%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU577^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 08:26:46 AM UTC 2026
% Result : Theorem 0.20s 0.33s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU577^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n018.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 13:53:56 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.26 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.bi2quG6kJl/E---3.1_108914.p
% 0.20/0.33 % Version: 3.5.1-ho
% 0.20/0.33 % Preprocessing class: HSMMSLSSLLLCHFA.
% 0.20/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.33 % Starting ehoh_best3_avoidappvar with 1500s (5) cores
% 0.20/0.33 % Starting ehoh_best3_rw with 300s (1) cores
% 0.20/0.33 % Starting almost_fo_3 with 300s (1) cores
% 0.20/0.33 % Starting new_ho_13 with 300s (1) cores
% 0.20/0.33 % almost_fo_3 with pid 108929 completed with status 0
% 0.20/0.33 % Result found by almost_fo_3
% 0.20/0.33 % Preprocessing class: HSMMSLSSLLLCHFA.
% 0.20/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.33 % Starting ehoh_best3_avoidappvar with 1500s (5) cores
% 0.20/0.33 % Starting ehoh_best3_rw with 300s (1) cores
% 0.20/0.33 % Starting almost_fo_3 with 300s (1) cores
% 0.20/0.33 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.20/0.33 % No SInE strategy applied
% 0.20/0.33 % Search class: HGHSM-FSLM31-SHFMMSBN
% 0.20/0.33 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.33 % Starting SubtermCWHack with 28s (1) cores
% 0.20/0.33 % SubtermCWHack with pid 108931 completed with status 0
% 0.20/0.33 % Result found by SubtermCWHack
% 0.20/0.33 % Preprocessing class: HSMMSLSSLLLCHFA.
% 0.20/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.33 % Starting ehoh_best3_avoidappvar with 1500s (5) cores
% 0.20/0.33 % Starting ehoh_best3_rw with 300s (1) cores
% 0.20/0.33 % Starting almost_fo_3 with 300s (1) cores
% 0.20/0.33 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.20/0.33 % No SInE strategy applied
% 0.20/0.33 % Search class: HGHSM-FSLM31-SHFMMSBN
% 0.20/0.33 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.33 % Starting SubtermCWHack with 28s (1) cores
% 0.20/0.33 % Preprocessing time : 0.004 s
% 0.20/0.33
% 0.20/0.33 % Proof found!
% 0.20/0.33 % SZS status Theorem
% 0.20/0.33 % SZS output start CNFRefutation
% 0.20/0.33 thf(decl_23, type, in: $i > $i > $o).
% 0.20/0.33 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.20/0.33 thf(decl_25, type, setextAx: $o).
% 0.20/0.33 thf(decl_26, type, emptyset: $i).
% 0.20/0.33 thf(decl_27, type, emptysetAx: $o).
% 0.20/0.33 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.20/0.33 thf(decl_29, type, setadjoinAx: $o).
% 0.20/0.33 thf(decl_30, type, powerset: $i > $i).
% 0.20/0.33 thf(decl_31, type, powersetAx: $o).
% 0.20/0.33 thf(decl_32, type, setunion: $i > $i).
% 0.20/0.33 thf(decl_33, type, setunionAx: $o).
% 0.20/0.33 thf(decl_34, type, omega: $i).
% 0.20/0.33 thf(decl_35, type, omega0Ax: $o).
% 0.20/0.33 thf(decl_36, type, omegaSAx: $o).
% 0.20/0.33 thf(decl_37, type, omegaIndAx: $o).
% 0.20/0.33 thf(decl_38, type, replAx: $o).
% 0.20/0.33 thf(decl_39, type, foundationAx: $o).
% 0.20/0.33 thf(decl_40, type, wellorderingAx: $o).
% 0.20/0.33 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.20/0.33 thf(decl_42, type, descrp: $o).
% 0.20/0.33 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.20/0.33 thf(decl_44, type, dsetconstrI: $o).
% 0.20/0.33 thf(decl_45, type, dsetconstrEL: $o).
% 0.20/0.33 thf(decl_46, type, dsetconstrER: $o).
% 0.20/0.33 thf(decl_47, type, exuE1: $o).
% 0.20/0.33 thf(decl_48, type, prop2set: $o > $i).
% 0.20/0.33 thf(decl_49, type, prop2setE: $o).
% 0.20/0.33 thf(decl_50, type, emptysetE: $o).
% 0.20/0.33 thf(decl_51, type, emptysetimpfalse: $o).
% 0.20/0.33 thf(decl_52, type, notinemptyset: $o).
% 0.20/0.33 thf(decl_53, type, exuE3e: $o).
% 0.20/0.33 thf(decl_54, type, setext: $o).
% 0.20/0.33 thf(decl_55, type, emptyI: $o).
% 0.20/0.33 thf(decl_56, type, noeltsimpempty: $o).
% 0.20/0.33 thf(decl_57, type, setbeta: $o).
% 0.20/0.33 thf(decl_58, type, nonempty: $i > $o).
% 0.20/0.33 thf(decl_59, type, nonemptyE1: $o).
% 0.20/0.33 thf(decl_60, type, nonemptyI: $o).
% 0.20/0.33 thf(decl_61, type, nonemptyI1: $o).
% 0.20/0.33 thf(decl_62, type, setadjoinIL: $o).
% 0.20/0.33 thf(decl_63, type, emptyinunitempty: $o).
% 0.20/0.33 thf(decl_64, type, setadjoinIR: $o).
% 0.20/0.33 thf(decl_65, type, setadjoinE: $o).
% 0.20/0.33 thf(decl_66, type, setadjoinOr: $o).
% 0.20/0.33 thf(decl_67, type, setoftrueEq: $o).
% 0.20/0.33 thf(decl_68, type, powersetI: $o).
% 0.20/0.33 thf(decl_69, type, emptyinPowerset: $o).
% 0.20/0.33 thf(decl_70, type, emptyInPowerset: $o).
% 0.20/0.33 thf(decl_71, type, powersetE: $o).
% 0.20/0.33 thf(decl_72, type, setunionI: $o).
% 0.20/0.33 thf(decl_73, type, setunionE: $o).
% 0.20/0.33 thf(decl_74, type, subPowSU: $o).
% 0.20/0.33 thf(decl_75, type, exuE2: $o).
% 0.20/0.33 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.20/0.33 thf(decl_77, type, uniqinunit: $o).
% 0.20/0.33 thf(decl_78, type, notinsingleton: $o).
% 0.20/0.33 thf(decl_79, type, eqinunit: $o).
% 0.20/0.33 thf(decl_80, type, singletonsswitch: $o).
% 0.20/0.33 thf(decl_81, type, upairsetE: $o).
% 0.20/0.33 thf(decl_82, type, upairsetIL: $o).
% 0.20/0.33 thf(decl_83, type, upairsetIR: $o).
% 0.20/0.33 thf(decl_84, type, emptyE1: $o).
% 0.20/0.33 thf(decl_85, type, vacuousDall: $o).
% 0.20/0.33 thf(decl_86, type, quantDeMorgan1: $o).
% 0.20/0.33 thf(decl_87, type, quantDeMorgan2: $o).
% 0.20/0.33 thf(decl_88, type, quantDeMorgan3: $o).
% 0.20/0.33 thf(decl_89, type, quantDeMorgan4: $o).
% 0.20/0.33 thf(decl_90, type, prop2setI: $o).
% 0.20/0.33 thf(decl_91, type, set2prop: $i > $o).
% 0.20/0.33 thf(decl_92, type, prop2set2propI: $o).
% 0.20/0.33 thf(decl_93, type, notdexE: $o).
% 0.20/0.33 thf(decl_94, type, notdallE: $o).
% 0.20/0.33 thf(decl_95, type, exuI1: $o).
% 0.20/0.33 thf(decl_96, type, exuI3: $o).
% 0.20/0.33 thf(decl_97, type, exuI2: $o).
% 0.20/0.33 thf(decl_98, type, inCongP: $o).
% 0.20/0.33 thf(decl_99, type, in__Cong: $o).
% 0.20/0.33 thf(decl_100, type, exuE3u: $o).
% 0.20/0.33 thf(decl_101, type, exu__Cong: $o).
% 0.20/0.33 thf(decl_102, type, emptyset__Cong: $o).
% 0.20/0.33 thf(decl_103, type, setadjoin__Cong: $o).
% 0.20/0.33 thf(decl_104, type, powerset__Cong: $o).
% 0.20/0.33 thf(decl_105, type, setunion__Cong: $o).
% 0.20/0.33 thf(decl_106, type, omega__Cong: $o).
% 0.20/0.33 thf(decl_107, type, exuEu: $o).
% 0.20/0.33 thf(decl_108, type, descr__Cong: $o).
% 0.20/0.33 thf(decl_109, type, dsetconstr__Cong: $o).
% 0.20/0.33 thf(decl_110, type, subset: $i > $i > $o).
% 0.20/0.33 thf(decl_113, type, subsetI1: $o).
% 0.20/0.33 thf(decl_114, type, eqimpsubset2: $o).
% 0.20/0.33 thf(decl_115, type, eqimpsubset1: $o).
% 0.20/0.33 thf(decl_116, type, subsetI2: $o).
% 0.20/0.33 thf(decl_117, type, emptysetsubset: $o).
% 0.20/0.33 thf(decl_118, type, subsetE: $o).
% 0.20/0.33 thf(decl_119, type, subsetE2: $o).
% 0.20/0.33 thf(decl_120, type, notsubsetI: $o).
% 0.20/0.33 thf(decl_121, type, notequalI1: $o).
% 0.20/0.33 thf(decl_122, type, notequalI2: $o).
% 0.20/0.33 thf(decl_123, type, subsetRefl: $o).
% 0.20/0.33 thf(decl_124, type, subsetTrans: $o).
% 0.20/0.33 thf(decl_125, type, setadjoinSub: $o).
% 0.20/0.33 thf(decl_126, type, setadjoinSub2: $o).
% 0.20/0.33 thf(decl_127, type, subset2powerset: $o).
% 0.20/0.33 thf(decl_128, type, setextsub: $o).
% 0.20/0.33 thf(decl_129, type, subsetemptysetimpeq: $o).
% 0.20/0.33 thf(decl_130, type, powersetI1: $o).
% 0.20/0.33 thf(decl_131, type, epred1_0: $o).
% 0.20/0.33 thf(decl_132, type, esk1_2: $i > $i > $i).
% 0.20/0.33 thf(decl_133, type, esk2_2: $i > $i > $i).
% 0.20/0.33 thf(decl_134, type, esk3_2: $i > $i > $i).
% 0.20/0.33 thf(decl_135, type, esk4_1: $i > $i).
% 0.20/0.33 thf(decl_136, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.20/0.33 thf(decl_137, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.20/0.33 thf(decl_138, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.20/0.33 thf(decl_139, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.20/0.33 thf(decl_140, type, esk9_1: $i > $i).
% 0.20/0.33 thf(decl_141, type, esk10_2: ($i > $o) > $i > $i).
% 0.20/0.33 thf(decl_142, type, esk11_2: ($i > $o) > $i > $i).
% 0.20/0.33 thf(decl_143, type, esk12_1: ($i > $o) > $i).
% 0.20/0.33 thf(decl_144, type, esk13_2: ($i > $o) > $i > $i).
% 0.20/0.33 thf(decl_145, type, esk14_1: ($i > $o) > $i).
% 0.20/0.33 thf(decl_146, type, esk15_2: $i > $i > $i).
% 0.20/0.33 thf(decl_147, type, esk16_2: $i > $i > $i).
% 0.20/0.33 thf(decl_148, type, esk17_1: $i > $i).
% 0.20/0.33 thf(decl_149, type, esk18_1: $i > $i).
% 0.20/0.33 thf(decl_150, type, esk19_1: $i > $i).
% 0.20/0.33 thf(decl_151, type, esk20_2: $i > $i > $i).
% 0.20/0.33 thf(decl_152, type, esk21_3: $i > $i > $o > $i).
% 0.20/0.33 thf(decl_153, type, esk22_2: ($i > $o) > $i > $i).
% 0.20/0.33 thf(decl_154, type, esk23_1: ($i > $o) > $i).
% 0.20/0.33 thf(decl_155, type, esk24_1: $i > $i).
% 0.20/0.33 thf(decl_156, type, esk25_2: $i > ($i > $o) > $i).
% 0.20/0.33 thf(decl_157, type, esk26_2: $i > ($i > $o) > $i).
% 0.20/0.33 thf(decl_158, type, esk27_2: $i > ($i > $o) > $i).
% 0.20/0.33 thf(decl_159, type, esk28_2: $i > ($i > $o) > $i).
% 0.20/0.33 thf(decl_160, type, esk29_2: $i > ($i > $o) > $i).
% 0.20/0.33 thf(decl_161, type, esk30_2: $i > ($i > $o) > $i).
% 0.20/0.33 thf(decl_162, type, esk31_2: ($i > $o) > $i > $i).
% 0.20/0.33 thf(decl_163, type, esk32_1: ($i > $o) > $i).
% 0.20/0.33 thf(decl_164, type, esk33_1: ($i > $o) > $i).
% 0.20/0.33 thf(decl_165, type, esk34_1: ($i > $o) > $i).
% 0.20/0.33 thf(decl_166, type, esk35_1: ($i > $o) > $i).
% 0.20/0.33 thf(decl_167, type, esk36_2: ($i > $o) > $i > $i).
% 0.20/0.33 thf(decl_168, type, esk37_1: ($i > $o) > $i).
% 0.20/0.33 thf(decl_169, type, esk38_2: ($i > $o) > $i > $i).
% 0.20/0.33 thf(decl_170, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 0.20/0.33 thf(decl_171, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 0.20/0.33 thf(decl_172, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.20/0.33 thf(decl_173, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 0.20/0.33 thf(decl_174, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.20/0.33 thf(decl_175, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 0.20/0.33 thf(decl_176, type, esk45_2: ($i > $o) > $i > $i).
% 0.20/0.33 thf(decl_177, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 0.20/0.33 thf(decl_178, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 0.20/0.33 thf(decl_179, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.20/0.33 thf(decl_180, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.20/0.33 thf(decl_181, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.20/0.33 thf(decl_182, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.20/0.33 thf(decl_183, type, esk52_2: $i > $i > $i).
% 0.20/0.33 thf(decl_184, type, esk53_2: $i > $i > $i).
% 0.20/0.33 thf(decl_185, type, esk54_0: $i).
% 0.20/0.33 thf(decl_186, type, esk55_0: $i).
% 0.20/0.33 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', replAx)).
% 0.20/0.33 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', exu)).
% 0.20/0.33 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', descrp)).
% 0.20/0.33 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', exuE1)).
% 0.20/0.33 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', exuE3e)).
% 0.20/0.33 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', nonempty)).
% 0.20/0.33 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', nonemptyI)).
% 0.20/0.33 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', exuE2)).
% 0.20/0.33 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.bi2quG6kJl/E---3.1_108914.p', exuI1)).
% 0.20/0.33 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', exuI3)).
% 0.20/0.33 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', exuI2)).
% 0.20/0.33 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', exuE3u)).
% 0.20/0.33 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', exu__Cong)).
% 0.20/0.33 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', exuEu)).
% 0.20/0.33 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', descr__Cong)).
% 0.20/0.33 thf(powersetE1, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', powersetE1)).
% 0.20/0.33 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', dsetconstrI)).
% 0.20/0.33 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', dsetconstrEL)).
% 0.20/0.33 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', dsetconstrER)).
% 0.20/0.33 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', setbeta)).
% 0.20/0.33 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', nonemptyE1)).
% 0.20/0.33 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', nonemptyI1)).
% 0.20/0.33 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', setoftrueEq)).
% 0.20/0.33 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', nonemptyImpWitness)).
% 0.20/0.33 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.bi2quG6kJl/E---3.1_108914.p', emptyE1)).
% 0.20/0.33 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', dsetconstr__Cong)).
% 0.20/0.33 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', setextAx)).
% 0.20/0.33 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', emptysetAx)).
% 0.20/0.33 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', setadjoinAx)).
% 0.20/0.33 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', powersetAx)).
% 0.20/0.33 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', setunionAx)).
% 0.20/0.33 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', omega0Ax)).
% 0.20/0.33 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', omegaSAx)).
% 0.20/0.33 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.bi2quG6kJl/E---3.1_108914.p', omegaIndAx)).
% 0.20/0.33 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.bi2quG6kJl/E---3.1_108914.p', foundationAx)).
% 0.20/0.33 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', wellorderingAx)).
% 0.20/0.33 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', prop2setE)).
% 0.20/0.33 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', emptysetE)).
% 0.20/0.33 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', emptysetimpfalse)).
% 0.20/0.33 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', notinemptyset)).
% 0.20/0.33 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.bi2quG6kJl/E---3.1_108914.p', setext)).
% 0.20/0.33 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', emptyI)).
% 0.20/0.33 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', noeltsimpempty)).
% 0.20/0.33 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', setadjoinIL)).
% 0.20/0.33 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', emptyinunitempty)).
% 0.20/0.33 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', setadjoinIR)).
% 0.20/0.33 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', setadjoinE)).
% 0.20/0.33 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', setadjoinOr)).
% 0.20/0.33 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', powersetI)).
% 0.20/0.33 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', emptyinPowerset)).
% 0.20/0.33 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', emptyInPowerset)).
% 0.20/0.33 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', powersetE)).
% 0.20/0.33 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', setunionI)).
% 0.20/0.33 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', setunionE)).
% 0.20/0.33 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', subPowSU)).
% 0.20/0.33 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', uniqinunit)).
% 0.20/0.33 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', notinsingleton)).
% 0.20/0.33 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', eqinunit)).
% 0.20/0.33 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', singletonsswitch)).
% 0.20/0.33 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', upairsetE)).
% 0.20/0.33 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', upairsetIL)).
% 0.20/0.33 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', upairsetIR)).
% 0.20/0.33 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', vacuousDall)).
% 0.20/0.33 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', quantDeMorgan1)).
% 0.20/0.33 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', quantDeMorgan2)).
% 0.20/0.33 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', quantDeMorgan3)).
% 0.20/0.33 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', quantDeMorgan4)).
% 0.20/0.33 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', prop2setI)).
% 0.20/0.33 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', prop2set2propI)).
% 0.20/0.33 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', notdexE)).
% 0.20/0.33 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', notdallE)).
% 0.20/0.33 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', inCongP)).
% 0.20/0.33 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', in__Cong)).
% 0.20/0.33 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', emptyset__Cong)).
% 0.20/0.33 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', setadjoin__Cong)).
% 0.20/0.33 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', powerset__Cong)).
% 0.20/0.33 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', setunion__Cong)).
% 0.20/0.33 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', omega__Cong)).
% 0.20/0.33 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', subsetI1)).
% 0.20/0.33 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', eqimpsubset2)).
% 0.20/0.33 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', eqimpsubset1)).
% 0.20/0.33 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', subsetI2)).
% 0.20/0.33 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', emptysetsubset)).
% 0.20/0.33 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', subsetE)).
% 0.20/0.33 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', subsetE2)).
% 0.20/0.33 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', notsubsetI)).
% 0.20/0.33 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', notequalI1)).
% 0.20/0.33 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', notequalI2)).
% 0.20/0.33 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', subsetRefl)).
% 0.20/0.33 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', subsetTrans)).
% 0.20/0.33 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', setadjoinSub)).
% 0.20/0.33 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', setadjoinSub2)).
% 0.20/0.33 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', subset2powerset)).
% 0.20/0.33 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', setextsub)).
% 0.20/0.33 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', subsetemptysetimpeq)).
% 0.20/0.33 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.bi2quG6kJl/E---3.1_108914.p', powersetI1)).
% 0.20/0.33 thf(c_0_96, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.20/0.33 thf(c_0_97, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.20/0.33 thf(c_0_98, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.20/0.33 thf(c_0_99, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.20/0.33 thf(c_0_100, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.20/0.33 thf(c_0_101, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.20/0.33 thf(c_0_102, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.20/0.33 thf(c_0_103, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.20/0.33 thf(c_0_104, 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])).
% 0.20/0.33 thf(c_0_105, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.20/0.33 thf(c_0_106, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.20/0.33 thf(c_0_107, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 0.20/0.33 thf(c_0_108, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.20/0.33 thf(c_0_109, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 0.20/0.33 thf(c_0_110, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))=>((exu @ (^[Z0:$i]:((X17 @ Z0))))=>((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 0.20/0.33 thf(c_0_111, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[powersetE1])).
% 0.20/0.33 thf(c_0_112, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X274:$i]:(((((X6 @ X2 @ X274)))&(![X275:$i]:(((((X6 @ X2 @ X275)))=>(((X274)=(X275)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_96, c_0_97])).
% 0.20/0.33 thf(c_0_113, plain, ((descrp)=(![X1:$i > $o]:((((?[X276:$i]:(((((X1 @ X276)))&(![X277:$i]:(((((X1 @ X277)))=>(((X276)=(X277))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_98, c_0_97])).
% 0.20/0.33 thf(c_0_114, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.20/0.33 thf(c_0_115, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.20/0.33 thf(c_0_116, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.20/0.33 thf(c_0_117, plain, ((exuE1)=(![X1:$i > $o]:((((?[X278:$i]:(((((X1 @ X278)))&(![X279:$i]:(((((X1 @ X279)))=>(((X278)=(X279))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_99, c_0_97])).
% 0.20/0.33 thf(c_0_118, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X280:$i]:(((((X1 @ X280)))&(![X281:$i]:(((((X1 @ X281)))=>(((X280)=(X281))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_100, c_0_97])).
% 0.20/0.33 thf(c_0_119, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.20/0.33 thf(c_0_120, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_101])).
% 0.20/0.33 thf(c_0_121, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_102, c_0_101])).
% 0.20/0.33 thf(c_0_122, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_101])).
% 0.20/0.33 thf(c_0_123, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.20/0.33 thf(c_0_124, plain, ((exuE2)=(![X1:$i > $o]:((((?[X282:$i]:(((((X1 @ X282)))&(![X283:$i]:(((((X1 @ X283)))=>(((X282)=(X283))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_103, c_0_97])).
% 0.20/0.33 thf(c_0_125, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_101])).
% 0.20/0.33 thf(c_0_126, 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])).
% 0.20/0.33 thf(c_0_127, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X284:$i]:(((((X1 @ X284)))&(![X285:$i]:(((((X1 @ X285)))=>(((X284)=(X285)))))))))))))), inference(apply_def,[status(thm)],[c_0_104, c_0_97])).
% 0.20/0.33 thf(c_0_128, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X286:$i]:(((((X1 @ X286)))&(![X287:$i]:(((((X1 @ X287)))=>(((X286)=(X287)))))))))))))))), inference(apply_def,[status(thm)],[c_0_105, c_0_97])).
% 0.20/0.33 thf(c_0_129, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X288:$i]:(((((X1 @ X288)))&(![X289:$i]:(((((X1 @ X289)))=>(((X288)=(X289)))))))))))))), inference(apply_def,[status(thm)],[c_0_106, c_0_97])).
% 0.20/0.33 thf(c_0_130, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X290:$i]:(((((X1 @ X290)))&(![X291:$i]:(((((X1 @ X291)))=>(((X290)=(X291))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_107, c_0_97])).
% 0.20/0.33 thf(c_0_131, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X292:$i]:(((((X1 @ X292)))&(![X293:$i]:(((((X1 @ X293)))=>(((X292)=(X293))))))))))<=>((?[X294:$i]:(((((X17 @ X294)))&(![X295:$i]:(((((X17 @ X295)))=>(((X294)=(X295)))))))))))))))), inference(apply_def,[status(thm)],[c_0_108, c_0_97])).
% 0.20/0.33 thf(c_0_132, plain, ((exuEu)=(![X1:$i > $o]:((((?[X296:$i]:(((((X1 @ X296)))&(![X297:$i]:(((((X1 @ X297)))=>(((X296)=(X297))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_109, c_0_97])).
% 0.20/0.33 thf(c_0_133, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X298:$i]:(((((X1 @ X298)))&(![X299:$i]:(((((X1 @ X299)))=>(((X298)=(X299))))))))))=>((((?[X300:$i]:(((((X17 @ X300)))&(![X301:$i]:(((((X17 @ X301)))=>(((X300)=(X301))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_110, c_0_97])).
% 0.20/0.33 thf(c_0_134, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 0.20/0.33 thf(c_0_135, plain, ((epred1_0)<=>![X331:$i]:(?[X332:$i]:((((![X333:$i]:(((in @ X333 @ X332)=>![X334:$i]:(((in @ X334 @ X333)=>(in @ X334 @ X331)))))&![X335:$i, X336:$i]:((((in @ X335 @ X331)&(in @ X336 @ X331))=>(![X337:$i]:(((in @ X337 @ X332)=>((in @ X335 @ X337)<=>(in @ X336 @ X337))))=>((X335)=(X336))))))&![X338:$i, X339:$i]:((((in @ X338 @ X332)&(in @ X339 @ X332))=>(![X340:$i]:(((in @ X340 @ X338)=>(in @ X340 @ X339)))|![X341:$i]:(((in @ X341 @ X339)=>(in @ X341 @ X338)))))))&![X342:$i]:(((![X343:$i]:(((in @ X343 @ X342)=>(in @ X343 @ X331)))&?[X344:$i]:((in @ X344 @ X342)))=>?[X345:$i, X346:$i]:(((((in @ X345 @ X332)&(in @ X346 @ X342))&~(?[X347:$i]:(((in @ X347 @ X345)&(in @ X347 @ X342)))))&![X348:$i]:(((in @ X348 @ X332)=>(![X349:$i]:(((in @ X349 @ X348)=>(in @ X349 @ X345)))|(in @ X346 @ X348)))))))))))), introduced(definition)).
% 0.20/0.33 thf(c_0_136, negated_conjecture, ~((![X302:$i, X303:$i]:((![X304:$i]:(((in @ X304 @ X302)<=>(in @ X304 @ X303)))=>((X302)=(X303))))=>(![X305:$i]:(~(in @ X305 @ emptyset))=>(![X306:$i, X307:$i, X308:$i]:(((in @ X308 @ (setadjoin @ X306 @ X307))<=>(((X308)=(X306))|(in @ X308 @ X307))))=>(![X309:$i, X310:$i]:(((in @ X310 @ (powerset @ X309))<=>![X311:$i]:(((in @ X311 @ X310)=>(in @ X311 @ X309)))))=>(![X312:$i, X313:$i]:(((in @ X313 @ (setunion @ X312))<=>?[X314:$i]:(((in @ X313 @ X314)&(in @ X314 @ X312)))))=>((in @ emptyset @ omega)=>(![X315:$i]:(((in @ X315 @ omega)=>(in @ (setadjoin @ X315 @ X315) @ omega)))=>(![X316:$i]:((((in @ emptyset @ X316)&![X317:$i]:((((in @ X317 @ omega)&(in @ X317 @ X316))=>(in @ (setadjoin @ X317 @ X317) @ X316))))=>![X318:$i]:(((in @ X318 @ omega)=>(in @ X318 @ X316)))))=>(![X319:$i > $i > $o, X320:$i]:((![X321:$i]:(((in @ X321 @ X320)=>?[X322:$i]:(((X319 @ X321 @ X322)&![X323:$i]:(((X319 @ X321 @ X323)=>((X322)=(X323))))))))=>?[X324:$i]:(![X325:$i]:(((in @ X325 @ X324)<=>?[X326:$i]:(((in @ X326 @ X320)&(X319 @ X326 @ X325))))))))=>(![X327:$i]:((?[X328:$i]:((in @ X328 @ X327))=>?[X329:$i]:(((in @ X329 @ X327)&~(?[X330:$i]:(((in @ X330 @ X329)&(in @ X330 @ X327))))))))=>((epred1_0)=>(![X350:$i > $o]:((?[X351:$i]:(((X350 @ X351)&![X352:$i]:(((X350 @ X352)=>((X351)=(X352))))))=>(X350 @ (descr @ (^[Z0:$i]:(X350 @ Z0))))))=>(![X353:$i, X354:$i > $o, X355:$i]:(((in @ X355 @ X353)=>((X354 @ X355)=>(in @ X355 @ (dsetconstr @ X353 @ X354)))))=>(![X356:$i, X357:$i > $o, X358:$i]:(((in @ X358 @ (dsetconstr @ X356 @ X357))=>(in @ X358 @ X356)))=>(![X359:$i, X360:$i > $o, X361:$i]:(((in @ X361 @ (dsetconstr @ X359 @ X360))=>(X360 @ X361)))=>(![X362:$i > $o]:((?[X363:$i]:(((X362 @ X363)&![X364:$i]:(((X362 @ X364)=>((X363)=(X364))))))=>?[X365:$i]:(((X362 @ X365)&![X366:$i]:(((X362 @ X366)=>((X365)=(X366))))))))=>(![X367:$o, X368:$i]:(((in @ X368 @ (prop2set @ ((X367))))=>(X367)))=>(![X369:$i]:(((in @ X369 @ emptyset)=>![X370:$o]:((X370))))=>(![X371:$i]:(((in @ X371 @ emptyset)=>~($true)))=>(![X372:$i]:(~(in @ X372 @ emptyset))=>(![X373:$i > $o]:((?[X374:$i]:(((X373 @ X374)&![X375:$i]:(((X373 @ X375)=>((X374)=(X375))))))=>?[X376:$i]:((X373 @ X376))))=>(![X377:$i, X378:$i]:((![X379:$i]:(((in @ X379 @ X377)=>(in @ X379 @ X378)))=>(![X380:$i]:(((in @ X380 @ X378)=>(in @ X380 @ X377)))=>((X377)=(X378)))))=>(![X381:$i]:((![X382:$i]:(~(in @ X382 @ X381))=>((X381)=(emptyset))))=>(![X383:$i]:((![X384:$i]:(~(in @ X384 @ X383))=>((X383)=(emptyset))))=>(![X385:$i, X386:$i > $o, X387:$i]:(((in @ X387 @ X385)=>((in @ X387 @ (dsetconstr @ X385 @ X386))<=>(X386 @ X387))))=>(![X388:$i]:((((X388)!=(emptyset))=>?[X389:$i]:((in @ X389 @ X388))))=>(![X390:$i, X391:$i > $o, X392:$i]:(((in @ X392 @ X390)=>((X391 @ X392)=>((dsetconstr @ X390 @ X391)!=(emptyset)))))=>(![X393:$i]:((?[X394:$i]:((in @ X394 @ X393))=>((X393)!=(emptyset))))=>(![X395:$i, X396:$i]:((in @ X395 @ (setadjoin @ X395 @ X396)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X397:$i, X398:$i, X399:$i]:(((in @ X399 @ X398)=>(in @ X399 @ (setadjoin @ X397 @ X398))))=>(![X400:$i, X401:$i, X402:$i]:(((in @ X402 @ (setadjoin @ X400 @ X401))=>![X403:$o]:(((((X402)=(X400))=>(X403))=>(((in @ X402 @ X401)=>(X403))=>(X403))))))=>(![X404:$i, X405:$i, X406:$i]:(((in @ X406 @ (setadjoin @ X404 @ X405))=>(((X406)=(X404))|(in @ X406 @ X405))))=>(![X407:$i]:(((dsetconstr @ X407 @ (^[Z0:$i]:($true)))=(X407)))=>(![X408:$i, X409:$i]:((![X410:$i]:(((in @ X410 @ X409)=>(in @ X410 @ X408)))=>(in @ X409 @ (powerset @ X408))))=>(![X411:$i]:((in @ emptyset @ (powerset @ X411)))=>(![X412:$i]:((in @ emptyset @ (powerset @ X412)))=>(![X413:$i, X414:$i, X415:$i]:(((in @ X414 @ (powerset @ X413))=>((in @ X415 @ X414)=>(in @ X415 @ X413))))=>(![X416:$i, X417:$i, X418:$i]:(((in @ X417 @ X418)=>((in @ X418 @ X416)=>(in @ X417 @ (setunion @ X416)))))=>(![X419:$i, X420:$i]:(((in @ X420 @ (setunion @ X419))=>![X421:$o]:((![X422:$i]:(((in @ X420 @ X422)=>((in @ X422 @ X419)=>(X421))))=>(X421)))))=>(![X423:$i, X424:$i]:(((in @ X424 @ X423)=>(in @ X424 @ (powerset @ (setunion @ X423)))))=>(![X425:$i > $o]:((?[X426:$i]:(((X425 @ X426)&![X427:$i]:(((X425 @ X427)=>((X426)=(X427))))))=>?[X428:$i]:(![X429:$i]:(((X425 @ X429)<=>((X429)=(X428)))))))=>(![X430:$i]:((((X430)!=(emptyset))=>?[X431:$i]:(((in @ X431 @ X430)&$true))))=>(![X432:$i, X433:$i]:(((in @ X432 @ (setadjoin @ X433 @ emptyset))=>((X432)=(X433))))=>(![X434:$i, X435:$i]:((((X434)!=(X435))=>~(in @ X435 @ (setadjoin @ X434 @ emptyset))))=>(![X436:$i, X437:$i]:((((X436)=(X437))=>(in @ X436 @ (setadjoin @ X437 @ emptyset))))=>(![X438:$i, X439:$i]:(((in @ X438 @ (setadjoin @ X439 @ emptyset))=>(in @ X439 @ (setadjoin @ X438 @ emptyset))))=>(![X440:$i, X441:$i, X442:$i]:(((in @ X442 @ (setadjoin @ X440 @ (setadjoin @ X441 @ emptyset)))=>(((X442)=(X440))|((X442)=(X441)))))=>(![X443:$i, X444:$i]:((in @ X443 @ (setadjoin @ X443 @ (setadjoin @ X444 @ emptyset))))=>(![X445:$i, X446:$i]:((in @ X446 @ (setadjoin @ X445 @ (setadjoin @ X446 @ emptyset))))=>(![X447:$i, X448:$i > $o]:((?[X449:$i]:(((in @ X449 @ X447)&(X448 @ X449)))=>(((dsetconstr @ X447 @ X448)=(emptyset))=>~($true))))=>(![X450:$i > $o, X451:$i]:(((in @ X451 @ emptyset)=>(X450 @ X451)))=>(![X452:$i, X453:$i > $o]:((~(![X454:$i]:(((in @ X454 @ X452)=>(X453 @ X454))))=>?[X455:$i]:(((in @ X455 @ X452)&~((X453 @ X455))))))=>(![X456:$i, X457:$i > $o]:((![X458:$i]:(((in @ X458 @ X456)=>~((X457 @ X458))))=>~(?[X459:$i]:(((in @ X459 @ X456)&(X457 @ X459))))))=>(![X460:$i, X461:$i > $o]:((~(?[X462:$i]:(((in @ X462 @ X460)&(X461 @ X462))))=>![X463:$i]:(((in @ X463 @ X460)=>~((X461 @ X463))))))=>(![X464:$i, X465:$i > $o]:((?[X466:$i]:(((in @ X466 @ X464)&~((X465 @ X466))))=>~(![X467:$i]:(((in @ X467 @ X464)=>(X465 @ X467))))))=>(![X468:$o]:(((X468)=>(in @ emptyset @ (prop2set @ ((X468))))))=>(![X469:$o]:(((X469)=>(set2prop @ (prop2set @ ((X469))))))=>(![X470:$i, X471:$i > $o]:((~(?[X472:$i]:(((in @ X472 @ X470)&(X471 @ X472))))=>![X473:$i]:(((in @ X473 @ X470)=>~((X471 @ X473))))))=>(![X474:$i, X475:$i > $o]:((~(![X476:$i]:(((in @ X476 @ X474)=>(X475 @ X476))))=>?[X477:$i]:(((in @ X477 @ X474)&~((X475 @ X477))))))=>(![X478:$i > $o]:((?[X479:$i]:(((X478 @ X479)&![X480:$i]:(((X478 @ X480)=>((X479)=(X480))))))=>?[X481:$i]:(((X478 @ X481)&![X482:$i]:(((X478 @ X482)=>((X481)=(X482))))))))=>(![X483:$i > $o]:((?[X484:$i]:((X483 @ X484))=>(![X485:$i, X486:$i]:(((X483 @ X485)=>((X483 @ X486)=>((X485)=(X486)))))=>?[X487:$i]:(((X483 @ X487)&![X488:$i]:(((X483 @ X488)=>((X487)=(X488)))))))))=>(![X489:$i > $o]:((?[X490:$i]:(![X491:$i]:(((X489 @ X491)<=>((X491)=(X490)))))=>?[X492:$i]:(((X489 @ X492)&![X493:$i]:(((X489 @ X493)=>((X492)=(X493))))))))=>(![X494:$i, X495:$i]:((((X494)=(X495))=>![X496:$i, X497:$i]:((((X496)=(X497))=>((in @ X496 @ X494)=>(in @ X497 @ X495))))))=>(![X498:$i, X499:$i]:((((X498)=(X499))=>![X500:$i, X501:$i]:((((X500)=(X501))=>((in @ X500 @ X498)<=>(in @ X501 @ X499))))))=>(![X502:$i > $o]:((?[X503:$i]:(((X502 @ X503)&![X504:$i]:(((X502 @ X504)=>((X503)=(X504))))))=>![X505:$i, X506:$i]:(((X502 @ X505)=>((X502 @ X506)=>((X505)=(X506)))))))=>(![X507:$i > $o, X508:$i > $o]:((![X509:$i, X510:$i]:((((X509)=(X510))=>((X507 @ X509)<=>(X508 @ X510))))=>(?[X511:$i]:(((X507 @ X511)&![X512:$i]:(((X507 @ X512)=>((X511)=(X512))))))<=>?[X513:$i]:(((X508 @ X513)&![X514:$i]:(((X508 @ X514)=>((X513)=(X514)))))))))=>(((emptyset)=(emptyset))=>(![X515:$i, X516:$i]:((((X515)=(X516))=>![X517:$i, X518:$i]:((((X517)=(X518))=>((setadjoin @ X515 @ X517)=(setadjoin @ X516 @ X518))))))=>(![X519:$i, X520:$i]:((((X519)=(X520))=>((powerset @ X519)=(powerset @ X520))))=>(![X521:$i, X522:$i]:((((X521)=(X522))=>((setunion @ X521)=(setunion @ X522))))=>(((omega)=(omega))=>(![X523:$i > $o]:((?[X524:$i]:(((X523 @ X524)&![X525:$i]:(((X523 @ X525)=>((X524)=(X525))))))=>![X526:$i, X527:$i]:(((X523 @ X526)=>((X523 @ X527)=>((X526)=(X527)))))))=>(![X528:$i > $o, X529:$i > $o]:((![X530:$i, X531:$i]:((((X530)=(X531))=>((X528 @ X530)<=>(X529 @ X531))))=>(?[X532:$i]:(((X528 @ X532)&![X533:$i]:(((X528 @ X533)=>((X532)=(X533))))))=>(?[X534:$i]:(((X529 @ X534)&![X535:$i]:(((X529 @ X535)=>((X534)=(X535))))))=>((descr @ X528)=(descr @ X529))))))=>(![X536:$i, X537:$i]:((((X536)=(X537))=>![X538:$i > $o, X539:$i > $o]:((![X540:$i]:(((in @ X540 @ X536)=>![X541:$i]:(((in @ X541 @ X537)=>(((X540)=(X541))=>((X538 @ X540)<=>(X539 @ X541)))))))=>((dsetconstr @ X536 @ X538)=(dsetconstr @ X537 @ X539))))))=>(![X542:$i, X543:$i]:((![X544:$i]:(((in @ X544 @ X542)=>(in @ X544 @ X543)))=>(subset @ X542 @ X543)))=>(![X545:$i, X546:$i]:((((X545)=(X546))=>(subset @ X546 @ X545)))=>(![X547:$i, X548:$i]:((((X547)=(X548))=>(subset @ X547 @ X548)))=>(![X549:$i, X550:$i]:((![X551:$i]:(((in @ X551 @ X549)=>(in @ X551 @ X550)))=>(subset @ X549 @ X550)))=>(![X552:$i]:((subset @ emptyset @ X552))=>(![X553:$i, X554:$i, X555:$i]:(((subset @ X553 @ X554)=>((in @ X555 @ X553)=>(in @ X555 @ X554))))=>(![X556:$i, X557:$i, X558:$i]:(((subset @ X556 @ X557)=>(~(in @ X558 @ X557)=>~(in @ X558 @ X556))))=>(![X559:$i, X560:$i, X561:$i]:(((in @ X561 @ X559)=>(~(in @ X561 @ X560)=>~(subset @ X559 @ X560))))=>(![X562:$i, X563:$i]:((~(subset @ X562 @ X563)=>((X562)!=(X563))))=>(![X564:$i, X565:$i, X566:$i]:(((in @ X566 @ X564)=>(~(in @ X566 @ X565)=>((X564)!=(X565)))))=>(![X567:$i]:((subset @ X567 @ X567))=>(![X568:$i, X569:$i, X570:$i]:(((subset @ X568 @ X569)=>((subset @ X569 @ X570)=>(subset @ X568 @ X570))))=>(![X571:$i, X572:$i]:((subset @ X572 @ (setadjoin @ X571 @ X572)))=>(![X573:$i, X574:$i, X575:$i]:(((subset @ X573 @ X575)=>(subset @ X573 @ (setadjoin @ X574 @ X575))))=>(![X576:$i, X577:$i]:(((subset @ X576 @ X577)=>(in @ X576 @ (powerset @ X577))))=>(![X578:$i, X579:$i]:(((subset @ X578 @ X579)=>((subset @ X579 @ X578)=>((X578)=(X579)))))=>(![X580:$i]:(((subset @ X580 @ emptyset)=>((X580)=(emptyset))))=>(![X581:$i, X582:$i]:(((subset @ X582 @ X581)=>(in @ X582 @ (powerset @ X581))))=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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)],[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_111, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_112]), foundationAx]), wellorderingAx]), c_0_113]), c_0_114]), c_0_115]), c_0_116]), c_0_117]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_118]), setext]), emptyI]), noeltsimpempty]), c_0_119]), c_0_120]), c_0_121]), c_0_122]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_123]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_124]), c_0_125]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_126]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_127]), c_0_128]), c_0_129]), inCongP]), in__Cong]), c_0_130]), c_0_131]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_132]), c_0_133]), c_0_134]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1])])]), c_0_135])).
% 0.20/0.33 thf(c_0_137, negated_conjecture, ![X583:$i, X584:$i, X586:$i, X587:$i, X588:$i, X589:$i, X590:$i, X591:$i, X592:$i, X593:$i, X594:$i, X596:$i, X597:$i, X599:$i, X600:$i, X601:$i, X602:$i, X603:$i, X605:$i, X606:$i > $i > $o, X607:$i, X609:$i, X612:$i, X614:$i, X615:$i, X616:$i, X617:$i, X619:$i, X620:$i > $o, X621:$i, X623:$i, X624:$i > $o, X625:$i, X626:$i, X627:$i > $o, X628:$i, X629:$i, X630:$i > $o, X631:$i, X632:$i > $o, X633:$i, X636:$i, X637:$o, X638:$i, X639:$i, X640:$o, X641:$i, X642:$i, X643:$i > $o, X644:$i, X647:$i, X648:$i, X651:$i, X653:$i, X655:$i, X656:$i > $o, X657:$i, X658:$i, X660:$i, X661:$i > $o, X662:$i, X663:$i, X664:$i, X665:$i, X666:$i, X667:$i, X668:$i, X669:$i, X670:$i, X671:$i, X672:$i, X673:$o, X674:$i, X675:$i, X676:$i, X677:$i, X678:$i, X679:$i, X681:$i, X682:$i, X683:$i, X684:$i, X685:$i, X686:$i, X687:$i, X688:$i, X689:$i, X690:$i, X691:$o, X693:$i, X694:$i, X695:$i > $o, X696:$i, X699:$i, X700:$i, X701:$i, X703:$i, X704:$i, X705:$i, X706:$i, X707:$i, X708:$i, X709:$i, X710:$i, X711:$i, X712:$i, X713:$i, X714:$i, X715:$i, X716:$i, X717:$i, X718:$i, X719:$i > $o, X720:$i, X721:$i > $o, X722:$i, X723:$i, X724:$i > $o, X725:$i, X727:$i, X728:$i > $o, X730:$i, X731:$i, X732:$i > $o, X734:$i, X735:$i, X736:$i > $o, X737:$i, X739:$o, X740:$o, X741:$i, X742:$i > $o, X744:$i, X745:$i, X746:$i > $o, X747:$i, X749:$i > $o, X750:$i, X753:$i, X754:$i > $o, X755:$i, X759:$i, X760:$i > $o, X761:$i, X764:$i, X765:$i, X766:$i, X767:$i, X768:$i, X769:$i, X770:$i, X771:$i, X772:$i, X773:$i > $o, X774:$i, X776:$i, X777:$i, X778:$i > $o, X779:$i > $o, X782:$i, X785:$i, X786:$i, X789:$i, X790:$i, X791:$i, X792:$i, X793:$i, X794:$i, X795:$i, X796:$i, X797:$i, X798:$i > $o, X799:$i, X801:$i, X802:$i, X803:$i > $o, X804:$i > $o, X807:$i, X809:$i, X811:$i, X812:$i, X813:$i > $o, X814:$i > $o, X817:$i, X818:$i, X820:$i, X821:$i, X822:$i, X823:$i, X824:$i, X825:$i, X827:$i, X828:$i, X829:$i, X830:$i, X831:$i, X832:$i, X833:$i, X834:$i, X835:$i, X836:$i, X837:$i, X838:$i, X839:$i, X840:$i, X841:$i, X842:$i, X843:$i, X844:$i, X845:$i, X846:$i, X847:$i, X848:$i, X849:$i, X850:$i, X851:$i, X852:$i, X853:$i, X854:$i, X855:$i, X856:$i, X857:$i]:((((~(in @ (esk1_2 @ X583 @ X584) @ X583)|~(in @ (esk1_2 @ X583 @ X584) @ X584)|((X583)=(X584)))&((in @ (esk1_2 @ X583 @ X584) @ X583)|(in @ (esk1_2 @ X583 @ X584) @ X584)|((X583)=(X584))))&(~(in @ X586 @ emptyset)&(((~(in @ X589 @ (setadjoin @ X587 @ X588))|(((X589)=(X587))|(in @ X589 @ X588)))&((((X589)!=(X587))|(in @ X589 @ (setadjoin @ X587 @ X588)))&(~(in @ X589 @ X588)|(in @ X589 @ (setadjoin @ X587 @ X588)))))&(((~(in @ X591 @ (powerset @ X590))|(~(in @ X592 @ X591)|(in @ X592 @ X590)))&(((in @ (esk2_2 @ X593 @ X594) @ X594)|(in @ X594 @ (powerset @ X593)))&(~(in @ (esk2_2 @ X593 @ X594) @ X593)|(in @ X594 @ (powerset @ X593)))))&(((((in @ X597 @ (esk3_2 @ X596 @ X597))|~(in @ X597 @ (setunion @ X596)))&((in @ (esk3_2 @ X596 @ X597) @ X596)|~(in @ X597 @ (setunion @ X596))))&(~(in @ X600 @ X601)|~(in @ X601 @ X599)|(in @ X600 @ (setunion @ X599))))&((in @ emptyset @ omega)&((~(in @ X602 @ omega)|(in @ (setadjoin @ X602 @ X602) @ omega))&(((((in @ (esk4_1 @ X603) @ omega)|~(in @ emptyset @ X603)|(~(in @ X605 @ omega)|(in @ X605 @ X603)))&((in @ (esk4_1 @ X603) @ X603)|~(in @ emptyset @ X603)|(~(in @ X605 @ omega)|(in @ X605 @ X603))))&(~(in @ (setadjoin @ (esk4_1 @ X603) @ (esk4_1 @ X603)) @ X603)|~(in @ emptyset @ X603)|(~(in @ X605 @ omega)|(in @ X605 @ X603))))&((((((in @ (esk8_3 @ X606 @ X607 @ X612) @ X607)|~(in @ X612 @ (esk7_2 @ X606 @ X607))|(in @ (esk5_2 @ X606 @ X607) @ X607))&((X606 @ (esk8_3 @ X606 @ X607 @ X612) @ X612)|~(in @ X612 @ (esk7_2 @ X606 @ X607))|(in @ (esk5_2 @ X606 @ X607) @ X607)))&(~(in @ X615 @ X607)|~(X606 @ X615 @ X614)|(in @ X614 @ (esk7_2 @ X606 @ X607))|(in @ (esk5_2 @ X606 @ X607) @ X607)))&(((((in @ (esk8_3 @ X606 @ X607 @ X612) @ X607)|~(in @ X612 @ (esk7_2 @ X606 @ X607))|((X606 @ (esk5_2 @ X606 @ X607) @ (esk6_3 @ X606 @ X607 @ X609))|~(X606 @ (esk5_2 @ X606 @ X607) @ X609)))&((X606 @ (esk8_3 @ X606 @ X607 @ X612) @ X612)|~(in @ X612 @ (esk7_2 @ X606 @ X607))|((X606 @ (esk5_2 @ X606 @ X607) @ (esk6_3 @ X606 @ X607 @ X609))|~(X606 @ (esk5_2 @ X606 @ X607) @ X609))))&(~(in @ X615 @ X607)|~(X606 @ X615 @ X614)|(in @ X614 @ (esk7_2 @ X606 @ X607))|((X606 @ (esk5_2 @ X606 @ X607) @ (esk6_3 @ X606 @ X607 @ X609))|~(X606 @ (esk5_2 @ X606 @ X607) @ X609))))&((((in @ (esk8_3 @ X606 @ X607 @ X612) @ X607)|~(in @ X612 @ (esk7_2 @ X606 @ X607))|(((X609)!=(esk6_3 @ X606 @ X607 @ X609))|~(X606 @ (esk5_2 @ X606 @ X607) @ X609)))&((X606 @ (esk8_3 @ X606 @ X607 @ X612) @ X612)|~(in @ X612 @ (esk7_2 @ X606 @ X607))|(((X609)!=(esk6_3 @ X606 @ X607 @ X609))|~(X606 @ (esk5_2 @ X606 @ X607) @ X609))))&(~(in @ X615 @ X607)|~(X606 @ X615 @ X614)|(in @ X614 @ (esk7_2 @ X606 @ X607))|(((X609)!=(esk6_3 @ X606 @ X607 @ X609))|~(X606 @ (esk5_2 @ X606 @ X607) @ X609))))))&((((in @ (esk9_1 @ X616) @ X616)|~(in @ X617 @ X616))&(~(in @ X619 @ (esk9_1 @ X616))|~(in @ X619 @ X616)|~(in @ X617 @ X616)))&((epred1_0)&((((X620 @ (esk10_2 @ X620 @ X621))|~(X620 @ X621)|(X620 @ (descr @ X620)))&(((X621)!=(esk10_2 @ X620 @ X621))|~(X620 @ X621)|(X620 @ (descr @ X620))))&((~(in @ X625 @ X623)|(~(X624 @ X625)|(in @ X625 @ (dsetconstr @ X623 @ X624))))&((~(in @ X628 @ (dsetconstr @ X626 @ X627))|(in @ X628 @ X626))&((~(in @ X631 @ (dsetconstr @ X629 @ X630))|(X630 @ X631))&(((((X632 @ (esk12_1 @ X632))|((X632 @ (esk11_2 @ X632 @ X633))|~(X632 @ X633)))&(~(X632 @ X636)|((esk12_1 @ X632)=(X636))|((X632 @ (esk11_2 @ X632 @ X633))|~(X632 @ X633))))&(((X632 @ (esk12_1 @ X632))|(((X633)!=(esk11_2 @ X632 @ X633))|~(X632 @ X633)))&(~(X632 @ X636)|((esk12_1 @ X632)=(X636))|(((X633)!=(esk11_2 @ X632 @ X633))|~(X632 @ X633)))))&((~(in @ X638 @ (prop2set @ ((X637))))|(X637))&((~(in @ X639 @ emptyset)|(X640))&((~(in @ X641 @ emptyset)|~($true))&(~(in @ X642 @ emptyset)&((((X643 @ (esk13_2 @ X643 @ X644))|~(X643 @ X644)|(X643 @ (esk14_1 @ X643)))&(((X644)!=(esk13_2 @ X643 @ X644))|~(X643 @ X644)|(X643 @ (esk14_1 @ X643))))&(((((in @ (esk16_2 @ X647 @ X648) @ X648)|((X647)=(X648))|(in @ (esk15_2 @ X647 @ X648) @ X647))&(~(in @ (esk16_2 @ X647 @ X648) @ X647)|((X647)=(X648))|(in @ (esk15_2 @ X647 @ X648) @ X647)))&(((in @ (esk16_2 @ X647 @ X648) @ X648)|((X647)=(X648))|~(in @ (esk15_2 @ X647 @ X648) @ X648))&(~(in @ (esk16_2 @ X647 @ X648) @ X647)|((X647)=(X648))|~(in @ (esk15_2 @ X647 @ X648) @ X648))))&(((in @ (esk17_1 @ X651) @ X651)|((X651)=(emptyset)))&(((in @ (esk18_1 @ X653) @ X653)|((X653)=(emptyset)))&(((~(in @ X657 @ (dsetconstr @ X655 @ X656))|(X656 @ X657)|~(in @ X657 @ X655))&(~(X656 @ X657)|(in @ X657 @ (dsetconstr @ X655 @ X656))|~(in @ X657 @ X655)))&((((X658)=(emptyset))|(in @ (esk19_1 @ X658) @ X658))&((~(in @ X662 @ X660)|(~(X661 @ X662)|((dsetconstr @ X660 @ X661)!=(emptyset))))&((~(in @ X664 @ X663)|((X663)!=(emptyset)))&((in @ X665 @ (setadjoin @ X665 @ X666))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X669 @ X668)|(in @ X669 @ (setadjoin @ X667 @ X668)))&(((((in @ X672 @ X671)|(X673)|((X672)=(X670))|~(in @ X672 @ (setadjoin @ X670 @ X671)))&(~(X673)|(X673)|((X672)=(X670))|~(in @ X672 @ (setadjoin @ X670 @ X671))))&(((in @ X672 @ X671)|(X673)|~(X673)|~(in @ X672 @ (setadjoin @ X670 @ X671)))&(~(X673)|(X673)|~(X673)|~(in @ X672 @ (setadjoin @ X670 @ X671)))))&((~(in @ X676 @ (setadjoin @ X674 @ X675))|(((X676)=(X674))|(in @ X676 @ X675)))&(((dsetconstr @ X677 @ (^[Z0:$i]:($true)))=(X677))&((((in @ (esk20_2 @ X678 @ X679) @ X679)|(in @ X679 @ (powerset @ X678)))&(~(in @ (esk20_2 @ X678 @ X679) @ X678)|(in @ X679 @ (powerset @ X678))))&((in @ emptyset @ (powerset @ X681))&((in @ emptyset @ (powerset @ X682))&((~(in @ X684 @ (powerset @ X683))|(~(in @ X685 @ X684)|(in @ X685 @ X683)))&((~(in @ X687 @ X688)|(~(in @ X688 @ X686)|(in @ X687 @ (setunion @ X686))))&((((in @ X690 @ (esk21_3 @ X689 @ X690 @ X691))|(X691)|~(in @ X690 @ (setunion @ X689)))&(((in @ (esk21_3 @ X689 @ X690 @ X691) @ X689)|(X691)|~(in @ X690 @ (setunion @ X689)))&(~(X691)|(X691)|~(in @ X690 @ (setunion @ X689)))))&((~(in @ X694 @ X693)|(in @ X694 @ (powerset @ (setunion @ X693))))&((((~(X695 @ X699)|((X699)=(esk23_1 @ X695))|((X695 @ (esk22_2 @ X695 @ X696))|~(X695 @ X696)))&(((X700)!=(esk23_1 @ X695))|(X695 @ X700)|((X695 @ (esk22_2 @ X695 @ X696))|~(X695 @ X696))))&((~(X695 @ X699)|((X699)=(esk23_1 @ X695))|(((X696)!=(esk22_2 @ X695 @ X696))|~(X695 @ X696)))&(((X700)!=(esk23_1 @ X695))|(X695 @ X700)|(((X696)!=(esk22_2 @ X695 @ X696))|~(X695 @ X696)))))&((((in @ (esk24_1 @ X701) @ X701)|((X701)=(emptyset)))&(($true)|((X701)=(emptyset))))&((~(in @ X703 @ (setadjoin @ X704 @ emptyset))|((X703)=(X704)))&((((X705)=(X706))|~(in @ X706 @ (setadjoin @ X705 @ emptyset)))&((((X707)!=(X708))|(in @ X707 @ (setadjoin @ X708 @ emptyset)))&((~(in @ X709 @ (setadjoin @ X710 @ emptyset))|(in @ X710 @ (setadjoin @ X709 @ emptyset)))&((~(in @ X713 @ (setadjoin @ X711 @ (setadjoin @ X712 @ emptyset)))|(((X713)=(X711))|((X713)=(X712))))&((in @ X714 @ (setadjoin @ X714 @ (setadjoin @ X715 @ emptyset)))&((in @ X717 @ (setadjoin @ X716 @ (setadjoin @ X717 @ emptyset)))&((~(in @ X720 @ X718)|~(X719 @ X720)|(((dsetconstr @ X718 @ X719)!=(emptyset))|~($true)))&((~(in @ X722 @ emptyset)|(X721 @ X722))&((((in @ (esk25_2 @ X723 @ X724) @ X723)|(~(in @ X725 @ X723)|(X724 @ X725)))&(~(X724 @ (esk25_2 @ X723 @ X724))|(~(in @ X725 @ X723)|(X724 @ X725))))&((((in @ (esk26_2 @ X727 @ X728) @ X727)|(~(in @ X730 @ X727)|~(X728 @ X730)))&((X728 @ (esk26_2 @ X727 @ X728))|(~(in @ X730 @ X727)|~(X728 @ X730))))&((((in @ (esk27_2 @ X731 @ X732) @ X731)|(~(in @ X734 @ X731)|~(X732 @ X734)))&((X732 @ (esk27_2 @ X731 @ X732))|(~(in @ X734 @ X731)|~(X732 @ X734))))&((((in @ (esk28_2 @ X735 @ X736) @ X735)|(~(in @ X737 @ X735)|(X736 @ X737)))&(~(X736 @ (esk28_2 @ X735 @ X736))|(~(in @ X737 @ X735)|(X736 @ X737))))&((~(X739)|(in @ emptyset @ (prop2set @ ((X739)))))&((~(X740)|(set2prop @ (prop2set @ ((X740)))))&((((in @ (esk29_2 @ X741 @ X742) @ X741)|(~(in @ X744 @ X741)|~(X742 @ X744)))&((X742 @ (esk29_2 @ X741 @ X742))|(~(in @ X744 @ X741)|~(X742 @ X744))))&((((in @ (esk30_2 @ X745 @ X746) @ X745)|(~(in @ X747 @ X745)|(X746 @ X747)))&(~(X746 @ (esk30_2 @ X745 @ X746))|(~(in @ X747 @ X745)|(X746 @ X747))))&(((((X749 @ (esk32_1 @ X749))|((X749 @ (esk31_2 @ X749 @ X750))|~(X749 @ X750)))&(~(X749 @ X753)|((esk32_1 @ X749)=(X753))|((X749 @ (esk31_2 @ X749 @ X750))|~(X749 @ X750))))&(((X749 @ (esk32_1 @ X749))|(((X750)!=(esk31_2 @ X749 @ X750))|~(X749 @ X750)))&(~(X749 @ X753)|((esk32_1 @ X749)=(X753))|(((X750)!=(esk31_2 @ X749 @ X750))|~(X749 @ X750)))))&(((((X754 @ (esk35_1 @ X754))|(X754 @ (esk33_1 @ X754))|~(X754 @ X755))&(~(X754 @ X759)|((esk35_1 @ X754)=(X759))|(X754 @ (esk33_1 @ X754))|~(X754 @ X755)))&((((X754 @ (esk35_1 @ X754))|(X754 @ (esk34_1 @ X754))|~(X754 @ X755))&(~(X754 @ X759)|((esk35_1 @ X754)=(X759))|(X754 @ (esk34_1 @ X754))|~(X754 @ X755)))&(((X754 @ (esk35_1 @ X754))|((esk33_1 @ X754)!=(esk34_1 @ X754))|~(X754 @ X755))&(~(X754 @ X759)|((esk35_1 @ X754)=(X759))|((esk33_1 @ X754)!=(esk34_1 @ X754))|~(X754 @ X755)))))&(((((X760 @ (esk37_1 @ X760))|(~(X760 @ (esk36_2 @ X760 @ X761))|((esk36_2 @ X760 @ X761)!=(X761))))&(~(X760 @ X764)|((esk37_1 @ X760)=(X764))|(~(X760 @ (esk36_2 @ X760 @ X761))|((esk36_2 @ X760 @ X761)!=(X761)))))&(((X760 @ (esk37_1 @ X760))|((X760 @ (esk36_2 @ X760 @ X761))|((esk36_2 @ X760 @ X761)=(X761))))&(~(X760 @ X764)|((esk37_1 @ X760)=(X764))|((X760 @ (esk36_2 @ X760 @ X761))|((esk36_2 @ X760 @ X761)=(X761))))))&((((X765)!=(X766))|(((X767)!=(X768))|(~(in @ X767 @ X765)|(in @ X768 @ X766))))&(((~(in @ X771 @ X769)|(in @ X772 @ X770)|((X771)!=(X772))|((X769)!=(X770)))&(~(in @ X772 @ X770)|(in @ X771 @ X769)|((X771)!=(X772))|((X769)!=(X770))))&((((X773 @ (esk38_2 @ X773 @ X774))|~(X773 @ X774)|(~(X773 @ X776)|(~(X773 @ X777)|((X776)=(X777)))))&(((X774)!=(esk38_2 @ X773 @ X774))|~(X773 @ X774)|(~(X773 @ X776)|(~(X773 @ X777)|((X776)=(X777))))))&(((((((X779 @ (esk42_2 @ X778 @ X779))|((X778 @ (esk41_3 @ X778 @ X779 @ X782))|~(X778 @ X782))|((esk39_2 @ X778 @ X779)=(esk40_2 @ X778 @ X779)))&(~(X779 @ X785)|((esk42_2 @ X778 @ X779)=(X785))|((X778 @ (esk41_3 @ X778 @ X779 @ X782))|~(X778 @ X782))|((esk39_2 @ X778 @ X779)=(esk40_2 @ X778 @ X779))))&(((X779 @ (esk42_2 @ X778 @ X779))|(((X782)!=(esk41_3 @ X778 @ X779 @ X782))|~(X778 @ X782))|((esk39_2 @ X778 @ X779)=(esk40_2 @ X778 @ X779)))&(~(X779 @ X785)|((esk42_2 @ X778 @ X779)=(X785))|(((X782)!=(esk41_3 @ X778 @ X779 @ X782))|~(X778 @ X782))|((esk39_2 @ X778 @ X779)=(esk40_2 @ X778 @ X779)))))&((((X778 @ (esk44_2 @ X778 @ X779))|((X779 @ (esk43_3 @ X778 @ X779 @ X786))|~(X779 @ X786))|((esk39_2 @ X778 @ X779)=(esk40_2 @ X778 @ X779)))&(~(X778 @ X789)|((esk44_2 @ X778 @ X779)=(X789))|((X779 @ (esk43_3 @ X778 @ X779 @ X786))|~(X779 @ X786))|((esk39_2 @ X778 @ X779)=(esk40_2 @ X778 @ X779))))&(((X778 @ (esk44_2 @ X778 @ X779))|(((X786)!=(esk43_3 @ X778 @ X779 @ X786))|~(X779 @ X786))|((esk39_2 @ X778 @ X779)=(esk40_2 @ X778 @ X779)))&(~(X778 @ X789)|((esk44_2 @ X778 @ X779)=(X789))|(((X786)!=(esk43_3 @ X778 @ X779 @ X786))|~(X779 @ X786))|((esk39_2 @ X778 @ X779)=(esk40_2 @ X778 @ X779))))))&((((((X779 @ (esk42_2 @ X778 @ X779))|((X778 @ (esk41_3 @ X778 @ X779 @ X782))|~(X778 @ X782))|(~(X778 @ (esk39_2 @ X778 @ X779))|~(X779 @ (esk40_2 @ X778 @ X779))))&(~(X779 @ X785)|((esk42_2 @ X778 @ X779)=(X785))|((X778 @ (esk41_3 @ X778 @ X779 @ X782))|~(X778 @ X782))|(~(X778 @ (esk39_2 @ X778 @ X779))|~(X779 @ (esk40_2 @ X778 @ X779)))))&(((X779 @ (esk42_2 @ X778 @ X779))|(((X782)!=(esk41_3 @ X778 @ X779 @ X782))|~(X778 @ X782))|(~(X778 @ (esk39_2 @ X778 @ X779))|~(X779 @ (esk40_2 @ X778 @ X779))))&(~(X779 @ X785)|((esk42_2 @ X778 @ X779)=(X785))|(((X782)!=(esk41_3 @ X778 @ X779 @ X782))|~(X778 @ X782))|(~(X778 @ (esk39_2 @ X778 @ X779))|~(X779 @ (esk40_2 @ X778 @ X779))))))&((((X778 @ (esk44_2 @ X778 @ X779))|((X779 @ (esk43_3 @ X778 @ X779 @ X786))|~(X779 @ X786))|(~(X778 @ (esk39_2 @ X778 @ X779))|~(X779 @ (esk40_2 @ X778 @ X779))))&(~(X778 @ X789)|((esk44_2 @ X778 @ X779)=(X789))|((X779 @ (esk43_3 @ X778 @ X779 @ X786))|~(X779 @ X786))|(~(X778 @ (esk39_2 @ X778 @ X779))|~(X779 @ (esk40_2 @ X778 @ X779)))))&(((X778 @ (esk44_2 @ X778 @ X779))|(((X786)!=(esk43_3 @ X778 @ X779 @ X786))|~(X779 @ X786))|(~(X778 @ (esk39_2 @ X778 @ X779))|~(X779 @ (esk40_2 @ X778 @ X779))))&(~(X778 @ X789)|((esk44_2 @ X778 @ X779)=(X789))|(((X786)!=(esk43_3 @ X778 @ X779 @ X786))|~(X779 @ X786))|(~(X778 @ (esk39_2 @ X778 @ X779))|~(X779 @ (esk40_2 @ X778 @ X779)))))))&(((((X779 @ (esk42_2 @ X778 @ X779))|((X778 @ (esk41_3 @ X778 @ X779 @ X782))|~(X778 @ X782))|((X778 @ (esk39_2 @ X778 @ X779))|(X779 @ (esk40_2 @ X778 @ X779))))&(~(X779 @ X785)|((esk42_2 @ X778 @ X779)=(X785))|((X778 @ (esk41_3 @ X778 @ X779 @ X782))|~(X778 @ X782))|((X778 @ (esk39_2 @ X778 @ X779))|(X779 @ (esk40_2 @ X778 @ X779)))))&(((X779 @ (esk42_2 @ X778 @ X779))|(((X782)!=(esk41_3 @ X778 @ X779 @ X782))|~(X778 @ X782))|((X778 @ (esk39_2 @ X778 @ X779))|(X779 @ (esk40_2 @ X778 @ X779))))&(~(X779 @ X785)|((esk42_2 @ X778 @ X779)=(X785))|(((X782)!=(esk41_3 @ X778 @ X779 @ X782))|~(X778 @ X782))|((X778 @ (esk39_2 @ X778 @ X779))|(X779 @ (esk40_2 @ X778 @ X779))))))&((((X778 @ (esk44_2 @ X778 @ X779))|((X779 @ (esk43_3 @ X778 @ X779 @ X786))|~(X779 @ X786))|((X778 @ (esk39_2 @ X778 @ X779))|(X779 @ (esk40_2 @ X778 @ X779))))&(~(X778 @ X789)|((esk44_2 @ X778 @ X779)=(X789))|((X779 @ (esk43_3 @ X778 @ X779 @ X786))|~(X779 @ X786))|((X778 @ (esk39_2 @ X778 @ X779))|(X779 @ (esk40_2 @ X778 @ X779)))))&(((X778 @ (esk44_2 @ X778 @ X779))|(((X786)!=(esk43_3 @ X778 @ X779 @ X786))|~(X779 @ X786))|((X778 @ (esk39_2 @ X778 @ X779))|(X779 @ (esk40_2 @ X778 @ X779))))&(~(X778 @ X789)|((esk44_2 @ X778 @ X779)=(X789))|(((X786)!=(esk43_3 @ X778 @ X779 @ X786))|~(X779 @ X786))|((X778 @ (esk39_2 @ X778 @ X779))|(X779 @ (esk40_2 @ X778 @ X779)))))))))&(((emptyset)=(emptyset))&((((X790)!=(X791))|(((X792)!=(X793))|((setadjoin @ X790 @ X792)=(setadjoin @ X791 @ X793))))&((((X794)!=(X795))|((powerset @ X794)=(powerset @ X795)))&((((X796)!=(X797))|((setunion @ X796)=(setunion @ X797)))&(((omega)=(omega))&((((X798 @ (esk45_2 @ X798 @ X799))|~(X798 @ X799)|(~(X798 @ X801)|(~(X798 @ X802)|((X801)=(X802)))))&(((X799)!=(esk45_2 @ X798 @ X799))|~(X798 @ X799)|(~(X798 @ X801)|(~(X798 @ X802)|((X801)=(X802))))))&((((((X804 @ (esk49_3 @ X803 @ X804 @ X809))|~(X804 @ X809)|((descr @ X803)=(descr @ X804))|((X803 @ (esk48_3 @ X803 @ X804 @ X807))|~(X803 @ X807))|((esk46_2 @ X803 @ X804)=(esk47_2 @ X803 @ X804)))&(((X809)!=(esk49_3 @ X803 @ X804 @ X809))|~(X804 @ X809)|((descr @ X803)=(descr @ X804))|((X803 @ (esk48_3 @ X803 @ X804 @ X807))|~(X803 @ X807))|((esk46_2 @ X803 @ X804)=(esk47_2 @ X803 @ X804))))&(((X804 @ (esk49_3 @ X803 @ X804 @ X809))|~(X804 @ X809)|((descr @ X803)=(descr @ X804))|(((X807)!=(esk48_3 @ X803 @ X804 @ X807))|~(X803 @ X807))|((esk46_2 @ X803 @ X804)=(esk47_2 @ X803 @ X804)))&(((X809)!=(esk49_3 @ X803 @ X804 @ X809))|~(X804 @ X809)|((descr @ X803)=(descr @ X804))|(((X807)!=(esk48_3 @ X803 @ X804 @ X807))|~(X803 @ X807))|((esk46_2 @ X803 @ X804)=(esk47_2 @ X803 @ X804)))))&(((((X804 @ (esk49_3 @ X803 @ X804 @ X809))|~(X804 @ X809)|((descr @ X803)=(descr @ X804))|((X803 @ (esk48_3 @ X803 @ X804 @ X807))|~(X803 @ X807))|(~(X803 @ (esk46_2 @ X803 @ X804))|~(X804 @ (esk47_2 @ X803 @ X804))))&(((X809)!=(esk49_3 @ X803 @ X804 @ X809))|~(X804 @ X809)|((descr @ X803)=(descr @ X804))|((X803 @ (esk48_3 @ X803 @ X804 @ X807))|~(X803 @ X807))|(~(X803 @ (esk46_2 @ X803 @ X804))|~(X804 @ (esk47_2 @ X803 @ X804)))))&(((X804 @ (esk49_3 @ X803 @ X804 @ X809))|~(X804 @ X809)|((descr @ X803)=(descr @ X804))|(((X807)!=(esk48_3 @ X803 @ X804 @ X807))|~(X803 @ X807))|(~(X803 @ (esk46_2 @ X803 @ X804))|~(X804 @ (esk47_2 @ X803 @ X804))))&(((X809)!=(esk49_3 @ X803 @ X804 @ X809))|~(X804 @ X809)|((descr @ X803)=(descr @ X804))|(((X807)!=(esk48_3 @ X803 @ X804 @ X807))|~(X803 @ X807))|(~(X803 @ (esk46_2 @ X803 @ X804))|~(X804 @ (esk47_2 @ X803 @ X804))))))&((((X804 @ (esk49_3 @ X803 @ X804 @ X809))|~(X804 @ X809)|((descr @ X803)=(descr @ X804))|((X803 @ (esk48_3 @ X803 @ X804 @ X807))|~(X803 @ X807))|((X803 @ (esk46_2 @ X803 @ X804))|(X804 @ (esk47_2 @ X803 @ X804))))&(((X809)!=(esk49_3 @ X803 @ X804 @ X809))|~(X804 @ X809)|((descr @ X803)=(descr @ X804))|((X803 @ (esk48_3 @ X803 @ X804 @ X807))|~(X803 @ X807))|((X803 @ (esk46_2 @ X803 @ X804))|(X804 @ (esk47_2 @ X803 @ X804)))))&(((X804 @ (esk49_3 @ X803 @ X804 @ X809))|~(X804 @ X809)|((descr @ X803)=(descr @ X804))|(((X807)!=(esk48_3 @ X803 @ X804 @ X807))|~(X803 @ X807))|((X803 @ (esk46_2 @ X803 @ X804))|(X804 @ (esk47_2 @ X803 @ X804))))&(((X809)!=(esk49_3 @ X803 @ X804 @ X809))|~(X804 @ X809)|((descr @ X803)=(descr @ X804))|(((X807)!=(esk48_3 @ X803 @ X804 @ X807))|~(X803 @ X807))|((X803 @ (esk46_2 @ X803 @ X804))|(X804 @ (esk47_2 @ X803 @ X804))))))))&((((in @ (esk50_4 @ X811 @ X812 @ X813 @ X814) @ X811)|((dsetconstr @ X811 @ X813)=(dsetconstr @ X812 @ X814))|((X811)!=(X812)))&(((in @ (esk51_4 @ X811 @ X812 @ X813 @ X814) @ X812)|((dsetconstr @ X811 @ X813)=(dsetconstr @ X812 @ X814))|((X811)!=(X812)))&((((esk50_4 @ X811 @ X812 @ X813 @ X814)=(esk51_4 @ X811 @ X812 @ X813 @ X814))|((dsetconstr @ X811 @ X813)=(dsetconstr @ X812 @ X814))|((X811)!=(X812)))&((~(X813 @ (esk50_4 @ X811 @ X812 @ X813 @ X814))|~(X814 @ (esk51_4 @ X811 @ X812 @ X813 @ X814))|((dsetconstr @ X811 @ X813)=(dsetconstr @ X812 @ X814))|((X811)!=(X812)))&((X813 @ (esk50_4 @ X811 @ X812 @ X813 @ X814))|(X814 @ (esk51_4 @ X811 @ X812 @ X813 @ X814))|((dsetconstr @ X811 @ X813)=(dsetconstr @ X812 @ X814))|((X811)!=(X812)))))))&((((in @ (esk52_2 @ X817 @ X818) @ X817)|(subset @ X817 @ X818))&(~(in @ (esk52_2 @ X817 @ X818) @ X818)|(subset @ X817 @ X818)))&((((X820)!=(X821))|(subset @ X821 @ X820))&((((X822)!=(X823))|(subset @ X822 @ X823))&((((in @ (esk53_2 @ X824 @ X825) @ X824)|(subset @ X824 @ X825))&(~(in @ (esk53_2 @ X824 @ X825) @ X825)|(subset @ X824 @ X825)))&((subset @ emptyset @ X827)&((~(subset @ X828 @ X829)|(~(in @ X830 @ X828)|(in @ X830 @ X829)))&((~(subset @ X831 @ X832)|((in @ X833 @ X832)|~(in @ X833 @ X831)))&((~(in @ X836 @ X834)|((in @ X836 @ X835)|~(subset @ X834 @ X835)))&(((subset @ X837 @ X838)|((X837)!=(X838)))&((~(in @ X841 @ X839)|((in @ X841 @ X840)|((X839)!=(X840))))&((subset @ X842 @ X842)&((~(subset @ X843 @ X844)|(~(subset @ X844 @ X845)|(subset @ X843 @ X845)))&((subset @ X847 @ (setadjoin @ X846 @ X847))&((~(subset @ X848 @ X850)|(subset @ X848 @ (setadjoin @ X849 @ X850)))&((~(subset @ X851 @ X852)|(in @ X851 @ (powerset @ X852)))&((~(subset @ X853 @ X854)|(~(subset @ X854 @ X853)|((X853)=(X854))))&((~(subset @ X855 @ emptyset)|((X855)=(emptyset)))&((~(subset @ X857 @ X856)|(in @ X857 @ (powerset @ X856)))&((in @ esk55_0 @ (powerset @ esk54_0))&~(subset @ esk55_0 @ esk54_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_136])])])])])])])).
% 0.20/0.33 thf(c_0_138, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:(((in @ X4 @ X3)|~((in @ X2 @ (powerset @ X3)))|~((in @ X4 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_137])).
% 0.20/0.33 thf(c_0_139, negated_conjecture, (in @ esk55_0 @ (powerset @ esk54_0)), inference(split_conjunct,[status(thm)],[c_0_137])).
% 0.20/0.33 thf(c_0_140, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ X3)|~((in @ (esk53_2 @ X2 @ X3) @ X3)))), inference(split_conjunct,[status(thm)],[c_0_137])).
% 0.20/0.33 thf(c_0_141, negated_conjecture, ![X2:$i]:(((in @ X2 @ esk54_0)|~((in @ X2 @ esk55_0)))), inference(spm,[status(thm)],[c_0_138, c_0_139])).
% 0.20/0.33 thf(c_0_142, negated_conjecture, ![X2:$i]:(((subset @ X2 @ esk54_0)|~((in @ (esk53_2 @ X2 @ esk54_0) @ esk55_0)))), inference(spm,[status(thm)],[c_0_140, c_0_141])).
% 0.20/0.33 thf(c_0_143, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (esk53_2 @ X2 @ X3) @ X2)|(subset @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_137])).
% 0.20/0.33 thf(c_0_144, negated_conjecture, ~((subset @ esk55_0 @ esk54_0)), inference(split_conjunct,[status(thm)],[c_0_137])).
% 0.20/0.33 thf(c_0_145, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_142, c_0_143]), c_0_144]), ['proof']).
% 0.20/0.33 % SZS output end CNFRefutation
% 0.20/0.33 % Parsed axioms : 204
% 0.20/0.33 % Removed by relevancy pruning/SinE : 0
% 0.20/0.33 % Initial clauses : 313
% 0.20/0.33 % Removed in clause preprocessing : 122
% 0.20/0.33 % Initial clauses in saturation : 191
% 0.20/0.33 % Processed clauses : 214
% 0.20/0.33 % ...of these trivial : 3
% 0.20/0.33 % ...subsumed : 91
% 0.20/0.33 % ...remaining for further processing : 120
% 0.20/0.33 % Other redundant clauses eliminated : 7
% 0.20/0.33 % Clauses deleted for lack of memory : 0
% 0.20/0.33 % Backward-subsumed : 0
% 0.20/0.33 % Backward-rewritten : 5
% 0.20/0.33 % Generated clauses : 756
% 0.20/0.33 % ...of the previous two non-redundant : 705
% 0.20/0.33 % ...aggressively subsumed : 0
% 0.20/0.33 % Contextual simplify-reflections : 0
% 0.20/0.33 % Paramodulations : 749
% 0.20/0.33 % Factorizations : 0
% 0.20/0.33 % NegExts : 0
% 0.20/0.33 % Equation resolutions : 7
% 0.20/0.33 % Disequality decompositions : 0
% 0.20/0.33 % Total rewrite steps : 61
% 0.20/0.33 % ...of those cached : 36
% 0.20/0.33 % Propositional unsat checks : 0
% 0.20/0.33 % Propositional check models : 0
% 0.20/0.33 % Propositional check unsatisfiable : 0
% 0.20/0.33 % Propositional clauses : 0
% 0.20/0.33 % Propositional clauses after purity: 0
% 0.20/0.33 % Propositional unsat core size : 0
% 0.20/0.33 % Propositional preprocessing time : 0.000
% 0.20/0.33 % Propositional encoding time : 0.000
% 0.20/0.33 % Propositional solver time : 0.000
% 0.20/0.33 % Success case prop preproc time : 0.000
% 0.20/0.33 % Success case prop encoding time : 0.000
% 0.20/0.33 % Success case prop solver time : 0.000
% 0.20/0.33 % Current number of processed clauses : 109
% 0.20/0.33 % Positive orientable unit clauses : 20
% 0.20/0.33 % Positive unorientable unit clauses: 0
% 0.20/0.33 % Negative unit clauses : 2
% 0.20/0.33 % Non-unit-clauses : 87
% 0.20/0.33 % Current number of unprocessed clauses: 669
% 0.20/0.33 % ...number of literals in the above : 2025
% 0.20/0.33 % Current number of archived formulas : 0
% 0.20/0.33 % Current number of archived clauses : 5
% 0.20/0.33 % Clause-clause subsumption calls (NU) : 849
% 0.20/0.33 % Rec. Clause-clause subsumption calls : 766
% 0.20/0.33 % Non-unit clause-clause subsumptions : 75
% 0.20/0.33 % Unit Clause-clause subsumption calls : 26
% 0.20/0.33 % Rewrite failures with RHS unbound : 0
% 0.20/0.33 % BW rewrite match attempts : 11
% 0.20/0.33 % BW rewrite match successes : 4
% 0.20/0.33 % Condensation attempts : 0
% 0.20/0.33 % Condensation successes : 0
% 0.20/0.33 % Termbank termtop insertions : 36135
% 0.20/0.33 % Search garbage collected termcells : 10288
% 0.20/0.33
% 0.20/0.33 % -------------------------------------------------
% 0.20/0.33 % User time : 0.037 s
% 0.20/0.33 % System time : 0.009 s
% 0.20/0.33 % Total time : 0.046 s
% 0.20/0.33 % Maximum resident set size: 6136 pages
% 0.20/0.33
% 0.20/0.33 % -------------------------------------------------
% 0.20/0.33 % User time : 0.041 s
% 0.20/0.33 % System time : 0.016 s
% 0.20/0.33 % Total time : 0.057 s
% 0.20/0.33 % Maximum resident set size: 5120 pages
% 0.20/0.33 % E exiting
%------------------------------------------------------------------------------