%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU548^1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:26:40 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU548^1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n014.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 13:49:15 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.24 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.aeonRqHjhB/E---3.1_2691731.p
% 0.20/0.28 % Version: 3.5.1-ho
% 0.20/0.28 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.20/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.20/0.28 % Starting sh5l with 300s (1) cores
% 0.20/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.20/0.28 % Starting new_bool_2 with 300s (1) cores
% 0.20/0.28 % new_bool_1 with pid 2691762 completed with status 0
% 0.20/0.28 % Result found by new_bool_1
% 0.20/0.28 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.20/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.20/0.28 % Starting sh5l with 300s (1) cores
% 0.20/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.20/0.28 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.20/0.28 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.28 % Search class: HGHSM-FFMM31-SHFMMSBN
% 0.20/0.28 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.28 % Starting SubtermCWHack with 31s (1) cores
% 0.20/0.28 % SubtermCWHack with pid 2691765 completed with status 0
% 0.20/0.28 % Result found by SubtermCWHack
% 0.20/0.28 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.20/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.20/0.28 % Starting sh5l with 300s (1) cores
% 0.20/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.20/0.28 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.20/0.28 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.28 % Search class: HGHSM-FFMM31-SHFMMSBN
% 0.20/0.28 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.28 % Starting SubtermCWHack with 31s (1) cores
% 0.20/0.28 % Preprocessing time : 0.002 s
% 0.20/0.28
% 0.20/0.28 % Proof found!
% 0.20/0.28 % SZS status Theorem
% 0.20/0.28 % SZS output start CNFRefutation
% 0.20/0.28 thf(decl_23, type, in: $i > $i > $o).
% 0.20/0.28 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.20/0.28 thf(decl_25, type, setextAx: $o).
% 0.20/0.28 thf(decl_26, type, emptyset: $i).
% 0.20/0.28 thf(decl_27, type, emptysetAx: $o).
% 0.20/0.28 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.20/0.28 thf(decl_29, type, setadjoinAx: $o).
% 0.20/0.28 thf(decl_30, type, powerset: $i > $i).
% 0.20/0.28 thf(decl_31, type, powersetAx: $o).
% 0.20/0.28 thf(decl_32, type, setunion: $i > $i).
% 0.20/0.28 thf(decl_33, type, setunionAx: $o).
% 0.20/0.28 thf(decl_34, type, omega: $i).
% 0.20/0.28 thf(decl_35, type, omega0Ax: $o).
% 0.20/0.28 thf(decl_36, type, omegaSAx: $o).
% 0.20/0.28 thf(decl_37, type, omegaIndAx: $o).
% 0.20/0.28 thf(decl_38, type, replAx: $o).
% 0.20/0.28 thf(decl_39, type, foundationAx: $o).
% 0.20/0.28 thf(decl_40, type, wellorderingAx: $o).
% 0.20/0.28 thf(decl_42, type, descrp: $o).
% 0.20/0.28 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.20/0.28 thf(decl_44, type, dsetconstrI: $o).
% 0.20/0.28 thf(decl_45, type, dsetconstrEL: $o).
% 0.20/0.28 thf(decl_46, type, dsetconstrER: $o).
% 0.20/0.28 thf(decl_47, type, exuE1: $o).
% 0.20/0.28 thf(decl_48, type, prop2set: $o > $i).
% 0.20/0.28 thf(decl_49, type, prop2setE: $o).
% 0.20/0.28 thf(decl_50, type, emptysetE: $o).
% 0.20/0.28 thf(decl_51, type, emptysetimpfalse: $o).
% 0.20/0.28 thf(decl_52, type, notinemptyset: $o).
% 0.20/0.28 thf(decl_53, type, exuE3e: $o).
% 0.20/0.28 thf(decl_54, type, setext: $o).
% 0.20/0.28 thf(decl_55, type, emptyI: $o).
% 0.20/0.28 thf(decl_56, type, noeltsimpempty: $o).
% 0.20/0.28 thf(decl_57, type, setbeta: $o).
% 0.20/0.28 thf(decl_58, type, nonempty: $i > $o).
% 0.20/0.28 thf(decl_59, type, nonemptyE1: $o).
% 0.20/0.28 thf(decl_60, type, nonemptyI: $o).
% 0.20/0.28 thf(decl_61, type, nonemptyI1: $o).
% 0.20/0.28 thf(decl_62, type, setadjoinIL: $o).
% 0.20/0.28 thf(decl_63, type, emptyinunitempty: $o).
% 0.20/0.28 thf(decl_64, type, setadjoinIR: $o).
% 0.20/0.28 thf(decl_65, type, setadjoinE: $o).
% 0.20/0.28 thf(decl_66, type, setadjoinOr: $o).
% 0.20/0.28 thf(decl_67, type, setoftrueEq: $o).
% 0.20/0.28 thf(decl_68, type, powersetI: $o).
% 0.20/0.28 thf(decl_69, type, emptyinPowerset: $o).
% 0.20/0.28 thf(decl_70, type, emptyInPowerset: $o).
% 0.20/0.28 thf(decl_71, type, powersetE: $o).
% 0.20/0.28 thf(decl_72, type, setunionI: $o).
% 0.20/0.28 thf(decl_73, type, setunionE: $o).
% 0.20/0.28 thf(decl_74, type, subPowSU: $o).
% 0.20/0.28 thf(decl_75, type, exuE2: $o).
% 0.20/0.28 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.20/0.28 thf(decl_77, type, uniqinunit: $o).
% 0.20/0.28 thf(decl_78, type, notinsingleton: $o).
% 0.20/0.28 thf(decl_79, type, eqinunit: $o).
% 0.20/0.28 thf(decl_80, type, singletonsswitch: $o).
% 0.20/0.28 thf(decl_81, type, upairsetE: $o).
% 0.20/0.28 thf(decl_82, type, upairsetIL: $o).
% 0.20/0.28 thf(decl_83, type, upairsetIR: $o).
% 0.20/0.28 thf(decl_84, type, emptyE1: $o).
% 0.20/0.28 thf(decl_85, type, vacuousDall: $o).
% 0.20/0.28 thf(decl_86, type, quantDeMorgan1: $o).
% 0.20/0.28 thf(decl_87, type, quantDeMorgan2: $o).
% 0.20/0.28 thf(decl_88, type, quantDeMorgan3: $o).
% 0.20/0.28 thf(decl_89, type, quantDeMorgan4: $o).
% 0.20/0.28 thf(decl_90, type, prop2setI: $o).
% 0.20/0.28 thf(decl_92, type, prop2set2propI: $o).
% 0.20/0.28 thf(decl_93, type, notdexE: $o).
% 0.20/0.28 thf(decl_94, type, notdallE: $o).
% 0.20/0.28 thf(decl_95, type, exuI1: $o).
% 0.20/0.28 thf(decl_96, type, exuI3: $o).
% 0.20/0.28 thf(decl_97, type, exuI2: $o).
% 0.20/0.28 thf(decl_98, type, inCongP: $o).
% 0.20/0.28 thf(decl_99, type, epred1_0: $o).
% 0.20/0.28 thf(decl_100, type, esk1_2: $i > $i > $i).
% 0.20/0.28 thf(decl_101, type, esk2_2: $i > $i > $i).
% 0.20/0.28 thf(decl_102, type, esk3_2: $i > $i > $i).
% 0.20/0.28 thf(decl_103, type, esk4_1: $i > $i).
% 0.20/0.28 thf(decl_104, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.20/0.28 thf(decl_105, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.20/0.28 thf(decl_106, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.20/0.28 thf(decl_107, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.20/0.28 thf(decl_108, type, esk9_1: $i > $i).
% 0.20/0.28 thf(decl_109, type, esk10_2: ($i > $o) > $i > $i).
% 0.20/0.28 thf(decl_110, type, esk11_1: ($i > $o) > $i).
% 0.20/0.28 thf(decl_111, type, esk12_2: ($i > $o) > $i > $i).
% 0.20/0.28 thf(decl_112, type, esk13_1: ($i > $o) > $i).
% 0.20/0.28 thf(decl_113, type, esk14_2: $i > $i > $i).
% 0.20/0.28 thf(decl_114, type, esk15_2: $i > $i > $i).
% 0.20/0.28 thf(decl_115, type, esk16_1: $i > $i).
% 0.20/0.28 thf(decl_116, type, esk17_1: $i > $i).
% 0.20/0.28 thf(decl_117, type, esk18_1: $i > $i).
% 0.20/0.28 thf(decl_118, type, esk19_2: $i > $i > $i).
% 0.20/0.28 thf(decl_119, type, esk20_3: $i > $i > $o > $i).
% 0.20/0.28 thf(decl_120, type, esk21_2: ($i > $o) > $i > $i).
% 0.20/0.28 thf(decl_121, type, esk22_1: ($i > $o) > $i).
% 0.20/0.28 thf(decl_122, type, esk23_1: $i > $i).
% 0.20/0.28 thf(decl_123, type, esk24_2: $i > ($i > $o) > $i).
% 0.20/0.28 thf(decl_124, type, esk25_2: $i > ($i > $o) > $i).
% 0.20/0.28 thf(decl_125, type, esk26_2: $i > ($i > $o) > $i).
% 0.20/0.28 thf(decl_126, type, esk27_2: $i > ($i > $o) > $i).
% 0.20/0.28 thf(decl_127, type, esk28_2: $i > ($i > $o) > $i).
% 0.20/0.28 thf(decl_128, type, esk29_2: $i > ($i > $o) > $i).
% 0.20/0.28 thf(decl_129, type, esk30_2: ($i > $o) > $i > $i).
% 0.20/0.28 thf(decl_130, type, esk31_1: ($i > $o) > $i).
% 0.20/0.28 thf(decl_131, type, esk32_1: ($i > $o) > $i).
% 0.20/0.28 thf(decl_132, type, esk33_1: ($i > $o) > $i).
% 0.20/0.28 thf(decl_133, type, esk34_1: ($i > $o) > $i).
% 0.20/0.28 thf(decl_134, type, esk35_2: ($i > $o) > $i > $i).
% 0.20/0.28 thf(decl_135, type, esk36_1: ($i > $o) > $i).
% 0.20/0.28 thf(decl_136, type, esk37_0: $i).
% 0.20/0.28 thf(decl_137, type, esk38_0: $i).
% 0.20/0.28 thf(decl_138, type, esk39_0: $i).
% 0.20/0.28 thf(decl_139, type, esk40_0: $i).
% 0.20/0.28 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', replAx)).
% 0.20/0.28 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', exu)).
% 0.20/0.28 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', exuI1)).
% 0.20/0.28 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', exuI3)).
% 0.20/0.28 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', exuI2)).
% 0.20/0.28 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/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', exuE1)).
% 0.20/0.28 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', nonemptyI)).
% 0.20/0.28 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', nonempty)).
% 0.20/0.28 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', exuE3e)).
% 0.20/0.28 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', exuE2)).
% 0.20/0.28 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/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', in__Cong)).
% 0.20/0.28 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/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', emptyE1)).
% 0.20/0.28 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', dsetconstrER)).
% 0.20/0.28 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', dsetconstrEL)).
% 0.20/0.28 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', dsetconstrI)).
% 0.20/0.28 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', nonemptyE1)).
% 0.20/0.28 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', setbeta)).
% 0.20/0.28 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', nonemptyI1)).
% 0.20/0.28 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', setoftrueEq)).
% 0.20/0.28 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', nonemptyImpWitness)).
% 0.20/0.28 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', upairsetIR)).
% 0.20/0.28 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', upairsetIL)).
% 0.20/0.28 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', vacuousDall)).
% 0.20/0.28 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', quantDeMorgan1)).
% 0.20/0.28 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', quantDeMorgan2)).
% 0.20/0.28 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', quantDeMorgan3)).
% 0.20/0.28 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', quantDeMorgan4)).
% 0.20/0.28 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', prop2setI)).
% 0.20/0.28 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/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', foundationAx)).
% 0.20/0.28 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', notdexE)).
% 0.20/0.28 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', notdallE)).
% 0.20/0.28 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', omegaIndAx)).
% 0.20/0.28 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', omegaSAx)).
% 0.20/0.28 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', omega0Ax)).
% 0.20/0.28 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', setunionAx)).
% 0.20/0.28 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/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', inCongP)).
% 0.20/0.28 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', powersetAx)).
% 0.20/0.28 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', wellorderingAx)).
% 0.20/0.28 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', emptysetimpfalse)).
% 0.20/0.28 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', emptysetE)).
% 0.20/0.28 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', prop2setE)).
% 0.20/0.28 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', notinemptyset)).
% 0.20/0.28 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', noeltsimpempty)).
% 0.20/0.28 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', emptyI)).
% 0.20/0.28 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', setext)).
% 0.20/0.28 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', powersetI)).
% 0.20/0.28 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', setadjoinOr)).
% 0.20/0.28 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', setadjoinE)).
% 0.20/0.28 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', setadjoinIR)).
% 0.20/0.28 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', emptyinunitempty)).
% 0.20/0.28 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', setadjoinIL)).
% 0.20/0.28 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', emptyinPowerset)).
% 0.20/0.28 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', subPowSU)).
% 0.20/0.28 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', setunionE)).
% 0.20/0.28 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', setunionI)).
% 0.20/0.28 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', powersetE)).
% 0.20/0.28 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', emptyInPowerset)).
% 0.20/0.28 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', notinsingleton)).
% 0.20/0.28 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', eqinunit)).
% 0.20/0.28 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', singletonsswitch)).
% 0.20/0.28 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', upairsetE)).
% 0.20/0.28 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', uniqinunit)).
% 0.20/0.28 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', setadjoinAx)).
% 0.20/0.28 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', emptysetAx)).
% 0.20/0.28 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.aeonRqHjhB/E---3.1_2691731.p', setextAx)).
% 0.20/0.28 thf(c_0_65, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.20/0.28 thf(c_0_66, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.20/0.28 thf(c_0_67, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 0.20/0.28 thf(c_0_68, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.20/0.28 thf(c_0_69, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.20/0.28 thf(c_0_70, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.20/0.28 thf(c_0_71, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.20/0.28 thf(c_0_72, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.20/0.28 thf(c_0_73, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.20/0.28 thf(c_0_74, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.20/0.29 thf(c_0_75, 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])).
% 0.20/0.29 thf(c_0_76, 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])).
% 0.20/0.29 thf(c_0_77, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X199:$i]:(((((X6 @ X2 @ X199)))&(![X200:$i]:(((((X6 @ X2 @ X200)))=>(((X199)=(X200)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_65, c_0_66])).
% 0.20/0.29 thf(c_0_78, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X207:$i]:(((((X1 @ X207)))&(![X208:$i]:(((((X1 @ X208)))=>(((X207)=(X208)))))))))))))), inference(apply_def,[status(thm)],[c_0_67, c_0_66])).
% 0.20/0.29 thf(c_0_79, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X209:$i]:(((((X1 @ X209)))&(![X210:$i]:(((((X1 @ X210)))=>(((X209)=(X210)))))))))))))))), inference(apply_def,[status(thm)],[c_0_68, c_0_66])).
% 0.20/0.29 thf(c_0_80, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X211:$i]:(((((X1 @ X211)))&(![X212:$i]:(((((X1 @ X212)))=>(((X211)=(X212)))))))))))))), inference(apply_def,[status(thm)],[c_0_69, c_0_66])).
% 0.20/0.29 thf(c_0_81, plain, ((exuE1)=(![X1:$i > $o]:((((?[X201:$i]:(((((X1 @ X201)))&(![X202:$i]:(((((X1 @ X202)))=>(((X201)=(X202))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_70, c_0_66])).
% 0.20/0.29 thf(c_0_82, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.20/0.29 thf(c_0_83, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.20/0.29 thf(c_0_84, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.20/0.29 thf(c_0_85, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_71, c_0_72])).
% 0.20/0.29 thf(c_0_86, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_72])).
% 0.20/0.29 thf(c_0_87, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.20/0.29 thf(c_0_88, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X203:$i]:(((((X1 @ X203)))&(![X204:$i]:(((((X1 @ X204)))=>(((X203)=(X204))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_73, c_0_66])).
% 0.20/0.29 thf(c_0_89, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_72])).
% 0.20/0.29 thf(c_0_90, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.20/0.29 thf(c_0_91, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_72])).
% 0.20/0.29 thf(c_0_92, plain, ((exuE2)=(![X1:$i > $o]:((((?[X205:$i]:(((((X1 @ X205)))&(![X206:$i]:(((((X1 @ X206)))=>(((X205)=(X206))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_74, c_0_66])).
% 0.20/0.29 thf(c_0_93, plain, ((epred1_0)<=>![X242:$i]:(?[X243:$i]:((((![X244:$i]:(((in @ X244 @ X243)=>![X245:$i]:(((in @ X245 @ X244)=>(in @ X245 @ X242)))))&![X246:$i, X247:$i]:((((in @ X246 @ X242)&(in @ X247 @ X242))=>(![X248:$i]:(((in @ X248 @ X243)=>((in @ X246 @ X248)<=>(in @ X247 @ X248))))=>((X246)=(X247))))))&![X249:$i, X250:$i]:((((in @ X249 @ X243)&(in @ X250 @ X243))=>(![X251:$i]:(((in @ X251 @ X249)=>(in @ X251 @ X250)))|![X252:$i]:(((in @ X252 @ X250)=>(in @ X252 @ X249)))))))&![X253:$i]:(((![X254:$i]:(((in @ X254 @ X253)=>(in @ X254 @ X242)))&?[X255:$i]:((in @ X255 @ X253)))=>?[X256:$i, X257:$i]:(((((in @ X256 @ X243)&(in @ X257 @ X253))&~(?[X258:$i]:(((in @ X258 @ X256)&(in @ X258 @ X253)))))&![X259:$i]:(((in @ X259 @ X243)=>(![X260:$i]:(((in @ X260 @ X259)=>(in @ X260 @ X256)))|(in @ X257 @ X259)))))))))))), introduced(definition)).
% 0.20/0.29 thf(c_0_94, negated_conjecture, ~((![X213:$i, X214:$i]:((![X215:$i]:(((in @ X215 @ X213)<=>(in @ X215 @ X214)))=>((X213)=(X214))))=>(![X216:$i]:(~(in @ X216 @ emptyset))=>(![X217:$i, X218:$i, X219:$i]:(((in @ X219 @ (setadjoin @ X217 @ X218))<=>(((X219)=(X217))|(in @ X219 @ X218))))=>(![X220:$i, X221:$i]:(((in @ X221 @ (powerset @ X220))<=>![X222:$i]:(((in @ X222 @ X221)=>(in @ X222 @ X220)))))=>(![X223:$i, X224:$i]:(((in @ X224 @ (setunion @ X223))<=>?[X225:$i]:(((in @ X224 @ X225)&(in @ X225 @ X223)))))=>((in @ emptyset @ omega)=>(![X226:$i]:(((in @ X226 @ omega)=>(in @ (setadjoin @ X226 @ X226) @ omega)))=>(![X227:$i]:((((in @ emptyset @ X227)&![X228:$i]:((((in @ X228 @ omega)&(in @ X228 @ X227))=>(in @ (setadjoin @ X228 @ X228) @ X227))))=>![X229:$i]:(((in @ X229 @ omega)=>(in @ X229 @ X227)))))=>(![X230:$i > $i > $o, X231:$i]:((![X232:$i]:(((in @ X232 @ X231)=>?[X233:$i]:(((X230 @ X232 @ X233)&![X234:$i]:(((X230 @ X232 @ X234)=>((X233)=(X234))))))))=>?[X235:$i]:(![X236:$i]:(((in @ X236 @ X235)<=>?[X237:$i]:(((in @ X237 @ X231)&(X230 @ X237 @ X236))))))))=>(![X238:$i]:((?[X239:$i]:((in @ X239 @ X238))=>?[X240:$i]:(((in @ X240 @ X238)&~(?[X241:$i]:(((in @ X241 @ X240)&(in @ X241 @ X238))))))))=>((epred1_0)=>((descrp)=>(![X261:$i, X262:$i > $o, X263:$i]:(((in @ X263 @ X261)=>((X262 @ X263)=>(in @ X263 @ (dsetconstr @ X261 @ X262)))))=>(![X264:$i, X265:$i > $o, X266:$i]:(((in @ X266 @ (dsetconstr @ X264 @ X265))=>(in @ X266 @ X264)))=>(![X267:$i, X268:$i > $o, X269:$i]:(((in @ X269 @ (dsetconstr @ X267 @ X268))=>(X268 @ X269)))=>(![X270:$i > $o]:((?[X271:$i]:(((X270 @ X271)&![X272:$i]:(((X270 @ X272)=>((X271)=(X272))))))=>?[X273:$i]:(((X270 @ X273)&![X274:$i]:(((X270 @ X274)=>((X273)=(X274))))))))=>(![X275:$o, X276:$i]:(((in @ X276 @ (prop2set @ ((X275))))=>(X275)))=>(![X277:$i]:(((in @ X277 @ emptyset)=>![X278:$o]:((X278))))=>(![X279:$i]:(((in @ X279 @ emptyset)=>~($true)))=>(![X280:$i]:(~(in @ X280 @ emptyset))=>(![X281:$i > $o]:((?[X282:$i]:(((X281 @ X282)&![X283:$i]:(((X281 @ X283)=>((X282)=(X283))))))=>?[X284:$i]:((X281 @ X284))))=>(![X285:$i, X286:$i]:((![X287:$i]:(((in @ X287 @ X285)=>(in @ X287 @ X286)))=>(![X288:$i]:(((in @ X288 @ X286)=>(in @ X288 @ X285)))=>((X285)=(X286)))))=>(![X289:$i]:((![X290:$i]:(~(in @ X290 @ X289))=>((X289)=(emptyset))))=>(![X291:$i]:((![X292:$i]:(~(in @ X292 @ X291))=>((X291)=(emptyset))))=>(![X293:$i, X294:$i > $o, X295:$i]:(((in @ X295 @ X293)=>((in @ X295 @ (dsetconstr @ X293 @ X294))<=>(X294 @ X295))))=>(![X296:$i]:((((X296)!=(emptyset))=>?[X297:$i]:((in @ X297 @ X296))))=>(![X298:$i, X299:$i > $o, X300:$i]:(((in @ X300 @ X298)=>((X299 @ X300)=>((dsetconstr @ X298 @ X299)!=(emptyset)))))=>(![X301:$i]:((?[X302:$i]:((in @ X302 @ X301))=>((X301)!=(emptyset))))=>(![X303:$i, X304:$i]:((in @ X303 @ (setadjoin @ X303 @ X304)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X305:$i, X306:$i, X307:$i]:(((in @ X307 @ X306)=>(in @ X307 @ (setadjoin @ X305 @ X306))))=>(![X308:$i, X309:$i, X310:$i]:(((in @ X310 @ (setadjoin @ X308 @ X309))=>![X311:$o]:(((((X310)=(X308))=>(X311))=>(((in @ X310 @ X309)=>(X311))=>(X311))))))=>(![X312:$i, X313:$i, X314:$i]:(((in @ X314 @ (setadjoin @ X312 @ X313))=>(((X314)=(X312))|(in @ X314 @ X313))))=>(![X315:$i]:(((dsetconstr @ X315 @ (^[Z0:$i]:($true)))=(X315)))=>(![X316:$i, X317:$i]:((![X318:$i]:(((in @ X318 @ X317)=>(in @ X318 @ X316)))=>(in @ X317 @ (powerset @ X316))))=>(![X319:$i]:((in @ emptyset @ (powerset @ X319)))=>(![X320:$i]:((in @ emptyset @ (powerset @ X320)))=>(![X321:$i, X322:$i, X323:$i]:(((in @ X322 @ (powerset @ X321))=>((in @ X323 @ X322)=>(in @ X323 @ X321))))=>(![X324:$i, X325:$i, X326:$i]:(((in @ X325 @ X326)=>((in @ X326 @ X324)=>(in @ X325 @ (setunion @ X324)))))=>(![X327:$i, X328:$i]:(((in @ X328 @ (setunion @ X327))=>![X329:$o]:((![X330:$i]:(((in @ X328 @ X330)=>((in @ X330 @ X327)=>(X329))))=>(X329)))))=>(![X331:$i, X332:$i]:(((in @ X332 @ X331)=>(in @ X332 @ (powerset @ (setunion @ X331)))))=>(![X333:$i > $o]:((?[X334:$i]:(((X333 @ X334)&![X335:$i]:(((X333 @ X335)=>((X334)=(X335))))))=>?[X336:$i]:(![X337:$i]:(((X333 @ X337)<=>((X337)=(X336)))))))=>(![X338:$i]:((((X338)!=(emptyset))=>?[X339:$i]:(((in @ X339 @ X338)&$true))))=>(![X340:$i, X341:$i]:(((in @ X340 @ (setadjoin @ X341 @ emptyset))=>((X340)=(X341))))=>(![X342:$i, X343:$i]:((((X342)!=(X343))=>~(in @ X343 @ (setadjoin @ X342 @ emptyset))))=>(![X344:$i, X345:$i]:((((X344)=(X345))=>(in @ X344 @ (setadjoin @ X345 @ emptyset))))=>(![X346:$i, X347:$i]:(((in @ X346 @ (setadjoin @ X347 @ emptyset))=>(in @ X347 @ (setadjoin @ X346 @ emptyset))))=>(![X348:$i, X349:$i, X350:$i]:(((in @ X350 @ (setadjoin @ X348 @ (setadjoin @ X349 @ emptyset)))=>(((X350)=(X348))|((X350)=(X349)))))=>(![X351:$i, X352:$i]:((in @ X351 @ (setadjoin @ X351 @ (setadjoin @ X352 @ emptyset))))=>(![X353:$i, X354:$i]:((in @ X354 @ (setadjoin @ X353 @ (setadjoin @ X354 @ emptyset))))=>(![X355:$i, X356:$i > $o]:((?[X357:$i]:(((in @ X357 @ X355)&(X356 @ X357)))=>(((dsetconstr @ X355 @ X356)=(emptyset))=>~($true))))=>(![X358:$i > $o, X359:$i]:(((in @ X359 @ emptyset)=>(X358 @ X359)))=>(![X360:$i, X361:$i > $o]:((~(![X362:$i]:(((in @ X362 @ X360)=>(X361 @ X362))))=>?[X363:$i]:(((in @ X363 @ X360)&~((X361 @ X363))))))=>(![X364:$i, X365:$i > $o]:((![X366:$i]:(((in @ X366 @ X364)=>~((X365 @ X366))))=>~(?[X367:$i]:(((in @ X367 @ X364)&(X365 @ X367))))))=>(![X368:$i, X369:$i > $o]:((~(?[X370:$i]:(((in @ X370 @ X368)&(X369 @ X370))))=>![X371:$i]:(((in @ X371 @ X368)=>~((X369 @ X371))))))=>(![X372:$i, X373:$i > $o]:((?[X374:$i]:(((in @ X374 @ X372)&~((X373 @ X374))))=>~(![X375:$i]:(((in @ X375 @ X372)=>(X373 @ X375))))))=>(![X376:$o]:(((X376)=>(in @ emptyset @ (prop2set @ ((X376))))))=>((prop2set2propI)=>(![X377:$i, X378:$i > $o]:((~(?[X379:$i]:(((in @ X379 @ X377)&(X378 @ X379))))=>![X380:$i]:(((in @ X380 @ X377)=>~((X378 @ X380))))))=>(![X381:$i, X382:$i > $o]:((~(![X383:$i]:(((in @ X383 @ X381)=>(X382 @ X383))))=>?[X384:$i]:(((in @ X384 @ X381)&~((X382 @ X384))))))=>(![X385:$i > $o]:((?[X386:$i]:(((X385 @ X386)&![X387:$i]:(((X385 @ X387)=>((X386)=(X387))))))=>?[X388:$i]:(((X385 @ X388)&![X389:$i]:(((X385 @ X389)=>((X388)=(X389))))))))=>(![X390:$i > $o]:((?[X391:$i]:((X390 @ X391))=>(![X392:$i, X393:$i]:(((X390 @ X392)=>((X390 @ X393)=>((X392)=(X393)))))=>?[X394:$i]:(((X390 @ X394)&![X395:$i]:(((X390 @ X395)=>((X394)=(X395)))))))))=>(![X396:$i > $o]:((?[X397:$i]:(![X398:$i]:(((X396 @ X398)<=>((X398)=(X397)))))=>?[X399:$i]:(((X396 @ X399)&![X400:$i]:(((X396 @ X400)=>((X399)=(X400))))))))=>(![X401:$i, X402:$i]:((((X401)=(X402))=>![X403:$i, X404:$i]:((((X403)=(X404))=>((in @ X403 @ X401)=>(in @ X404 @ X402))))))=>![X4:$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)],[c_0_75, upairsetIR]), upairsetIL]), c_0_76]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), foundationAx]), notdexE]), c_0_77]), notdallE]), omegaIndAx]), c_0_78]), omegaSAx]), c_0_79]), omega0Ax]), c_0_80]), setunionAx]), inCongP]), powersetAx]), wellorderingAx]), emptysetimpfalse]), emptysetE]), prop2setE]), c_0_81]), c_0_82]), c_0_83]), c_0_84]), notinemptyset]), c_0_85]), c_0_86]), c_0_87]), noeltsimpempty]), emptyI]), setext]), c_0_88]), c_0_89]), powersetI]), c_0_90]), setadjoinOr]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), emptyinPowerset]), c_0_91]), c_0_92]), subPowSU]), setunionE]), setunionI]), powersetE]), emptyInPowerset]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), uniqinunit]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_93])).
% 0.20/0.29 thf(c_0_95, negated_conjecture, ![X405:$i, X406:$i, X408:$i, X409:$i, X410:$i, X411:$i, X412:$i, X413:$i, X414:$i, X415:$i, X416:$i, X418:$i, X419:$i, X421:$i, X422:$i, X423:$i, X424:$i, X425:$i, X427:$i, X428:$i > $i > $o, X429:$i, X431:$i, X434:$i, X436:$i, X437:$i, X438:$i, X439:$i, X441:$i, X442:$i, X443:$i > $o, X444:$i, X445:$i, X446:$i > $o, X447:$i, X448:$i, X449:$i > $o, X450:$i, X451:$i > $o, X452:$i, X455:$i, X456:$o, X457:$i, X458:$i, X459:$o, X460:$i, X461:$i, X462:$i > $o, X463:$i, X466:$i, X467:$i, X470:$i, X472:$i, X474:$i, X475:$i > $o, X476:$i, X477:$i, X479:$i, X480:$i > $o, X481:$i, X482:$i, X483:$i, X484:$i, X485:$i, X486:$i, X487:$i, X488:$i, X489:$i, X490:$i, X491:$i, X492:$o, X493:$i, X494:$i, X495:$i, X496:$i, X497:$i, X498:$i, X500:$i, X501:$i, X502:$i, X503:$i, X504:$i, X505:$i, X506:$i, X507:$i, X508:$i, X509:$i, X510:$o, X512:$i, X513:$i, X514:$i > $o, X515:$i, X518:$i, X519:$i, X520:$i, X522:$i, X523:$i, X524:$i, X525:$i, X526:$i, X527:$i, X528:$i, X529:$i, X530:$i, X531:$i, X532:$i, X533:$i, X534:$i, X535:$i, X536:$i, X537:$i, X538:$i > $o, X539:$i, X540:$i > $o, X541:$i, X542:$i, X543:$i > $o, X544:$i, X546:$i, X547:$i > $o, X549:$i, X550:$i, X551:$i > $o, X553:$i, X554:$i, X555:$i > $o, X556:$i, X558:$o, X559:$i, X560:$i > $o, X562:$i, X563:$i, X564:$i > $o, X565:$i, X567:$i > $o, X568:$i, X571:$i, X572:$i > $o, X573:$i, X577:$i, X578:$i > $o, X579:$i, X582:$i, X583:$i, X584:$i, X585:$i, X586:$i]:((((~(in @ (esk1_2 @ X405 @ X406) @ X405)|~(in @ (esk1_2 @ X405 @ X406) @ X406)|((X405)=(X406)))&((in @ (esk1_2 @ X405 @ X406) @ X405)|(in @ (esk1_2 @ X405 @ X406) @ X406)|((X405)=(X406))))&(~(in @ X408 @ emptyset)&(((~(in @ X411 @ (setadjoin @ X409 @ X410))|(((X411)=(X409))|(in @ X411 @ X410)))&((((X411)!=(X409))|(in @ X411 @ (setadjoin @ X409 @ X410)))&(~(in @ X411 @ X410)|(in @ X411 @ (setadjoin @ X409 @ X410)))))&(((~(in @ X413 @ (powerset @ X412))|(~(in @ X414 @ X413)|(in @ X414 @ X412)))&(((in @ (esk2_2 @ X415 @ X416) @ X416)|(in @ X416 @ (powerset @ X415)))&(~(in @ (esk2_2 @ X415 @ X416) @ X415)|(in @ X416 @ (powerset @ X415)))))&(((((in @ X419 @ (esk3_2 @ X418 @ X419))|~(in @ X419 @ (setunion @ X418)))&((in @ (esk3_2 @ X418 @ X419) @ X418)|~(in @ X419 @ (setunion @ X418))))&(~(in @ X422 @ X423)|~(in @ X423 @ X421)|(in @ X422 @ (setunion @ X421))))&((in @ emptyset @ omega)&((~(in @ X424 @ omega)|(in @ (setadjoin @ X424 @ X424) @ omega))&(((((in @ (esk4_1 @ X425) @ omega)|~(in @ emptyset @ X425)|(~(in @ X427 @ omega)|(in @ X427 @ X425)))&((in @ (esk4_1 @ X425) @ X425)|~(in @ emptyset @ X425)|(~(in @ X427 @ omega)|(in @ X427 @ X425))))&(~(in @ (setadjoin @ (esk4_1 @ X425) @ (esk4_1 @ X425)) @ X425)|~(in @ emptyset @ X425)|(~(in @ X427 @ omega)|(in @ X427 @ X425))))&((((((in @ (esk8_3 @ X428 @ X429 @ X434) @ X429)|~(in @ X434 @ (esk7_2 @ X428 @ X429))|(in @ (esk5_2 @ X428 @ X429) @ X429))&((X428 @ (esk8_3 @ X428 @ X429 @ X434) @ X434)|~(in @ X434 @ (esk7_2 @ X428 @ X429))|(in @ (esk5_2 @ X428 @ X429) @ X429)))&(~(in @ X437 @ X429)|~(X428 @ X437 @ X436)|(in @ X436 @ (esk7_2 @ X428 @ X429))|(in @ (esk5_2 @ X428 @ X429) @ X429)))&(((((in @ (esk8_3 @ X428 @ X429 @ X434) @ X429)|~(in @ X434 @ (esk7_2 @ X428 @ X429))|((X428 @ (esk5_2 @ X428 @ X429) @ (esk6_3 @ X428 @ X429 @ X431))|~(X428 @ (esk5_2 @ X428 @ X429) @ X431)))&((X428 @ (esk8_3 @ X428 @ X429 @ X434) @ X434)|~(in @ X434 @ (esk7_2 @ X428 @ X429))|((X428 @ (esk5_2 @ X428 @ X429) @ (esk6_3 @ X428 @ X429 @ X431))|~(X428 @ (esk5_2 @ X428 @ X429) @ X431))))&(~(in @ X437 @ X429)|~(X428 @ X437 @ X436)|(in @ X436 @ (esk7_2 @ X428 @ X429))|((X428 @ (esk5_2 @ X428 @ X429) @ (esk6_3 @ X428 @ X429 @ X431))|~(X428 @ (esk5_2 @ X428 @ X429) @ X431))))&((((in @ (esk8_3 @ X428 @ X429 @ X434) @ X429)|~(in @ X434 @ (esk7_2 @ X428 @ X429))|(((X431)!=(esk6_3 @ X428 @ X429 @ X431))|~(X428 @ (esk5_2 @ X428 @ X429) @ X431)))&((X428 @ (esk8_3 @ X428 @ X429 @ X434) @ X434)|~(in @ X434 @ (esk7_2 @ X428 @ X429))|(((X431)!=(esk6_3 @ X428 @ X429 @ X431))|~(X428 @ (esk5_2 @ X428 @ X429) @ X431))))&(~(in @ X437 @ X429)|~(X428 @ X437 @ X436)|(in @ X436 @ (esk7_2 @ X428 @ X429))|(((X431)!=(esk6_3 @ X428 @ X429 @ X431))|~(X428 @ (esk5_2 @ X428 @ X429) @ X431))))))&((((in @ (esk9_1 @ X438) @ X438)|~(in @ X439 @ X438))&(~(in @ X441 @ (esk9_1 @ X438))|~(in @ X441 @ X438)|~(in @ X439 @ X438)))&((epred1_0)&((descrp)&((~(in @ X444 @ X442)|(~(X443 @ X444)|(in @ X444 @ (dsetconstr @ X442 @ X443))))&((~(in @ X447 @ (dsetconstr @ X445 @ X446))|(in @ X447 @ X445))&((~(in @ X450 @ (dsetconstr @ X448 @ X449))|(X449 @ X450))&(((((X451 @ (esk11_1 @ X451))|((X451 @ (esk10_2 @ X451 @ X452))|~(X451 @ X452)))&(~(X451 @ X455)|((esk11_1 @ X451)=(X455))|((X451 @ (esk10_2 @ X451 @ X452))|~(X451 @ X452))))&(((X451 @ (esk11_1 @ X451))|(((X452)!=(esk10_2 @ X451 @ X452))|~(X451 @ X452)))&(~(X451 @ X455)|((esk11_1 @ X451)=(X455))|(((X452)!=(esk10_2 @ X451 @ X452))|~(X451 @ X452)))))&((~(in @ X457 @ (prop2set @ ((X456))))|(X456))&((~(in @ X458 @ emptyset)|(X459))&((~(in @ X460 @ emptyset)|~($true))&(~(in @ X461 @ emptyset)&((((X462 @ (esk12_2 @ X462 @ X463))|~(X462 @ X463)|(X462 @ (esk13_1 @ X462)))&(((X463)!=(esk12_2 @ X462 @ X463))|~(X462 @ X463)|(X462 @ (esk13_1 @ X462))))&(((((in @ (esk15_2 @ X466 @ X467) @ X467)|((X466)=(X467))|(in @ (esk14_2 @ X466 @ X467) @ X466))&(~(in @ (esk15_2 @ X466 @ X467) @ X466)|((X466)=(X467))|(in @ (esk14_2 @ X466 @ X467) @ X466)))&(((in @ (esk15_2 @ X466 @ X467) @ X467)|((X466)=(X467))|~(in @ (esk14_2 @ X466 @ X467) @ X467))&(~(in @ (esk15_2 @ X466 @ X467) @ X466)|((X466)=(X467))|~(in @ (esk14_2 @ X466 @ X467) @ X467))))&(((in @ (esk16_1 @ X470) @ X470)|((X470)=(emptyset)))&(((in @ (esk17_1 @ X472) @ X472)|((X472)=(emptyset)))&(((~(in @ X476 @ (dsetconstr @ X474 @ X475))|(X475 @ X476)|~(in @ X476 @ X474))&(~(X475 @ X476)|(in @ X476 @ (dsetconstr @ X474 @ X475))|~(in @ X476 @ X474)))&((((X477)=(emptyset))|(in @ (esk18_1 @ X477) @ X477))&((~(in @ X481 @ X479)|(~(X480 @ X481)|((dsetconstr @ X479 @ X480)!=(emptyset))))&((~(in @ X483 @ X482)|((X482)!=(emptyset)))&((in @ X484 @ (setadjoin @ X484 @ X485))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X488 @ X487)|(in @ X488 @ (setadjoin @ X486 @ X487)))&(((((in @ X491 @ X490)|(X492)|((X491)=(X489))|~(in @ X491 @ (setadjoin @ X489 @ X490)))&(~(X492)|(X492)|((X491)=(X489))|~(in @ X491 @ (setadjoin @ X489 @ X490))))&(((in @ X491 @ X490)|(X492)|~(X492)|~(in @ X491 @ (setadjoin @ X489 @ X490)))&(~(X492)|(X492)|~(X492)|~(in @ X491 @ (setadjoin @ X489 @ X490)))))&((~(in @ X495 @ (setadjoin @ X493 @ X494))|(((X495)=(X493))|(in @ X495 @ X494)))&(((dsetconstr @ X496 @ (^[Z0:$i]:($true)))=(X496))&((((in @ (esk19_2 @ X497 @ X498) @ X498)|(in @ X498 @ (powerset @ X497)))&(~(in @ (esk19_2 @ X497 @ X498) @ X497)|(in @ X498 @ (powerset @ X497))))&((in @ emptyset @ (powerset @ X500))&((in @ emptyset @ (powerset @ X501))&((~(in @ X503 @ (powerset @ X502))|(~(in @ X504 @ X503)|(in @ X504 @ X502)))&((~(in @ X506 @ X507)|(~(in @ X507 @ X505)|(in @ X506 @ (setunion @ X505))))&((((in @ X509 @ (esk20_3 @ X508 @ X509 @ X510))|(X510)|~(in @ X509 @ (setunion @ X508)))&(((in @ (esk20_3 @ X508 @ X509 @ X510) @ X508)|(X510)|~(in @ X509 @ (setunion @ X508)))&(~(X510)|(X510)|~(in @ X509 @ (setunion @ X508)))))&((~(in @ X513 @ X512)|(in @ X513 @ (powerset @ (setunion @ X512))))&((((~(X514 @ X518)|((X518)=(esk22_1 @ X514))|((X514 @ (esk21_2 @ X514 @ X515))|~(X514 @ X515)))&(((X519)!=(esk22_1 @ X514))|(X514 @ X519)|((X514 @ (esk21_2 @ X514 @ X515))|~(X514 @ X515))))&((~(X514 @ X518)|((X518)=(esk22_1 @ X514))|(((X515)!=(esk21_2 @ X514 @ X515))|~(X514 @ X515)))&(((X519)!=(esk22_1 @ X514))|(X514 @ X519)|(((X515)!=(esk21_2 @ X514 @ X515))|~(X514 @ X515)))))&((((in @ (esk23_1 @ X520) @ X520)|((X520)=(emptyset)))&(($true)|((X520)=(emptyset))))&((~(in @ X522 @ (setadjoin @ X523 @ emptyset))|((X522)=(X523)))&((((X524)=(X525))|~(in @ X525 @ (setadjoin @ X524 @ emptyset)))&((((X526)!=(X527))|(in @ X526 @ (setadjoin @ X527 @ emptyset)))&((~(in @ X528 @ (setadjoin @ X529 @ emptyset))|(in @ X529 @ (setadjoin @ X528 @ emptyset)))&((~(in @ X532 @ (setadjoin @ X530 @ (setadjoin @ X531 @ emptyset)))|(((X532)=(X530))|((X532)=(X531))))&((in @ X533 @ (setadjoin @ X533 @ (setadjoin @ X534 @ emptyset)))&((in @ X536 @ (setadjoin @ X535 @ (setadjoin @ X536 @ emptyset)))&((~(in @ X539 @ X537)|~(X538 @ X539)|(((dsetconstr @ X537 @ X538)!=(emptyset))|~($true)))&((~(in @ X541 @ emptyset)|(X540 @ X541))&((((in @ (esk24_2 @ X542 @ X543) @ X542)|(~(in @ X544 @ X542)|(X543 @ X544)))&(~(X543 @ (esk24_2 @ X542 @ X543))|(~(in @ X544 @ X542)|(X543 @ X544))))&((((in @ (esk25_2 @ X546 @ X547) @ X546)|(~(in @ X549 @ X546)|~(X547 @ X549)))&((X547 @ (esk25_2 @ X546 @ X547))|(~(in @ X549 @ X546)|~(X547 @ X549))))&((((in @ (esk26_2 @ X550 @ X551) @ X550)|(~(in @ X553 @ X550)|~(X551 @ X553)))&((X551 @ (esk26_2 @ X550 @ X551))|(~(in @ X553 @ X550)|~(X551 @ X553))))&((((in @ (esk27_2 @ X554 @ X555) @ X554)|(~(in @ X556 @ X554)|(X555 @ X556)))&(~(X555 @ (esk27_2 @ X554 @ X555))|(~(in @ X556 @ X554)|(X555 @ X556))))&((~(X558)|(in @ emptyset @ (prop2set @ ((X558)))))&((prop2set2propI)&((((in @ (esk28_2 @ X559 @ X560) @ X559)|(~(in @ X562 @ X559)|~(X560 @ X562)))&((X560 @ (esk28_2 @ X559 @ X560))|(~(in @ X562 @ X559)|~(X560 @ X562))))&((((in @ (esk29_2 @ X563 @ X564) @ X563)|(~(in @ X565 @ X563)|(X564 @ X565)))&(~(X564 @ (esk29_2 @ X563 @ X564))|(~(in @ X565 @ X563)|(X564 @ X565))))&(((((X567 @ (esk31_1 @ X567))|((X567 @ (esk30_2 @ X567 @ X568))|~(X567 @ X568)))&(~(X567 @ X571)|((esk31_1 @ X567)=(X571))|((X567 @ (esk30_2 @ X567 @ X568))|~(X567 @ X568))))&(((X567 @ (esk31_1 @ X567))|(((X568)!=(esk30_2 @ X567 @ X568))|~(X567 @ X568)))&(~(X567 @ X571)|((esk31_1 @ X567)=(X571))|(((X568)!=(esk30_2 @ X567 @ X568))|~(X567 @ X568)))))&(((((X572 @ (esk34_1 @ X572))|(X572 @ (esk32_1 @ X572))|~(X572 @ X573))&(~(X572 @ X577)|((esk34_1 @ X572)=(X577))|(X572 @ (esk32_1 @ X572))|~(X572 @ X573)))&((((X572 @ (esk34_1 @ X572))|(X572 @ (esk33_1 @ X572))|~(X572 @ X573))&(~(X572 @ X577)|((esk34_1 @ X572)=(X577))|(X572 @ (esk33_1 @ X572))|~(X572 @ X573)))&(((X572 @ (esk34_1 @ X572))|((esk32_1 @ X572)!=(esk33_1 @ X572))|~(X572 @ X573))&(~(X572 @ X577)|((esk34_1 @ X572)=(X577))|((esk32_1 @ X572)!=(esk33_1 @ X572))|~(X572 @ X573)))))&(((((X578 @ (esk36_1 @ X578))|(~(X578 @ (esk35_2 @ X578 @ X579))|((esk35_2 @ X578 @ X579)!=(X579))))&(~(X578 @ X582)|((esk36_1 @ X578)=(X582))|(~(X578 @ (esk35_2 @ X578 @ X579))|((esk35_2 @ X578 @ X579)!=(X579)))))&(((X578 @ (esk36_1 @ X578))|((X578 @ (esk35_2 @ X578 @ X579))|((esk35_2 @ X578 @ X579)=(X579))))&(~(X578 @ X582)|((esk36_1 @ X578)=(X582))|((X578 @ (esk35_2 @ X578 @ X579))|((esk35_2 @ X578 @ X579)=(X579))))))&((((X583)!=(X584))|(((X585)!=(X586))|(~(in @ X585 @ X583)|(in @ X586 @ X584))))&(((esk37_0)=(esk38_0))&(((esk39_0)=(esk40_0))&((~(in @ esk39_0 @ esk37_0)|~(in @ esk40_0 @ esk38_0))&((in @ esk39_0 @ esk37_0)|(in @ esk40_0 @ esk38_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_94])])])])])])])).
% 0.20/0.29 thf(c_0_96, negated_conjecture, ((in @ esk39_0 @ esk37_0)|(in @ esk40_0 @ esk38_0)), inference(split_conjunct,[status(thm)],[c_0_95])).
% 0.20/0.29 thf(c_0_97, negated_conjecture, ((esk39_0)=(esk40_0)), inference(split_conjunct,[status(thm)],[c_0_95])).
% 0.20/0.29 thf(c_0_98, negated_conjecture, ((esk37_0)=(esk38_0)), inference(split_conjunct,[status(thm)],[c_0_95])).
% 0.20/0.29 thf(c_0_99, negated_conjecture, (~((in @ esk39_0 @ esk37_0))|~((in @ esk40_0 @ esk38_0))), inference(split_conjunct,[status(thm)],[c_0_95])).
% 0.20/0.29 thf(c_0_100, negated_conjecture, (in @ esk40_0 @ esk37_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_96, c_0_97]), c_0_98])])).
% 0.20/0.29 thf(c_0_101, 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_99, c_0_97]), c_0_100]), c_0_98]), c_0_100])]), ['proof']).
% 0.20/0.29 % SZS output end CNFRefutation
% 0.20/0.29 % Parsed axioms : 143
% 0.20/0.29 % Removed by relevancy pruning/SinE : 78
% 0.20/0.29 % Initial clauses : 134
% 0.20/0.29 % Removed in clause preprocessing : 6
% 0.20/0.29 % Initial clauses in saturation : 128
% 0.20/0.29 % Processed clauses : 25
% 0.20/0.29 % ...of these trivial : 1
% 0.20/0.29 % ...subsumed : 6
% 0.20/0.29 % ...remaining for further processing : 17
% 0.20/0.29 % Other redundant clauses eliminated : 1
% 0.20/0.29 % Clauses deleted for lack of memory : 0
% 0.20/0.29 % Backward-subsumed : 0
% 0.20/0.29 % Backward-rewritten : 2
% 0.20/0.29 % Generated clauses : 2
% 0.20/0.29 % ...of the previous two non-redundant : 3
% 0.20/0.29 % ...aggressively subsumed : 0
% 0.20/0.29 % Contextual simplify-reflections : 0
% 0.20/0.29 % Paramodulations : 1
% 0.20/0.29 % Factorizations : 0
% 0.20/0.29 % NegExts : 0
% 0.20/0.29 % Equation resolutions : 1
% 0.20/0.29 % Disequality decompositions : 0
% 0.20/0.29 % Total rewrite steps : 9
% 0.20/0.29 % ...of those cached : 3
% 0.20/0.29 % Propositional unsat checks : 0
% 0.20/0.29 % Propositional check models : 0
% 0.20/0.29 % Propositional check unsatisfiable : 0
% 0.20/0.29 % Propositional clauses : 0
% 0.20/0.29 % Propositional clauses after purity: 0
% 0.20/0.29 % Propositional unsat core size : 0
% 0.20/0.29 % Propositional preprocessing time : 0.000
% 0.20/0.29 % Propositional encoding time : 0.000
% 0.20/0.29 % Propositional solver time : 0.000
% 0.20/0.29 % Success case prop preproc time : 0.000
% 0.20/0.29 % Success case prop encoding time : 0.000
% 0.20/0.29 % Success case prop solver time : 0.000
% 0.20/0.29 % Current number of processed clauses : 14
% 0.20/0.29 % Positive orientable unit clauses : 12
% 0.20/0.29 % Positive unorientable unit clauses: 0
% 0.20/0.29 % Negative unit clauses : 1
% 0.20/0.29 % Non-unit-clauses : 1
% 0.20/0.29 % Current number of unprocessed clauses: 106
% 0.20/0.29 % ...number of literals in the above : 345
% 0.20/0.29 % Current number of archived formulas : 0
% 0.20/0.29 % Current number of archived clauses : 2
% 0.20/0.29 % Clause-clause subsumption calls (NU) : 0
% 0.20/0.29 % Rec. Clause-clause subsumption calls : 0
% 0.20/0.29 % Non-unit clause-clause subsumptions : 0
% 0.20/0.29 % Unit Clause-clause subsumption calls : 0
% 0.20/0.29 % Rewrite failures with RHS unbound : 0
% 0.20/0.29 % BW rewrite match attempts : 2
% 0.20/0.29 % BW rewrite match successes : 2
% 0.20/0.29 % Condensation attempts : 0
% 0.20/0.29 % Condensation successes : 0
% 0.20/0.29 % Termbank termtop insertions : 16882
% 0.20/0.29 % Search garbage collected termcells : 6908
% 0.20/0.29
% 0.20/0.29 % -------------------------------------------------
% 0.20/0.29 % User time : 0.015 s
% 0.20/0.29 % System time : 0.007 s
% 0.20/0.29 % Total time : 0.022 s
% 0.20/0.29 % Maximum resident set size: 5572 pages
% 0.20/0.29
% 0.20/0.29 % -------------------------------------------------
% 0.20/0.29 % User time : 0.019 s
% 0.20/0.29 % System time : 0.012 s
% 0.20/0.29 % Total time : 0.031 s
% 0.20/0.29 % Maximum resident set size: 4608 pages
% 0.20/0.29 % E exiting
%------------------------------------------------------------------------------