%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU591^1 : 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 : n010.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 08:26:50 AM UTC 2026
% Result : Theorem 0.23s 0.31s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU591^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n010.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 13:54:18 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running higher-order theorem proving
% 0.10/0.24 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p
% 0.23/0.31 % Version: 3.5.1-ho
% 0.23/0.31 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.23/0.31 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.31 % Starting ehoh_best5 with 300s (1) cores
% 0.23/0.31 % Starting almost_fo_3_lam with 300s (1) cores
% 0.23/0.31 % Starting new_bool_5 with 300s (1) cores
% 0.23/0.31 % Starting pre_casc_3 with 300s (1) cores
% 0.23/0.31 % Starting ho_unfolding_8 with 300s (1) cores
% 0.23/0.31 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.23/0.31 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.31 % Starting new_ho_5 with 300s (1) cores
% 0.23/0.31 % ho_unfolding_8 with pid 2897153 completed with status 0
% 0.23/0.31 % Result found by ho_unfolding_8
% 0.23/0.31 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.23/0.31 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.31 % Starting ehoh_best5 with 300s (1) cores
% 0.23/0.31 % Starting almost_fo_3_lam with 300s (1) cores
% 0.23/0.31 % Starting new_bool_5 with 300s (1) cores
% 0.23/0.31 % Starting pre_casc_3 with 300s (1) cores
% 0.23/0.31 % Starting ho_unfolding_8 with 300s (1) cores
% 0.23/0.31 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.31 % No SInE strategy applied
% 0.23/0.31 % Search class: HGHSM-FSLM31-MHFMMSBN
% 0.23/0.31 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.31 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.31 % SubtermCWHack with pid 2897160 completed with status 0
% 0.23/0.31 % Result found by SubtermCWHack
% 0.23/0.31 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.23/0.31 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.31 % Starting ehoh_best5 with 300s (1) cores
% 0.23/0.31 % Starting almost_fo_3_lam with 300s (1) cores
% 0.23/0.31 % Starting new_bool_5 with 300s (1) cores
% 0.23/0.31 % Starting pre_casc_3 with 300s (1) cores
% 0.23/0.31 % Starting ho_unfolding_8 with 300s (1) cores
% 0.23/0.31 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.31 % No SInE strategy applied
% 0.23/0.31 % Search class: HGHSM-FSLM31-MHFMMSBN
% 0.23/0.31 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.31 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.31 % Preprocessing time : 0.004 s
% 0.23/0.31
% 0.23/0.31 % Proof found!
% 0.23/0.31 % SZS status Theorem
% 0.23/0.31 % SZS output start CNFRefutation
% 0.23/0.31 thf(decl_23, type, in: $i > $i > $o).
% 0.23/0.31 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.23/0.31 thf(decl_25, type, setextAx: $o).
% 0.23/0.31 thf(decl_26, type, emptyset: $i).
% 0.23/0.31 thf(decl_27, type, emptysetAx: $o).
% 0.23/0.31 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.23/0.31 thf(decl_29, type, setadjoinAx: $o).
% 0.23/0.31 thf(decl_30, type, powerset: $i > $i).
% 0.23/0.31 thf(decl_31, type, powersetAx: $o).
% 0.23/0.31 thf(decl_32, type, setunion: $i > $i).
% 0.23/0.31 thf(decl_33, type, setunionAx: $o).
% 0.23/0.31 thf(decl_34, type, omega: $i).
% 0.23/0.31 thf(decl_35, type, omega0Ax: $o).
% 0.23/0.31 thf(decl_36, type, omegaSAx: $o).
% 0.23/0.31 thf(decl_37, type, omegaIndAx: $o).
% 0.23/0.31 thf(decl_38, type, replAx: $o).
% 0.23/0.31 thf(decl_39, type, foundationAx: $o).
% 0.23/0.31 thf(decl_40, type, wellorderingAx: $o).
% 0.23/0.31 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.23/0.31 thf(decl_42, type, descrp: $o).
% 0.23/0.31 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.23/0.31 thf(decl_44, type, dsetconstrI: $o).
% 0.23/0.31 thf(decl_45, type, dsetconstrEL: $o).
% 0.23/0.31 thf(decl_46, type, dsetconstrER: $o).
% 0.23/0.31 thf(decl_47, type, exuE1: $o).
% 0.23/0.31 thf(decl_48, type, prop2set: $o > $i).
% 0.23/0.31 thf(decl_49, type, prop2setE: $o).
% 0.23/0.31 thf(decl_50, type, emptysetE: $o).
% 0.23/0.31 thf(decl_51, type, emptysetimpfalse: $o).
% 0.23/0.31 thf(decl_52, type, notinemptyset: $o).
% 0.23/0.31 thf(decl_53, type, exuE3e: $o).
% 0.23/0.31 thf(decl_54, type, setext: $o).
% 0.23/0.31 thf(decl_55, type, emptyI: $o).
% 0.23/0.31 thf(decl_56, type, noeltsimpempty: $o).
% 0.23/0.31 thf(decl_57, type, setbeta: $o).
% 0.23/0.31 thf(decl_58, type, nonempty: $i > $o).
% 0.23/0.31 thf(decl_59, type, nonemptyE1: $o).
% 0.23/0.31 thf(decl_60, type, nonemptyI: $o).
% 0.23/0.31 thf(decl_61, type, nonemptyI1: $o).
% 0.23/0.31 thf(decl_62, type, setadjoinIL: $o).
% 0.23/0.31 thf(decl_63, type, emptyinunitempty: $o).
% 0.23/0.31 thf(decl_64, type, setadjoinIR: $o).
% 0.23/0.31 thf(decl_65, type, setadjoinE: $o).
% 0.23/0.31 thf(decl_66, type, setadjoinOr: $o).
% 0.23/0.31 thf(decl_67, type, setoftrueEq: $o).
% 0.23/0.31 thf(decl_68, type, powersetI: $o).
% 0.23/0.31 thf(decl_69, type, emptyinPowerset: $o).
% 0.23/0.31 thf(decl_70, type, emptyInPowerset: $o).
% 0.23/0.31 thf(decl_71, type, powersetE: $o).
% 0.23/0.31 thf(decl_72, type, setunionI: $o).
% 0.23/0.31 thf(decl_73, type, setunionE: $o).
% 0.23/0.31 thf(decl_74, type, subPowSU: $o).
% 0.23/0.31 thf(decl_75, type, exuE2: $o).
% 0.23/0.31 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.23/0.31 thf(decl_77, type, uniqinunit: $o).
% 0.23/0.31 thf(decl_78, type, notinsingleton: $o).
% 0.23/0.31 thf(decl_79, type, eqinunit: $o).
% 0.23/0.31 thf(decl_80, type, singletonsswitch: $o).
% 0.23/0.31 thf(decl_81, type, upairsetE: $o).
% 0.23/0.31 thf(decl_82, type, upairsetIL: $o).
% 0.23/0.31 thf(decl_83, type, upairsetIR: $o).
% 0.23/0.31 thf(decl_84, type, emptyE1: $o).
% 0.23/0.31 thf(decl_85, type, vacuousDall: $o).
% 0.23/0.31 thf(decl_86, type, quantDeMorgan1: $o).
% 0.23/0.31 thf(decl_87, type, quantDeMorgan2: $o).
% 0.23/0.31 thf(decl_88, type, quantDeMorgan3: $o).
% 0.23/0.31 thf(decl_89, type, quantDeMorgan4: $o).
% 0.23/0.31 thf(decl_90, type, prop2setI: $o).
% 0.23/0.31 thf(decl_91, type, set2prop: $i > $o).
% 0.23/0.31 thf(decl_92, type, prop2set2propI: $o).
% 0.23/0.31 thf(decl_93, type, notdexE: $o).
% 0.23/0.31 thf(decl_94, type, notdallE: $o).
% 0.23/0.31 thf(decl_95, type, exuI1: $o).
% 0.23/0.31 thf(decl_96, type, exuI3: $o).
% 0.23/0.31 thf(decl_97, type, exuI2: $o).
% 0.23/0.31 thf(decl_98, type, inCongP: $o).
% 0.23/0.31 thf(decl_99, type, in__Cong: $o).
% 0.23/0.31 thf(decl_100, type, exuE3u: $o).
% 0.23/0.31 thf(decl_101, type, exu__Cong: $o).
% 0.23/0.31 thf(decl_102, type, emptyset__Cong: $o).
% 0.23/0.31 thf(decl_103, type, setadjoin__Cong: $o).
% 0.23/0.31 thf(decl_104, type, powerset__Cong: $o).
% 0.23/0.31 thf(decl_105, type, setunion__Cong: $o).
% 0.23/0.31 thf(decl_106, type, omega__Cong: $o).
% 0.23/0.31 thf(decl_107, type, exuEu: $o).
% 0.23/0.31 thf(decl_108, type, descr__Cong: $o).
% 0.23/0.31 thf(decl_109, type, dsetconstr__Cong: $o).
% 0.23/0.31 thf(decl_110, type, subset: $i > $i > $o).
% 0.23/0.31 thf(decl_113, type, subsetI1: $o).
% 0.23/0.31 thf(decl_114, type, eqimpsubset2: $o).
% 0.23/0.31 thf(decl_115, type, eqimpsubset1: $o).
% 0.23/0.31 thf(decl_116, type, subsetI2: $o).
% 0.23/0.31 thf(decl_117, type, emptysetsubset: $o).
% 0.23/0.31 thf(decl_118, type, subsetE: $o).
% 0.23/0.31 thf(decl_119, type, subsetE2: $o).
% 0.23/0.31 thf(decl_120, type, notsubsetI: $o).
% 0.23/0.31 thf(decl_121, type, notequalI1: $o).
% 0.23/0.31 thf(decl_122, type, notequalI2: $o).
% 0.23/0.31 thf(decl_123, type, subsetRefl: $o).
% 0.23/0.31 thf(decl_124, type, subsetTrans: $o).
% 0.23/0.31 thf(decl_125, type, setadjoinSub: $o).
% 0.23/0.31 thf(decl_126, type, setadjoinSub2: $o).
% 0.23/0.31 thf(decl_127, type, subset2powerset: $o).
% 0.23/0.31 thf(decl_128, type, setextsub: $o).
% 0.23/0.31 thf(decl_129, type, subsetemptysetimpeq: $o).
% 0.23/0.31 thf(decl_130, type, powersetI1: $o).
% 0.23/0.31 thf(decl_131, type, powersetE1: $o).
% 0.23/0.31 thf(decl_132, type, inPowerset: $o).
% 0.23/0.31 thf(decl_133, type, powersetsubset: $o).
% 0.23/0.31 thf(decl_134, type, sepInPowerset: $o).
% 0.23/0.31 thf(decl_135, type, sepSubset: $o).
% 0.23/0.31 thf(decl_136, type, binunion: $i > $i > $i).
% 0.23/0.31 thf(decl_137, type, binunionIL: $o).
% 0.23/0.31 thf(decl_138, type, upairset2IR: $o).
% 0.23/0.31 thf(decl_139, type, binunionIR: $o).
% 0.23/0.31 thf(decl_140, type, binunionEcases: $o).
% 0.23/0.31 thf(decl_141, type, binunionE: $o).
% 0.23/0.31 thf(decl_142, type, binunionLsub: $o).
% 0.23/0.31 thf(decl_143, type, binunionRsub: $o).
% 0.23/0.31 thf(decl_144, type, binintersect: $i > $i > $i).
% 0.23/0.31 thf(decl_145, type, binintersectI: $o).
% 0.23/0.31 thf(decl_146, type, binintersectSubset5: $o).
% 0.23/0.31 thf(decl_147, type, epred1_0: $o).
% 0.23/0.31 thf(decl_148, type, esk1_2: $i > $i > $i).
% 0.23/0.31 thf(decl_149, type, esk2_2: $i > $i > $i).
% 0.23/0.31 thf(decl_150, type, esk3_2: $i > $i > $i).
% 0.23/0.31 thf(decl_151, type, esk4_1: $i > $i).
% 0.23/0.31 thf(decl_152, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.23/0.31 thf(decl_153, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.23/0.31 thf(decl_154, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.23/0.31 thf(decl_155, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.23/0.31 thf(decl_156, type, esk9_1: $i > $i).
% 0.23/0.31 thf(decl_157, type, esk10_2: ($i > $o) > $i > $i).
% 0.23/0.31 thf(decl_158, type, esk11_2: ($i > $o) > $i > $i).
% 0.23/0.31 thf(decl_159, type, esk12_1: ($i > $o) > $i).
% 0.23/0.31 thf(decl_160, type, esk13_2: ($i > $o) > $i > $i).
% 0.23/0.31 thf(decl_161, type, esk14_1: ($i > $o) > $i).
% 0.23/0.31 thf(decl_162, type, esk15_2: $i > $i > $i).
% 0.23/0.31 thf(decl_163, type, esk16_2: $i > $i > $i).
% 0.23/0.31 thf(decl_164, type, esk17_1: $i > $i).
% 0.23/0.31 thf(decl_165, type, esk18_1: $i > $i).
% 0.23/0.31 thf(decl_166, type, esk19_1: $i > $i).
% 0.23/0.31 thf(decl_167, type, esk20_2: $i > $i > $i).
% 0.23/0.31 thf(decl_168, type, esk21_3: $i > $i > $o > $i).
% 0.23/0.31 thf(decl_169, type, esk22_2: ($i > $o) > $i > $i).
% 0.23/0.31 thf(decl_170, type, esk23_1: ($i > $o) > $i).
% 0.23/0.31 thf(decl_171, type, esk24_1: $i > $i).
% 0.23/0.31 thf(decl_172, type, esk25_2: $i > ($i > $o) > $i).
% 0.23/0.31 thf(decl_173, type, esk26_2: $i > ($i > $o) > $i).
% 0.23/0.31 thf(decl_174, type, esk27_2: $i > ($i > $o) > $i).
% 0.23/0.31 thf(decl_175, type, esk28_2: $i > ($i > $o) > $i).
% 0.23/0.31 thf(decl_176, type, esk29_2: $i > ($i > $o) > $i).
% 0.23/0.31 thf(decl_177, type, esk30_2: $i > ($i > $o) > $i).
% 0.23/0.31 thf(decl_178, type, esk31_2: ($i > $o) > $i > $i).
% 0.23/0.31 thf(decl_179, type, esk32_1: ($i > $o) > $i).
% 0.23/0.31 thf(decl_180, type, esk33_1: ($i > $o) > $i).
% 0.23/0.31 thf(decl_181, type, esk34_1: ($i > $o) > $i).
% 0.23/0.31 thf(decl_182, type, esk35_1: ($i > $o) > $i).
% 0.23/0.31 thf(decl_183, type, esk36_2: ($i > $o) > $i > $i).
% 0.23/0.31 thf(decl_184, type, esk37_1: ($i > $o) > $i).
% 0.23/0.31 thf(decl_185, type, esk38_2: ($i > $o) > $i > $i).
% 0.23/0.31 thf(decl_186, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 0.23/0.31 thf(decl_187, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 0.23/0.31 thf(decl_188, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.23/0.31 thf(decl_189, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 0.23/0.31 thf(decl_190, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.23/0.31 thf(decl_191, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 0.23/0.31 thf(decl_192, type, esk45_2: ($i > $o) > $i > $i).
% 0.23/0.31 thf(decl_193, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 0.23/0.31 thf(decl_194, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 0.23/0.31 thf(decl_195, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.23/0.31 thf(decl_196, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.23/0.31 thf(decl_197, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.23/0.31 thf(decl_198, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.23/0.31 thf(decl_199, type, esk52_2: $i > $i > $i).
% 0.23/0.31 thf(decl_200, type, esk53_2: $i > $i > $i).
% 0.23/0.31 thf(decl_201, type, esk54_0: $i).
% 0.23/0.31 thf(decl_202, type, esk55_0: $i).
% 0.23/0.31 thf(decl_203, type, esk56_0: $i).
% 0.23/0.31 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', replAx)).
% 0.23/0.31 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', exu)).
% 0.23/0.31 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', descrp)).
% 0.23/0.31 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', exuE1)).
% 0.23/0.31 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', exuE3e)).
% 0.23/0.31 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', nonempty)).
% 0.23/0.31 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', nonemptyI)).
% 0.23/0.31 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', exuE2)).
% 0.23/0.31 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.ztcc3Uqwbc/E---3.1_2897136.p', exuI1)).
% 0.23/0.31 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', exuI3)).
% 0.23/0.31 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', exuI2)).
% 0.23/0.31 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.ztcc3Uqwbc/E---3.1_2897136.p', exuE3u)).
% 0.23/0.31 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', exu__Cong)).
% 0.23/0.31 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', exuEu)).
% 0.23/0.31 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', descr__Cong)).
% 0.23/0.31 thf(binintersectEL, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', binintersectEL)).
% 0.23/0.31 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', dsetconstrI)).
% 0.23/0.31 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', dsetconstrEL)).
% 0.23/0.31 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', dsetconstrER)).
% 0.23/0.31 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', setbeta)).
% 0.23/0.31 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', nonemptyE1)).
% 0.23/0.31 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', nonemptyI1)).
% 0.23/0.31 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', setoftrueEq)).
% 0.23/0.31 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', nonemptyImpWitness)).
% 0.23/0.31 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.ztcc3Uqwbc/E---3.1_2897136.p', emptyE1)).
% 0.23/0.31 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', dsetconstr__Cong)).
% 0.23/0.31 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', sepInPowerset)).
% 0.23/0.31 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', sepSubset)).
% 0.23/0.31 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', setextAx)).
% 0.23/0.31 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', emptysetAx)).
% 0.23/0.31 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', setadjoinAx)).
% 0.23/0.31 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', powersetAx)).
% 0.23/0.31 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', setunionAx)).
% 0.23/0.31 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', omega0Ax)).
% 0.23/0.31 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', omegaSAx)).
% 0.23/0.31 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', omegaIndAx)).
% 0.23/0.31 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', foundationAx)).
% 0.23/0.31 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.ztcc3Uqwbc/E---3.1_2897136.p', wellorderingAx)).
% 0.23/0.31 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', prop2setE)).
% 0.23/0.31 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', emptysetE)).
% 0.23/0.31 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', emptysetimpfalse)).
% 0.23/0.31 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', notinemptyset)).
% 0.23/0.31 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', setext)).
% 0.23/0.31 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', emptyI)).
% 0.23/0.31 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', noeltsimpempty)).
% 0.23/0.31 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', setadjoinIL)).
% 0.23/0.31 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', emptyinunitempty)).
% 0.23/0.31 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', setadjoinIR)).
% 0.23/0.31 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.ztcc3Uqwbc/E---3.1_2897136.p', setadjoinE)).
% 0.23/0.31 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', setadjoinOr)).
% 0.23/0.31 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', powersetI)).
% 0.23/0.31 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', emptyinPowerset)).
% 0.23/0.31 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', emptyInPowerset)).
% 0.23/0.31 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', powersetE)).
% 0.23/0.31 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', setunionI)).
% 0.23/0.31 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.ztcc3Uqwbc/E---3.1_2897136.p', setunionE)).
% 0.23/0.31 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', subPowSU)).
% 0.23/0.31 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', uniqinunit)).
% 0.23/0.31 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', notinsingleton)).
% 0.23/0.31 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', eqinunit)).
% 0.23/0.31 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', singletonsswitch)).
% 0.23/0.31 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', upairsetE)).
% 0.23/0.31 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', upairsetIL)).
% 0.23/0.31 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', upairsetIR)).
% 0.23/0.31 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', vacuousDall)).
% 0.23/0.31 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', quantDeMorgan1)).
% 0.23/0.31 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', quantDeMorgan2)).
% 0.23/0.31 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', quantDeMorgan3)).
% 0.23/0.31 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', quantDeMorgan4)).
% 0.23/0.31 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', prop2setI)).
% 0.23/0.31 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', prop2set2propI)).
% 0.23/0.31 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', notdexE)).
% 0.23/0.31 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', notdallE)).
% 0.23/0.31 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', inCongP)).
% 0.23/0.31 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', in__Cong)).
% 0.23/0.31 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', emptyset__Cong)).
% 0.23/0.31 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', setadjoin__Cong)).
% 0.23/0.31 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', powerset__Cong)).
% 0.23/0.31 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', setunion__Cong)).
% 0.23/0.31 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', omega__Cong)).
% 0.23/0.31 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', subsetI1)).
% 0.23/0.31 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', eqimpsubset2)).
% 0.23/0.31 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', eqimpsubset1)).
% 0.23/0.31 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', subsetI2)).
% 0.23/0.31 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', emptysetsubset)).
% 0.23/0.31 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', subsetE)).
% 0.23/0.31 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', subsetE2)).
% 0.23/0.31 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', notsubsetI)).
% 0.23/0.31 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', notequalI1)).
% 0.23/0.31 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', notequalI2)).
% 0.23/0.31 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', subsetRefl)).
% 0.23/0.31 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', subsetTrans)).
% 0.23/0.31 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', setadjoinSub)).
% 0.23/0.31 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', setadjoinSub2)).
% 0.23/0.31 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', subset2powerset)).
% 0.23/0.31 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', setextsub)).
% 0.23/0.31 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', subsetemptysetimpeq)).
% 0.23/0.31 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', powersetI1)).
% 0.23/0.31 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', powersetE1)).
% 0.23/0.31 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', inPowerset)).
% 0.23/0.31 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', powersetsubset)).
% 0.23/0.31 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', binunionIL)).
% 0.23/0.31 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', upairset2IR)).
% 0.23/0.31 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', binunionIR)).
% 0.23/0.31 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', binunionEcases)).
% 0.23/0.31 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', binunionE)).
% 0.23/0.31 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', binunionLsub)).
% 0.23/0.31 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', binunionRsub)).
% 0.23/0.31 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', binintersectI)).
% 0.23/0.31 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', binintersectSubset5)).
% 0.23/0.31 thf(binintersect, axiom, ((binintersect)=(^[X4:$i, X5:$i]:(dsetconstr @ X4 @ (^[X2:$i]:((in @ X2 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ztcc3Uqwbc/E---3.1_2897136.p', binintersect)).
% 0.23/0.31 thf(c_0_111, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.23/0.31 thf(c_0_112, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.23/0.31 thf(c_0_113, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.23/0.31 thf(c_0_114, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.23/0.31 thf(c_0_115, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.23/0.31 thf(c_0_116, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.23/0.31 thf(c_0_117, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.23/0.31 thf(c_0_118, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.23/0.31 thf(c_0_119, 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])).
% 0.23/0.31 thf(c_0_120, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.23/0.31 thf(c_0_121, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.23/0.31 thf(c_0_122, 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])).
% 0.23/0.31 thf(c_0_123, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.23/0.31 thf(c_0_124, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 0.23/0.31 thf(c_0_125, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 0.23/0.31 thf(c_0_126, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[binintersectEL])).
% 0.23/0.31 thf(c_0_127, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X310:$i]:(((((X6 @ X2 @ X310)))&(![X311:$i]:(((((X6 @ X2 @ X311)))=>(((X310)=(X311)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_111, c_0_112])).
% 0.23/0.31 thf(c_0_128, plain, ((descrp)=(![X1:$i > $o]:((((?[X312:$i]:(((((X1 @ X312)))&(![X313:$i]:(((((X1 @ X313)))=>(((X312)=(X313))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_113, c_0_112])).
% 0.23/0.31 thf(c_0_129, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.23/0.31 thf(c_0_130, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.23/0.31 thf(c_0_131, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.23/0.31 thf(c_0_132, plain, ((exuE1)=(![X1:$i > $o]:((((?[X314:$i]:(((((X1 @ X314)))&(![X315:$i]:(((((X1 @ X315)))=>(((X314)=(X315))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_114, c_0_112])).
% 0.23/0.31 thf(c_0_133, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X316:$i]:(((((X1 @ X316)))&(![X317:$i]:(((((X1 @ X317)))=>(((X316)=(X317))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_115, c_0_112])).
% 0.23/0.31 thf(c_0_134, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.23/0.31 thf(c_0_135, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_116])).
% 0.23/0.31 thf(c_0_136, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_117, c_0_116])).
% 0.23/0.31 thf(c_0_137, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_116])).
% 0.23/0.31 thf(c_0_138, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.23/0.31 thf(c_0_139, plain, ((exuE2)=(![X1:$i > $o]:((((?[X318:$i]:(((((X1 @ X318)))&(![X319:$i]:(((((X1 @ X319)))=>(((X318)=(X319))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_118, c_0_112])).
% 0.23/0.31 thf(c_0_140, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_116])).
% 0.23/0.31 thf(c_0_141, 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])).
% 0.23/0.31 thf(c_0_142, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X320:$i]:(((((X1 @ X320)))&(![X321:$i]:(((((X1 @ X321)))=>(((X320)=(X321)))))))))))))), inference(apply_def,[status(thm)],[c_0_119, c_0_112])).
% 0.23/0.31 thf(c_0_143, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X322:$i]:(((((X1 @ X322)))&(![X323:$i]:(((((X1 @ X323)))=>(((X322)=(X323)))))))))))))))), inference(apply_def,[status(thm)],[c_0_120, c_0_112])).
% 0.23/0.31 thf(c_0_144, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X324:$i]:(((((X1 @ X324)))&(![X325:$i]:(((((X1 @ X325)))=>(((X324)=(X325)))))))))))))), inference(apply_def,[status(thm)],[c_0_121, c_0_112])).
% 0.23/0.31 thf(c_0_145, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X326:$i]:(((((X1 @ X326)))&(![X327:$i]:(((((X1 @ X327)))=>(((X326)=(X327))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_122, c_0_112])).
% 0.23/0.31 thf(c_0_146, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X328:$i]:(((((X1 @ X328)))&(![X329:$i]:(((((X1 @ X329)))=>(((X328)=(X329))))))))))<=>((?[X330:$i]:(((((X17 @ X330)))&(![X331:$i]:(((((X17 @ X331)))=>(((X330)=(X331)))))))))))))))), inference(apply_def,[status(thm)],[c_0_123, c_0_112])).
% 0.23/0.31 thf(c_0_147, plain, ((exuEu)=(![X1:$i > $o]:((((?[X332:$i]:(((((X1 @ X332)))&(![X333:$i]:(((((X1 @ X333)))=>(((X332)=(X333))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_124, c_0_112])).
% 0.23/0.31 thf(c_0_148, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X334:$i]:(((((X1 @ X334)))&(![X335:$i]:(((((X1 @ X335)))=>(((X334)=(X335))))))))))=>((((?[X336:$i]:(((((X17 @ X336)))&(![X337:$i]:(((((X17 @ X337)))=>(((X336)=(X337))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_125, c_0_112])).
% 0.23/0.31 thf(c_0_149, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 0.23/0.31 thf(c_0_150, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 0.23/0.31 thf(c_0_151, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 0.23/0.31 thf(c_0_152, plain, ((epred1_0)<=>![X367:$i]:(?[X368:$i]:((((![X369:$i]:(((in @ X369 @ X368)=>![X370:$i]:(((in @ X370 @ X369)=>(in @ X370 @ X367)))))&![X371:$i, X372:$i]:((((in @ X371 @ X367)&(in @ X372 @ X367))=>(![X373:$i]:(((in @ X373 @ X368)=>((in @ X371 @ X373)<=>(in @ X372 @ X373))))=>((X371)=(X372))))))&![X374:$i, X375:$i]:((((in @ X374 @ X368)&(in @ X375 @ X368))=>(![X376:$i]:(((in @ X376 @ X374)=>(in @ X376 @ X375)))|![X377:$i]:(((in @ X377 @ X375)=>(in @ X377 @ X374)))))))&![X378:$i]:(((![X379:$i]:(((in @ X379 @ X378)=>(in @ X379 @ X367)))&?[X380:$i]:((in @ X380 @ X378)))=>?[X381:$i, X382:$i]:(((((in @ X381 @ X368)&(in @ X382 @ X378))&~(?[X383:$i]:(((in @ X383 @ X381)&(in @ X383 @ X378)))))&![X384:$i]:(((in @ X384 @ X368)=>(![X385:$i]:(((in @ X385 @ X384)=>(in @ X385 @ X381)))|(in @ X382 @ X384)))))))))))), introduced(definition)).
% 0.23/0.31 thf(c_0_153, negated_conjecture, ~((![X338:$i, X339:$i]:((![X340:$i]:(((in @ X340 @ X338)<=>(in @ X340 @ X339)))=>((X338)=(X339))))=>(![X341:$i]:(~(in @ X341 @ emptyset))=>(![X342:$i, X343:$i, X344:$i]:(((in @ X344 @ (setadjoin @ X342 @ X343))<=>(((X344)=(X342))|(in @ X344 @ X343))))=>(![X345:$i, X346:$i]:(((in @ X346 @ (powerset @ X345))<=>![X347:$i]:(((in @ X347 @ X346)=>(in @ X347 @ X345)))))=>(![X348:$i, X349:$i]:(((in @ X349 @ (setunion @ X348))<=>?[X350:$i]:(((in @ X349 @ X350)&(in @ X350 @ X348)))))=>((in @ emptyset @ omega)=>(![X351:$i]:(((in @ X351 @ omega)=>(in @ (setadjoin @ X351 @ X351) @ omega)))=>(![X352:$i]:((((in @ emptyset @ X352)&![X353:$i]:((((in @ X353 @ omega)&(in @ X353 @ X352))=>(in @ (setadjoin @ X353 @ X353) @ X352))))=>![X354:$i]:(((in @ X354 @ omega)=>(in @ X354 @ X352)))))=>(![X355:$i > $i > $o, X356:$i]:((![X357:$i]:(((in @ X357 @ X356)=>?[X358:$i]:(((X355 @ X357 @ X358)&![X359:$i]:(((X355 @ X357 @ X359)=>((X358)=(X359))))))))=>?[X360:$i]:(![X361:$i]:(((in @ X361 @ X360)<=>?[X362:$i]:(((in @ X362 @ X356)&(X355 @ X362 @ X361))))))))=>(![X363:$i]:((?[X364:$i]:((in @ X364 @ X363))=>?[X365:$i]:(((in @ X365 @ X363)&~(?[X366:$i]:(((in @ X366 @ X365)&(in @ X366 @ X363))))))))=>((epred1_0)=>(![X386:$i > $o]:((?[X387:$i]:(((X386 @ X387)&![X388:$i]:(((X386 @ X388)=>((X387)=(X388))))))=>(X386 @ (descr @ (^[Z0:$i]:(X386 @ Z0))))))=>(![X389:$i, X390:$i > $o, X391:$i]:(((in @ X391 @ X389)=>((X390 @ X391)=>(in @ X391 @ (dsetconstr @ X389 @ X390)))))=>(![X392:$i, X393:$i > $o, X394:$i]:(((in @ X394 @ (dsetconstr @ X392 @ X393))=>(in @ X394 @ X392)))=>(![X395:$i, X396:$i > $o, X397:$i]:(((in @ X397 @ (dsetconstr @ X395 @ X396))=>(X396 @ X397)))=>(![X398:$i > $o]:((?[X399:$i]:(((X398 @ X399)&![X400:$i]:(((X398 @ X400)=>((X399)=(X400))))))=>?[X401:$i]:(((X398 @ X401)&![X402:$i]:(((X398 @ X402)=>((X401)=(X402))))))))=>(![X403:$o, X404:$i]:(((in @ X404 @ (prop2set @ ((X403))))=>(X403)))=>(![X405:$i]:(((in @ X405 @ emptyset)=>![X406:$o]:((X406))))=>(![X407:$i]:(((in @ X407 @ emptyset)=>~($true)))=>(![X408:$i]:(~(in @ X408 @ emptyset))=>(![X409:$i > $o]:((?[X410:$i]:(((X409 @ X410)&![X411:$i]:(((X409 @ X411)=>((X410)=(X411))))))=>?[X412:$i]:((X409 @ X412))))=>(![X413:$i, X414:$i]:((![X415:$i]:(((in @ X415 @ X413)=>(in @ X415 @ X414)))=>(![X416:$i]:(((in @ X416 @ X414)=>(in @ X416 @ X413)))=>((X413)=(X414)))))=>(![X417:$i]:((![X418:$i]:(~(in @ X418 @ X417))=>((X417)=(emptyset))))=>(![X419:$i]:((![X420:$i]:(~(in @ X420 @ X419))=>((X419)=(emptyset))))=>(![X421:$i, X422:$i > $o, X423:$i]:(((in @ X423 @ X421)=>((in @ X423 @ (dsetconstr @ X421 @ X422))<=>(X422 @ X423))))=>(![X424:$i]:((((X424)!=(emptyset))=>?[X425:$i]:((in @ X425 @ X424))))=>(![X426:$i, X427:$i > $o, X428:$i]:(((in @ X428 @ X426)=>((X427 @ X428)=>((dsetconstr @ X426 @ X427)!=(emptyset)))))=>(![X429:$i]:((?[X430:$i]:((in @ X430 @ X429))=>((X429)!=(emptyset))))=>(![X431:$i, X432:$i]:((in @ X431 @ (setadjoin @ X431 @ X432)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X433:$i, X434:$i, X435:$i]:(((in @ X435 @ X434)=>(in @ X435 @ (setadjoin @ X433 @ X434))))=>(![X436:$i, X437:$i, X438:$i]:(((in @ X438 @ (setadjoin @ X436 @ X437))=>![X439:$o]:(((((X438)=(X436))=>(X439))=>(((in @ X438 @ X437)=>(X439))=>(X439))))))=>(![X440:$i, X441:$i, X442:$i]:(((in @ X442 @ (setadjoin @ X440 @ X441))=>(((X442)=(X440))|(in @ X442 @ X441))))=>(![X443:$i]:(((dsetconstr @ X443 @ (^[Z0:$i]:($true)))=(X443)))=>(![X444:$i, X445:$i]:((![X446:$i]:(((in @ X446 @ X445)=>(in @ X446 @ X444)))=>(in @ X445 @ (powerset @ X444))))=>(![X447:$i]:((in @ emptyset @ (powerset @ X447)))=>(![X448:$i]:((in @ emptyset @ (powerset @ X448)))=>(![X449:$i, X450:$i, X451:$i]:(((in @ X450 @ (powerset @ X449))=>((in @ X451 @ X450)=>(in @ X451 @ X449))))=>(![X452:$i, X453:$i, X454:$i]:(((in @ X453 @ X454)=>((in @ X454 @ X452)=>(in @ X453 @ (setunion @ X452)))))=>(![X455:$i, X456:$i]:(((in @ X456 @ (setunion @ X455))=>![X457:$o]:((![X458:$i]:(((in @ X456 @ X458)=>((in @ X458 @ X455)=>(X457))))=>(X457)))))=>(![X459:$i, X460:$i]:(((in @ X460 @ X459)=>(in @ X460 @ (powerset @ (setunion @ X459)))))=>(![X461:$i > $o]:((?[X462:$i]:(((X461 @ X462)&![X463:$i]:(((X461 @ X463)=>((X462)=(X463))))))=>?[X464:$i]:(![X465:$i]:(((X461 @ X465)<=>((X465)=(X464)))))))=>(![X466:$i]:((((X466)!=(emptyset))=>?[X467:$i]:(((in @ X467 @ X466)&$true))))=>(![X468:$i, X469:$i]:(((in @ X468 @ (setadjoin @ X469 @ emptyset))=>((X468)=(X469))))=>(![X470:$i, X471:$i]:((((X470)!=(X471))=>~(in @ X471 @ (setadjoin @ X470 @ emptyset))))=>(![X472:$i, X473:$i]:((((X472)=(X473))=>(in @ X472 @ (setadjoin @ X473 @ emptyset))))=>(![X474:$i, X475:$i]:(((in @ X474 @ (setadjoin @ X475 @ emptyset))=>(in @ X475 @ (setadjoin @ X474 @ emptyset))))=>(![X476:$i, X477:$i, X478:$i]:(((in @ X478 @ (setadjoin @ X476 @ (setadjoin @ X477 @ emptyset)))=>(((X478)=(X476))|((X478)=(X477)))))=>(![X479:$i, X480:$i]:((in @ X479 @ (setadjoin @ X479 @ (setadjoin @ X480 @ emptyset))))=>(![X481:$i, X482:$i]:((in @ X482 @ (setadjoin @ X481 @ (setadjoin @ X482 @ emptyset))))=>(![X483:$i, X484:$i > $o]:((?[X485:$i]:(((in @ X485 @ X483)&(X484 @ X485)))=>(((dsetconstr @ X483 @ X484)=(emptyset))=>~($true))))=>(![X486:$i > $o, X487:$i]:(((in @ X487 @ emptyset)=>(X486 @ X487)))=>(![X488:$i, X489:$i > $o]:((~(![X490:$i]:(((in @ X490 @ X488)=>(X489 @ X490))))=>?[X491:$i]:(((in @ X491 @ X488)&~((X489 @ X491))))))=>(![X492:$i, X493:$i > $o]:((![X494:$i]:(((in @ X494 @ X492)=>~((X493 @ X494))))=>~(?[X495:$i]:(((in @ X495 @ X492)&(X493 @ X495))))))=>(![X496:$i, X497:$i > $o]:((~(?[X498:$i]:(((in @ X498 @ X496)&(X497 @ X498))))=>![X499:$i]:(((in @ X499 @ X496)=>~((X497 @ X499))))))=>(![X500:$i, X501:$i > $o]:((?[X502:$i]:(((in @ X502 @ X500)&~((X501 @ X502))))=>~(![X503:$i]:(((in @ X503 @ X500)=>(X501 @ X503))))))=>(![X504:$o]:(((X504)=>(in @ emptyset @ (prop2set @ ((X504))))))=>(![X505:$o]:(((X505)=>(set2prop @ (prop2set @ ((X505))))))=>(![X506:$i, X507:$i > $o]:((~(?[X508:$i]:(((in @ X508 @ X506)&(X507 @ X508))))=>![X509:$i]:(((in @ X509 @ X506)=>~((X507 @ X509))))))=>(![X510:$i, X511:$i > $o]:((~(![X512:$i]:(((in @ X512 @ X510)=>(X511 @ X512))))=>?[X513:$i]:(((in @ X513 @ X510)&~((X511 @ X513))))))=>(![X514:$i > $o]:((?[X515:$i]:(((X514 @ X515)&![X516:$i]:(((X514 @ X516)=>((X515)=(X516))))))=>?[X517:$i]:(((X514 @ X517)&![X518:$i]:(((X514 @ X518)=>((X517)=(X518))))))))=>(![X519:$i > $o]:((?[X520:$i]:((X519 @ X520))=>(![X521:$i, X522:$i]:(((X519 @ X521)=>((X519 @ X522)=>((X521)=(X522)))))=>?[X523:$i]:(((X519 @ X523)&![X524:$i]:(((X519 @ X524)=>((X523)=(X524)))))))))=>(![X525:$i > $o]:((?[X526:$i]:(![X527:$i]:(((X525 @ X527)<=>((X527)=(X526)))))=>?[X528:$i]:(((X525 @ X528)&![X529:$i]:(((X525 @ X529)=>((X528)=(X529))))))))=>(![X530:$i, X531:$i]:((((X530)=(X531))=>![X532:$i, X533:$i]:((((X532)=(X533))=>((in @ X532 @ X530)=>(in @ X533 @ X531))))))=>(![X534:$i, X535:$i]:((((X534)=(X535))=>![X536:$i, X537:$i]:((((X536)=(X537))=>((in @ X536 @ X534)<=>(in @ X537 @ X535))))))=>(![X538:$i > $o]:((?[X539:$i]:(((X538 @ X539)&![X540:$i]:(((X538 @ X540)=>((X539)=(X540))))))=>![X541:$i, X542:$i]:(((X538 @ X541)=>((X538 @ X542)=>((X541)=(X542)))))))=>(![X543:$i > $o, X544:$i > $o]:((![X545:$i, X546:$i]:((((X545)=(X546))=>((X543 @ X545)<=>(X544 @ X546))))=>(?[X547:$i]:(((X543 @ X547)&![X548:$i]:(((X543 @ X548)=>((X547)=(X548))))))<=>?[X549:$i]:(((X544 @ X549)&![X550:$i]:(((X544 @ X550)=>((X549)=(X550)))))))))=>(((emptyset)=(emptyset))=>(![X551:$i, X552:$i]:((((X551)=(X552))=>![X553:$i, X554:$i]:((((X553)=(X554))=>((setadjoin @ X551 @ X553)=(setadjoin @ X552 @ X554))))))=>(![X555:$i, X556:$i]:((((X555)=(X556))=>((powerset @ X555)=(powerset @ X556))))=>(![X557:$i, X558:$i]:((((X557)=(X558))=>((setunion @ X557)=(setunion @ X558))))=>(((omega)=(omega))=>(![X559:$i > $o]:((?[X560:$i]:(((X559 @ X560)&![X561:$i]:(((X559 @ X561)=>((X560)=(X561))))))=>![X562:$i, X563:$i]:(((X559 @ X562)=>((X559 @ X563)=>((X562)=(X563)))))))=>(![X564:$i > $o, X565:$i > $o]:((![X566:$i, X567:$i]:((((X566)=(X567))=>((X564 @ X566)<=>(X565 @ X567))))=>(?[X568:$i]:(((X564 @ X568)&![X569:$i]:(((X564 @ X569)=>((X568)=(X569))))))=>(?[X570:$i]:(((X565 @ X570)&![X571:$i]:(((X565 @ X571)=>((X570)=(X571))))))=>((descr @ X564)=(descr @ X565))))))=>(![X572:$i, X573:$i]:((((X572)=(X573))=>![X574:$i > $o, X575:$i > $o]:((![X576:$i]:(((in @ X576 @ X572)=>![X577:$i]:(((in @ X577 @ X573)=>(((X576)=(X577))=>((X574 @ X576)<=>(X575 @ X577)))))))=>((dsetconstr @ X572 @ X574)=(dsetconstr @ X573 @ X575))))))=>(![X578:$i, X579:$i]:((![X580:$i]:(((in @ X580 @ X578)=>(in @ X580 @ X579)))=>(subset @ X578 @ X579)))=>(![X581:$i, X582:$i]:((((X581)=(X582))=>(subset @ X582 @ X581)))=>(![X583:$i, X584:$i]:((((X583)=(X584))=>(subset @ X583 @ X584)))=>(![X585:$i, X586:$i]:((![X587:$i]:(((in @ X587 @ X585)=>(in @ X587 @ X586)))=>(subset @ X585 @ X586)))=>(![X588:$i]:((subset @ emptyset @ X588))=>(![X589:$i, X590:$i, X591:$i]:(((subset @ X589 @ X590)=>((in @ X591 @ X589)=>(in @ X591 @ X590))))=>(![X592:$i, X593:$i, X594:$i]:(((subset @ X592 @ X593)=>(~(in @ X594 @ X593)=>~(in @ X594 @ X592))))=>(![X595:$i, X596:$i, X597:$i]:(((in @ X597 @ X595)=>(~(in @ X597 @ X596)=>~(subset @ X595 @ X596))))=>(![X598:$i, X599:$i]:((~(subset @ X598 @ X599)=>((X598)!=(X599))))=>(![X600:$i, X601:$i, X602:$i]:(((in @ X602 @ X600)=>(~(in @ X602 @ X601)=>((X600)!=(X601)))))=>(![X603:$i]:((subset @ X603 @ X603))=>(![X604:$i, X605:$i, X606:$i]:(((subset @ X604 @ X605)=>((subset @ X605 @ X606)=>(subset @ X604 @ X606))))=>(![X607:$i, X608:$i]:((subset @ X608 @ (setadjoin @ X607 @ X608)))=>(![X609:$i, X610:$i, X611:$i]:(((subset @ X609 @ X611)=>(subset @ X609 @ (setadjoin @ X610 @ X611))))=>(![X612:$i, X613:$i]:(((subset @ X612 @ X613)=>(in @ X612 @ (powerset @ X613))))=>(![X614:$i, X615:$i]:(((subset @ X614 @ X615)=>((subset @ X615 @ X614)=>((X614)=(X615)))))=>(![X616:$i]:(((subset @ X616 @ emptyset)=>((X616)=(emptyset))))=>(![X617:$i, X618:$i]:(((subset @ X618 @ X617)=>(in @ X618 @ (powerset @ X617))))=>(![X619:$i, X620:$i]:(((in @ X620 @ (powerset @ X619))=>(subset @ X620 @ X619)))=>(![X621:$i]:((in @ X621 @ (powerset @ X621)))=>(![X622:$i, X623:$i]:(((subset @ X622 @ X623)=>(subset @ (powerset @ X622) @ (powerset @ X623))))=>(![X624:$i, X625:$i > $o]:((in @ (dsetconstr @ X624 @ X625) @ (powerset @ X624)))=>(![X626:$i, X627:$i > $o]:((subset @ (dsetconstr @ X626 @ X627) @ X626))=>(![X628:$i, X629:$i, X630:$i]:(((in @ X630 @ X628)=>(in @ X630 @ (binunion @ X628 @ X629))))=>(![X631:$i, X632:$i]:((in @ X632 @ (setadjoin @ X631 @ (setadjoin @ X632 @ emptyset))))=>(![X633:$i, X634:$i, X635:$i]:(((in @ X635 @ X634)=>(in @ X635 @ (binunion @ X633 @ X634))))=>(![X636:$i, X637:$i, X638:$i, X639:$o]:(((in @ X638 @ (binunion @ X636 @ X637))=>(((in @ X638 @ X636)=>(X639))=>(((in @ X638 @ X637)=>(X639))=>(X639)))))=>(![X640:$i, X641:$i, X642:$i]:(((in @ X642 @ (binunion @ X640 @ X641))=>((in @ X642 @ X640)|(in @ X642 @ X641))))=>(![X643:$i, X644:$i]:((subset @ X643 @ (binunion @ X643 @ X644)))=>(![X645:$i, X646:$i]:((subset @ X646 @ (binunion @ X645 @ X646)))=>(![X647:$i, X648:$i, X649:$i]:(((in @ X649 @ X647)=>((in @ X649 @ X648)=>(in @ X649 @ (binintersect @ X647 @ X648)))))=>(![X650:$i, X651:$i, X652:$i]:(((subset @ X652 @ X650)=>((subset @ X652 @ X651)=>(subset @ X652 @ (binintersect @ X650 @ X651)))))=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ 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)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(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_126, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_127]), foundationAx]), wellorderingAx]), c_0_128]), c_0_129]), c_0_130]), c_0_131]), c_0_132]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_133]), setext]), emptyI]), noeltsimpempty]), c_0_134]), c_0_135]), c_0_136]), c_0_137]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_138]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_139]), c_0_140]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_141]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_142]), c_0_143]), c_0_144]), inCongP]), in__Cong]), c_0_145]), c_0_146]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_147]), c_0_148]), c_0_149]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_150]), c_0_151]), binunionIL]), upairset2IR]), binunionIR]), binunionEcases]), binunionE]), binunionLsub]), binunionRsub]), binintersectI]), binintersectSubset5])])]), c_0_152])).
% 0.23/0.31 thf(c_0_154, plain, ![X653:$i, X654:$i]:(((binintersect @ X653 @ X654)=(dsetconstr @ X653 @ (^[Z0:$i]:((in @ Z0 @ X654)))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[binintersect])])).
% 0.23/0.31 thf(c_0_155, negated_conjecture, ![X657:$i, X658:$i, X660:$i, X661:$i, X662:$i, X663:$i, X664:$i, X665:$i, X666:$i, X667:$i, X668:$i, X670:$i, X671:$i, X673:$i, X674:$i, X675:$i, X676:$i, X677:$i, X679:$i, X680:$i > $i > $o, X681:$i, X683:$i, X686:$i, X688:$i, X689:$i, X690:$i, X691:$i, X693:$i, X694:$i > $o, X695:$i, X697:$i, X698:$i > $o, X699:$i, X700:$i, X701:$i > $o, X702:$i, X703:$i, X704:$i > $o, X705:$i, X706:$i > $o, X707:$i, X710:$i, X711:$o, X712:$i, X713:$i, X714:$o, X715:$i, X716:$i, X717:$i > $o, X718:$i, X721:$i, X722:$i, X725:$i, X727:$i, X729:$i, X730:$i > $o, X731:$i, X732:$i, X734:$i, X735:$i > $o, X736:$i, X737:$i, X738:$i, X739:$i, X740:$i, X741:$i, X742:$i, X743:$i, X744:$i, X745:$i, X746:$i, X747:$o, X748:$i, X749:$i, X750:$i, X751:$i, X752:$i, X753:$i, X755:$i, X756:$i, X757:$i, X758:$i, X759:$i, X760:$i, X761:$i, X762:$i, X763:$i, X764:$i, X765:$o, X767:$i, X768:$i, X769:$i > $o, X770:$i, X773:$i, X774:$i, X775:$i, X777:$i, X778:$i, X779:$i, X780:$i, X781:$i, X782:$i, X783:$i, X784:$i, X785:$i, X786:$i, X787:$i, X788:$i, X789:$i, X790:$i, X791:$i, X792:$i, X793:$i > $o, X794:$i, X795:$i > $o, X796:$i, X797:$i, X798:$i > $o, X799:$i, X801:$i, X802:$i > $o, X804:$i, X805:$i, X806:$i > $o, X808:$i, X809:$i, X810:$i > $o, X811:$i, X813:$o, X814:$o, X815:$i, X816:$i > $o, X818:$i, X819:$i, X820:$i > $o, X821:$i, X823:$i > $o, X824:$i, X827:$i, X828:$i > $o, X829:$i, X833:$i, X834:$i > $o, X835:$i, X838:$i, X839:$i, X840:$i, X841:$i, X842:$i, X843:$i, X844:$i, X845:$i, X846:$i, X847:$i > $o, X848:$i, X850:$i, X851:$i, X852:$i > $o, X853:$i > $o, X856:$i, X859:$i, X860:$i, X863:$i, X864:$i, X865:$i, X866:$i, X867:$i, X868:$i, X869:$i, X870:$i, X871:$i, X872:$i > $o, X873:$i, X875:$i, X876:$i, X877:$i > $o, X878:$i > $o, X881:$i, X883:$i, X885:$i, X886:$i, X887:$i > $o, X888:$i > $o, X891:$i, X892:$i, X894:$i, X895:$i, X896:$i, X897:$i, X898:$i, X899:$i, X901:$i, X902:$i, X903:$i, X904:$i, X905:$i, X906:$i, X907:$i, X908:$i, X909:$i, X910:$i, X911:$i, X912:$i, X913:$i, X914:$i, X915:$i, X916:$i, X917:$i, X918:$i, X919:$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 > $o, X939:$i, X940:$i > $o, X941:$i, X942:$i, X943:$i, X944:$i, X945:$i, X946:$i, X947:$i, X948:$i, X949:$i, X950:$i, X951:$i, X952:$o, X953:$i, X954:$i, X955:$i, X956:$i, X957:$i, X958:$i, X959:$i, X960:$i, X961:$i, X962:$i, X963:$i, X964:$i, X965:$i]:((((~(in @ (esk1_2 @ X657 @ X658) @ X657)|~(in @ (esk1_2 @ X657 @ X658) @ X658)|((X657)=(X658)))&((in @ (esk1_2 @ X657 @ X658) @ X657)|(in @ (esk1_2 @ X657 @ X658) @ X658)|((X657)=(X658))))&(~(in @ X660 @ emptyset)&(((~(in @ X663 @ (setadjoin @ X661 @ X662))|(((X663)=(X661))|(in @ X663 @ X662)))&((((X663)!=(X661))|(in @ X663 @ (setadjoin @ X661 @ X662)))&(~(in @ X663 @ X662)|(in @ X663 @ (setadjoin @ X661 @ X662)))))&(((~(in @ X665 @ (powerset @ X664))|(~(in @ X666 @ X665)|(in @ X666 @ X664)))&(((in @ (esk2_2 @ X667 @ X668) @ X668)|(in @ X668 @ (powerset @ X667)))&(~(in @ (esk2_2 @ X667 @ X668) @ X667)|(in @ X668 @ (powerset @ X667)))))&(((((in @ X671 @ (esk3_2 @ X670 @ X671))|~(in @ X671 @ (setunion @ X670)))&((in @ (esk3_2 @ X670 @ X671) @ X670)|~(in @ X671 @ (setunion @ X670))))&(~(in @ X674 @ X675)|~(in @ X675 @ X673)|(in @ X674 @ (setunion @ X673))))&((in @ emptyset @ omega)&((~(in @ X676 @ omega)|(in @ (setadjoin @ X676 @ X676) @ omega))&(((((in @ (esk4_1 @ X677) @ omega)|~(in @ emptyset @ X677)|(~(in @ X679 @ omega)|(in @ X679 @ X677)))&((in @ (esk4_1 @ X677) @ X677)|~(in @ emptyset @ X677)|(~(in @ X679 @ omega)|(in @ X679 @ X677))))&(~(in @ (setadjoin @ (esk4_1 @ X677) @ (esk4_1 @ X677)) @ X677)|~(in @ emptyset @ X677)|(~(in @ X679 @ omega)|(in @ X679 @ X677))))&((((((in @ (esk8_3 @ X680 @ X681 @ X686) @ X681)|~(in @ X686 @ (esk7_2 @ X680 @ X681))|(in @ (esk5_2 @ X680 @ X681) @ X681))&((X680 @ (esk8_3 @ X680 @ X681 @ X686) @ X686)|~(in @ X686 @ (esk7_2 @ X680 @ X681))|(in @ (esk5_2 @ X680 @ X681) @ X681)))&(~(in @ X689 @ X681)|~(X680 @ X689 @ X688)|(in @ X688 @ (esk7_2 @ X680 @ X681))|(in @ (esk5_2 @ X680 @ X681) @ X681)))&(((((in @ (esk8_3 @ X680 @ X681 @ X686) @ X681)|~(in @ X686 @ (esk7_2 @ X680 @ X681))|((X680 @ (esk5_2 @ X680 @ X681) @ (esk6_3 @ X680 @ X681 @ X683))|~(X680 @ (esk5_2 @ X680 @ X681) @ X683)))&((X680 @ (esk8_3 @ X680 @ X681 @ X686) @ X686)|~(in @ X686 @ (esk7_2 @ X680 @ X681))|((X680 @ (esk5_2 @ X680 @ X681) @ (esk6_3 @ X680 @ X681 @ X683))|~(X680 @ (esk5_2 @ X680 @ X681) @ X683))))&(~(in @ X689 @ X681)|~(X680 @ X689 @ X688)|(in @ X688 @ (esk7_2 @ X680 @ X681))|((X680 @ (esk5_2 @ X680 @ X681) @ (esk6_3 @ X680 @ X681 @ X683))|~(X680 @ (esk5_2 @ X680 @ X681) @ X683))))&((((in @ (esk8_3 @ X680 @ X681 @ X686) @ X681)|~(in @ X686 @ (esk7_2 @ X680 @ X681))|(((X683)!=(esk6_3 @ X680 @ X681 @ X683))|~(X680 @ (esk5_2 @ X680 @ X681) @ X683)))&((X680 @ (esk8_3 @ X680 @ X681 @ X686) @ X686)|~(in @ X686 @ (esk7_2 @ X680 @ X681))|(((X683)!=(esk6_3 @ X680 @ X681 @ X683))|~(X680 @ (esk5_2 @ X680 @ X681) @ X683))))&(~(in @ X689 @ X681)|~(X680 @ X689 @ X688)|(in @ X688 @ (esk7_2 @ X680 @ X681))|(((X683)!=(esk6_3 @ X680 @ X681 @ X683))|~(X680 @ (esk5_2 @ X680 @ X681) @ X683))))))&((((in @ (esk9_1 @ X690) @ X690)|~(in @ X691 @ X690))&(~(in @ X693 @ (esk9_1 @ X690))|~(in @ X693 @ X690)|~(in @ X691 @ X690)))&((epred1_0)&((((X694 @ (esk10_2 @ X694 @ X695))|~(X694 @ X695)|(X694 @ (descr @ X694)))&(((X695)!=(esk10_2 @ X694 @ X695))|~(X694 @ X695)|(X694 @ (descr @ X694))))&((~(in @ X699 @ X697)|(~(X698 @ X699)|(in @ X699 @ (dsetconstr @ X697 @ X698))))&((~(in @ X702 @ (dsetconstr @ X700 @ X701))|(in @ X702 @ X700))&((~(in @ X705 @ (dsetconstr @ X703 @ X704))|(X704 @ X705))&(((((X706 @ (esk12_1 @ X706))|((X706 @ (esk11_2 @ X706 @ X707))|~(X706 @ X707)))&(~(X706 @ X710)|((esk12_1 @ X706)=(X710))|((X706 @ (esk11_2 @ X706 @ X707))|~(X706 @ X707))))&(((X706 @ (esk12_1 @ X706))|(((X707)!=(esk11_2 @ X706 @ X707))|~(X706 @ X707)))&(~(X706 @ X710)|((esk12_1 @ X706)=(X710))|(((X707)!=(esk11_2 @ X706 @ X707))|~(X706 @ X707)))))&((~(in @ X712 @ (prop2set @ ((X711))))|(X711))&((~(in @ X713 @ emptyset)|(X714))&((~(in @ X715 @ emptyset)|~($true))&(~(in @ X716 @ emptyset)&((((X717 @ (esk13_2 @ X717 @ X718))|~(X717 @ X718)|(X717 @ (esk14_1 @ X717)))&(((X718)!=(esk13_2 @ X717 @ X718))|~(X717 @ X718)|(X717 @ (esk14_1 @ X717))))&(((((in @ (esk16_2 @ X721 @ X722) @ X722)|((X721)=(X722))|(in @ (esk15_2 @ X721 @ X722) @ X721))&(~(in @ (esk16_2 @ X721 @ X722) @ X721)|((X721)=(X722))|(in @ (esk15_2 @ X721 @ X722) @ X721)))&(((in @ (esk16_2 @ X721 @ X722) @ X722)|((X721)=(X722))|~(in @ (esk15_2 @ X721 @ X722) @ X722))&(~(in @ (esk16_2 @ X721 @ X722) @ X721)|((X721)=(X722))|~(in @ (esk15_2 @ X721 @ X722) @ X722))))&(((in @ (esk17_1 @ X725) @ X725)|((X725)=(emptyset)))&(((in @ (esk18_1 @ X727) @ X727)|((X727)=(emptyset)))&(((~(in @ X731 @ (dsetconstr @ X729 @ X730))|(X730 @ X731)|~(in @ X731 @ X729))&(~(X730 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X878))|(((X881)!=(esk48_3 @ X877 @ X878 @ X881))|~(X877 @ X881))|((X877 @ (esk46_2 @ X877 @ X878))|(X878 @ (esk47_2 @ X877 @ X878))))&(((X883)!=(esk49_3 @ X877 @ X878 @ X883))|~(X878 @ X883)|((descr @ X877)=(descr @ X878))|(((X881)!=(esk48_3 @ X877 @ X878 @ X881))|~(X877 @ X881))|((X877 @ (esk46_2 @ X877 @ X878))|(X878 @ (esk47_2 @ X877 @ X878))))))))&((((in @ (esk50_4 @ X885 @ X886 @ X887 @ X888) @ X885)|((dsetconstr @ X885 @ X887)=(dsetconstr @ X886 @ X888))|((X885)!=(X886)))&(((in @ (esk51_4 @ X885 @ X886 @ X887 @ X888) @ X886)|((dsetconstr @ X885 @ X887)=(dsetconstr @ X886 @ X888))|((X885)!=(X886)))&((((esk50_4 @ X885 @ X886 @ X887 @ X888)=(esk51_4 @ X885 @ X886 @ X887 @ X888))|((dsetconstr @ X885 @ X887)=(dsetconstr @ X886 @ X888))|((X885)!=(X886)))&((~(X887 @ (esk50_4 @ X885 @ X886 @ X887 @ X888))|~(X888 @ (esk51_4 @ X885 @ X886 @ X887 @ X888))|((dsetconstr @ X885 @ X887)=(dsetconstr @ X886 @ X888))|((X885)!=(X886)))&((X887 @ (esk50_4 @ X885 @ X886 @ X887 @ X888))|(X888 @ (esk51_4 @ X885 @ X886 @ X887 @ X888))|((dsetconstr @ X885 @ X887)=(dsetconstr @ X886 @ X888))|((X885)!=(X886)))))))&((((in @ (esk52_2 @ X891 @ X892) @ X891)|(subset @ X891 @ X892))&(~(in @ (esk52_2 @ X891 @ X892) @ X892)|(subset @ X891 @ X892)))&((((X894)!=(X895))|(subset @ X895 @ X894))&((((X896)!=(X897))|(subset @ X896 @ X897))&((((in @ (esk53_2 @ X898 @ X899) @ X898)|(subset @ X898 @ X899))&(~(in @ (esk53_2 @ X898 @ X899) @ X899)|(subset @ X898 @ X899)))&((subset @ emptyset @ X901)&((~(subset @ X902 @ X903)|(~(in @ X904 @ X902)|(in @ X904 @ X903)))&((~(subset @ X905 @ X906)|((in @ X907 @ X906)|~(in @ X907 @ X905)))&((~(in @ X910 @ X908)|((in @ X910 @ X909)|~(subset @ X908 @ X909)))&(((subset @ X911 @ X912)|((X911)!=(X912)))&((~(in @ X915 @ X913)|((in @ X915 @ X914)|((X913)!=(X914))))&((subset @ X916 @ X916)&((~(subset @ X917 @ X918)|(~(subset @ X918 @ X919)|(subset @ X917 @ X919)))&((subset @ X921 @ (setadjoin @ X920 @ X921))&((~(subset @ X922 @ X924)|(subset @ X922 @ (setadjoin @ X923 @ X924)))&((~(subset @ X925 @ X926)|(in @ X925 @ (powerset @ X926)))&((~(subset @ X927 @ X928)|(~(subset @ X928 @ X927)|((X927)=(X928))))&((~(subset @ X929 @ emptyset)|((X929)=(emptyset)))&((~(subset @ X931 @ X930)|(in @ X931 @ (powerset @ X930)))&((~(in @ X933 @ (powerset @ X932))|(subset @ X933 @ X932))&((in @ X934 @ (powerset @ X934))&((~(subset @ X935 @ X936)|(subset @ (powerset @ X935) @ (powerset @ X936)))&((in @ (dsetconstr @ X937 @ X938) @ (powerset @ X937))&((subset @ (dsetconstr @ X939 @ X940) @ X939)&((~(in @ X943 @ X941)|(in @ X943 @ (binunion @ X941 @ X942)))&((in @ X945 @ (setadjoin @ X944 @ (setadjoin @ X945 @ emptyset)))&((~(in @ X948 @ X947)|(in @ X948 @ (binunion @ X946 @ X947)))&(((((in @ X951 @ X950)|(X952)|(in @ X951 @ X949)|~(in @ X951 @ (binunion @ X949 @ X950)))&(~(X952)|(X952)|(in @ X951 @ X949)|~(in @ X951 @ (binunion @ X949 @ X950))))&(((in @ X951 @ X950)|(X952)|~(X952)|~(in @ X951 @ (binunion @ X949 @ X950)))&(~(X952)|(X952)|~(X952)|~(in @ X951 @ (binunion @ X949 @ X950)))))&((~(in @ X955 @ (binunion @ X953 @ X954))|((in @ X955 @ X953)|(in @ X955 @ X954)))&((subset @ X956 @ (binunion @ X956 @ X957))&((subset @ X959 @ (binunion @ X958 @ X959))&((~(in @ X962 @ X960)|(~(in @ X962 @ X961)|(in @ X962 @ (binintersect @ X960 @ X961))))&((~(subset @ X965 @ X963)|(~(subset @ X965 @ X964)|(subset @ X965 @ (binintersect @ X963 @ X964))))&((in @ esk56_0 @ (binintersect @ esk54_0 @ esk55_0))&~(in @ esk56_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_153])])])])])])])).
% 0.23/0.31 thf(c_0_156, plain, ![X655:$i, X656:$i]:(((binintersect @ X655 @ X656)=(dsetconstr @ X655 @ (^[Z0:$i]:((in @ Z0 @ X656)))))), inference(variable_rename,[status(thm)],[c_0_154])).
% 0.23/0.31 thf(c_0_157, negated_conjecture, (in @ esk56_0 @ (binintersect @ esk54_0 @ esk55_0)), inference(split_conjunct,[status(thm)],[c_0_155])).
% 0.23/0.31 thf(c_0_158, plain, ![X2:$i, X3:$i]:(((binintersect @ X2 @ X3)=(dsetconstr @ X2 @ (^[Z0:$i]:((in @ Z0 @ X3)))))), inference(split_conjunct,[status(thm)],[c_0_156])).
% 0.23/0.31 thf(c_0_159, negated_conjecture, ![X3:$i, X2:$i, X1:$i > $o]:(((in @ X2 @ X3)|~((in @ X2 @ (dsetconstr @ X3 @ X1))))), inference(split_conjunct,[status(thm)],[c_0_155])).
% 0.23/0.31 thf(c_0_160, negated_conjecture, (in @ esk56_0 @ (dsetconstr @ esk54_0 @ (^[Z0:$i]:((in @ Z0 @ esk55_0))))), inference(rw,[status(thm)],[c_0_157, c_0_158])).
% 0.23/0.31 thf(c_0_161, negated_conjecture, ~((in @ esk56_0 @ esk54_0)), inference(split_conjunct,[status(thm)],[c_0_155])).
% 0.23/0.31 thf(c_0_162, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_159, c_0_160]), c_0_161]), ['proof']).
% 0.23/0.31 % SZS output end CNFRefutation
% 0.23/0.31 % Parsed axioms : 235
% 0.23/0.31 % Removed by relevancy pruning/SinE : 0
% 0.23/0.31 % Initial clauses : 347
% 0.23/0.31 % Removed in clause preprocessing : 142
% 0.23/0.31 % Initial clauses in saturation : 205
% 0.23/0.31 % Processed clauses : 94
% 0.23/0.31 % ...of these trivial : 5
% 0.23/0.31 % ...subsumed : 23
% 0.23/0.31 % ...remaining for further processing : 66
% 0.23/0.31 % Other redundant clauses eliminated : 6
% 0.23/0.31 % Clauses deleted for lack of memory : 0
% 0.23/0.31 % Backward-subsumed : 0
% 0.23/0.31 % Backward-rewritten : 2
% 0.23/0.31 % Generated clauses : 195
% 0.23/0.31 % ...of the previous two non-redundant : 154
% 0.23/0.31 % ...aggressively subsumed : 0
% 0.23/0.31 % Contextual simplify-reflections : 0
% 0.23/0.31 % Paramodulations : 189
% 0.23/0.31 % Factorizations : 0
% 0.23/0.31 % NegExts : 0
% 0.23/0.31 % Equation resolutions : 6
% 0.23/0.31 % Disequality decompositions : 0
% 0.23/0.31 % Total rewrite steps : 38
% 0.23/0.31 % ...of those cached : 16
% 0.23/0.31 % Propositional unsat checks : 0
% 0.23/0.31 % Propositional check models : 0
% 0.23/0.31 % Propositional check unsatisfiable : 0
% 0.23/0.31 % Propositional clauses : 0
% 0.23/0.31 % Propositional clauses after purity: 0
% 0.23/0.31 % Propositional unsat core size : 0
% 0.23/0.31 % Propositional preprocessing time : 0.000
% 0.23/0.31 % Propositional encoding time : 0.000
% 0.23/0.31 % Propositional solver time : 0.000
% 0.23/0.31 % Success case prop preproc time : 0.000
% 0.23/0.31 % Success case prop encoding time : 0.000
% 0.23/0.31 % Success case prop solver time : 0.000
% 0.23/0.31 % Current number of processed clauses : 58
% 0.23/0.31 % Positive orientable unit clauses : 26
% 0.23/0.31 % Positive unorientable unit clauses: 0
% 0.23/0.31 % Negative unit clauses : 2
% 0.23/0.31 % Non-unit-clauses : 30
% 0.23/0.31 % Current number of unprocessed clauses: 264
% 0.23/0.31 % ...number of literals in the above : 861
% 0.23/0.31 % Current number of archived formulas : 0
% 0.23/0.31 % Current number of archived clauses : 3
% 0.23/0.31 % Clause-clause subsumption calls (NU) : 112
% 0.23/0.31 % Rec. Clause-clause subsumption calls : 108
% 0.23/0.31 % Non-unit clause-clause subsumptions : 14
% 0.23/0.31 % Unit Clause-clause subsumption calls : 25
% 0.23/0.31 % Rewrite failures with RHS unbound : 0
% 0.23/0.31 % BW rewrite match attempts : 5
% 0.23/0.31 % BW rewrite match successes : 2
% 0.23/0.31 % Condensation attempts : 0
% 0.23/0.31 % Condensation successes : 0
% 0.23/0.31 % Termbank termtop insertions : 31414
% 0.23/0.31 % Search garbage collected termcells : 11226
% 0.23/0.31
% 0.23/0.31 % -------------------------------------------------
% 0.23/0.31 % User time : 0.028 s
% 0.23/0.31 % System time : 0.010 s
% 0.23/0.31 % Total time : 0.038 s
% 0.23/0.31 % Maximum resident set size: 6168 pages
% 0.23/0.31
% 0.23/0.31 % -------------------------------------------------
% 0.23/0.31 % User time : 0.033 s
% 0.23/0.31 % System time : 0.019 s
% 0.23/0.31 % Total time : 0.051 s
% 0.23/0.31 % Maximum resident set size: 5120 pages
% 0.23/0.31 % E exiting
%------------------------------------------------------------------------------