: $o).
% 0.08/0.28 thf(decl_83, type, upairsetIR: $o).
% 0.08/0.28 thf(decl_84, type, emptyE1: $o).
% 0.08/0.28 thf(decl_85, type, vacuousDall: $o).
% 0.08/0.28 thf(decl_86, type, quantDeMorgan1: $o).
% 0.08/0.28 thf(decl_87, type, quantDeMorgan2: $o).
% 0.08/0.28 thf(decl_88, type, quantDeMorgan3: $o).
% 0.08/0.28 thf(decl_89, type, quantDeMorgan4: $o).
% 0.08/0.28 thf(decl_90, type, prop2setI: $o).
% 0.08/0.28 thf(decl_91, type, set2prop: $i > $o).
% 0.08/0.28 thf(decl_92, type, prop2set2propI: $o).
% 0.08/0.28 thf(decl_93, type, notdexE: $o).
% 0.08/0.28 thf(decl_94, type, notdallE: $o).
% 0.08/0.28 thf(decl_95, type, exuI1: $o).
% 0.08/0.28 thf(decl_96, type, exuI3: $o).
% 0.08/0.28 thf(decl_97, type, exuI2: $o).
% 0.08/0.28 thf(decl_98, type, inCongP: $o).
% 0.08/0.28 thf(decl_99, type, epred1_0: $o).
% 0.08/0.28 thf(decl_100, type, esk1_2: $i > $i > $i).
% 0.08/0.28 thf(decl_101, type, esk2_2: $i > $i > $i).
% 0.08/0.28 thf(decl_102, type, esk3_2: $i > $i > $i).
% 0.08/0.28 thf(decl_103, type, esk4_1: $i > $i).
% 0.08/0.28 thf(decl_104, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.08/0.28 thf(decl_105, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.08/0.28 thf(decl_106, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.08/0.28 thf(decl_107, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.08/0.28 thf(decl_108, type, esk9_1: $i > $i).
% 0.08/0.28 thf(decl_109, type, esk10_2: ($i > $o) > $i > $i).
% 0.08/0.28 thf(decl_110, type, esk11_2: ($i > $o) > $i > $i).
% 0.08/0.28 thf(decl_111, type, esk12_1: ($i > $o) > $i).
% 0.08/0.28 thf(decl_112, type, esk13_2: ($i > $o) > $i > $i).
% 0.08/0.28 thf(decl_113, type, esk14_1: ($i > $o) > $i).
% 0.08/0.28 thf(decl_114, type, esk15_2: $i > $i > $i).
% 0.08/0.28 thf(decl_115, type, esk16_2: $i > $i > $i).
% 0.08/0.28 thf(decl_116, type, esk17_1: $i > $i).
% 0.08/0.28 thf(decl_117, type, esk18_1: $i > $i).
% 0.08/0.28 thf(decl_118, type, esk19_1: $i > $i).
% 0.08/0.28 thf(decl_119, type, esk20_2: $i > $i > $i).
% 0.08/0.28 thf(decl_120, type, esk21_3: $i > $i > $o > $i).
% 0.08/0.28 thf(decl_121, type, esk22_2: ($i > $o) > $i > $i).
% 0.08/0.28 thf(decl_122, type, esk23_1: ($i > $o) > $i).
% 0.08/0.28 thf(decl_123, type, esk24_1: $i > $i).
% 0.08/0.28 thf(decl_124, type, esk25_2: $i > ($i > $o) > $i).
% 0.08/0.28 thf(decl_125, type, esk26_2: $i > ($i > $o) > $i).
% 0.08/0.28 thf(decl_126, type, esk27_2: $i > ($i > $o) > $i).
% 0.08/0.28 thf(decl_127, type, esk28_2: $i > ($i > $o) > $i).
% 0.08/0.28 thf(decl_128, type, esk29_2: $i > ($i > $o) > $i).
% 0.08/0.28 thf(decl_129, type, esk30_2: $i > ($i > $o) > $i).
% 0.08/0.28 thf(decl_130, type, esk31_2: ($i > $o) > $i > $i).
% 0.08/0.28 thf(decl_131, type, esk32_1: ($i > $o) > $i).
% 0.08/0.28 thf(decl_132, type, esk33_1: ($i > $o) > $i).
% 0.08/0.28 thf(decl_133, type, esk34_1: ($i > $o) > $i).
% 0.08/0.28 thf(decl_134, type, esk35_1: ($i > $o) > $i).
% 0.08/0.28 thf(decl_135, type, esk36_2: ($i > $o) > $i > $i).
% 0.08/0.28 thf(decl_136, type, esk37_1: ($i > $o) > $i).
% 0.08/0.28 thf(decl_137, type, esk38_0: $i).
% 0.08/0.28 thf(decl_138, type, esk39_0: $i).
% 0.08/0.28 thf(decl_139, type, esk40_0: $i).
% 0.08/0.28 thf(decl_140, type, esk41_0: $i).
% 0.08/0.28 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', exuI1)).
% 0.08/0.28 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', exu)).
% 0.08/0.28 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', exuI3)).
% 0.08/0.28 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', exuI2)).
% 0.08/0.28 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', exuE1)).
% 0.08/0.28 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', descrp)).
% 0.08/0.28 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', nonemptyI)).
% 0.08/0.28 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', nonempty)).
% 0.08/0.28 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', exuE3e)).
% 0.08/0.28 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', replAx)).
% 0.08/0.28 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', exuE2)).
% 0.08/0.28 thf(in__Cong, 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)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', in__Cong)).
% 0.08/0.28 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', emptyE1)).
% 0.08/0.28 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', dsetconstrER)).
% 0.08/0.28 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', dsetconstrEL)).
% 0.08/0.28 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', dsetconstrI)).
% 0.08/0.28 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', nonemptyE1)).
% 0.08/0.28 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', setbeta)).
% 0.08/0.28 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', nonemptyI1)).
% 0.08/0.28 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', setoftrueEq)).
% 0.08/0.28 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', nonemptyImpWitness)).
% 0.08/0.28 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', wellorderingAx)).
% 0.08/0.28 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', quantDeMorgan3)).
% 0.08/0.28 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', upairsetIR)).
% 0.08/0.28 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', vacuousDall)).
% 0.08/0.28 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', quantDeMorgan4)).
% 0.08/0.28 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', prop2setI)).
% 0.08/0.28 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', prop2set2propI)).
% 0.08/0.28 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', notdexE)).
% 0.08/0.28 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', notdallE)).
% 0.08/0.28 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', inCongP)).
% 0.08/0.28 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', foundationAx)).
% 0.08/0.28 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', prop2setE)).
% 0.08/0.28 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', noeltsimpempty)).
% 0.08/0.28 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', emptyI)).
% 0.08/0.28 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', setext)).
% 0.08/0.28 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', notinemptyset)).
% 0.08/0.28 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', emptysetimpfalse)).
% 0.08/0.28 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', emptysetE)).
% 0.08/0.28 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', setadjoinE)).
% 0.08/0.28 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', setadjoinIR)).
% 0.08/0.28 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', emptyinunitempty)).
% 0.08/0.28 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', setadjoinIL)).
% 0.08/0.28 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', setadjoinOr)).
% 0.08/0.28 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', setunionE)).
% 0.08/0.28 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', setunionI)).
% 0.08/0.28 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', powersetE)).
% 0.08/0.28 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', emptyInPowerset)).
% 0.08/0.28 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', emptyinPowerset)).
% 0.08/0.28 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', powersetI)).
% 0.08/0.28 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', subPowSU)).
% 0.08/0.28 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', upairsetE)).
% 0.08/0.28 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', singletonsswitch)).
% 0.08/0.28 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', eqinunit)).
% 0.08/0.28 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', notinsingleton)).
% 0.08/0.28 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', uniqinunit)).
% 0.08/0.28 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', quantDeMorgan1)).
% 0.08/0.28 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', upairsetIL)).
% 0.08/0.28 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', quantDeMorgan2)).
% 0.08/0.28 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', omegaIndAx)).
% 0.08/0.28 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', omegaSAx)).
% 0.08/0.28 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', omega0Ax)).
% 0.08/0.28 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', setunionAx)).
% 0.08/0.28 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', powersetAx)).
% 0.08/0.28 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', setadjoinAx)).
% 0.08/0.28 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', emptysetAx)).
% 0.08/0.28 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.EFxTpa1KTz/E---3.1_1277323.p', setextAx)).
% 0.08/0.28 thf(c_0_67, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 0.08/0.28 thf(c_0_68, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.08/0.28 thf(c_0_69, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.08/0.28 thf(c_0_70, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.08/0.28 thf(c_0_71, 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])).
% 0.08/0.28 thf(c_0_72, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.08/0.28 thf(c_0_73, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.08/0.28 thf(c_0_74, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.08/0.28 thf(c_0_75, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.08/0.28 thf(c_0_76, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.08/0.28 thf(c_0_77, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.08/0.28 thf(c_0_78, 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)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[in__Cong])).
% 0.08/0.28 thf(c_0_79, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
% 0.08/0.28 thf(c_0_80, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X211:$i]:(((((X1 @ X211)))&(![X212:$i]:(((((X1 @ X212)))=>(((X211)=(X212)))))))))))))), inference(apply_def,[status(thm)],[c_0_67, c_0_68])).
% 0.08/0.28 thf(c_0_81, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X213:$i]:(((((X1 @ X213)))&(![X214:$i]:(((((X1 @ X214)))=>(((X213)=(X214)))))))))))))))), inference(apply_def,[status(thm)],[c_0_69, c_0_68])).
% 0.08/0.28 thf(c_0_82, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X215:$i]:(((((X1 @ X215)))&(![X216:$i]:(((((X1 @ X216)))=>(((X215)=(X216)))))))))))))), inference(apply_def,[status(thm)],[c_0_70, c_0_68])).
% 0.08/0.28 thf(c_0_83, plain, ((exuE1)=(![X1:$i > $o]:((((?[X205:$i]:(((((X1 @ X205)))&(![X206:$i]:(((((X1 @ X206)))=>(((X205)=(X206))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_71, c_0_68])).
% 0.08/0.28 thf(c_0_84, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.08/0.28 thf(c_0_85, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.08/0.28 thf(c_0_86, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.08/0.28 thf(c_0_87, plain, ((descrp)=(![X1:$i > $o]:((((?[X203:$i]:(((((X1 @ X203)))&(![X204:$i]:(((((X1 @ X204)))=>(((X203)=(X204))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_72, c_0_68])).
% 0.08/0.28 thf(c_0_88, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_73, c_0_74])).
% 0.08/0.28 thf(c_0_89, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_74])).
% 0.08/0.28 thf(c_0_90, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X207:$i]:(((((X1 @ X207)))&(![X208:$i]:(((((X1 @ X208)))=>(((X207)=(X208))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_75, c_0_68])).
% 0.08/0.28 thf(c_0_91, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.08/0.28 thf(c_0_92, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X201:$i]:(((((X6 @ X2 @ X201)))&(![X202:$i]:(((((X6 @ X2 @ X202)))=>(((X201)=(X202)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_76, c_0_68])).
% 0.08/0.28 thf(c_0_93, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_74])).
% 0.08/0.28 thf(c_0_94, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.08/0.28 thf(c_0_95, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_74])).
% 0.08/0.28 thf(c_0_96, plain, ((exuE2)=(![X1:$i > $o]:((((?[X209:$i]:(((((X1 @ X209)))&(![X210:$i]:(((((X1 @ X210)))=>(((X209)=(X210))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_77, c_0_68])).
% 0.08/0.28 thf(c_0_97, plain, ((epred1_0)<=>![X246:$i]:(?[X247:$i]:((((![X248:$i]:(((in @ X248 @ X247)=>![X249:$i]:(((in @ X249 @ X248)=>(in @ X249 @ X246)))))&![X250:$i, X251:$i]:((((in @ X250 @ X246)&(in @ X251 @ X246))=>(![X252:$i]:(((in @ X252 @ X247)=>((in @ X250 @ X252)<=>(in @ X251 @ X252))))=>((X250)=(X251))))))&![X253:$i, X254:$i]:((((in @ X253 @ X247)&(in @ X254 @ X247))=>(![X255:$i]:(((in @ X255 @ X253)=>(in @ X255 @ X254)))|![X256:$i]:(((in @ X256 @ X254)=>(in @ X256 @ X253)))))))&![X257:$i]:(((![X258:$i]:(((in @ X258 @ X257)=>(in @ X258 @ X246)))&?[X259:$i]:((in @ X259 @ X257)))=>?[X260:$i, X261:$i]:(((((in @ X260 @ X247)&(in @ X261 @ X257))&~(?[X262:$i]:(((in @ X262 @ X260)&(in @ X262 @ X257)))))&![X263:$i]:(((in @ X263 @ X247)=>(![X264:$i]:(((in @ X264 @ X263)=>(in @ X264 @ X260)))|(in @ X261 @ X263)))))))))))), introduced(definition)).
% 0.08/0.28 thf(c_0_98, negated_conjecture, ~((![X217:$i, X218:$i]:((![X219:$i]:(((in @ X219 @ X217)<=>(in @ X219 @ X218)))=>((X217)=(X218))))=>(![X220:$i]:(~(in @ X220 @ emptyset))=>(![X221:$i, X222:$i, X223:$i]:(((in @ X223 @ (setadjoin @ X221 @ X222))<=>(((X223)=(X221))|(in @ X223 @ X222))))=>(![X224:$i, X225:$i]:(((in @ X225 @ (powerset @ X224))<=>![X226:$i]:(((in @ X226 @ X225)=>(in @ X226 @ X224)))))=>(![X227:$i, X228:$i]:(((in @ X228 @ (setunion @ X227))<=>?[X229:$i]:(((in @ X228 @ X229)&(in @ X229 @ X227)))))=>((in @ emptyset @ omega)=>(![X230:$i]:(((in @ X230 @ omega)=>(in @ (setadjoin @ X230 @ X230) @ omega)))=>(![X231:$i]:((((in @ emptyset @ X231)&![X232:$i]:((((in @ X232 @ omega)&(in @ X232 @ X231))=>(in @ (setadjoin @ X232 @ X232) @ X231))))=>![X233:$i]:(((in @ X233 @ omega)=>(in @ X233 @ X231)))))=>(![X234:$i > $i > $o, X235:$i]:((![X236:$i]:(((in @ X236 @ X235)=>?[X237:$i]:(((X234 @ X236 @ X237)&![X238:$i]:(((X234 @ X236 @ X238)=>((X237)=(X238))))))))=>?[X239:$i]:(![X240:$i]:(((in @ X240 @ X239)<=>?[X241:$i]:(((in @ X241 @ X235)&(X234 @ X241 @ X240))))))))=>(![X242:$i]:((?[X243:$i]:((in @ X243 @ X242))=>?[X244:$i]:(((in @ X244 @ X242)&~(?[X245:$i]:(((in @ X245 @ X244)&(in @ X245 @ X242))))))))=>((epred1_0)=>(![X265:$i > $o]:((?[X266:$i]:(((X265 @ X266)&![X267:$i]:(((X265 @ X267)=>((X266)=(X267))))))=>(X265 @ (descr @ (^[Z0:$i]:(X265 @ Z0))))))=>(![X268:$i, X269:$i > $o, X270:$i]:(((in @ X270 @ X268)=>((X269 @ X270)=>(in @ X270 @ (dsetconstr @ X268 @ X269)))))=>(![X271:$i, X272:$i > $o, X273:$i]:(((in @ X273 @ (dsetconstr @ X271 @ X272))=>(in @ X273 @ X271)))=>(![X274:$i, X275:$i > $o, X276:$i]:(((in @ X276 @ (dsetconstr @ X274 @ X275))=>(X275 @ X276)))=>(![X277:$i > $o]:((?[X278:$i]:(((X277 @ X278)&![X279:$i]:(((X277 @ X279)=>((X278)=(X279))))))=>?[X280:$i]:(((X277 @ X280)&![X281:$i]:(((X277 @ X281)=>((X280)=(X281))))))))=>(![X282:$o, X283:$i]:(((in @ X283 @ (prop2set @ ((X282))))=>(X282)))=>(![X284:$i]:(((in @ X284 @ emptyset)=>![X285:$o]:((X285))))=>(![X286:$i]:(((in @ X286 @ emptyset)=>~($true)))=>(![X287:$i]:(~(in @ X287 @ emptyset))=>(![X288:$i > $o]:((?[X289:$i]:(((X288 @ X289)&![X290:$i]:(((X288 @ X290)=>((X289)=(X290))))))=>?[X291:$i]:((X288 @ X291))))=>(![X292:$i, X293:$i]:((![X294:$i]:(((in @ X294 @ X292)=>(in @ X294 @ X293)))=>(![X295:$i]:(((in @ X295 @ X293)=>(in @ X295 @ X292)))=>((X292)=(X293)))))=>(![X296:$i]:((![X297:$i]:(~(in @ X297 @ X296))=>((X296)=(emptyset))))=>(![X298:$i]:((![X299:$i]:(~(in @ X299 @ X298))=>((X298)=(emptyset))))=>(![X300:$i, X301:$i > $o, X302:$i]:(((in @ X302 @ X300)=>((in @ X302 @ (dsetconstr @ X300 @ X301))<=>(X301 @ X302))))=>(![X303:$i]:((((X303)!=(emptyset))=>?[X304:$i]:((in @ X304 @ X303))))=>(![X305:$i, X306:$i > $o, X307:$i]:(((in @ X307 @ X305)=>((X306 @ X307)=>((dsetconstr @ X305 @ X306)!=(emptyset)))))=>(![X308:$i]:((?[X309:$i]:((in @ X309 @ X308))=>((X308)!=(emptyset))))=>(![X310:$i, X311:$i]:((in @ X310 @ (setadjoin @ X310 @ X311)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X312:$i, X313:$i, X314:$i]:(((in @ X314 @ X313)=>(in @ X314 @ (setadjoin @ X312 @ X313))))=>(![X315:$i, X316:$i, X317:$i]:(((in @ X317 @ (setadjoin @ X315 @ X316))=>![X318:$o]:(((((X317)=(X315))=>(X318))=>(((in @ X317 @ X316)=>(X318))=>(X318))))))=>(![X319:$i, X320:$i, X321:$i]:(((in @ X321 @ (setadjoin @ X319 @ X320))=>(((X321)=(X319))|(in @ X321 @ X320))))=>(![X322:$i]:(((dsetconstr @ X322 @ (^[Z0:$i]:($true)))=(X322)))=>(![X323:$i, X324:$i]:((![X325:$i]:(((in @ X325 @ X324)=>(in @ X325 @ X323)))=>(in @ X324 @ (powerset @ X323))))=>(![X326:$i]:((in @ emptyset @ (powerset @ X326)))=>(![X327:$i]:((in @ emptyset @ (powerset @ X327)))=>(![X328:$i, X329:$i, X330:$i]:(((in @ X329 @ (powerset @ X328))=>((in @ X330 @ X329)=>(in @ X330 @ X328))))=>(![X331:$i, X332:$i, X333:$i]:(((in @ X332 @ X333)=>((in @ X333 @ X331)=>(in @ X332 @ (setunion @ X331)))))=>(![X334:$i, X335:$i]:(((in @ X335 @ (setunion @ X334))=>![X336:$o]:((![X337:$i]:(((in @ X335 @ X337)=>((in @ X337 @ X334)=>(X336))))=>(X336)))))=>(![X338:$i, X339:$i]:(((in @ X339 @ X338)=>(in @ X339 @ (powerset @ (setunion @ X338)))))=>(![X340:$i > $o]:((?[X341:$i]:(((X340 @ X341)&![X342:$i]:(((X340 @ X342)=>((X341)=(X342))))))=>?[X343:$i]:(![X344:$i]:(((X340 @ X344)<=>((X344)=(X343)))))))=>(![X345:$i]:((((X345)!=(emptyset))=>?[X346:$i]:(((in @ X346 @ X345)&$true))))=>(![X347:$i, X348:$i]:(((in @ X347 @ (setadjoin @ X348 @ emptyset))=>((X347)=(X348))))=>(![X349:$i, X350:$i]:((((X349)!=(X350))=>~(in @ X350 @ (setadjoin @ X349 @ emptyset))))=>(![X351:$i, X352:$i]:((((X351)=(X352))=>(in @ X351 @ (setadjoin @ X352 @ emptyset))))=>(![X353:$i, X354:$i]:(((in @ X353 @ (setadjoin @ X354 @ emptyset))=>(in @ X354 @ (setadjoin @ X353 @ emptyset))))=>(![X355:$i, X356:$i, X357:$i]:(((in @ X357 @ (setadjoin @ X355 @ (setadjoin @ X356 @ emptyset)))=>(((X357)=(X355))|((X357)=(X356)))))=>(![X358:$i, X359:$i]:((in @ X358 @ (setadjoin @ X358 @ (setadjoin @ X359 @ emptyset))))=>(![X360:$i, X361:$i]:((in @ X361 @ (setadjoin @ X360 @ (setadjoin @ X361 @ emptyset))))=>(![X362:$i, X363:$i > $o]:((?[X364:$i]:(((in @ X364 @ X362)&(X363 @ X364)))=>(((dsetconstr @ X362 @ X363)=(emptyset))=>~($true))))=>(![X365:$i > $o, X366:$i]:(((in @ X366 @ emptyset)=>(X365 @ X366)))=>(![X367:$i, X368:$i > $o]:((~(![X369:$i]:(((in @ X369 @ X367)=>(X368 @ X369))))=>?[X370:$i]:(((in @ X370 @ X367)&~((X368 @ X370))))))=>(![X371:$i, X372:$i > $o]:((![X373:$i]:(((in @ X373 @ X371)=>~((X372 @ X373))))=>~(?[X374:$i]:(((in @ X374 @ X371)&(X372 @ X374))))))=>(![X375:$i, X376:$i > $o]:((~(?[X377:$i]:(((in @ X377 @ X375)&(X376 @ X377))))=>![X378:$i]:(((in @ X378 @ X375)=>~((X376 @ X378))))))=>(![X379:$i, X380:$i > $o]:((?[X381:$i]:(((in @ X381 @ X379)&~((X380 @ X381))))=>~(![X382:$i]:(((in @ X382 @ X379)=>(X380 @ X382))))))=>(![X383:$o]:(((X383)=>(in @ emptyset @ (prop2set @ ((X383))))))=>(![X384:$o]:(((X384)=>(set2prop @ (prop2set @ ((X384))))))=>(![X385:$i, X386:$i > $o]:((~(?[X387:$i]:(((in @ X387 @ X385)&(X386 @ X387))))=>![X388:$i]:(((in @ X388 @ X385)=>~((X386 @ X388))))))=>(![X389:$i, X390:$i > $o]:((~(![X391:$i]:(((in @ X391 @ X389)=>(X390 @ X391))))=>?[X392:$i]:(((in @ X392 @ X389)&~((X390 @ X392))))))=>(![X393:$i > $o]:((?[X394:$i]:(((X393 @ X394)&![X395:$i]:(((X393 @ X395)=>((X394)=(X395))))))=>?[X396:$i]:(((X393 @ X396)&![X397:$i]:(((X393 @ X397)=>((X396)=(X397))))))))=>(![X398:$i > $o]:((?[X399:$i]:((X398 @ X399))=>(![X400:$i, X401:$i]:(((X398 @ X400)=>((X398 @ X401)=>((X400)=(X401)))))=>?[X402:$i]:(((X398 @ X402)&![X403:$i]:(((X398 @ X403)=>((X402)=(X403)))))))))=>(![X404:$i > $o]:((?[X405:$i]:(![X406:$i]:(((X404 @ X406)<=>((X406)=(X405)))))=>?[X407:$i]:(((X404 @ X407)&![X408:$i]:(((X404 @ X408)=>((X407)=(X408))))))))=>(![X409:$i, X410:$i]:((((X409)=(X410))=>![X411:$i, X412:$i]:((((X411)=(X412))=>((in @ X411 @ X409)=>(in @ X412 @ X410))))))=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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)],[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_78, wellorderingAx]), quantDeMorgan3]), upairsetIR]), vacuousDall]), c_0_79]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_80]), c_0_81]), c_0_82]), inCongP]), c_0_83]), c_0_84]), c_0_85]), c_0_86]), c_0_87]), c_0_88]), c_0_89]), foundationAx]), prop2setE]), noeltsimpempty]), emptyI]), setext]), c_0_90]), notinemptyset]), emptysetimpfalse]), emptysetE]), c_0_91]), c_0_92]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), c_0_93]), setadjoinOr]), setunionE]), setunionI]), powersetE]), emptyInPowerset]), emptyinPowerset]), powersetI]), c_0_94]), subPowSU]), upairsetE]), singletonsswitch]), eqinunit]), notinsingleton]), uniqinunit]), c_0_95]), c_0_96]), quantDeMorgan1]), upairsetIL]), quantDeMorgan2]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_97])).
% 0.08/0.28 thf(c_0_99, negated_conjecture, ![X413:$i, X414:$i, X416:$i, X417:$i, X418:$i, X419:$i, X420:$i, X421:$i, X422:$i, X423:$i, X424:$i, X426:$i, X427:$i, X429:$i, X430:$i, X431:$i, X432:$i, X433:$i, X435:$i, X436:$i > $i > $o, X437:$i, X439:$i, X442:$i, X444:$i, X445:$i, X446:$i, X447:$i, X449:$i, X450:$i > $o, X451:$i, X453:$i, X454:$i > $o, X455:$i, X456:$i, X457:$i > $o, X458:$i, X459:$i, X460:$i > $o, X461:$i, X462:$i > $o, X463:$i, X466:$i, X467:$o, X468:$i, X469:$i, X470:$o, X471:$i, X472:$i, X473:$i > $o, X474:$i, X477:$i, X478:$i, X481:$i, X483:$i, X485:$i, X486:$i > $o, X487:$i, X488:$i, X490:$i, X491:$i > $o, X492:$i, X493:$i, X494:$i, X495:$i, X496:$i, X497:$i, X498:$i, X499:$i, X500:$i, X501:$i, X502:$i, X503:$o, X504:$i, X505:$i, X506:$i, X507:$i, X508:$i, X509:$i, X511:$i, X512:$i, X513:$i, X514:$i, X515:$i, X516:$i, X517:$i, X518:$i, X519:$i, X520:$i, X521:$o, X523:$i, X524:$i, X525:$i > $o, X526:$i, X529:$i, X530:$i, X531:$i, X533:$i, X534:$i, X535:$i, X536:$i, X537:$i, X538:$i, X539:$i, X540:$i, X541:$i, X542:$i, X543:$i, X544:$i, X545:$i, X546:$i, X547:$i, X548:$i, X549:$i > $o, X550:$i, X551:$i > $o, X552:$i, X553:$i, X554:$i > $o, X555:$i, X557:$i, X558:$i > $o, X560:$i, X561:$i, X562:$i > $o, X564:$i, X565:$i, X566:$i > $o, X567:$i, X569:$o, X570:$o, X571:$i, X572:$i > $o, X574:$i, X575:$i, X576:$i > $o, X577:$i, X579:$i > $o, X580:$i, X583:$i, X584:$i > $o, X585:$i, X589:$i, X590:$i > $o, X591:$i, X594:$i, X595:$i, X596:$i, X597:$i, X598:$i]:((((~(in @ (esk1_2 @ X413 @ X414) @ X413)|~(in @ (esk1_2 @ X413 @ X414) @ X414)|((X413)=(X414)))&((in @ (esk1_2 @ X413 @ X414) @ X413)|(in @ (esk1_2 @ X413 @ X414) @ X414)|((X413)=(X414))))&(~(in @ X416 @ emptyset)&(((~(in @ X419 @ (setadjoin @ X417 @ X418))|(((X419)=(X417))|(in @ X419 @ X418)))&((((X419)!=(X417))|(in @ X419 @ (setadjoin @ X417 @ X418)))&(~(in @ X419 @ X418)|(in @ X419 @ (setadjoin @ X417 @ X418)))))&(((~(in @ X421 @ (powerset @ X420))|(~(in @ X422 @ X421)|(in @ X422 @ X420)))&(((in @ (esk2_2 @ X423 @ X424) @ X424)|(in @ X424 @ (powerset @ X423)))&(~(in @ (esk2_2 @ X423 @ X424) @ X423)|(in @ X424 @ (powerset @ X423)))))&(((((in @ X427 @ (esk3_2 @ X426 @ X427))|~(in @ X427 @ (setunion @ X426)))&((in @ (esk3_2 @ X426 @ X427) @ X426)|~(in @ X427 @ (setunion @ X426))))&(~(in @ X430 @ X431)|~(in @ X431 @ X429)|(in @ X430 @ (setunion @ X429))))&((in @ emptyset @ omega)&((~(in @ X432 @ omega)|(in @ (setadjoin @ X432 @ X432) @ omega))&(((((in @ (esk4_1 @ X433) @ omega)|~(in @ emptyset @ X433)|(~(in @ X435 @ omega)|(in @ X435 @ X433)))&((in @ (esk4_1 @ X433) @ X433)|~(in @ emptyset @ X433)|(~(in @ X435 @ omega)|(in @ X435 @ X433))))&(~(in @ (setadjoin @ (esk4_1 @ X433) @ (esk4_1 @ X433)) @ X433)|~(in @ emptyset @ X433)|(~(in @ X435 @ omega)|(in @ X435 @ X433))))&((((((in @ (esk8_3 @ X436 @ X437 @ X442) @ X437)|~(in @ X442 @ (esk7_2 @ X436 @ X437))|(in @ (esk5_2 @ X436 @ X437) @ X437))&((X436 @ (esk8_3 @ X436 @ X437 @ X442) @ X442)|~(in @ X442 @ (esk7_2 @ X436 @ X437))|(in @ (esk5_2 @ X436 @ X437) @ X437)))&(~(in @ X445 @ X437)|~(X436 @ X445 @ X444)|(in @ X444 @ (esk7_2 @ X436 @ X437))|(in @ (esk5_2 @ X436 @ X437) @ X437)))&(((((in @ (esk8_3 @ X436 @ X437 @ X442) @ X437)|~(in @ X442 @ (esk7_2 @ X436 @ X437))|((X436 @ (esk5_2 @ X436 @ X437) @ (esk6_3 @ X436 @ X437 @ X439))|~(X436 @ (esk5_2 @ X436 @ X437) @ X439)))&((X436 @ (esk8_3 @ X436 @ X437 @ X442) @ X442)|~(in @ X442 @ (esk7_2 @ X436 @ X437))|((X436 @ (esk5_2 @ X436 @ X437) @ (esk6_3 @ X436 @ X437 @ X439))|~(X436 @ (esk5_2 @ X436 @ X437) @ X439))))&(~(in @ X445 @ X437)|~(X436 @ X445 @ X444)|(in @ X444 @ (esk7_2 @ X436 @ X437))|((X436 @ (esk5_2 @ X436 @ X437) @ (esk6_3 @ X436 @ X437 @ X439))|~(X436 @ (esk5_2 @ X436 @ X437) @ X439))))&((((in @ (esk8_3 @ X436 @ X437 @ X442) @ X437)|~(in @ X442 @ (esk7_2 @ X436 @ X437))|(((X439)!=(esk6_3 @ X436 @ X437 @ X439))|~(X436 @ (esk5_2 @ X436 @ X437) @ X439)))&((X436 @ (esk8_3 @ X436 @ X437 @ X442) @ X442)|~(in @ X442 @ (esk7_2 @ X436 @ X437))|(((X439)!=(esk6_3 @ X436 @ X437 @ X439))|~(X436 @ (esk5_2 @ X436 @ X437) @ X439))))&(~(in @ X445 @ X437)|~(X436 @ X445 @ X444)|(in @ X444 @ (esk7_2 @ X436 @ X437))|(((X439)!=(esk6_3 @ X436 @ X437 @ X439))|~(X436 @ (esk5_2 @ X436 @ X437) @ X439))))))&((((in @ (esk9_1 @ X446) @ X446)|~(in @ X447 @ X446))&(~(in @ X449 @ (esk9_1 @ X446))|~(in @ X449 @ X446)|~(in @ X447 @ X446)))&((epred1_0)&((((X450 @ (esk10_2 @ X450 @ X451))|~(X450 @ X451)|(X450 @ (descr @ X450)))&(((X451)!=(esk10_2 @ X450 @ X451))|~(X450 @ X451)|(X450 @ (descr @ X450))))&((~(in @ X455 @ X453)|(~(X454 @ X455)|(in @ X455 @ (dsetconstr @ X453 @ X454))))&((~(in @ X458 @ (dsetconstr @ X456 @ X457))|(in @ X458 @ X456))&((~(in @ X461 @ (dsetconstr @ X459 @ X460))|(X460 @ X461))&(((((X462 @ (esk12_1 @ X462))|((X462 @ (esk11_2 @ X462 @ X463))|~(X462 @ X463)))&(~(X462 @ X466)|((esk12_1 @ X462)=(X466))|((X462 @ (esk11_2 @ X462 @ X463))|~(X462 @ X463))))&(((X462 @ (esk12_1 @ X462))|(((X463)!=(esk11_2 @ X462 @ X463))|~(X462 @ X463)))&(~(X462 @ X466)|((esk12_1 @ X462)=(X466))|(((X463)!=(esk11_2 @ X462 @ X463))|~(X462 @ X463)))))&((~(in @ X468 @ (prop2set @ ((X467))))|(X467))&((~(in @ X469 @ emptyset)|(X470))&((~(in @ X471 @ emptyset)|~($true))&(~(in @ X472 @ emptyset)&((((X473 @ (esk13_2 @ X473 @ X474))|~(X473 @ X474)|(X473 @ (esk14_1 @ X473)))&(((X474)!=(esk13_2 @ X473 @ X474))|~(X473 @ X474)|(X473 @ (esk14_1 @ X473))))&(((((in @ (esk16_2 @ X477 @ X478) @ X478)|((X477)=(X478))|(in @ (esk15_2 @ X477 @ X478) @ X477))&(~(in @ (esk16_2 @ X477 @ X478) @ X477)|((X477)=(X478))|(in @ (esk15_2 @ X477 @ X478) @ X477)))&(((in @ (esk16_2 @ X477 @ X478) @ X478)|((X477)=(X478))|~(in @ (esk15_2 @ X477 @ X478) @ X478))&(~(in @ (esk16_2 @ X477 @ X478) @ X477)|((X477)=(X478))|~(in @ (esk15_2 @ X477 @ X478) @ X478))))&(((in @ (esk17_1 @ X481) @ X481)|((X481)=(emptyset)))&(((in @ (esk18_1 @ X483) @ X483)|((X483)=(emptyset)))&(((~(in @ X487 @ (dsetconstr @ X485 @ X486))|(X486 @ X487)|~(in @ X487 @ X485))&(~(X486 @ X487)|(in @ X487 @ (dsetconstr @ X485 @ X486))|~(in @ X487 @ X485)))&((((X488)=(emptyset))|(in @ (esk19_1 @ X488) @ X488))&((~(in @ X492 @ X490)|(~(X491 @ X492)|((dsetconstr @ X490 @ X491)!=(emptyset))))&((~(in @ X494 @ X493)|((X493)!=(emptyset)))&((in @ X495 @ (setadjoin @ X495 @ X496))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X499 @ X498)|(in @ X499 @ (setadjoin @ X497 @ X498)))&(((((in @ X502 @ X501)|(X503)|((X502)=(X500))|~(in @ X502 @ (setadjoin @ X500 @ X501)))&(~(X503)|(X503)|((X502)=(X500))|~(in @ X502 @ (setadjoin @ X500 @ X501))))&(((in @ X502 @ X501)|(X503)|~(X503)|~(in @ X502 @ (setadjoin @ X500 @ X501)))&(~(X503)|(X503)|~(X503)|~(in @ X502 @ (setadjoin @ X500 @ X501)))))&((~(in @ X506 @ (setadjoin @ X504 @ X505))|(((X506)=(X504))|(in @ X506 @ X505)))&(((dsetconstr @ X507 @ (^[Z0:$i]:($true)))=(X507))&((((in @ (esk20_2 @ X508 @ X509) @ X509)|(in @ X509 @ (powerset @ X508)))&(~(in @ (esk20_2 @ X508 @ X509) @ X508)|(in @ X509 @ (powerset @ X508))))&((in @ emptyset @ (powerset @ X511))&((in @ emptyset @ (powerset @ X512))&((~(in @ X514 @ (powerset @ X513))|(~(in @ X515 @ X514)|(in @ X515 @ X513)))&((~(in @ X517 @ X518)|(~(in @ X518 @ X516)|(in @ X517 @ (setunion @ X516))))&((((in @ X520 @ (esk21_3 @ X519 @ X520 @ X521))|(X521)|~(in @ X520 @ (setunion @ X519)))&(((in @ (esk21_3 @ X519 @ X520 @ X521) @ X519)|(X521)|~(in @ X520 @ (setunion @ X519)))&(~(X521)|(X521)|~(in @ X520 @ (setunion @ X519)))))&((~(in @ X524 @ X523)|(in @ X524 @ (powerset @ (setunion @ X523))))&((((~(X525 @ X529)|((X529)=(esk23_1 @ X525))|((X525 @ (esk22_2 @ X525 @ X526))|~(X525 @ X526)))&(((X530)!=(esk23_1 @ X525))|(X525 @ X530)|((X525 @ (esk22_2 @ X525 @ X526))|~(X525 @ X526))))&((~(X525 @ X529)|((X529)=(esk23_1 @ X525))|(((X526)!=(esk22_2 @ X525 @ X526))|~(X525 @ X526)))&(((X530)!=(esk23_1 @ X525))|(X525 @ X530)|(((X526)!=(esk22_2 @ X525 @ X526))|~(X525 @ X526)))))&((((in @ (esk24_1 @ X531) @ X531)|((X531)=(emptyset)))&(($true)|((X531)=(emptyset))))&((~(in @ X533 @ (setadjoin @ X534 @ emptyset))|((X533)=(X534)))&((((X535)=(X536))|~(in @ X536 @ (setadjoin @ X535 @ emptyset)))&((((X537)!=(X538))|(in @ X537 @ (setadjoin @ X538 @ emptyset)))&((~(in @ X539 @ (setadjoin @ X540 @ emptyset))|(in @ X540 @ (setadjoin @ X539 @ emptyset)))&((~(in @ X543 @ (setadjoin @ X541 @ (setadjoin @ X542 @ emptyset)))|(((X543)=(X541))|((X543)=(X542))))&((in @ X544 @ (setadjoin @ X544 @ (setadjoin @ X545 @ emptyset)))&((in @ X547 @ (setadjoin @ X546 @ (setadjoin @ X547 @ emptyset)))&((~(in @ X550 @ X548)|~(X549 @ X550)|(((dsetconstr @ X548 @ X549)!=(emptyset))|~($true)))&((~(in @ X552 @ emptyset)|(X551 @ X552))&((((in @ (esk25_2 @ X553 @ X554) @ X553)|(~(in @ X555 @ X553)|(X554 @ X555)))&(~(X554 @ (esk25_2 @ X553 @ X554))|(~(in @ X555 @ X553)|(X554 @ X555))))&((((in @ (esk26_2 @ X557 @ X558) @ X557)|(~(in @ X560 @ X557)|~(X558 @ X560)))&((X558 @ (esk26_2 @ X557 @ X558))|(~(in @ X560 @ X557)|~(X558 @ X560))))&((((in @ (esk27_2 @ X561 @ X562) @ X561)|(~(in @ X564 @ X561)|~(X562 @ X564)))&((X562 @ (esk27_2 @ X561 @ X562))|(~(in @ X564 @ X561)|~(X562 @ X564))))&((((in @ (esk28_2 @ X565 @ X566) @ X565)|(~(in @ X567 @ X565)|(X566 @ X567)))&(~(X566 @ (esk28_2 @ X565 @ X566))|(~(in @ X567 @ X565)|(X566 @ X567))))&((~(X569)|(in @ emptyset @ (prop2set @ ((X569)))))&((~(X570)|(set2prop @ (prop2set @ ((X570)))))&((((in @ (esk29_2 @ X571 @ X572) @ X571)|(~(in @ X574 @ X571)|~(X572 @ X574)))&((X572 @ (esk29_2 @ X571 @ X572))|(~(in @ X574 @ X571)|~(X572 @ X574))))&((((in @ (esk30_2 @ X575 @ X576) @ X575)|(~(in @ X577 @ X575)|(X576 @ X577)))&(~(X576 @ (esk30_2 @ X575 @ X576))|(~(in @ X577 @ X575)|(X576 @ X577))))&(((((X579 @ (esk32_1 @ X579))|((X579 @ (esk31_2 @ X579 @ X580))|~(X579 @ X580)))&(~(X579 @ X583)|((esk32_1 @ X579)=(X583))|((X579 @ (esk31_2 @ X579 @ X580))|~(X579 @ X580))))&(((X579 @ (esk32_1 @ X579))|(((X580)!=(esk31_2 @ X579 @ X580))|~(X579 @ X580)))&(~(X579 @ X583)|((esk32_1 @ X579)=(X583))|(((X580)!=(esk31_2 @ X579 @ X580))|~(X579 @ X580)))))&(((((X584 @ (esk35_1 @ X584))|(X584 @ (esk33_1 @ X584))|~(X584 @ X585))&(~(X584 @ X589)|((esk35_1 @ X584)=(X589))|(X584 @ (esk33_1 @ X584))|~(X584 @ X585)))&((((X584 @ (esk35_1 @ X584))|(X584 @ (esk34_1 @ X584))|~(X584 @ X585))&(~(X584 @ X589)|((esk35_1 @ X584)=(X589))|(X584 @ (esk34_1 @ X584))|~(X584 @ X585)))&(((X584 @ (esk35_1 @ X584))|((esk33_1 @ X584)!=(esk34_1 @ X584))|~(X584 @ X585))&(~(X584 @ X589)|((esk35_1 @ X584)=(X589))|((esk33_1 @ X584)!=(esk34_1 @ X584))|~(X584 @ X585)))))&(((((X590 @ (esk37_1 @ X590))|(~(X590 @ (esk36_2 @ X590 @ X591))|((esk36_2 @ X590 @ X591)!=(X591))))&(~(X590 @ X594)|((esk37_1 @ X590)=(X594))|(~(X590 @ (esk36_2 @ X590 @ X591))|((esk36_2 @ X590 @ X591)!=(X591)))))&(((X590 @ (esk37_1 @ X590))|((X590 @ (esk36_2 @ X590 @ X591))|((esk36_2 @ X590 @ X591)=(X591))))&(~(X590 @ X594)|((esk37_1 @ X590)=(X594))|((X590 @ (esk36_2 @ X590 @ X591))|((esk36_2 @ X590 @ X591)=(X591))))))&((((X595)!=(X596))|(((X597)!=(X598))|(~(in @ X597 @ X595)|(in @ X598 @ X596))))&(((esk38_0)=(esk39_0))&(((esk40_0)=(esk41_0))&((~(in @ esk40_0 @ esk38_0)|~(in @ esk41_0 @ esk39_0))&((in @ esk40_0 @ esk38_0)|(in @ esk41_0 @ esk39_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_98])])])])])])])).
% 0.08/0.28 thf(c_0_100, negated_conjecture, ((in @ esk40_0 @ esk38_0)|(in @ esk41_0 @ esk39_0)), inference(split_conjunct,[status(thm)],[c_0_99])).
% 0.08/0.28 thf(c_0_101, negated_conjecture, ((esk40_0)=(esk41_0)), inference(split_conjunct,[status(thm)],[c_0_99])).
% 0.08/0.28 thf(c_0_102, negated_conjecture, ((esk38_0)=(esk39_0)), inference(split_conjunct,[status(thm)],[c_0_99])).
% 0.08/0.28 thf(c_0_103, negated_conjecture, (~((in @ esk40_0 @ esk38_0))|~((in @ esk41_0 @ esk39_0))), inference(split_conjunct,[status(thm)],[c_0_99])).
% 0.08/0.28 thf(c_0_104, negated_conjecture, (in @ esk41_0 @ esk38_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_100, c_0_101]), c_0_102])])).
% 0.08/0.28 thf(c_0_105, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_103, c_0_101]), c_0_104]), c_0_102]), c_0_104])]), ['proof']).
% 0.08/0.28 % SZS output end CNFRefutation
% 0.08/0.28 % Parsed axioms : 143
% 0.08/0.28 % Removed by relevancy pruning/SinE : 76
% 0.08/0.28 % Initial clauses : 135
% 0.08/0.28 % Removed in clause preprocessing : 6
% 0.08/0.28 % Initial clauses in saturation : 129
% 0.08/0.28 % Processed clauses : 21
% 0.08/0.28 % ...of these trivial : 1
% 0.08/0.28 % ...subsumed : 5
% 0.08/0.28 % ...remaining for further processing : 14
% 0.08/0.28 % Other redundant clauses eliminated : 1
% 0.08/0.28 % Clauses deleted for lack of memory : 0
% 0.08/0.28 % Backward-subsumed : 0
% 0.08/0.28 % Backward-rewritten : 1
% 0.08/0.28 % Generated clauses : 1
% 0.08/0.28 % ...of the previous two non-redundant : 1
% 0.08/0.28 % ...aggressively subsumed : 0
% 0.08/0.28 % Contextual simplify-reflections : 0
% 0.08/0.28 % Paramodulations : 0
% 0.08/0.28 % Factorizations : 0
% 0.08/0.28 % NegExts : 0
% 0.08/0.28 % Equation resolutions : 1
% 0.08/0.28 % Disequality decompositions : 0
% 0.08/0.28 % Total rewrite steps : 8
% 0.08/0.28 % ...of those cached : 3
% 0.08/0.28 % Propositional unsat checks : 0
% 0.08/0.28 % Propositional check models : 0
% 0.08/0.28 % Propositional check unsatisfiable : 0
% 0.08/0.28 % Propositional clauses : 0
% 0.08/0.28 % Propositional clauses after purity: 0
% 0.08/0.28 % Propositional unsat core size : 0
% 0.08/0.28 % Propositional preprocessing time : 0.000
% 0.08/0.28 % Propositional encoding time : 0.000
% 0.08/0.28 % Propositional solver time : 0.000
% 0.08/0.28 % Success case prop preproc time : 0.000
% 0.08/0.28 % Success case prop encoding time : 0.000
% 0.08/0.28 % Success case prop solver time : 0.000
% 0.08/0.28 % Current number of processed clauses : 12
% 0.08/0.28 % Positive orientable unit clauses : 10
% 0.08/0.28 % Positive unorientable unit clauses: 0
% 0.08/0.28 % Negative unit clauses : 2
% 0.08/0.28 % Non-unit-clauses : 0
% 0.08/0.28 % Current number of unprocessed clauses: 109
% 0.08/0.28 % ...number of literals in the above : 353
% 0.08/0.28 % Current number of archived formulas : 0
% 0.08/0.28 % Current number of archived clauses : 1
% 0.08/0.28 % Clause-clause subsumption calls (NU) : 0
% 0.08/0.28 % Rec. Clause-clause subsumption calls : 0
% 0.08/0.28 % Non-unit clause-clause subsumptions : 0
% 0.08/0.28 % Unit Clause-clause subsumption calls : 0
% 0.08/0.28 % Rewrite failures with RHS unbound : 0
% 0.08/0.28 % BW rewrite match attempts : 1
% 0.08/0.28 % BW rewrite match successes : 1
% 0.08/0.28 % Condensation attempts : 0
% 0.08/0.28 % Condensation successes : 0
% 0.08/0.28 % Termbank termtop insertions : 17279
% 0.08/0.28 % Search garbage collected termcells : 7089
% 0.08/0.28
% 0.08/0.28 % -------------------------------------------------
% 0.08/0.28 % User time : 0.017 s
% 0.08/0.28 % System time : 0.001 s
% 0.08/0.28 % Total time : 0.018 s
% 0.08/0.28 % Maximum resident set size: 5828 pages
% 0.08/0.28
% 0.08/0.28 % -------------------------------------------------
% 0.08/0.28 % User time : 0.020 s
% 0.08/0.28 % System time : 0.007 s
% 0.08/0.28 % Total time : 0.027 s
% 0.08/0.28 % Maximum resident set size: 4608 pages
% 0.08/0.28 % E exiting
%------------------------------------------------------------------------------