%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU595^1 : 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 : n003.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 08:26:51 AM UTC 2026
% Result : Theorem 0.19s 0.32s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU595^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n003.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 13:57:44 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.19/0.26 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.KY8l8zcYYR/E---3.1_2542043.p
% 0.19/0.32 % Version: 3.5.1-ho
% 0.19/0.32 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.19/0.32 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.32 % Starting ehoh_best5 with 300s (1) cores
% 0.19/0.32 % Starting almost_fo_3_lam with 300s (1) cores
% 0.19/0.32 % Starting new_bool_5 with 300s (1) cores
% 0.19/0.32 % Starting pre_casc_3 with 300s (1) cores
% 0.19/0.32 % Starting ho_unfolding_8 with 300s (1) cores
% 0.19/0.32 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.19/0.32 % Starting new_bool_3 with 300s (1) cores
% 0.19/0.32 % Starting new_ho_5 with 300s (1) cores
% 0.19/0.32 % ho_unfolding_8 with pid 2542060 completed with status 0
% 0.19/0.32 % Result found by ho_unfolding_8
% 0.19/0.32 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.19/0.32 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.32 % Starting ehoh_best5 with 300s (1) cores
% 0.19/0.32 % Starting almost_fo_3_lam with 300s (1) cores
% 0.19/0.32 % Starting new_bool_5 with 300s (1) cores
% 0.19/0.32 % Starting pre_casc_3 with 300s (1) cores
% 0.19/0.32 % Starting ho_unfolding_8 with 300s (1) cores
% 0.19/0.32 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.19/0.32 % No SInE strategy applied
% 0.19/0.32 % Search class: HGHSM-FSLM31-MHFMMSBN
% 0.19/0.32 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.32 % Starting SubtermCWHack with 28s (1) cores
% 0.19/0.32 % SubtermCWHack with pid 2542068 completed with status 0
% 0.19/0.32 % Result found by SubtermCWHack
% 0.19/0.32 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.19/0.32 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.32 % Starting ehoh_best5 with 300s (1) cores
% 0.19/0.32 % Starting almost_fo_3_lam with 300s (1) cores
% 0.19/0.32 % Starting new_bool_5 with 300s (1) cores
% 0.19/0.32 % Starting pre_casc_3 with 300s (1) cores
% 0.19/0.32 % Starting ho_unfolding_8 with 300s (1) cores
% 0.19/0.32 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.19/0.32 % No SInE strategy applied
% 0.19/0.32 % Search class: HGHSM-FSLM31-MHFMMSBN
% 0.19/0.32 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.32 % Starting SubtermCWHack with 28s (1) cores
% 0.19/0.32 % Preprocessing time : 0.004 s
% 0.19/0.32
% 0.19/0.32 % Proof found!
% 0.19/0.32 % SZS status Theorem
% 0.19/0.32 % SZS output start CNFRefutation
% 0.19/0.32 thf(decl_23, type, in: $i > $i > $o).
% 0.19/0.32 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.19/0.32 thf(decl_25, type, setextAx: $o).
% 0.19/0.32 thf(decl_26, type, emptyset: $i).
% 0.19/0.32 thf(decl_27, type, emptysetAx: $o).
% 0.19/0.32 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.19/0.32 thf(decl_29, type, setadjoinAx: $o).
% 0.19/0.32 thf(decl_30, type, powerset: $i > $i).
% 0.19/0.32 thf(decl_31, type, powersetAx: $o).
% 0.19/0.32 thf(decl_32, type, setunion: $i > $i).
% 0.19/0.32 thf(decl_33, type, setunionAx: $o).
% 0.19/0.32 thf(decl_34, type, omega: $i).
% 0.19/0.32 thf(decl_35, type, omega0Ax: $o).
% 0.19/0.32 thf(decl_36, type, omegaSAx: $o).
% 0.19/0.32 thf(decl_37, type, omegaIndAx: $o).
% 0.19/0.32 thf(decl_38, type, replAx: $o).
% 0.19/0.32 thf(decl_39, type, foundationAx: $o).
% 0.19/0.32 thf(decl_40, type, wellorderingAx: $o).
% 0.19/0.32 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.19/0.32 thf(decl_42, type, descrp: $o).
% 0.19/0.32 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.19/0.32 thf(decl_44, type, dsetconstrI: $o).
% 0.19/0.32 thf(decl_45, type, dsetconstrEL: $o).
% 0.19/0.32 thf(decl_46, type, dsetconstrER: $o).
% 0.19/0.32 thf(decl_47, type, exuE1: $o).
% 0.19/0.32 thf(decl_48, type, prop2set: $o > $i).
% 0.19/0.32 thf(decl_49, type, prop2setE: $o).
% 0.19/0.32 thf(decl_50, type, emptysetE: $o).
% 0.19/0.32 thf(decl_51, type, emptysetimpfalse: $o).
% 0.19/0.32 thf(decl_52, type, notinemptyset: $o).
% 0.19/0.32 thf(decl_53, type, exuE3e: $o).
% 0.19/0.32 thf(decl_54, type, setext: $o).
% 0.19/0.32 thf(decl_55, type, emptyI: $o).
% 0.19/0.32 thf(decl_56, type, noeltsimpempty: $o).
% 0.19/0.32 thf(decl_57, type, setbeta: $o).
% 0.19/0.32 thf(decl_58, type, nonempty: $i > $o).
% 0.19/0.32 thf(decl_59, type, nonemptyE1: $o).
% 0.19/0.32 thf(decl_60, type, nonemptyI: $o).
% 0.19/0.32 thf(decl_61, type, nonemptyI1: $o).
% 0.19/0.32 thf(decl_62, type, setadjoinIL: $o).
% 0.19/0.32 thf(decl_63, type, emptyinunitempty: $o).
% 0.19/0.32 thf(decl_64, type, setadjoinIR: $o).
% 0.19/0.32 thf(decl_65, type, setadjoinE: $o).
% 0.19/0.32 thf(decl_66, type, setadjoinOr: $o).
% 0.19/0.32 thf(decl_67, type, setoftrueEq: $o).
% 0.19/0.32 thf(decl_68, type, powersetI: $o).
% 0.19/0.32 thf(decl_69, type, emptyinPowerset: $o).
% 0.19/0.32 thf(decl_70, type, emptyInPowerset: $o).
% 0.19/0.32 thf(decl_71, type, powersetE: $o).
% 0.19/0.32 thf(decl_72, type, setunionI: $o).
% 0.19/0.32 thf(decl_73, type, setunionE: $o).
% 0.19/0.32 thf(decl_74, type, subPowSU: $o).
% 0.19/0.32 thf(decl_75, type, exuE2: $o).
% 0.19/0.32 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.19/0.32 thf(decl_77, type, uniqinunit: $o).
% 0.19/0.32 thf(decl_78, type, notinsingleton: $o).
% 0.19/0.32 thf(decl_79, type, eqinunit: $o).
% 0.19/0.32 thf(decl_80, type, singletonsswitch: $o).
% 0.19/0.32 thf(decl_81, type, upairsetE: $o).
% 0.19/0.32 thf(decl_82, type, upairsetIL: $o).
% 0.19/0.32 thf(decl_83, type, upairsetIR: $o).
% 0.19/0.32 thf(decl_84, type, emptyE1: $o).
% 0.19/0.32 thf(decl_85, type, vacuousDall: $o).
% 0.19/0.32 thf(decl_86, type, quantDeMorgan1: $o).
% 0.19/0.32 thf(decl_87, type, quantDeMorgan2: $o).
% 0.19/0.32 thf(decl_88, type, quantDeMorgan3: $o).
% 0.19/0.32 thf(decl_89, type, quantDeMorgan4: $o).
% 0.19/0.32 thf(decl_90, type, prop2setI: $o).
% 0.19/0.32 thf(decl_91, type, set2prop: $i > $o).
% 0.19/0.32 thf(decl_92, type, prop2set2propI: $o).
% 0.19/0.32 thf(decl_93, type, notdexE: $o).
% 0.19/0.32 thf(decl_94, type, notdallE: $o).
% 0.19/0.32 thf(decl_95, type, exuI1: $o).
% 0.19/0.32 thf(decl_96, type, exuI3: $o).
% 0.19/0.32 thf(decl_97, type, exuI2: $o).
% 0.19/0.32 thf(decl_98, type, inCongP: $o).
% 0.19/0.32 thf(decl_99, type, in__Cong: $o).
% 0.19/0.32 thf(decl_100, type, exuE3u: $o).
% 0.19/0.32 thf(decl_101, type, exu__Cong: $o).
% 0.19/0.32 thf(decl_102, type, emptyset__Cong: $o).
% 0.19/0.32 thf(decl_103, type, setadjoin__Cong: $o).
% 0.19/0.32 thf(decl_104, type, powerset__Cong: $o).
% 0.19/0.32 thf(decl_105, type, setunion__Cong: $o).
% 0.19/0.32 thf(decl_106, type, omega__Cong: $o).
% 0.19/0.32 thf(decl_107, type, exuEu: $o).
% 0.19/0.32 thf(decl_108, type, descr__Cong: $o).
% 0.19/0.32 thf(decl_109, type, dsetconstr__Cong: $o).
% 0.19/0.32 thf(decl_110, type, subset: $i > $i > $o).
% 0.19/0.32 thf(decl_113, type, subsetI1: $o).
% 0.19/0.32 thf(decl_114, type, eqimpsubset2: $o).
% 0.19/0.32 thf(decl_115, type, eqimpsubset1: $o).
% 0.19/0.32 thf(decl_116, type, subsetI2: $o).
% 0.19/0.32 thf(decl_117, type, emptysetsubset: $o).
% 0.19/0.32 thf(decl_118, type, subsetE: $o).
% 0.19/0.32 thf(decl_119, type, subsetE2: $o).
% 0.19/0.32 thf(decl_120, type, notsubsetI: $o).
% 0.19/0.32 thf(decl_121, type, notequalI1: $o).
% 0.19/0.32 thf(decl_122, type, notequalI2: $o).
% 0.19/0.32 thf(decl_123, type, subsetRefl: $o).
% 0.19/0.32 thf(decl_124, type, subsetTrans: $o).
% 0.19/0.32 thf(decl_125, type, setadjoinSub: $o).
% 0.19/0.32 thf(decl_126, type, setadjoinSub2: $o).
% 0.19/0.32 thf(decl_127, type, subset2powerset: $o).
% 0.19/0.32 thf(decl_128, type, setextsub: $o).
% 0.19/0.32 thf(decl_129, type, subsetemptysetimpeq: $o).
% 0.19/0.32 thf(decl_130, type, powersetI1: $o).
% 0.19/0.32 thf(decl_131, type, powersetE1: $o).
% 0.19/0.32 thf(decl_132, type, inPowerset: $o).
% 0.19/0.32 thf(decl_133, type, powersetsubset: $o).
% 0.19/0.32 thf(decl_134, type, sepInPowerset: $o).
% 0.19/0.32 thf(decl_135, type, sepSubset: $o).
% 0.19/0.32 thf(decl_136, type, binunion: $i > $i > $i).
% 0.19/0.32 thf(decl_137, type, binunionIL: $o).
% 0.19/0.32 thf(decl_138, type, upairset2IR: $o).
% 0.19/0.32 thf(decl_139, type, binunionIR: $o).
% 0.19/0.32 thf(decl_140, type, binunionEcases: $o).
% 0.19/0.32 thf(decl_141, type, binunionE: $o).
% 0.19/0.32 thf(decl_142, type, binunionLsub: $o).
% 0.19/0.32 thf(decl_143, type, binunionRsub: $o).
% 0.19/0.32 thf(decl_144, type, binintersect: $i > $i > $i).
% 0.19/0.32 thf(decl_145, type, binintersectI: $o).
% 0.19/0.32 thf(decl_146, type, binintersectSubset5: $o).
% 0.19/0.32 thf(decl_147, type, binintersectEL: $o).
% 0.19/0.32 thf(decl_148, type, binintersectLsub: $o).
% 0.19/0.32 thf(decl_149, type, binintersectSubset2: $o).
% 0.19/0.32 thf(decl_150, type, binintersectSubset3: $o).
% 0.19/0.32 thf(decl_151, type, epred1_0: $o).
% 0.19/0.32 thf(decl_152, type, esk1_2: $i > $i > $i).
% 0.19/0.32 thf(decl_153, type, esk2_2: $i > $i > $i).
% 0.19/0.32 thf(decl_154, type, esk3_2: $i > $i > $i).
% 0.19/0.32 thf(decl_155, type, esk4_1: $i > $i).
% 0.19/0.32 thf(decl_156, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.19/0.32 thf(decl_157, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.19/0.32 thf(decl_158, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.19/0.32 thf(decl_159, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.19/0.32 thf(decl_160, type, esk9_1: $i > $i).
% 0.19/0.32 thf(decl_161, type, esk10_2: ($i > $o) > $i > $i).
% 0.19/0.32 thf(decl_162, type, esk11_2: ($i > $o) > $i > $i).
% 0.19/0.32 thf(decl_163, type, esk12_1: ($i > $o) > $i).
% 0.19/0.32 thf(decl_164, type, esk13_2: ($i > $o) > $i > $i).
% 0.19/0.32 thf(decl_165, type, esk14_1: ($i > $o) > $i).
% 0.19/0.32 thf(decl_166, type, esk15_2: $i > $i > $i).
% 0.19/0.32 thf(decl_167, type, esk16_2: $i > $i > $i).
% 0.19/0.32 thf(decl_168, type, esk17_1: $i > $i).
% 0.19/0.32 thf(decl_169, type, esk18_1: $i > $i).
% 0.19/0.32 thf(decl_170, type, esk19_1: $i > $i).
% 0.19/0.32 thf(decl_171, type, esk20_2: $i > $i > $i).
% 0.19/0.32 thf(decl_172, type, esk21_3: $i > $i > $o > $i).
% 0.19/0.32 thf(decl_173, type, esk22_2: ($i > $o) > $i > $i).
% 0.19/0.32 thf(decl_174, type, esk23_1: ($i > $o) > $i).
% 0.19/0.32 thf(decl_175, type, esk24_1: $i > $i).
% 0.19/0.32 thf(decl_176, type, esk25_2: $i > ($i > $o) > $i).
% 0.19/0.32 thf(decl_177, type, esk26_2: $i > ($i > $o) > $i).
% 0.19/0.32 thf(decl_178, type, esk27_2: $i > ($i > $o) > $i).
% 0.19/0.32 thf(decl_179, type, esk28_2: $i > ($i > $o) > $i).
% 0.19/0.32 thf(decl_180, type, esk29_2: $i > ($i > $o) > $i).
% 0.19/0.32 thf(decl_181, type, esk30_2: $i > ($i > $o) > $i).
% 0.19/0.32 thf(decl_182, type, esk31_2: ($i > $o) > $i > $i).
% 0.19/0.32 thf(decl_183, type, esk32_1: ($i > $o) > $i).
% 0.19/0.32 thf(decl_184, type, esk33_1: ($i > $o) > $i).
% 0.19/0.32 thf(decl_185, type, esk34_1: ($i > $o) > $i).
% 0.19/0.32 thf(decl_186, type, esk35_1: ($i > $o) > $i).
% 0.19/0.32 thf(decl_187, type, esk36_2: ($i > $o) > $i > $i).
% 0.19/0.32 thf(decl_188, type, esk37_1: ($i > $o) > $i).
% 0.19/0.32 thf(decl_189, type, esk38_2: ($i > $o) > $i > $i).
% 0.19/0.32 thf(decl_190, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 0.19/0.32 thf(decl_191, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 0.19/0.32 thf(decl_192, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.19/0.32 thf(decl_193, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 0.19/0.32 thf(decl_194, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.19/0.32 thf(decl_195, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 0.19/0.32 thf(decl_196, type, esk45_2: ($i > $o) > $i > $i).
% 0.19/0.32 thf(decl_197, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 0.19/0.32 thf(decl_198, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 0.19/0.32 thf(decl_199, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.19/0.32 thf(decl_200, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.19/0.32 thf(decl_201, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.19/0.32 thf(decl_202, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.19/0.32 thf(decl_203, type, esk52_2: $i > $i > $i).
% 0.19/0.32 thf(decl_204, type, esk53_2: $i > $i > $i).
% 0.19/0.32 thf(decl_205, type, esk54_0: $i).
% 0.19/0.32 thf(decl_206, type, esk55_0: $i).
% 0.19/0.32 thf(decl_207, type, esk56_0: $i).
% 0.19/0.32 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', replAx)).
% 0.19/0.32 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', exu)).
% 0.19/0.32 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', descrp)).
% 0.19/0.32 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', exuE1)).
% 0.19/0.32 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', exuE3e)).
% 0.19/0.32 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', nonempty)).
% 0.19/0.32 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', nonemptyI)).
% 0.19/0.32 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', exuE2)).
% 0.19/0.32 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.KY8l8zcYYR/E---3.1_2542043.p', exuI1)).
% 0.19/0.32 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', exuI3)).
% 0.19/0.32 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', exuI2)).
% 0.19/0.32 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.KY8l8zcYYR/E---3.1_2542043.p', exuE3u)).
% 0.19/0.32 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', exu__Cong)).
% 0.19/0.32 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', exuEu)).
% 0.19/0.32 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', descr__Cong)).
% 0.19/0.32 thf(binintersectER, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', binintersectER)).
% 0.19/0.32 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', dsetconstrI)).
% 0.19/0.32 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', dsetconstrEL)).
% 0.19/0.32 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', dsetconstrER)).
% 0.19/0.32 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', setbeta)).
% 0.19/0.32 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', nonemptyE1)).
% 0.19/0.32 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', nonemptyI1)).
% 0.19/0.32 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', setoftrueEq)).
% 0.19/0.32 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', nonemptyImpWitness)).
% 0.19/0.32 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.KY8l8zcYYR/E---3.1_2542043.p', emptyE1)).
% 0.19/0.32 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', dsetconstr__Cong)).
% 0.19/0.32 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', sepInPowerset)).
% 0.19/0.32 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', sepSubset)).
% 0.19/0.32 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', setextAx)).
% 0.19/0.32 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', emptysetAx)).
% 0.19/0.32 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', setadjoinAx)).
% 0.19/0.32 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', powersetAx)).
% 0.19/0.32 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', setunionAx)).
% 0.19/0.32 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', omega0Ax)).
% 0.19/0.32 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', omegaSAx)).
% 0.19/0.32 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', omegaIndAx)).
% 0.19/0.32 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', foundationAx)).
% 0.19/0.32 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.KY8l8zcYYR/E---3.1_2542043.p', wellorderingAx)).
% 0.19/0.32 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', prop2setE)).
% 0.19/0.32 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', emptysetE)).
% 0.19/0.32 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', emptysetimpfalse)).
% 0.19/0.32 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', notinemptyset)).
% 0.19/0.32 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', setext)).
% 0.19/0.32 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', emptyI)).
% 0.19/0.32 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', noeltsimpempty)).
% 0.19/0.32 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', setadjoinIL)).
% 0.19/0.32 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', emptyinunitempty)).
% 0.19/0.32 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', setadjoinIR)).
% 0.19/0.32 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.KY8l8zcYYR/E---3.1_2542043.p', setadjoinE)).
% 0.19/0.32 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', setadjoinOr)).
% 0.19/0.32 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', powersetI)).
% 0.19/0.32 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', emptyinPowerset)).
% 0.19/0.32 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', emptyInPowerset)).
% 0.19/0.32 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', powersetE)).
% 0.19/0.32 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', setunionI)).
% 0.19/0.32 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.KY8l8zcYYR/E---3.1_2542043.p', setunionE)).
% 0.19/0.32 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', subPowSU)).
% 0.19/0.32 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', uniqinunit)).
% 0.19/0.32 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', notinsingleton)).
% 0.19/0.32 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', eqinunit)).
% 0.19/0.32 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', singletonsswitch)).
% 0.19/0.32 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', upairsetE)).
% 0.19/0.32 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', upairsetIL)).
% 0.19/0.32 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', upairsetIR)).
% 0.19/0.32 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', vacuousDall)).
% 0.19/0.32 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', quantDeMorgan1)).
% 0.19/0.32 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', quantDeMorgan2)).
% 0.19/0.32 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', quantDeMorgan3)).
% 0.19/0.32 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', quantDeMorgan4)).
% 0.19/0.32 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', prop2setI)).
% 0.19/0.32 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', prop2set2propI)).
% 0.19/0.32 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', notdexE)).
% 0.19/0.32 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', notdallE)).
% 0.19/0.32 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', inCongP)).
% 0.19/0.32 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', in__Cong)).
% 0.19/0.32 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', emptyset__Cong)).
% 0.19/0.32 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', setadjoin__Cong)).
% 0.19/0.32 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', powerset__Cong)).
% 0.19/0.32 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', setunion__Cong)).
% 0.19/0.32 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', omega__Cong)).
% 0.19/0.32 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', subsetI1)).
% 0.19/0.32 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', eqimpsubset2)).
% 0.19/0.32 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', eqimpsubset1)).
% 0.19/0.32 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', subsetI2)).
% 0.19/0.32 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', emptysetsubset)).
% 0.19/0.32 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', subsetE)).
% 0.19/0.32 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', subsetE2)).
% 0.19/0.32 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', notsubsetI)).
% 0.19/0.32 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', notequalI1)).
% 0.19/0.32 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', notequalI2)).
% 0.19/0.32 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', subsetRefl)).
% 0.19/0.32 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', subsetTrans)).
% 0.19/0.32 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', setadjoinSub)).
% 0.19/0.32 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', setadjoinSub2)).
% 0.19/0.32 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', subset2powerset)).
% 0.19/0.32 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', setextsub)).
% 0.19/0.32 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', subsetemptysetimpeq)).
% 0.19/0.32 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', powersetI1)).
% 0.19/0.32 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', powersetE1)).
% 0.19/0.32 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', inPowerset)).
% 0.19/0.32 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', powersetsubset)).
% 0.19/0.32 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', binunionIL)).
% 0.19/0.32 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', upairset2IR)).
% 0.19/0.32 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', binunionIR)).
% 0.19/0.32 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', binunionEcases)).
% 0.19/0.32 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', binunionE)).
% 0.19/0.32 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', binunionLsub)).
% 0.19/0.32 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', binunionRsub)).
% 0.19/0.32 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', binintersectI)).
% 0.19/0.32 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', binintersectSubset5)).
% 0.19/0.32 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', binintersectEL)).
% 0.19/0.32 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', binintersectLsub)).
% 0.19/0.32 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', binintersectSubset2)).
% 0.19/0.32 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', binintersectSubset3)).
% 0.19/0.32 thf(binintersect, axiom, ((binintersect)=(^[X4:$i, X5:$i]:(dsetconstr @ X4 @ (^[X2:$i]:((in @ X2 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.KY8l8zcYYR/E---3.1_2542043.p', binintersect)).
% 0.19/0.32 thf(c_0_115, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.19/0.32 thf(c_0_116, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.19/0.32 thf(c_0_117, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.19/0.32 thf(c_0_118, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.19/0.32 thf(c_0_119, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.19/0.32 thf(c_0_120, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.19/0.32 thf(c_0_121, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.19/0.32 thf(c_0_122, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.19/0.32 thf(c_0_123, 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])).
% 0.19/0.32 thf(c_0_124, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.19/0.32 thf(c_0_125, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.19/0.32 thf(c_0_126, 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])).
% 0.19/0.32 thf(c_0_127, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.19/0.32 thf(c_0_128, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 0.19/0.32 thf(c_0_129, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 0.19/0.32 thf(c_0_130, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[binintersectER])).
% 0.19/0.32 thf(c_0_131, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X319:$i]:(((((X6 @ X2 @ X319)))&(![X320:$i]:(((((X6 @ X2 @ X320)))=>(((X319)=(X320)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_115, c_0_116])).
% 0.19/0.32 thf(c_0_132, plain, ((descrp)=(![X1:$i > $o]:((((?[X321:$i]:(((((X1 @ X321)))&(![X322:$i]:(((((X1 @ X322)))=>(((X321)=(X322))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_117, c_0_116])).
% 0.19/0.32 thf(c_0_133, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.19/0.32 thf(c_0_134, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.19/0.32 thf(c_0_135, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.19/0.32 thf(c_0_136, plain, ((exuE1)=(![X1:$i > $o]:((((?[X323:$i]:(((((X1 @ X323)))&(![X324:$i]:(((((X1 @ X324)))=>(((X323)=(X324))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_118, c_0_116])).
% 0.19/0.32 thf(c_0_137, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X325:$i]:(((((X1 @ X325)))&(![X326:$i]:(((((X1 @ X326)))=>(((X325)=(X326))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_119, c_0_116])).
% 0.19/0.32 thf(c_0_138, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.19/0.32 thf(c_0_139, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_120])).
% 0.19/0.32 thf(c_0_140, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_121, c_0_120])).
% 0.19/0.32 thf(c_0_141, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_120])).
% 0.19/0.32 thf(c_0_142, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.19/0.32 thf(c_0_143, plain, ((exuE2)=(![X1:$i > $o]:((((?[X327:$i]:(((((X1 @ X327)))&(![X328:$i]:(((((X1 @ X328)))=>(((X327)=(X328))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_122, c_0_116])).
% 0.19/0.32 thf(c_0_144, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_120])).
% 0.19/0.32 thf(c_0_145, 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])).
% 0.19/0.32 thf(c_0_146, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X329:$i]:(((((X1 @ X329)))&(![X330:$i]:(((((X1 @ X330)))=>(((X329)=(X330)))))))))))))), inference(apply_def,[status(thm)],[c_0_123, c_0_116])).
% 0.19/0.32 thf(c_0_147, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X331:$i]:(((((X1 @ X331)))&(![X332:$i]:(((((X1 @ X332)))=>(((X331)=(X332)))))))))))))))), inference(apply_def,[status(thm)],[c_0_124, c_0_116])).
% 0.19/0.32 thf(c_0_148, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X333:$i]:(((((X1 @ X333)))&(![X334:$i]:(((((X1 @ X334)))=>(((X333)=(X334)))))))))))))), inference(apply_def,[status(thm)],[c_0_125, c_0_116])).
% 0.19/0.32 thf(c_0_149, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X335:$i]:(((((X1 @ X335)))&(![X336:$i]:(((((X1 @ X336)))=>(((X335)=(X336))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_126, c_0_116])).
% 0.19/0.32 thf(c_0_150, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X337:$i]:(((((X1 @ X337)))&(![X338:$i]:(((((X1 @ X338)))=>(((X337)=(X338))))))))))<=>((?[X339:$i]:(((((X17 @ X339)))&(![X340:$i]:(((((X17 @ X340)))=>(((X339)=(X340)))))))))))))))), inference(apply_def,[status(thm)],[c_0_127, c_0_116])).
% 0.19/0.32 thf(c_0_151, plain, ((exuEu)=(![X1:$i > $o]:((((?[X341:$i]:(((((X1 @ X341)))&(![X342:$i]:(((((X1 @ X342)))=>(((X341)=(X342))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_128, c_0_116])).
% 0.19/0.32 thf(c_0_152, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X343:$i]:(((((X1 @ X343)))&(![X344:$i]:(((((X1 @ X344)))=>(((X343)=(X344))))))))))=>((((?[X345:$i]:(((((X17 @ X345)))&(![X346:$i]:(((((X17 @ X346)))=>(((X345)=(X346))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_129, c_0_116])).
% 0.19/0.32 thf(c_0_153, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 0.19/0.32 thf(c_0_154, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 0.19/0.32 thf(c_0_155, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 0.19/0.32 thf(c_0_156, plain, ((epred1_0)<=>![X376:$i]:(?[X377:$i]:((((![X378:$i]:(((in @ X378 @ X377)=>![X379:$i]:(((in @ X379 @ X378)=>(in @ X379 @ X376)))))&![X380:$i, X381:$i]:((((in @ X380 @ X376)&(in @ X381 @ X376))=>(![X382:$i]:(((in @ X382 @ X377)=>((in @ X380 @ X382)<=>(in @ X381 @ X382))))=>((X380)=(X381))))))&![X383:$i, X384:$i]:((((in @ X383 @ X377)&(in @ X384 @ X377))=>(![X385:$i]:(((in @ X385 @ X383)=>(in @ X385 @ X384)))|![X386:$i]:(((in @ X386 @ X384)=>(in @ X386 @ X383)))))))&![X387:$i]:(((![X388:$i]:(((in @ X388 @ X387)=>(in @ X388 @ X376)))&?[X389:$i]:((in @ X389 @ X387)))=>?[X390:$i, X391:$i]:(((((in @ X390 @ X377)&(in @ X391 @ X387))&~(?[X392:$i]:(((in @ X392 @ X390)&(in @ X392 @ X387)))))&![X393:$i]:(((in @ X393 @ X377)=>(![X394:$i]:(((in @ X394 @ X393)=>(in @ X394 @ X390)))|(in @ X391 @ X393)))))))))))), introduced(definition)).
% 0.19/0.32 thf(c_0_157, negated_conjecture, ~((![X347:$i, X348:$i]:((![X349:$i]:(((in @ X349 @ X347)<=>(in @ X349 @ X348)))=>((X347)=(X348))))=>(![X350:$i]:(~(in @ X350 @ emptyset))=>(![X351:$i, X352:$i, X353:$i]:(((in @ X353 @ (setadjoin @ X351 @ X352))<=>(((X353)=(X351))|(in @ X353 @ X352))))=>(![X354:$i, X355:$i]:(((in @ X355 @ (powerset @ X354))<=>![X356:$i]:(((in @ X356 @ X355)=>(in @ X356 @ X354)))))=>(![X357:$i, X358:$i]:(((in @ X358 @ (setunion @ X357))<=>?[X359:$i]:(((in @ X358 @ X359)&(in @ X359 @ X357)))))=>((in @ emptyset @ omega)=>(![X360:$i]:(((in @ X360 @ omega)=>(in @ (setadjoin @ X360 @ X360) @ omega)))=>(![X361:$i]:((((in @ emptyset @ X361)&![X362:$i]:((((in @ X362 @ omega)&(in @ X362 @ X361))=>(in @ (setadjoin @ X362 @ X362) @ X361))))=>![X363:$i]:(((in @ X363 @ omega)=>(in @ X363 @ X361)))))=>(![X364:$i > $i > $o, X365:$i]:((![X366:$i]:(((in @ X366 @ X365)=>?[X367:$i]:(((X364 @ X366 @ X367)&![X368:$i]:(((X364 @ X366 @ X368)=>((X367)=(X368))))))))=>?[X369:$i]:(![X370:$i]:(((in @ X370 @ X369)<=>?[X371:$i]:(((in @ X371 @ X365)&(X364 @ X371 @ X370))))))))=>(![X372:$i]:((?[X373:$i]:((in @ X373 @ X372))=>?[X374:$i]:(((in @ X374 @ X372)&~(?[X375:$i]:(((in @ X375 @ X374)&(in @ X375 @ X372))))))))=>((epred1_0)=>(![X395:$i > $o]:((?[X396:$i]:(((X395 @ X396)&![X397:$i]:(((X395 @ X397)=>((X396)=(X397))))))=>(X395 @ (descr @ (^[Z0:$i]:(X395 @ Z0))))))=>(![X398:$i, X399:$i > $o, X400:$i]:(((in @ X400 @ X398)=>((X399 @ X400)=>(in @ X400 @ (dsetconstr @ X398 @ X399)))))=>(![X401:$i, X402:$i > $o, X403:$i]:(((in @ X403 @ (dsetconstr @ X401 @ X402))=>(in @ X403 @ X401)))=>(![X404:$i, X405:$i > $o, X406:$i]:(((in @ X406 @ (dsetconstr @ X404 @ X405))=>(X405 @ X406)))=>(![X407:$i > $o]:((?[X408:$i]:(((X407 @ X408)&![X409:$i]:(((X407 @ X409)=>((X408)=(X409))))))=>?[X410:$i]:(((X407 @ X410)&![X411:$i]:(((X407 @ X411)=>((X410)=(X411))))))))=>(![X412:$o, X413:$i]:(((in @ X413 @ (prop2set @ ((X412))))=>(X412)))=>(![X414:$i]:(((in @ X414 @ emptyset)=>![X415:$o]:((X415))))=>(![X416:$i]:(((in @ X416 @ emptyset)=>~($true)))=>(![X417:$i]:(~(in @ X417 @ emptyset))=>(![X418:$i > $o]:((?[X419:$i]:(((X418 @ X419)&![X420:$i]:(((X418 @ X420)=>((X419)=(X420))))))=>?[X421:$i]:((X418 @ X421))))=>(![X422:$i, X423:$i]:((![X424:$i]:(((in @ X424 @ X422)=>(in @ X424 @ X423)))=>(![X425:$i]:(((in @ X425 @ X423)=>(in @ X425 @ X422)))=>((X422)=(X423)))))=>(![X426:$i]:((![X427:$i]:(~(in @ X427 @ X426))=>((X426)=(emptyset))))=>(![X428:$i]:((![X429:$i]:(~(in @ X429 @ X428))=>((X428)=(emptyset))))=>(![X430:$i, X431:$i > $o, X432:$i]:(((in @ X432 @ X430)=>((in @ X432 @ (dsetconstr @ X430 @ X431))<=>(X431 @ X432))))=>(![X433:$i]:((((X433)!=(emptyset))=>?[X434:$i]:((in @ X434 @ X433))))=>(![X435:$i, X436:$i > $o, X437:$i]:(((in @ X437 @ X435)=>((X436 @ X437)=>((dsetconstr @ X435 @ X436)!=(emptyset)))))=>(![X438:$i]:((?[X439:$i]:((in @ X439 @ X438))=>((X438)!=(emptyset))))=>(![X440:$i, X441:$i]:((in @ X440 @ (setadjoin @ X440 @ X441)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X442:$i, X443:$i, X444:$i]:(((in @ X444 @ X443)=>(in @ X444 @ (setadjoin @ X442 @ X443))))=>(![X445:$i, X446:$i, X447:$i]:(((in @ X447 @ (setadjoin @ X445 @ X446))=>![X448:$o]:(((((X447)=(X445))=>(X448))=>(((in @ X447 @ X446)=>(X448))=>(X448))))))=>(![X449:$i, X450:$i, X451:$i]:(((in @ X451 @ (setadjoin @ X449 @ X450))=>(((X451)=(X449))|(in @ X451 @ X450))))=>(![X452:$i]:(((dsetconstr @ X452 @ (^[Z0:$i]:($true)))=(X452)))=>(![X453:$i, X454:$i]:((![X455:$i]:(((in @ X455 @ X454)=>(in @ X455 @ X453)))=>(in @ X454 @ (powerset @ X453))))=>(![X456:$i]:((in @ emptyset @ (powerset @ X456)))=>(![X457:$i]:((in @ emptyset @ (powerset @ X457)))=>(![X458:$i, X459:$i, X460:$i]:(((in @ X459 @ (powerset @ X458))=>((in @ X460 @ X459)=>(in @ X460 @ X458))))=>(![X461:$i, X462:$i, X463:$i]:(((in @ X462 @ X463)=>((in @ X463 @ X461)=>(in @ X462 @ (setunion @ X461)))))=>(![X464:$i, X465:$i]:(((in @ X465 @ (setunion @ X464))=>![X466:$o]:((![X467:$i]:(((in @ X465 @ X467)=>((in @ X467 @ X464)=>(X466))))=>(X466)))))=>(![X468:$i, X469:$i]:(((in @ X469 @ X468)=>(in @ X469 @ (powerset @ (setunion @ X468)))))=>(![X470:$i > $o]:((?[X471:$i]:(((X470 @ X471)&![X472:$i]:(((X470 @ X472)=>((X471)=(X472))))))=>?[X473:$i]:(![X474:$i]:(((X470 @ X474)<=>((X474)=(X473)))))))=>(![X475:$i]:((((X475)!=(emptyset))=>?[X476:$i]:(((in @ X476 @ X475)&$true))))=>(![X477:$i, X478:$i]:(((in @ X477 @ (setadjoin @ X478 @ emptyset))=>((X477)=(X478))))=>(![X479:$i, X480:$i]:((((X479)!=(X480))=>~(in @ X480 @ (setadjoin @ X479 @ emptyset))))=>(![X481:$i, X482:$i]:((((X481)=(X482))=>(in @ X481 @ (setadjoin @ X482 @ emptyset))))=>(![X483:$i, X484:$i]:(((in @ X483 @ (setadjoin @ X484 @ emptyset))=>(in @ X484 @ (setadjoin @ X483 @ emptyset))))=>(![X485:$i, X486:$i, X487:$i]:(((in @ X487 @ (setadjoin @ X485 @ (setadjoin @ X486 @ emptyset)))=>(((X487)=(X485))|((X487)=(X486)))))=>(![X488:$i, X489:$i]:((in @ X488 @ (setadjoin @ X488 @ (setadjoin @ X489 @ emptyset))))=>(![X490:$i, X491:$i]:((in @ X491 @ (setadjoin @ X490 @ (setadjoin @ X491 @ emptyset))))=>(![X492:$i, X493:$i > $o]:((?[X494:$i]:(((in @ X494 @ X492)&(X493 @ X494)))=>(((dsetconstr @ X492 @ X493)=(emptyset))=>~($true))))=>(![X495:$i > $o, X496:$i]:(((in @ X496 @ emptyset)=>(X495 @ X496)))=>(![X497:$i, X498:$i > $o]:((~(![X499:$i]:(((in @ X499 @ X497)=>(X498 @ X499))))=>?[X500:$i]:(((in @ X500 @ X497)&~((X498 @ X500))))))=>(![X501:$i, X502:$i > $o]:((![X503:$i]:(((in @ X503 @ X501)=>~((X502 @ X503))))=>~(?[X504:$i]:(((in @ X504 @ X501)&(X502 @ X504))))))=>(![X505:$i, X506:$i > $o]:((~(?[X507:$i]:(((in @ X507 @ X505)&(X506 @ X507))))=>![X508:$i]:(((in @ X508 @ X505)=>~((X506 @ X508))))))=>(![X509:$i, X510:$i > $o]:((?[X511:$i]:(((in @ X511 @ X509)&~((X510 @ X511))))=>~(![X512:$i]:(((in @ X512 @ X509)=>(X510 @ X512))))))=>(![X513:$o]:(((X513)=>(in @ emptyset @ (prop2set @ ((X513))))))=>(![X514:$o]:(((X514)=>(set2prop @ (prop2set @ ((X514))))))=>(![X515:$i, X516:$i > $o]:((~(?[X517:$i]:(((in @ X517 @ X515)&(X516 @ X517))))=>![X518:$i]:(((in @ X518 @ X515)=>~((X516 @ X518))))))=>(![X519:$i, X520:$i > $o]:((~(![X521:$i]:(((in @ X521 @ X519)=>(X520 @ X521))))=>?[X522:$i]:(((in @ X522 @ X519)&~((X520 @ X522))))))=>(![X523:$i > $o]:((?[X524:$i]:(((X523 @ X524)&![X525:$i]:(((X523 @ X525)=>((X524)=(X525))))))=>?[X526:$i]:(((X523 @ X526)&![X527:$i]:(((X523 @ X527)=>((X526)=(X527))))))))=>(![X528:$i > $o]:((?[X529:$i]:((X528 @ X529))=>(![X530:$i, X531:$i]:(((X528 @ X530)=>((X528 @ X531)=>((X530)=(X531)))))=>?[X532:$i]:(((X528 @ X532)&![X533:$i]:(((X528 @ X533)=>((X532)=(X533)))))))))=>(![X534:$i > $o]:((?[X535:$i]:(![X536:$i]:(((X534 @ X536)<=>((X536)=(X535)))))=>?[X537:$i]:(((X534 @ X537)&![X538:$i]:(((X534 @ X538)=>((X537)=(X538))))))))=>(![X539:$i, X540:$i]:((((X539)=(X540))=>![X541:$i, X542:$i]:((((X541)=(X542))=>((in @ X541 @ X539)=>(in @ X542 @ X540))))))=>(![X543:$i, X544:$i]:((((X543)=(X544))=>![X545:$i, X546:$i]:((((X545)=(X546))=>((in @ X545 @ X543)<=>(in @ X546 @ X544))))))=>(![X547:$i > $o]:((?[X548:$i]:(((X547 @ X548)&![X549:$i]:(((X547 @ X549)=>((X548)=(X549))))))=>![X550:$i, X551:$i]:(((X547 @ X550)=>((X547 @ X551)=>((X550)=(X551)))))))=>(![X552:$i > $o, X553:$i > $o]:((![X554:$i, X555:$i]:((((X554)=(X555))=>((X552 @ X554)<=>(X553 @ X555))))=>(?[X556:$i]:(((X552 @ X556)&![X557:$i]:(((X552 @ X557)=>((X556)=(X557))))))<=>?[X558:$i]:(((X553 @ X558)&![X559:$i]:(((X553 @ X559)=>((X558)=(X559)))))))))=>(((emptyset)=(emptyset))=>(![X560:$i, X561:$i]:((((X560)=(X561))=>![X562:$i, X563:$i]:((((X562)=(X563))=>((setadjoin @ X560 @ X562)=(setadjoin @ X561 @ X563))))))=>(![X564:$i, X565:$i]:((((X564)=(X565))=>((powerset @ X564)=(powerset @ X565))))=>(![X566:$i, X567:$i]:((((X566)=(X567))=>((setunion @ X566)=(setunion @ X567))))=>(((omega)=(omega))=>(![X568:$i > $o]:((?[X569:$i]:(((X568 @ X569)&![X570:$i]:(((X568 @ X570)=>((X569)=(X570))))))=>![X571:$i, X572:$i]:(((X568 @ X571)=>((X568 @ X572)=>((X571)=(X572)))))))=>(![X573:$i > $o, X574:$i > $o]:((![X575:$i, X576:$i]:((((X575)=(X576))=>((X573 @ X575)<=>(X574 @ X576))))=>(?[X577:$i]:(((X573 @ X577)&![X578:$i]:(((X573 @ X578)=>((X577)=(X578))))))=>(?[X579:$i]:(((X574 @ X579)&![X580:$i]:(((X574 @ X580)=>((X579)=(X580))))))=>((descr @ X573)=(descr @ X574))))))=>(![X581:$i, X582:$i]:((((X581)=(X582))=>![X583:$i > $o, X584:$i > $o]:((![X585:$i]:(((in @ X585 @ X581)=>![X586:$i]:(((in @ X586 @ X582)=>(((X585)=(X586))=>((X583 @ X585)<=>(X584 @ X586)))))))=>((dsetconstr @ X581 @ X583)=(dsetconstr @ X582 @ X584))))))=>(![X587:$i, X588:$i]:((![X589:$i]:(((in @ X589 @ X587)=>(in @ X589 @ X588)))=>(subset @ X587 @ X588)))=>(![X590:$i, X591:$i]:((((X590)=(X591))=>(subset @ X591 @ X590)))=>(![X592:$i, X593:$i]:((((X592)=(X593))=>(subset @ X592 @ X593)))=>(![X594:$i, X595:$i]:((![X596:$i]:(((in @ X596 @ X594)=>(in @ X596 @ X595)))=>(subset @ X594 @ X595)))=>(![X597:$i]:((subset @ emptyset @ X597))=>(![X598:$i, X599:$i, X600:$i]:(((subset @ X598 @ X599)=>((in @ X600 @ X598)=>(in @ X600 @ X599))))=>(![X601:$i, X602:$i, X603:$i]:(((subset @ X601 @ X602)=>(~(in @ X603 @ X602)=>~(in @ X603 @ X601))))=>(![X604:$i, X605:$i, X606:$i]:(((in @ X606 @ X604)=>(~(in @ X606 @ X605)=>~(subset @ X604 @ X605))))=>(![X607:$i, X608:$i]:((~(subset @ X607 @ X608)=>((X607)!=(X608))))=>(![X609:$i, X610:$i, X611:$i]:(((in @ X611 @ X609)=>(~(in @ X611 @ X610)=>((X609)!=(X610)))))=>(![X612:$i]:((subset @ X612 @ X612))=>(![X613:$i, X614:$i, X615:$i]:(((subset @ X613 @ X614)=>((subset @ X614 @ X615)=>(subset @ X613 @ X615))))=>(![X616:$i, X617:$i]:((subset @ X617 @ (setadjoin @ X616 @ X617)))=>(![X618:$i, X619:$i, X620:$i]:(((subset @ X618 @ X620)=>(subset @ X618 @ (setadjoin @ X619 @ X620))))=>(![X621:$i, X622:$i]:(((subset @ X621 @ X622)=>(in @ X621 @ (powerset @ X622))))=>(![X623:$i, X624:$i]:(((subset @ X623 @ X624)=>((subset @ X624 @ X623)=>((X623)=(X624)))))=>(![X625:$i]:(((subset @ X625 @ emptyset)=>((X625)=(emptyset))))=>(![X626:$i, X627:$i]:(((subset @ X627 @ X626)=>(in @ X627 @ (powerset @ X626))))=>(![X628:$i, X629:$i]:(((in @ X629 @ (powerset @ X628))=>(subset @ X629 @ X628)))=>(![X630:$i]:((in @ X630 @ (powerset @ X630)))=>(![X631:$i, X632:$i]:(((subset @ X631 @ X632)=>(subset @ (powerset @ X631) @ (powerset @ X632))))=>(![X633:$i, X634:$i > $o]:((in @ (dsetconstr @ X633 @ X634) @ (powerset @ X633)))=>(![X635:$i, X636:$i > $o]:((subset @ (dsetconstr @ X635 @ X636) @ X635))=>(![X637:$i, X638:$i, X639:$i]:(((in @ X639 @ X637)=>(in @ X639 @ (binunion @ X637 @ X638))))=>(![X640:$i, X641:$i]:((in @ X641 @ (setadjoin @ X640 @ (setadjoin @ X641 @ emptyset))))=>(![X642:$i, X643:$i, X644:$i]:(((in @ X644 @ X643)=>(in @ X644 @ (binunion @ X642 @ X643))))=>(![X645:$i, X646:$i, X647:$i, X648:$o]:(((in @ X647 @ (binunion @ X645 @ X646))=>(((in @ X647 @ X645)=>(X648))=>(((in @ X647 @ X646)=>(X648))=>(X648)))))=>(![X649:$i, X650:$i, X651:$i]:(((in @ X651 @ (binunion @ X649 @ X650))=>((in @ X651 @ X649)|(in @ X651 @ X650))))=>(![X652:$i, X653:$i]:((subset @ X652 @ (binunion @ X652 @ X653)))=>(![X654:$i, X655:$i]:((subset @ X655 @ (binunion @ X654 @ X655)))=>(![X656:$i, X657:$i, X658:$i]:(((in @ X658 @ X656)=>((in @ X658 @ X657)=>(in @ X658 @ (binintersect @ X656 @ X657)))))=>(![X659:$i, X660:$i, X661:$i]:(((subset @ X661 @ X659)=>((subset @ X661 @ X660)=>(subset @ X661 @ (binintersect @ X659 @ X660)))))=>(![X662:$i, X663:$i, X664:$i]:(((in @ X664 @ (binintersect @ X662 @ X663))=>(in @ X664 @ X662)))=>(![X665:$i, X666:$i]:((subset @ (binintersect @ X665 @ X666) @ X665))=>(![X667:$i, X668:$i]:(((subset @ X667 @ X668)=>((binintersect @ X667 @ X668)=(X667))))=>(![X669:$i, X670:$i]:((((binintersect @ X669 @ X670)=(X670))=>(subset @ X670 @ X669)))=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(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_130, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_131]), foundationAx]), wellorderingAx]), c_0_132]), c_0_133]), c_0_134]), c_0_135]), c_0_136]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_137]), setext]), emptyI]), noeltsimpempty]), c_0_138]), c_0_139]), c_0_140]), c_0_141]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_142]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_143]), c_0_144]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_145]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_146]), c_0_147]), c_0_148]), inCongP]), in__Cong]), c_0_149]), c_0_150]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_151]), c_0_152]), c_0_153]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_154]), c_0_155]), binunionIL]), upairset2IR]), binunionIR]), binunionEcases]), binunionE]), binunionLsub]), binunionRsub]), binintersectI]), binintersectSubset5]), binintersectEL]), binintersectLsub]), binintersectSubset2]), binintersectSubset3])])]), c_0_156])).
% 0.19/0.32 thf(c_0_158, plain, ![X671:$i, X672:$i]:(((binintersect @ X671 @ X672)=(dsetconstr @ X671 @ (^[Z0:$i]:((in @ Z0 @ X672)))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[binintersect])])).
% 0.19/0.32 thf(c_0_159, negated_conjecture, ![X675:$i, X676:$i, X678:$i, X679:$i, X680:$i, X681:$i, X682:$i, X683:$i, X684:$i, X685:$i, X686:$i, X688:$i, X689:$i, X691:$i, X692:$i, X693:$i, X694:$i, X695:$i, X697:$i, X698:$i > $i > $o, X699:$i, X701:$i, X704:$i, X706:$i, X707:$i, X708:$i, X709:$i, X711:$i, X712:$i > $o, X713:$i, X715:$i, X716:$i > $o, X717:$i, X718:$i, X719:$i > $o, X720:$i, X721:$i, X722:$i > $o, X723:$i, X724:$i > $o, X725:$i, X728:$i, X729:$o, X730:$i, X731:$i, X732:$o, X733:$i, X734:$i, X735:$i > $o, X736:$i, X739:$i, X740:$i, X743:$i, X745:$i, X747:$i, X748:$i > $o, X749:$i, X750:$i, X752:$i, X753:$i > $o, X754:$i, X755:$i, X756:$i, X757:$i, X758:$i, X759:$i, X760:$i, X761:$i, X762:$i, X763:$i, X764:$i, X765:$o, X766:$i, X767:$i, X768:$i, X769:$i, X770:$i, X771:$i, X773:$i, X774:$i, X775:$i, X776:$i, X777:$i, X778:$i, X779:$i, X780:$i, X781:$i, X782:$i, X783:$o, X785:$i, X786:$i, X787:$i > $o, X788:$i, X791:$i, X792:$i, X793:$i, X795:$i, X796:$i, X797:$i, X798:$i, X799:$i, X800:$i, X801:$i, X802:$i, X803:$i, X804:$i, X805:$i, X806:$i, X807:$i, X808:$i, X809:$i, X810:$i, X811:$i > $o, X812:$i, X813:$i > $o, X814:$i, X815:$i, X816:$i > $o, X817:$i, X819:$i, X820:$i > $o, X822:$i, X823:$i, X824:$i > $o, X826:$i, X827:$i, X828:$i > $o, X829:$i, X831:$o, X832:$o, X833:$i, X834:$i > $o, X836:$i, X837:$i, X838:$i > $o, X839:$i, X841:$i > $o, X842:$i, X845:$i, X846:$i > $o, X847:$i, X851:$i, X852:$i > $o, X853:$i, X856:$i, X857:$i, X858:$i, X859:$i, X860:$i, X861:$i, X862:$i, X863:$i, X864:$i, X865:$i > $o, X866:$i, X868:$i, X869:$i, X870:$i > $o, X871:$i > $o, X874:$i, X877:$i, X878:$i, X881:$i, X882:$i, X883:$i, X884:$i, X885:$i, X886:$i, X887:$i, X888:$i, X889:$i, X890:$i > $o, X891:$i, X893:$i, X894:$i, X895:$i > $o, X896:$i > $o, X899:$i, X901:$i, X903:$i, X904:$i, X905:$i > $o, X906:$i > $o, X909:$i, X910:$i, X912:$i, X913:$i, X914:$i, X915:$i, X916:$i, X917:$i, X919:$i, X920:$i, X921:$i, X922:$i, X923:$i, X924:$i, X925:$i, X926:$i, X927:$i, X928:$i, X929:$i, X930:$i, X931:$i, X932:$i, X933:$i, X934:$i, X935:$i, X936:$i, X937:$i, X938:$i, X939:$i, X940:$i, X941:$i, X942:$i, X943:$i, X944:$i, X945:$i, X946:$i, X947:$i, X948:$i, X949:$i, X950:$i, X951:$i, X952:$i, X953:$i, X954:$i, X955:$i, X956:$i > $o, X957:$i, X958:$i > $o, X959:$i, X960:$i, X961:$i, X962:$i, X963:$i, X964:$i, X965:$i, X966:$i, X967:$i, X968:$i, X969:$i, X970:$o, X971:$i, X972:$i, X973:$i, X974:$i, X975:$i, X976:$i, X977:$i, X978:$i, X979:$i, X980:$i, X981:$i, X982:$i, X983:$i, X984:$i, X985:$i, X986:$i, X987:$i, X988:$i, X989:$i, X990:$i, X991:$i, X992:$i]:((((~(in @ (esk1_2 @ X675 @ X676) @ X675)|~(in @ (esk1_2 @ X675 @ X676) @ X676)|((X675)=(X676)))&((in @ (esk1_2 @ X675 @ X676) @ X675)|(in @ (esk1_2 @ X675 @ X676) @ X676)|((X675)=(X676))))&(~(in @ X678 @ emptyset)&(((~(in @ X681 @ (setadjoin @ X679 @ X680))|(((X681)=(X679))|(in @ X681 @ X680)))&((((X681)!=(X679))|(in @ X681 @ (setadjoin @ X679 @ X680)))&(~(in @ X681 @ X680)|(in @ X681 @ (setadjoin @ X679 @ X680)))))&(((~(in @ X683 @ (powerset @ X682))|(~(in @ X684 @ X683)|(in @ X684 @ X682)))&(((in @ (esk2_2 @ X685 @ X686) @ X686)|(in @ X686 @ (powerset @ X685)))&(~(in @ (esk2_2 @ X685 @ X686) @ X685)|(in @ X686 @ (powerset @ X685)))))&(((((in @ X689 @ (esk3_2 @ X688 @ X689))|~(in @ X689 @ (setunion @ X688)))&((in @ (esk3_2 @ X688 @ X689) @ X688)|~(in @ X689 @ (setunion @ X688))))&(~(in @ X692 @ X693)|~(in @ X693 @ X691)|(in @ X692 @ (setunion @ X691))))&((in @ emptyset @ omega)&((~(in @ X694 @ omega)|(in @ (setadjoin @ X694 @ X694) @ omega))&(((((in @ (esk4_1 @ X695) @ omega)|~(in @ emptyset @ X695)|(~(in @ X697 @ omega)|(in @ X697 @ X695)))&((in @ (esk4_1 @ X695) @ X695)|~(in @ emptyset @ X695)|(~(in @ X697 @ omega)|(in @ X697 @ X695))))&(~(in @ (setadjoin @ (esk4_1 @ X695) @ (esk4_1 @ X695)) @ X695)|~(in @ emptyset @ X695)|(~(in @ X697 @ omega)|(in @ X697 @ X695))))&((((((in @ (esk8_3 @ X698 @ X699 @ X704) @ X699)|~(in @ X704 @ (esk7_2 @ X698 @ X699))|(in @ (esk5_2 @ X698 @ X699) @ X699))&((X698 @ (esk8_3 @ X698 @ X699 @ X704) @ X704)|~(in @ X704 @ (esk7_2 @ X698 @ X699))|(in @ (esk5_2 @ X698 @ X699) @ X699)))&(~(in @ X707 @ X699)|~(X698 @ X707 @ X706)|(in @ X706 @ (esk7_2 @ X698 @ X699))|(in @ (esk5_2 @ X698 @ X699) @ X699)))&(((((in @ (esk8_3 @ X698 @ X699 @ X704) @ X699)|~(in @ X704 @ (esk7_2 @ X698 @ X699))|((X698 @ (esk5_2 @ X698 @ X699) @ (esk6_3 @ X698 @ X699 @ X701))|~(X698 @ (esk5_2 @ X698 @ X699) @ X701)))&((X698 @ (esk8_3 @ X698 @ X699 @ X704) @ X704)|~(in @ X704 @ (esk7_2 @ X698 @ X699))|((X698 @ (esk5_2 @ X698 @ X699) @ (esk6_3 @ X698 @ X699 @ X701))|~(X698 @ (esk5_2 @ X698 @ X699) @ X701))))&(~(in @ X707 @ X699)|~(X698 @ X707 @ X706)|(in @ X706 @ (esk7_2 @ X698 @ X699))|((X698 @ (esk5_2 @ X698 @ X699) @ (esk6_3 @ X698 @ X699 @ X701))|~(X698 @ (esk5_2 @ X698 @ X699) @ X701))))&((((in @ (esk8_3 @ X698 @ X699 @ X704) @ X699)|~(in @ X704 @ (esk7_2 @ X698 @ X699))|(((X701)!=(esk6_3 @ X698 @ X699 @ X701))|~(X698 @ (esk5_2 @ X698 @ X699) @ 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X896)))))&(((X896 @ (esk49_3 @ X895 @ X896 @ X901))|~(X896 @ X901)|((descr @ X895)=(descr @ X896))|(((X899)!=(esk48_3 @ X895 @ X896 @ X899))|~(X895 @ X899))|((X895 @ (esk46_2 @ X895 @ X896))|(X896 @ (esk47_2 @ X895 @ X896))))&(((X901)!=(esk49_3 @ X895 @ X896 @ X901))|~(X896 @ X901)|((descr @ X895)=(descr @ X896))|(((X899)!=(esk48_3 @ X895 @ X896 @ X899))|~(X895 @ X899))|((X895 @ (esk46_2 @ X895 @ X896))|(X896 @ (esk47_2 @ X895 @ X896))))))))&((((in @ (esk50_4 @ X903 @ X904 @ X905 @ X906) @ X903)|((dsetconstr @ X903 @ X905)=(dsetconstr @ X904 @ X906))|((X903)!=(X904)))&(((in @ (esk51_4 @ X903 @ X904 @ X905 @ X906) @ X904)|((dsetconstr @ X903 @ X905)=(dsetconstr @ X904 @ X906))|((X903)!=(X904)))&((((esk50_4 @ X903 @ X904 @ X905 @ X906)=(esk51_4 @ X903 @ X904 @ X905 @ X906))|((dsetconstr @ X903 @ X905)=(dsetconstr @ X904 @ X906))|((X903)!=(X904)))&((~(X905 @ (esk50_4 @ X903 @ X904 @ X905 @ X906))|~(X906 @ (esk51_4 @ X903 @ X904 @ X905 @ X906))|((dsetconstr @ X903 @ X905)=(dsetconstr @ X904 @ X906))|((X903)!=(X904)))&((X905 @ (esk50_4 @ X903 @ X904 @ X905 @ X906))|(X906 @ (esk51_4 @ X903 @ X904 @ X905 @ X906))|((dsetconstr @ X903 @ X905)=(dsetconstr @ X904 @ X906))|((X903)!=(X904)))))))&((((in @ (esk52_2 @ X909 @ X910) @ X909)|(subset @ X909 @ X910))&(~(in @ (esk52_2 @ X909 @ X910) @ X910)|(subset @ X909 @ X910)))&((((X912)!=(X913))|(subset @ X913 @ X912))&((((X914)!=(X915))|(subset @ X914 @ X915))&((((in @ (esk53_2 @ X916 @ X917) @ X916)|(subset @ X916 @ X917))&(~(in @ (esk53_2 @ X916 @ X917) @ X917)|(subset @ X916 @ X917)))&((subset @ emptyset @ X919)&((~(subset @ X920 @ X921)|(~(in @ X922 @ X920)|(in @ X922 @ X921)))&((~(subset @ X923 @ X924)|((in @ X925 @ X924)|~(in @ X925 @ X923)))&((~(in @ X928 @ X926)|((in @ X928 @ X927)|~(subset @ X926 @ X927)))&(((subset @ X929 @ X930)|((X929)!=(X930)))&((~(in @ X933 @ X931)|((in @ X933 @ X932)|((X931)!=(X932))))&((subset @ X934 @ X934)&((~(subset @ X935 @ X936)|(~(subset @ X936 @ X937)|(subset @ X935 @ X937)))&((subset @ X939 @ (setadjoin @ X938 @ X939))&((~(subset @ X940 @ X942)|(subset @ X940 @ (setadjoin @ X941 @ X942)))&((~(subset @ X943 @ X944)|(in @ X943 @ (powerset @ X944)))&((~(subset @ X945 @ X946)|(~(subset @ X946 @ X945)|((X945)=(X946))))&((~(subset @ X947 @ emptyset)|((X947)=(emptyset)))&((~(subset @ X949 @ X948)|(in @ X949 @ (powerset @ X948)))&((~(in @ X951 @ (powerset @ X950))|(subset @ X951 @ X950))&((in @ X952 @ (powerset @ X952))&((~(subset @ X953 @ X954)|(subset @ (powerset @ X953) @ (powerset @ X954)))&((in @ (dsetconstr @ X955 @ X956) @ (powerset @ X955))&((subset @ (dsetconstr @ X957 @ X958) @ X957)&((~(in @ X961 @ X959)|(in @ X961 @ (binunion @ X959 @ X960)))&((in @ X963 @ (setadjoin @ X962 @ (setadjoin @ X963 @ emptyset)))&((~(in @ X966 @ X965)|(in @ X966 @ (binunion @ X964 @ X965)))&(((((in @ X969 @ X968)|(X970)|(in @ X969 @ X967)|~(in @ X969 @ (binunion @ X967 @ X968)))&(~(X970)|(X970)|(in @ X969 @ X967)|~(in @ X969 @ (binunion @ X967 @ X968))))&(((in @ X969 @ X968)|(X970)|~(X970)|~(in @ X969 @ (binunion @ X967 @ X968)))&(~(X970)|(X970)|~(X970)|~(in @ X969 @ (binunion @ X967 @ X968)))))&((~(in @ X973 @ (binunion @ X971 @ X972))|((in @ X973 @ X971)|(in @ X973 @ X972)))&((subset @ X974 @ (binunion @ X974 @ X975))&((subset @ X977 @ (binunion @ X976 @ X977))&((~(in @ X980 @ X978)|(~(in @ X980 @ X979)|(in @ X980 @ (binintersect @ X978 @ X979))))&((~(subset @ X983 @ X981)|(~(subset @ X983 @ X982)|(subset @ X983 @ (binintersect @ X981 @ X982))))&((~(in @ X986 @ (binintersect @ X984 @ X985))|(in @ X986 @ X984))&((subset @ (binintersect @ X987 @ X988) @ X987)&((~(subset @ X989 @ X990)|((binintersect @ X989 @ X990)=(X989)))&((((binintersect @ X991 @ X992)!=(X992))|(subset @ X992 @ X991))&((in @ esk56_0 @ (binintersect @ esk54_0 @ esk55_0))&~(in @ esk56_0 @ esk55_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_157])])])])])])])).
% 0.19/0.32 thf(c_0_160, plain, ![X673:$i, X674:$i]:(((binintersect @ X673 @ X674)=(dsetconstr @ X673 @ (^[Z0:$i]:((in @ Z0 @ X674)))))), inference(variable_rename,[status(thm)],[c_0_158])).
% 0.19/0.32 thf(c_0_161, negated_conjecture, (in @ esk56_0 @ (binintersect @ esk54_0 @ esk55_0)), inference(split_conjunct,[status(thm)],[c_0_159])).
% 0.19/0.32 thf(c_0_162, plain, ![X2:$i, X3:$i]:(((binintersect @ X2 @ X3)=(dsetconstr @ X2 @ (^[Z0:$i]:((in @ Z0 @ X3)))))), inference(split_conjunct,[status(thm)],[c_0_160])).
% 0.19/0.32 thf(c_0_163, negated_conjecture, ![X3:$i, X2:$i, X1:$i > $o]:(((X1 @ X2)|~((in @ X2 @ (dsetconstr @ X3 @ X1))))), inference(split_conjunct,[status(thm)],[c_0_159])).
% 0.19/0.32 thf(c_0_164, negated_conjecture, (in @ esk56_0 @ (dsetconstr @ esk54_0 @ (^[Z0:$i]:((in @ Z0 @ esk55_0))))), inference(rw,[status(thm)],[c_0_161, c_0_162])).
% 0.19/0.32 thf(c_0_165, negated_conjecture, ~((in @ esk56_0 @ esk55_0)), inference(split_conjunct,[status(thm)],[c_0_159])).
% 0.19/0.32 thf(c_0_166, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_163, c_0_164]), c_0_165]), ['proof']).
% 0.19/0.32 % SZS output end CNFRefutation
% 0.19/0.32 % Parsed axioms : 243
% 0.19/0.32 % Removed by relevancy pruning/SinE : 0
% 0.19/0.32 % Initial clauses : 355
% 0.19/0.32 % Removed in clause preprocessing : 146
% 0.19/0.32 % Initial clauses in saturation : 209
% 0.19/0.32 % Processed clauses : 56
% 0.19/0.32 % ...of these trivial : 5
% 0.19/0.32 % ...subsumed : 8
% 0.19/0.32 % ...remaining for further processing : 43
% 0.19/0.32 % Other redundant clauses eliminated : 6
% 0.19/0.32 % Clauses deleted for lack of memory : 0
% 0.19/0.32 % Backward-subsumed : 0
% 0.19/0.32 % Backward-rewritten : 2
% 0.19/0.32 % Generated clauses : 47
% 0.19/0.32 % ...of the previous two non-redundant : 29
% 0.19/0.32 % ...aggressively subsumed : 0
% 0.19/0.32 % Contextual simplify-reflections : 0
% 0.19/0.32 % Paramodulations : 41
% 0.19/0.32 % Factorizations : 0
% 0.19/0.32 % NegExts : 0
% 0.19/0.32 % Equation resolutions : 6
% 0.19/0.32 % Disequality decompositions : 0
% 0.19/0.32 % Total rewrite steps : 24
% 0.19/0.32 % ...of those cached : 8
% 0.19/0.32 % Propositional unsat checks : 0
% 0.19/0.32 % Propositional check models : 0
% 0.19/0.32 % Propositional check unsatisfiable : 0
% 0.19/0.32 % Propositional clauses : 0
% 0.19/0.32 % Propositional clauses after purity: 0
% 0.19/0.32 % Propositional unsat core size : 0
% 0.19/0.32 % Propositional preprocessing time : 0.000
% 0.19/0.32 % Propositional encoding time : 0.000
% 0.19/0.32 % Propositional solver time : 0.000
% 0.19/0.32 % Success case prop preproc time : 0.000
% 0.19/0.32 % Success case prop encoding time : 0.000
% 0.19/0.32 % Success case prop solver time : 0.000
% 0.19/0.32 % Current number of processed clauses : 35
% 0.19/0.32 % Positive orientable unit clauses : 24
% 0.19/0.32 % Positive unorientable unit clauses: 0
% 0.19/0.32 % Negative unit clauses : 2
% 0.19/0.32 % Non-unit-clauses : 9
% 0.19/0.32 % Current number of unprocessed clauses: 180
% 0.19/0.32 % ...number of literals in the above : 654
% 0.19/0.32 % Current number of archived formulas : 0
% 0.19/0.32 % Current number of archived clauses : 3
% 0.19/0.32 % Clause-clause subsumption calls (NU) : 18
% 0.19/0.32 % Rec. Clause-clause subsumption calls : 17
% 0.19/0.32 % Non-unit clause-clause subsumptions : 1
% 0.19/0.32 % Unit Clause-clause subsumption calls : 2
% 0.19/0.32 % Rewrite failures with RHS unbound : 0
% 0.19/0.32 % BW rewrite match attempts : 5
% 0.19/0.32 % BW rewrite match successes : 2
% 0.19/0.32 % Condensation attempts : 0
% 0.19/0.32 % Condensation successes : 0
% 0.19/0.32 % Termbank termtop insertions : 30058
% 0.19/0.32 % Search garbage collected termcells : 11435
% 0.19/0.32
% 0.19/0.32 % -------------------------------------------------
% 0.19/0.32 % User time : 0.023 s
% 0.19/0.32 % System time : 0.010 s
% 0.19/0.32 % Total time : 0.033 s
% 0.19/0.32 % Maximum resident set size: 6428 pages
% 0.19/0.32
% 0.19/0.32 % -------------------------------------------------
% 0.19/0.32 % User time : 0.032 s
% 0.19/0.32 % System time : 0.013 s
% 0.19/0.32 % Total time : 0.045 s
% 0.19/0.32 % Maximum resident set size: 5120 pages
% 0.19/0.32 % E exiting
%------------------------------------------------------------------------------