%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU592^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:24:38 AM UTC 2026
% Result : Theorem 0.33s 0.46s
% Output : CNFRefutation 0.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU592^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.25 % Computer : n018.cluster.edu
% 0.11/0.25 % Model : x86_64 x86_64
% 0.11/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.25 % Memory : 8046.5625MB
% 0.11/0.25 % OS : Linux 6.8.0-71-generic
% 0.11/0.25 % CPULimit : 300
% 0.11/0.25 % WCLimit : 300
% 0.11/0.25 % DateTime : Tue Sep 29 13:55:41 UTC 2026
% 0.11/0.25 % CPUTime :
% 0.11/0.25 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.33 Running higher-order theorem proving
% 0.24/0.37 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.aXV7tgFpRG/E---3.1_114554.p
% 0.33/0.46 % Version: 3.5.1-ho
% 0.33/0.46 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.33/0.46 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.33/0.46 % Starting ehoh_best5 with 300s (1) cores
% 0.33/0.46 % Starting almost_fo_3_lam with 300s (1) cores
% 0.33/0.46 % Starting new_bool_5 with 300s (1) cores
% 0.33/0.46 % Starting pre_casc_3 with 300s (1) cores
% 0.33/0.46 % Starting ho_unfolding_8 with 300s (1) cores
% 0.33/0.46 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.33/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.33/0.46 % Starting new_ho_5 with 300s (1) cores
% 0.33/0.46 % new_ho_10_cnf2 with pid 114572 completed with status 0
% 0.33/0.46 % Result found by new_ho_10_cnf2
% 0.33/0.46 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.33/0.46 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.33/0.46 % Starting ehoh_best5 with 300s (1) cores
% 0.33/0.46 % Starting almost_fo_3_lam with 300s (1) cores
% 0.33/0.46 % Starting new_bool_5 with 300s (1) cores
% 0.33/0.46 % Starting pre_casc_3 with 300s (1) cores
% 0.33/0.46 % Starting ho_unfolding_8 with 300s (1) cores
% 0.33/0.46 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.33/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.33/0.46 % No SInE strategy applied
% 0.33/0.46 % Search class: HGHSM-FSLS31-SHFMMSBN
% 0.33/0.46 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.33/0.46 % Starting SubtermCWHack with 28s (1) cores
% 0.33/0.46 % SubtermCWHack with pid 114579 completed with status 0
% 0.33/0.46 % Result found by SubtermCWHack
% 0.33/0.46 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.33/0.46 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.33/0.46 % Starting ehoh_best5 with 300s (1) cores
% 0.33/0.46 % Starting almost_fo_3_lam with 300s (1) cores
% 0.33/0.46 % Starting new_bool_5 with 300s (1) cores
% 0.33/0.46 % Starting pre_casc_3 with 300s (1) cores
% 0.33/0.46 % Starting ho_unfolding_8 with 300s (1) cores
% 0.33/0.46 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.33/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.33/0.46 % No SInE strategy applied
% 0.33/0.46 % Search class: HGHSM-FSLS31-SHFMMSBN
% 0.33/0.46 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.33/0.46 % Starting SubtermCWHack with 28s (1) cores
% 0.33/0.46 % Preprocessing time : 0.004 s
% 0.33/0.46
% 0.33/0.46 % Proof found!
% 0.33/0.46 % SZS status Theorem
% 0.33/0.46 % SZS output start CNFRefutation
% 0.33/0.46 thf(decl_23, type, in: $i > $i > $o).
% 0.33/0.46 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.33/0.46 thf(decl_25, type, setextAx: $o).
% 0.33/0.46 thf(decl_26, type, emptyset: $i).
% 0.33/0.46 thf(decl_27, type, emptysetAx: $o).
% 0.33/0.46 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.33/0.46 thf(decl_29, type, setadjoinAx: $o).
% 0.33/0.46 thf(decl_30, type, powerset: $i > $i).
% 0.33/0.46 thf(decl_31, type, powersetAx: $o).
% 0.33/0.46 thf(decl_32, type, setunion: $i > $i).
% 0.33/0.46 thf(decl_33, type, setunionAx: $o).
% 0.33/0.46 thf(decl_34, type, omega: $i).
% 0.33/0.46 thf(decl_35, type, omega0Ax: $o).
% 0.33/0.46 thf(decl_36, type, omegaSAx: $o).
% 0.33/0.46 thf(decl_37, type, omegaIndAx: $o).
% 0.33/0.46 thf(decl_38, type, replAx: $o).
% 0.33/0.46 thf(decl_39, type, foundationAx: $o).
% 0.33/0.46 thf(decl_40, type, wellorderingAx: $o).
% 0.33/0.46 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.33/0.46 thf(decl_42, type, descrp: $o).
% 0.33/0.46 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.33/0.46 thf(decl_44, type, dsetconstrI: $o).
% 0.33/0.46 thf(decl_45, type, dsetconstrEL: $o).
% 0.33/0.46 thf(decl_46, type, dsetconstrER: $o).
% 0.33/0.46 thf(decl_47, type, exuE1: $o).
% 0.33/0.46 thf(decl_48, type, prop2set: $o > $i).
% 0.33/0.46 thf(decl_49, type, prop2setE: $o).
% 0.33/0.46 thf(decl_50, type, emptysetE: $o).
% 0.33/0.46 thf(decl_51, type, emptysetimpfalse: $o).
% 0.33/0.46 thf(decl_52, type, notinemptyset: $o).
% 0.33/0.46 thf(decl_53, type, exuE3e: $o).
% 0.33/0.46 thf(decl_54, type, setext: $o).
% 0.33/0.46 thf(decl_55, type, emptyI: $o).
% 0.33/0.46 thf(decl_56, type, noeltsimpempty: $o).
% 0.33/0.46 thf(decl_57, type, setbeta: $o).
% 0.33/0.46 thf(decl_58, type, nonempty: $i > $o).
% 0.33/0.46 thf(decl_59, type, nonemptyE1: $o).
% 0.33/0.46 thf(decl_60, type, nonemptyI: $o).
% 0.33/0.46 thf(decl_61, type, nonemptyI1: $o).
% 0.33/0.46 thf(decl_62, type, setadjoinIL: $o).
% 0.33/0.46 thf(decl_63, type, emptyinunitempty: $o).
% 0.33/0.46 thf(decl_64, type, setadjoinIR: $o).
% 0.33/0.46 thf(decl_65, type, setadjoinE: $o).
% 0.33/0.46 thf(decl_66, type, setadjoinOr: $o).
% 0.33/0.46 thf(decl_67, type, setoftrueEq: $o).
% 0.33/0.46 thf(decl_68, type, powersetI: $o).
% 0.33/0.46 thf(decl_69, type, emptyinPowerset: $o).
% 0.33/0.46 thf(decl_70, type, emptyInPowerset: $o).
% 0.33/0.46 thf(decl_71, type, powersetE: $o).
% 0.33/0.46 thf(decl_72, type, setunionI: $o).
% 0.33/0.46 thf(decl_73, type, setunionE: $o).
% 0.33/0.46 thf(decl_74, type, subPowSU: $o).
% 0.33/0.46 thf(decl_75, type, exuE2: $o).
% 0.33/0.46 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.33/0.46 thf(decl_77, type, uniqinunit: $o).
% 0.33/0.46 thf(decl_78, type, notinsingleton: $o).
% 0.33/0.46 thf(decl_79, type, eqinunit: $o).
% 0.33/0.46 thf(decl_80, type, singletonsswitch: $o).
% 0.33/0.46 thf(decl_81, type, upairsetE: $o).
% 0.33/0.46 thf(decl_82, type, upairsetIL: $o).
% 0.33/0.46 thf(decl_83, type, upairsetIR: $o).
% 0.33/0.46 thf(decl_84, type, emptyE1: $o).
% 0.33/0.46 thf(decl_85, type, vacuousDall: $o).
% 0.33/0.46 thf(decl_86, type, quantDeMorgan1: $o).
% 0.33/0.46 thf(decl_87, type, quantDeMorgan2: $o).
% 0.33/0.46 thf(decl_88, type, quantDeMorgan3: $o).
% 0.33/0.46 thf(decl_89, type, quantDeMorgan4: $o).
% 0.33/0.46 thf(decl_90, type, prop2setI: $o).
% 0.33/0.46 thf(decl_91, type, set2prop: $i > $o).
% 0.33/0.46 thf(decl_92, type, prop2set2propI: $o).
% 0.33/0.46 thf(decl_93, type, notdexE: $o).
% 0.33/0.46 thf(decl_94, type, notdallE: $o).
% 0.33/0.46 thf(decl_95, type, exuI1: $o).
% 0.33/0.46 thf(decl_96, type, exuI3: $o).
% 0.33/0.46 thf(decl_97, type, exuI2: $o).
% 0.33/0.46 thf(decl_98, type, inCongP: $o).
% 0.33/0.46 thf(decl_99, type, in__Cong: $o).
% 0.33/0.46 thf(decl_100, type, exuE3u: $o).
% 0.33/0.46 thf(decl_101, type, exu__Cong: $o).
% 0.33/0.46 thf(decl_102, type, emptyset__Cong: $o).
% 0.33/0.46 thf(decl_103, type, setadjoin__Cong: $o).
% 0.33/0.46 thf(decl_104, type, powerset__Cong: $o).
% 0.33/0.46 thf(decl_105, type, setunion__Cong: $o).
% 0.33/0.46 thf(decl_106, type, omega__Cong: $o).
% 0.33/0.46 thf(decl_107, type, exuEu: $o).
% 0.33/0.46 thf(decl_108, type, descr__Cong: $o).
% 0.33/0.46 thf(decl_109, type, dsetconstr__Cong: $o).
% 0.33/0.46 thf(decl_110, type, subset: $i > $i > $o).
% 0.33/0.46 thf(decl_113, type, subsetI1: $o).
% 0.33/0.46 thf(decl_114, type, eqimpsubset2: $o).
% 0.33/0.46 thf(decl_115, type, eqimpsubset1: $o).
% 0.33/0.46 thf(decl_116, type, subsetI2: $o).
% 0.33/0.46 thf(decl_117, type, emptysetsubset: $o).
% 0.33/0.46 thf(decl_118, type, subsetE: $o).
% 0.33/0.46 thf(decl_119, type, subsetE2: $o).
% 0.33/0.46 thf(decl_120, type, notsubsetI: $o).
% 0.33/0.46 thf(decl_121, type, notequalI1: $o).
% 0.33/0.46 thf(decl_122, type, notequalI2: $o).
% 0.33/0.46 thf(decl_123, type, subsetRefl: $o).
% 0.33/0.46 thf(decl_124, type, subsetTrans: $o).
% 0.33/0.46 thf(decl_125, type, setadjoinSub: $o).
% 0.33/0.46 thf(decl_126, type, setadjoinSub2: $o).
% 0.33/0.46 thf(decl_127, type, subset2powerset: $o).
% 0.33/0.46 thf(decl_128, type, setextsub: $o).
% 0.33/0.46 thf(decl_129, type, subsetemptysetimpeq: $o).
% 0.33/0.46 thf(decl_130, type, powersetI1: $o).
% 0.33/0.46 thf(decl_131, type, powersetE1: $o).
% 0.33/0.46 thf(decl_132, type, inPowerset: $o).
% 0.33/0.46 thf(decl_133, type, powersetsubset: $o).
% 0.33/0.46 thf(decl_134, type, sepInPowerset: $o).
% 0.33/0.46 thf(decl_135, type, sepSubset: $o).
% 0.33/0.46 thf(decl_136, type, binunion: $i > $i > $i).
% 0.33/0.46 thf(decl_137, type, binunionIL: $o).
% 0.33/0.46 thf(decl_138, type, upairset2IR: $o).
% 0.33/0.46 thf(decl_139, type, binunionIR: $o).
% 0.33/0.46 thf(decl_140, type, binunionEcases: $o).
% 0.33/0.46 thf(decl_141, type, binunionE: $o).
% 0.33/0.46 thf(decl_142, type, binunionLsub: $o).
% 0.33/0.46 thf(decl_143, type, binunionRsub: $o).
% 0.33/0.46 thf(decl_144, type, binintersect: $i > $i > $i).
% 0.33/0.46 thf(decl_145, type, binintersectI: $o).
% 0.33/0.46 thf(decl_146, type, binintersectSubset5: $o).
% 0.33/0.46 thf(decl_147, type, binintersectEL: $o).
% 0.33/0.46 thf(decl_148, type, epred1_0: $o).
% 0.33/0.46 thf(decl_149, type, esk1_2: $i > $i > $i).
% 0.33/0.46 thf(decl_150, type, esk2_2: $i > $i > $i).
% 0.33/0.46 thf(decl_151, type, esk3_2: $i > $i > $i).
% 0.33/0.46 thf(decl_152, type, esk4_1: $i > $i).
% 0.33/0.46 thf(decl_153, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.33/0.46 thf(decl_154, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.33/0.46 thf(decl_155, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.33/0.46 thf(decl_156, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.33/0.46 thf(decl_157, type, esk9_1: $i > $i).
% 0.33/0.46 thf(decl_158, type, esk10_2: ($i > $o) > $i > $i).
% 0.33/0.46 thf(decl_159, type, esk11_2: ($i > $o) > $i > $i).
% 0.33/0.46 thf(decl_160, type, esk12_1: ($i > $o) > $i).
% 0.33/0.46 thf(decl_161, type, esk13_2: ($i > $o) > $i > $i).
% 0.33/0.46 thf(decl_162, type, esk14_1: ($i > $o) > $i).
% 0.33/0.46 thf(decl_163, type, esk15_2: $i > $i > $i).
% 0.33/0.46 thf(decl_164, type, esk16_2: $i > $i > $i).
% 0.33/0.46 thf(decl_165, type, esk17_1: $i > $i).
% 0.33/0.46 thf(decl_166, type, esk18_1: $i > $i).
% 0.33/0.46 thf(decl_167, type, esk19_1: $i > $i).
% 0.33/0.46 thf(decl_168, type, esk20_2: $i > $i > $i).
% 0.33/0.46 thf(decl_169, type, esk21_3: $i > $i > $o > $i).
% 0.33/0.46 thf(decl_170, type, esk22_2: ($i > $o) > $i > $i).
% 0.33/0.46 thf(decl_171, type, esk23_1: ($i > $o) > $i).
% 0.33/0.46 thf(decl_172, type, esk24_1: $i > $i).
% 0.33/0.46 thf(decl_173, type, esk25_2: $i > ($i > $o) > $i).
% 0.33/0.46 thf(decl_174, type, esk26_2: $i > ($i > $o) > $i).
% 0.33/0.46 thf(decl_175, type, esk27_2: $i > ($i > $o) > $i).
% 0.33/0.46 thf(decl_176, type, esk28_2: $i > ($i > $o) > $i).
% 0.33/0.46 thf(decl_177, type, esk29_2: $i > ($i > $o) > $i).
% 0.33/0.46 thf(decl_178, type, esk30_2: $i > ($i > $o) > $i).
% 0.33/0.46 thf(decl_179, type, esk31_2: ($i > $o) > $i > $i).
% 0.33/0.46 thf(decl_180, type, esk32_1: ($i > $o) > $i).
% 0.33/0.46 thf(decl_181, type, esk33_1: ($i > $o) > $i).
% 0.33/0.46 thf(decl_182, type, esk34_1: ($i > $o) > $i).
% 0.33/0.46 thf(decl_183, type, esk35_1: ($i > $o) > $i).
% 0.33/0.46 thf(decl_184, type, esk36_2: ($i > $o) > $i > $i).
% 0.33/0.46 thf(decl_185, type, esk37_1: ($i > $o) > $i).
% 0.33/0.46 thf(decl_186, type, esk38_2: ($i > $o) > $i > $i).
% 0.33/0.46 thf(decl_187, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 0.33/0.46 thf(decl_188, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 0.33/0.46 thf(decl_189, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.33/0.46 thf(decl_190, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 0.33/0.46 thf(decl_191, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.33/0.46 thf(decl_192, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 0.33/0.46 thf(decl_193, type, esk45_2: ($i > $o) > $i > $i).
% 0.33/0.46 thf(decl_194, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 0.33/0.46 thf(decl_195, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 0.33/0.46 thf(decl_196, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.33/0.46 thf(decl_197, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.33/0.46 thf(decl_198, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.33/0.46 thf(decl_199, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.33/0.46 thf(decl_200, type, esk52_2: $i > $i > $i).
% 0.33/0.46 thf(decl_201, type, esk53_2: $i > $i > $i).
% 0.33/0.46 thf(decl_202, type, esk54_0: $i).
% 0.33/0.46 thf(decl_203, type, esk55_0: $i).
% 0.33/0.46 thf(decl_209, type, epred2_1: $i > $i > $o).
% 0.33/0.46 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', replAx)).
% 0.33/0.46 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', exu)).
% 0.33/0.46 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', descrp)).
% 0.33/0.46 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', exuE1)).
% 0.33/0.46 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', exuE3e)).
% 0.33/0.46 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', nonempty)).
% 0.33/0.46 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', nonemptyI)).
% 0.33/0.46 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', exuE2)).
% 0.33/0.46 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.aXV7tgFpRG/E---3.1_114554.p', exuI1)).
% 0.33/0.46 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', exuI3)).
% 0.33/0.46 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', exuI2)).
% 0.33/0.46 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.aXV7tgFpRG/E---3.1_114554.p', exuE3u)).
% 0.33/0.46 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', exu__Cong)).
% 0.33/0.46 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', exuEu)).
% 0.33/0.46 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', descr__Cong)).
% 0.33/0.46 thf(binintersectLsub, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', binintersectLsub)).
% 0.33/0.46 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', dsetconstrI)).
% 0.33/0.46 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', dsetconstrEL)).
% 0.33/0.46 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', dsetconstrER)).
% 0.33/0.46 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', setbeta)).
% 0.33/0.46 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', nonemptyE1)).
% 0.33/0.46 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', nonemptyI1)).
% 0.33/0.46 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', setoftrueEq)).
% 0.33/0.46 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', nonemptyImpWitness)).
% 0.33/0.46 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.aXV7tgFpRG/E---3.1_114554.p', emptyE1)).
% 0.33/0.46 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', dsetconstr__Cong)).
% 0.33/0.46 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', sepInPowerset)).
% 0.33/0.46 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', sepSubset)).
% 0.33/0.46 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', setextAx)).
% 0.33/0.46 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', emptysetAx)).
% 0.33/0.46 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', setadjoinAx)).
% 0.33/0.46 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', powersetAx)).
% 0.33/0.46 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', setunionAx)).
% 0.33/0.46 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', omega0Ax)).
% 0.33/0.46 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', omegaSAx)).
% 0.33/0.46 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', omegaIndAx)).
% 0.33/0.46 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', foundationAx)).
% 0.33/0.46 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.aXV7tgFpRG/E---3.1_114554.p', wellorderingAx)).
% 0.33/0.46 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', prop2setE)).
% 0.33/0.46 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', emptysetE)).
% 0.33/0.46 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', emptysetimpfalse)).
% 0.33/0.46 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', notinemptyset)).
% 0.33/0.46 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', setext)).
% 0.33/0.46 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', emptyI)).
% 0.33/0.46 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', noeltsimpempty)).
% 0.33/0.46 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', setadjoinIL)).
% 0.33/0.46 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', emptyinunitempty)).
% 0.33/0.46 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', setadjoinIR)).
% 0.33/0.46 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.aXV7tgFpRG/E---3.1_114554.p', setadjoinE)).
% 0.33/0.46 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', setadjoinOr)).
% 0.33/0.46 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', powersetI)).
% 0.33/0.46 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', emptyinPowerset)).
% 0.33/0.46 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', emptyInPowerset)).
% 0.33/0.46 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', powersetE)).
% 0.33/0.46 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', setunionI)).
% 0.33/0.46 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.aXV7tgFpRG/E---3.1_114554.p', setunionE)).
% 0.33/0.46 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', subPowSU)).
% 0.33/0.46 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', uniqinunit)).
% 0.33/0.46 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', notinsingleton)).
% 0.33/0.46 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', eqinunit)).
% 0.33/0.46 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', singletonsswitch)).
% 0.33/0.46 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', upairsetE)).
% 0.33/0.46 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', upairsetIL)).
% 0.33/0.46 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', upairsetIR)).
% 0.33/0.46 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', vacuousDall)).
% 0.33/0.46 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', quantDeMorgan1)).
% 0.33/0.46 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', quantDeMorgan2)).
% 0.33/0.46 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', quantDeMorgan3)).
% 0.33/0.46 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', quantDeMorgan4)).
% 0.33/0.46 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', prop2setI)).
% 0.33/0.46 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', prop2set2propI)).
% 0.33/0.46 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', notdexE)).
% 0.33/0.46 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', notdallE)).
% 0.33/0.46 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', inCongP)).
% 0.33/0.46 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', in__Cong)).
% 0.33/0.46 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', emptyset__Cong)).
% 0.33/0.46 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', setadjoin__Cong)).
% 0.33/0.46 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', powerset__Cong)).
% 0.33/0.46 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', setunion__Cong)).
% 0.33/0.46 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', omega__Cong)).
% 0.33/0.46 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', subsetI1)).
% 0.33/0.46 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', eqimpsubset2)).
% 0.33/0.46 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', eqimpsubset1)).
% 0.33/0.46 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', subsetI2)).
% 0.33/0.46 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', emptysetsubset)).
% 0.33/0.46 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', subsetE)).
% 0.33/0.46 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', subsetE2)).
% 0.33/0.46 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', notsubsetI)).
% 0.33/0.46 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', notequalI1)).
% 0.33/0.46 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', notequalI2)).
% 0.33/0.46 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', subsetRefl)).
% 0.33/0.46 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', subsetTrans)).
% 0.33/0.46 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', setadjoinSub)).
% 0.33/0.46 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', setadjoinSub2)).
% 0.33/0.46 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', subset2powerset)).
% 0.33/0.46 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', setextsub)).
% 0.33/0.46 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', subsetemptysetimpeq)).
% 0.33/0.46 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', powersetI1)).
% 0.33/0.46 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', powersetE1)).
% 0.33/0.46 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', inPowerset)).
% 0.33/0.46 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', powersetsubset)).
% 0.33/0.46 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', binunionIL)).
% 0.33/0.46 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', upairset2IR)).
% 0.33/0.46 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', binunionIR)).
% 0.33/0.46 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', binunionEcases)).
% 0.33/0.46 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', binunionE)).
% 0.33/0.46 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', binunionLsub)).
% 0.33/0.46 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', binunionRsub)).
% 0.33/0.46 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', binintersectI)).
% 0.33/0.46 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', binintersectSubset5)).
% 0.33/0.46 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', binintersectEL)).
% 0.33/0.46 thf(binintersect, axiom, ((binintersect)=(^[X4:$i, X5:$i]:(dsetconstr @ X4 @ (^[X2:$i]:((in @ X2 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.aXV7tgFpRG/E---3.1_114554.p', binintersect)).
% 0.33/0.46 thf(c_0_112, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.33/0.46 thf(c_0_113, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.33/0.46 thf(c_0_114, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.33/0.46 thf(c_0_115, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.33/0.46 thf(c_0_116, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.33/0.46 thf(c_0_117, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.33/0.46 thf(c_0_118, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.33/0.46 thf(c_0_119, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.33/0.46 thf(c_0_120, 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])).
% 0.33/0.46 thf(c_0_121, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.33/0.46 thf(c_0_122, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.33/0.46 thf(c_0_123, 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])).
% 0.33/0.46 thf(c_0_124, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.33/0.46 thf(c_0_125, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 0.33/0.46 thf(c_0_126, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 0.33/0.46 thf(c_0_127, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[binintersectLsub])).
% 0.33/0.46 thf(c_0_128, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X312:$i]:(((((X6 @ X2 @ X312)))&(![X313:$i]:(((((X6 @ X2 @ X313)))=>(((X312)=(X313)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_112, c_0_113])).
% 0.33/0.46 thf(c_0_129, plain, ((descrp)=(![X1:$i > $o]:((((?[X314:$i]:(((((X1 @ X314)))&(![X315:$i]:(((((X1 @ X315)))=>(((X314)=(X315))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_114, c_0_113])).
% 0.33/0.46 thf(c_0_130, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.33/0.46 thf(c_0_131, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.33/0.46 thf(c_0_132, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.33/0.46 thf(c_0_133, plain, ((exuE1)=(![X1:$i > $o]:((((?[X316:$i]:(((((X1 @ X316)))&(![X317:$i]:(((((X1 @ X317)))=>(((X316)=(X317))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_115, c_0_113])).
% 0.33/0.46 thf(c_0_134, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X318:$i]:(((((X1 @ X318)))&(![X319:$i]:(((((X1 @ X319)))=>(((X318)=(X319))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_116, c_0_113])).
% 0.33/0.46 thf(c_0_135, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.33/0.46 thf(c_0_136, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_117])).
% 0.33/0.46 thf(c_0_137, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_118, c_0_117])).
% 0.33/0.46 thf(c_0_138, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_117])).
% 0.33/0.46 thf(c_0_139, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.33/0.46 thf(c_0_140, plain, ((exuE2)=(![X1:$i > $o]:((((?[X320:$i]:(((((X1 @ X320)))&(![X321:$i]:(((((X1 @ X321)))=>(((X320)=(X321))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_119, c_0_113])).
% 0.33/0.46 thf(c_0_141, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_117])).
% 0.33/0.46 thf(c_0_142, 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])).
% 0.33/0.46 thf(c_0_143, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X322:$i]:(((((X1 @ X322)))&(![X323:$i]:(((((X1 @ X323)))=>(((X322)=(X323)))))))))))))), inference(apply_def,[status(thm)],[c_0_120, c_0_113])).
% 0.33/0.46 thf(c_0_144, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X324:$i]:(((((X1 @ X324)))&(![X325:$i]:(((((X1 @ X325)))=>(((X324)=(X325)))))))))))))))), inference(apply_def,[status(thm)],[c_0_121, c_0_113])).
% 0.33/0.46 thf(c_0_145, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X326:$i]:(((((X1 @ X326)))&(![X327:$i]:(((((X1 @ X327)))=>(((X326)=(X327)))))))))))))), inference(apply_def,[status(thm)],[c_0_122, c_0_113])).
% 0.33/0.46 thf(c_0_146, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X328:$i]:(((((X1 @ X328)))&(![X329:$i]:(((((X1 @ X329)))=>(((X328)=(X329))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_123, c_0_113])).
% 0.33/0.46 thf(c_0_147, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X330:$i]:(((((X1 @ X330)))&(![X331:$i]:(((((X1 @ X331)))=>(((X330)=(X331))))))))))<=>((?[X332:$i]:(((((X17 @ X332)))&(![X333:$i]:(((((X17 @ X333)))=>(((X332)=(X333)))))))))))))))), inference(apply_def,[status(thm)],[c_0_124, c_0_113])).
% 0.33/0.46 thf(c_0_148, plain, ((exuEu)=(![X1:$i > $o]:((((?[X334:$i]:(((((X1 @ X334)))&(![X335:$i]:(((((X1 @ X335)))=>(((X334)=(X335))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_125, c_0_113])).
% 0.33/0.46 thf(c_0_149, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X336:$i]:(((((X1 @ X336)))&(![X337:$i]:(((((X1 @ X337)))=>(((X336)=(X337))))))))))=>((((?[X338:$i]:(((((X17 @ X338)))&(![X339:$i]:(((((X17 @ X339)))=>(((X338)=(X339))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_126, c_0_113])).
% 0.33/0.46 thf(c_0_150, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 0.33/0.46 thf(c_0_151, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 0.33/0.46 thf(c_0_152, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 0.33/0.46 thf(c_0_153, plain, ((epred1_0)<=>![X369:$i]:(?[X370:$i]:((((![X371:$i]:(((in @ X371 @ X370)=>![X372:$i]:(((in @ X372 @ X371)=>(in @ X372 @ X369)))))&![X373:$i, X374:$i]:((((in @ X373 @ X369)&(in @ X374 @ X369))=>(![X375:$i]:(((in @ X375 @ X370)=>((in @ X373 @ X375)<=>(in @ X374 @ X375))))=>((X373)=(X374))))))&![X376:$i, X377:$i]:((((in @ X376 @ X370)&(in @ X377 @ X370))=>(![X378:$i]:(((in @ X378 @ X376)=>(in @ X378 @ X377)))|![X379:$i]:(((in @ X379 @ X377)=>(in @ X379 @ X376)))))))&![X380:$i]:(((![X381:$i]:(((in @ X381 @ X380)=>(in @ X381 @ X369)))&?[X382:$i]:((in @ X382 @ X380)))=>?[X383:$i, X384:$i]:(((((in @ X383 @ X370)&(in @ X384 @ X380))&~(?[X385:$i]:(((in @ X385 @ X383)&(in @ X385 @ X380)))))&![X386:$i]:(((in @ X386 @ X370)=>(![X387:$i]:(((in @ X387 @ X386)=>(in @ X387 @ X383)))|(in @ X384 @ X386)))))))))))), introduced(definition)).
% 0.33/0.46 thf(c_0_154, negated_conjecture, ~((![X340:$i, X341:$i]:((![X342:$i]:(((in @ X342 @ X340)<=>(in @ X342 @ X341)))=>((X340)=(X341))))=>(![X343:$i]:(~(in @ X343 @ emptyset))=>(![X344:$i, X345:$i, X346:$i]:(((in @ X346 @ (setadjoin @ X344 @ X345))<=>(((X346)=(X344))|(in @ X346 @ X345))))=>(![X347:$i, X348:$i]:(((in @ X348 @ (powerset @ X347))<=>![X349:$i]:(((in @ X349 @ X348)=>(in @ X349 @ X347)))))=>(![X350:$i, X351:$i]:(((in @ X351 @ (setunion @ X350))<=>?[X352:$i]:(((in @ X351 @ X352)&(in @ X352 @ X350)))))=>((in @ emptyset @ omega)=>(![X353:$i]:(((in @ X353 @ omega)=>(in @ (setadjoin @ X353 @ X353) @ omega)))=>(![X354:$i]:((((in @ emptyset @ X354)&![X355:$i]:((((in @ X355 @ omega)&(in @ X355 @ X354))=>(in @ (setadjoin @ X355 @ X355) @ X354))))=>![X356:$i]:(((in @ X356 @ omega)=>(in @ X356 @ X354)))))=>(![X357:$i > $i > $o, X358:$i]:((![X359:$i]:(((in @ X359 @ X358)=>?[X360:$i]:(((X357 @ X359 @ X360)&![X361:$i]:(((X357 @ X359 @ X361)=>((X360)=(X361))))))))=>?[X362:$i]:(![X363:$i]:(((in @ X363 @ X362)<=>?[X364:$i]:(((in @ X364 @ X358)&(X357 @ X364 @ X363))))))))=>(![X365:$i]:((?[X366:$i]:((in @ X366 @ X365))=>?[X367:$i]:(((in @ X367 @ X365)&~(?[X368:$i]:(((in @ X368 @ X367)&(in @ X368 @ X365))))))))=>((epred1_0)=>(![X388:$i > $o]:((?[X389:$i]:(((X388 @ X389)&![X390:$i]:(((X388 @ X390)=>((X389)=(X390))))))=>(X388 @ (descr @ (^[Z0:$i]:(X388 @ Z0))))))=>(![X391:$i, X392:$i > $o, X393:$i]:(((in @ X393 @ X391)=>((X392 @ X393)=>(in @ X393 @ (dsetconstr @ X391 @ X392)))))=>(![X394:$i, X395:$i > $o, X396:$i]:(((in @ X396 @ (dsetconstr @ X394 @ X395))=>(in @ X396 @ X394)))=>(![X397:$i, X398:$i > $o, X399:$i]:(((in @ X399 @ (dsetconstr @ X397 @ X398))=>(X398 @ X399)))=>(![X400:$i > $o]:((?[X401:$i]:(((X400 @ X401)&![X402:$i]:(((X400 @ X402)=>((X401)=(X402))))))=>?[X403:$i]:(((X400 @ X403)&![X404:$i]:(((X400 @ X404)=>((X403)=(X404))))))))=>(![X405:$o, X406:$i]:(((in @ X406 @ (prop2set @ ((X405))))=>(X405)))=>(![X407:$i]:(((in @ X407 @ emptyset)=>![X408:$o]:((X408))))=>(![X409:$i]:(((in @ X409 @ emptyset)=>~($true)))=>(![X410:$i]:(~(in @ X410 @ emptyset))=>(![X411:$i > $o]:((?[X412:$i]:(((X411 @ X412)&![X413:$i]:(((X411 @ X413)=>((X412)=(X413))))))=>?[X414:$i]:((X411 @ X414))))=>(![X415:$i, X416:$i]:((![X417:$i]:(((in @ X417 @ X415)=>(in @ X417 @ X416)))=>(![X418:$i]:(((in @ X418 @ X416)=>(in @ X418 @ X415)))=>((X415)=(X416)))))=>(![X419:$i]:((![X420:$i]:(~(in @ X420 @ X419))=>((X419)=(emptyset))))=>(![X421:$i]:((![X422:$i]:(~(in @ X422 @ X421))=>((X421)=(emptyset))))=>(![X423:$i, X424:$i > $o, X425:$i]:(((in @ X425 @ X423)=>((in @ X425 @ (dsetconstr @ X423 @ X424))<=>(X424 @ X425))))=>(![X426:$i]:((((X426)!=(emptyset))=>?[X427:$i]:((in @ X427 @ X426))))=>(![X428:$i, X429:$i > $o, X430:$i]:(((in @ X430 @ X428)=>((X429 @ X430)=>((dsetconstr @ X428 @ X429)!=(emptyset)))))=>(![X431:$i]:((?[X432:$i]:((in @ X432 @ X431))=>((X431)!=(emptyset))))=>(![X433:$i, X434:$i]:((in @ X433 @ (setadjoin @ X433 @ X434)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X435:$i, X436:$i, X437:$i]:(((in @ X437 @ X436)=>(in @ X437 @ (setadjoin @ X435 @ X436))))=>(![X438:$i, X439:$i, X440:$i]:(((in @ X440 @ (setadjoin @ X438 @ X439))=>![X441:$o]:(((((X440)=(X438))=>(X441))=>(((in @ X440 @ X439)=>(X441))=>(X441))))))=>(![X442:$i, X443:$i, X444:$i]:(((in @ X444 @ (setadjoin @ X442 @ X443))=>(((X444)=(X442))|(in @ X444 @ X443))))=>(![X445:$i]:(((dsetconstr @ X445 @ (^[Z0:$i]:($true)))=(X445)))=>(![X446:$i, X447:$i]:((![X448:$i]:(((in @ X448 @ X447)=>(in @ X448 @ X446)))=>(in @ X447 @ (powerset @ X446))))=>(![X449:$i]:((in @ emptyset @ (powerset @ X449)))=>(![X450:$i]:((in @ emptyset @ (powerset @ X450)))=>(![X451:$i, X452:$i, X453:$i]:(((in @ X452 @ (powerset @ X451))=>((in @ X453 @ X452)=>(in @ X453 @ X451))))=>(![X454:$i, X455:$i, X456:$i]:(((in @ X455 @ X456)=>((in @ X456 @ X454)=>(in @ X455 @ (setunion @ X454)))))=>(![X457:$i, X458:$i]:(((in @ X458 @ (setunion @ X457))=>![X459:$o]:((![X460:$i]:(((in @ X458 @ X460)=>((in @ X460 @ X457)=>(X459))))=>(X459)))))=>(![X461:$i, X462:$i]:(((in @ X462 @ X461)=>(in @ X462 @ (powerset @ (setunion @ X461)))))=>(![X463:$i > $o]:((?[X464:$i]:(((X463 @ X464)&![X465:$i]:(((X463 @ X465)=>((X464)=(X465))))))=>?[X466:$i]:(![X467:$i]:(((X463 @ X467)<=>((X467)=(X466)))))))=>(![X468:$i]:((((X468)!=(emptyset))=>?[X469:$i]:(((in @ X469 @ X468)&$true))))=>(![X470:$i, X471:$i]:(((in @ X470 @ (setadjoin @ X471 @ emptyset))=>((X470)=(X471))))=>(![X472:$i, X473:$i]:((((X472)!=(X473))=>~(in @ X473 @ (setadjoin @ X472 @ emptyset))))=>(![X474:$i, X475:$i]:((((X474)=(X475))=>(in @ X474 @ (setadjoin @ X475 @ emptyset))))=>(![X476:$i, X477:$i]:(((in @ X476 @ (setadjoin @ X477 @ emptyset))=>(in @ X477 @ (setadjoin @ X476 @ emptyset))))=>(![X478:$i, X479:$i, X480:$i]:(((in @ X480 @ (setadjoin @ X478 @ (setadjoin @ X479 @ emptyset)))=>(((X480)=(X478))|((X480)=(X479)))))=>(![X481:$i, X482:$i]:((in @ X481 @ (setadjoin @ X481 @ (setadjoin @ X482 @ emptyset))))=>(![X483:$i, X484:$i]:((in @ X484 @ (setadjoin @ X483 @ (setadjoin @ X484 @ emptyset))))=>(![X485:$i, X486:$i > $o]:((?[X487:$i]:(((in @ X487 @ X485)&(X486 @ X487)))=>(((dsetconstr @ X485 @ X486)=(emptyset))=>~($true))))=>(![X488:$i > $o, X489:$i]:(((in @ X489 @ emptyset)=>(X488 @ X489)))=>(![X490:$i, X491:$i > $o]:((~(![X492:$i]:(((in @ X492 @ X490)=>(X491 @ X492))))=>?[X493:$i]:(((in @ X493 @ X490)&~((X491 @ X493))))))=>(![X494:$i, X495:$i > $o]:((![X496:$i]:(((in @ X496 @ X494)=>~((X495 @ X496))))=>~(?[X497:$i]:(((in @ X497 @ X494)&(X495 @ X497))))))=>(![X498:$i, X499:$i > $o]:((~(?[X500:$i]:(((in @ X500 @ X498)&(X499 @ X500))))=>![X501:$i]:(((in @ X501 @ X498)=>~((X499 @ X501))))))=>(![X502:$i, X503:$i > $o]:((?[X504:$i]:(((in @ X504 @ X502)&~((X503 @ X504))))=>~(![X505:$i]:(((in @ X505 @ X502)=>(X503 @ X505))))))=>(![X506:$o]:(((X506)=>(in @ emptyset @ (prop2set @ ((X506))))))=>(![X507:$o]:(((X507)=>(set2prop @ (prop2set @ ((X507))))))=>(![X508:$i, X509:$i > $o]:((~(?[X510:$i]:(((in @ X510 @ X508)&(X509 @ X510))))=>![X511:$i]:(((in @ X511 @ X508)=>~((X509 @ X511))))))=>(![X512:$i, X513:$i > $o]:((~(![X514:$i]:(((in @ X514 @ X512)=>(X513 @ X514))))=>?[X515:$i]:(((in @ X515 @ X512)&~((X513 @ X515))))))=>(![X516:$i > $o]:((?[X517:$i]:(((X516 @ X517)&![X518:$i]:(((X516 @ X518)=>((X517)=(X518))))))=>?[X519:$i]:(((X516 @ X519)&![X520:$i]:(((X516 @ X520)=>((X519)=(X520))))))))=>(![X521:$i > $o]:((?[X522:$i]:((X521 @ X522))=>(![X523:$i, X524:$i]:(((X521 @ X523)=>((X521 @ X524)=>((X523)=(X524)))))=>?[X525:$i]:(((X521 @ X525)&![X526:$i]:(((X521 @ X526)=>((X525)=(X526)))))))))=>(![X527:$i > $o]:((?[X528:$i]:(![X529:$i]:(((X527 @ X529)<=>((X529)=(X528)))))=>?[X530:$i]:(((X527 @ X530)&![X531:$i]:(((X527 @ X531)=>((X530)=(X531))))))))=>(![X532:$i, X533:$i]:((((X532)=(X533))=>![X534:$i, X535:$i]:((((X534)=(X535))=>((in @ X534 @ X532)=>(in @ X535 @ X533))))))=>(![X536:$i, X537:$i]:((((X536)=(X537))=>![X538:$i, X539:$i]:((((X538)=(X539))=>((in @ X538 @ X536)<=>(in @ X539 @ X537))))))=>(![X540:$i > $o]:((?[X541:$i]:(((X540 @ X541)&![X542:$i]:(((X540 @ X542)=>((X541)=(X542))))))=>![X543:$i, X544:$i]:(((X540 @ X543)=>((X540 @ X544)=>((X543)=(X544)))))))=>(![X545:$i > $o, X546:$i > $o]:((![X547:$i, X548:$i]:((((X547)=(X548))=>((X545 @ X547)<=>(X546 @ X548))))=>(?[X549:$i]:(((X545 @ X549)&![X550:$i]:(((X545 @ X550)=>((X549)=(X550))))))<=>?[X551:$i]:(((X546 @ X551)&![X552:$i]:(((X546 @ X552)=>((X551)=(X552)))))))))=>(((emptyset)=(emptyset))=>(![X553:$i, X554:$i]:((((X553)=(X554))=>![X555:$i, X556:$i]:((((X555)=(X556))=>((setadjoin @ X553 @ X555)=(setadjoin @ X554 @ X556))))))=>(![X557:$i, X558:$i]:((((X557)=(X558))=>((powerset @ X557)=(powerset @ X558))))=>(![X559:$i, X560:$i]:((((X559)=(X560))=>((setunion @ X559)=(setunion @ X560))))=>(((omega)=(omega))=>(![X561:$i > $o]:((?[X562:$i]:(((X561 @ X562)&![X563:$i]:(((X561 @ X563)=>((X562)=(X563))))))=>![X564:$i, X565:$i]:(((X561 @ X564)=>((X561 @ X565)=>((X564)=(X565)))))))=>(![X566:$i > $o, X567:$i > $o]:((![X568:$i, X569:$i]:((((X568)=(X569))=>((X566 @ X568)<=>(X567 @ X569))))=>(?[X570:$i]:(((X566 @ X570)&![X571:$i]:(((X566 @ X571)=>((X570)=(X571))))))=>(?[X572:$i]:(((X567 @ X572)&![X573:$i]:(((X567 @ X573)=>((X572)=(X573))))))=>((descr @ X566)=(descr @ X567))))))=>(![X574:$i, X575:$i]:((((X574)=(X575))=>![X576:$i > $o, X577:$i > $o]:((![X578:$i]:(((in @ X578 @ X574)=>![X579:$i]:(((in @ X579 @ X575)=>(((X578)=(X579))=>((X576 @ X578)<=>(X577 @ X579)))))))=>((dsetconstr @ X574 @ X576)=(dsetconstr @ X575 @ X577))))))=>(![X580:$i, X581:$i]:((![X582:$i]:(((in @ X582 @ X580)=>(in @ X582 @ X581)))=>(subset @ X580 @ X581)))=>(![X583:$i, X584:$i]:((((X583)=(X584))=>(subset @ X584 @ X583)))=>(![X585:$i, X586:$i]:((((X585)=(X586))=>(subset @ X585 @ X586)))=>(![X587:$i, X588:$i]:((![X589:$i]:(((in @ X589 @ X587)=>(in @ X589 @ X588)))=>(subset @ X587 @ X588)))=>(![X590:$i]:((subset @ emptyset @ X590))=>(![X591:$i, X592:$i, X593:$i]:(((subset @ X591 @ X592)=>((in @ X593 @ X591)=>(in @ X593 @ X592))))=>(![X594:$i, X595:$i, X596:$i]:(((subset @ X594 @ X595)=>(~(in @ X596 @ X595)=>~(in @ X596 @ X594))))=>(![X597:$i, X598:$i, X599:$i]:(((in @ X599 @ X597)=>(~(in @ X599 @ X598)=>~(subset @ X597 @ X598))))=>(![X600:$i, X601:$i]:((~(subset @ X600 @ X601)=>((X600)!=(X601))))=>(![X602:$i, X603:$i, X604:$i]:(((in @ X604 @ X602)=>(~(in @ X604 @ X603)=>((X602)!=(X603)))))=>(![X605:$i]:((subset @ X605 @ X605))=>(![X606:$i, X607:$i, X608:$i]:(((subset @ X606 @ X607)=>((subset @ X607 @ X608)=>(subset @ X606 @ X608))))=>(![X609:$i, X610:$i]:((subset @ X610 @ (setadjoin @ X609 @ X610)))=>(![X611:$i, X612:$i, X613:$i]:(((subset @ X611 @ X613)=>(subset @ X611 @ (setadjoin @ X612 @ X613))))=>(![X614:$i, X615:$i]:(((subset @ X614 @ X615)=>(in @ X614 @ (powerset @ X615))))=>(![X616:$i, X617:$i]:(((subset @ X616 @ X617)=>((subset @ X617 @ X616)=>((X616)=(X617)))))=>(![X618:$i]:(((subset @ X618 @ emptyset)=>((X618)=(emptyset))))=>(![X619:$i, X620:$i]:(((subset @ X620 @ X619)=>(in @ X620 @ (powerset @ X619))))=>(![X621:$i, X622:$i]:(((in @ X622 @ (powerset @ X621))=>(subset @ X622 @ X621)))=>(![X623:$i]:((in @ X623 @ (powerset @ X623)))=>(![X624:$i, X625:$i]:(((subset @ X624 @ X625)=>(subset @ (powerset @ X624) @ (powerset @ X625))))=>(![X626:$i, X627:$i > $o]:((in @ (dsetconstr @ X626 @ X627) @ (powerset @ X626)))=>(![X628:$i, X629:$i > $o]:((subset @ (dsetconstr @ X628 @ X629) @ X628))=>(![X630:$i, X631:$i, X632:$i]:(((in @ X632 @ X630)=>(in @ X632 @ (binunion @ X630 @ X631))))=>(![X633:$i, X634:$i]:((in @ X634 @ (setadjoin @ X633 @ (setadjoin @ X634 @ emptyset))))=>(![X635:$i, X636:$i, X637:$i]:(((in @ X637 @ X636)=>(in @ X637 @ (binunion @ X635 @ X636))))=>(![X638:$i, X639:$i, X640:$i, X641:$o]:(((in @ X640 @ (binunion @ X638 @ X639))=>(((in @ X640 @ X638)=>(X641))=>(((in @ X640 @ X639)=>(X641))=>(X641)))))=>(![X642:$i, X643:$i, X644:$i]:(((in @ X644 @ (binunion @ X642 @ X643))=>((in @ X644 @ X642)|(in @ X644 @ X643))))=>(![X645:$i, X646:$i]:((subset @ X645 @ (binunion @ X645 @ X646)))=>(![X647:$i, X648:$i]:((subset @ X648 @ (binunion @ X647 @ X648)))=>(![X649:$i, X650:$i, X651:$i]:(((in @ X651 @ X649)=>((in @ X651 @ X650)=>(in @ X651 @ (binintersect @ X649 @ X650)))))=>(![X652:$i, X653:$i, X654:$i]:(((subset @ X654 @ X652)=>((subset @ X654 @ X653)=>(subset @ X654 @ (binintersect @ X652 @ X653)))))=>(![X655:$i, X656:$i, X657:$i]:(((in @ X657 @ (binintersect @ X655 @ X656))=>(in @ X657 @ X655)))=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(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_127, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_128]), foundationAx]), wellorderingAx]), c_0_129]), c_0_130]), c_0_131]), c_0_132]), c_0_133]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_134]), setext]), emptyI]), noeltsimpempty]), c_0_135]), c_0_136]), c_0_137]), c_0_138]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_139]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_140]), c_0_141]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_142]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_143]), c_0_144]), c_0_145]), inCongP]), in__Cong]), c_0_146]), c_0_147]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_148]), c_0_149]), c_0_150]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_151]), c_0_152]), binunionIL]), upairset2IR]), binunionIR]), binunionEcases]), binunionE]), binunionLsub]), binunionRsub]), binintersectI]), binintersectSubset5]), binintersectEL])])]), c_0_153])).
% 0.33/0.46 thf(c_0_155, plain, ![X658:$i, X659:$i]:(((binintersect @ X658 @ X659)=(dsetconstr @ X658 @ (^[Z0:$i]:((in @ Z0 @ X659)))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[binintersect])])).
% 0.33/0.46 thf(c_0_156, negated_conjecture, ![X662:$i, X663:$i, X665:$i, X666:$i, X667:$i, X668:$i, X669:$i, X670:$i, X671:$i, X672:$i, X673:$i, X675:$i, X676:$i, X678:$i, X679:$i, X680:$i, X681:$i, X682:$i, X684:$i, X685:$i > $i > $o, X686:$i, X688:$i, X691:$i, X693:$i, X694:$i, X695:$i, X696:$i, X698:$i, X699:$i > $o, X700:$i, X702:$i, X703:$i > $o, X704:$i, X705:$i, X706:$i > $o, X707:$i, X708:$i, X709:$i > $o, X710:$i, X711:$i > $o, X712:$i, X715:$i, X716:$o, X717:$i, X718:$i, X719:$o, X720:$i, X721:$i, X722:$i > $o, X723:$i, X726:$i, X727:$i, X730:$i, X732:$i, X734:$i, X735:$i > $o, X736:$i, X737:$i, X739:$i, X740:$i > $o, X741:$i, X742:$i, X743:$i, X744:$i, X745:$i, X746:$i, X747:$i, X748:$i, X749:$i, X750:$i, X751:$i, X752:$o, X753:$i, X754:$i, X755:$i, X756:$i, X757:$i, X758:$i, X760:$i, X761:$i, X762:$i, X763:$i, X764:$i, X765:$i, X766:$i, X767:$i, X768:$i, X769:$i, X770:$o, X772:$i, X773:$i, X774:$i > $o, X775:$i, X778:$i, X779:$i, X780:$i, X782:$i, X783:$i, X784:$i, X785:$i, X786:$i, X787:$i, X788:$i, X789:$i, X790:$i, X791:$i, X792:$i, X793:$i, X794:$i, X795:$i, X796:$i, X797:$i, X798:$i > $o, X799:$i, X800:$i > $o, X801:$i, X802:$i, X803:$i > $o, X804:$i, X806:$i, X807:$i > $o, X809:$i, X810:$i, X811:$i > $o, X813:$i, X814:$i, X815:$i > $o, X816:$i, X818:$o, X819:$o, X820:$i, X821:$i > $o, X823:$i, X824:$i, X825:$i > $o, X826:$i, X828:$i > $o, X829:$i, X832:$i, X833:$i > $o, X834:$i, X838:$i, X839:$i > $o, X840:$i, X843:$i, X844:$i, X845:$i, X846:$i, X847:$i, X848:$i, X849:$i, X850:$i, X851:$i, X852:$i > $o, X853:$i, X855:$i, X856:$i, X857:$i > $o, X858:$i > $o, X861:$i, X864:$i, X865:$i, X868:$i, X869:$i, X870:$i, X871:$i, X872:$i, X873:$i, X874:$i, X875:$i, X876:$i, X877:$i > $o, X878:$i, X880:$i, X881:$i, X882:$i > $o, X883:$i > $o, X886:$i, X888:$i, X890:$i, X891:$i, X892:$i > $o, X893:$i > $o, X896:$i, X897:$i, X899:$i, X900:$i, X901:$i, X902:$i, X903:$i, X904:$i, X906:$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, X939:$i, X940:$i, X941:$i, X942:$i, X943:$i > $o, X944:$i, X945:$i > $o, X946:$i, X947:$i, X948:$i, X949:$i, X950:$i, X951:$i, X952:$i, X953:$i, X954:$i, X955:$i, X956:$i, X957:$o, X958:$i, X959:$i, X960:$i, X961:$i, X962:$i, X963:$i, X964:$i, X965:$i, X966:$i, X967:$i, X968:$i, X969:$i, X970:$i, X971:$i, X972:$i, X973:$i]:((((~(in @ (esk1_2 @ X662 @ X663) @ X662)|~(in @ (esk1_2 @ X662 @ X663) @ X663)|((X662)=(X663)))&((in @ (esk1_2 @ X662 @ X663) @ X662)|(in @ (esk1_2 @ X662 @ X663) @ X663)|((X662)=(X663))))&(~(in @ X665 @ emptyset)&(((~(in @ X668 @ (setadjoin @ X666 @ X667))|(((X668)=(X666))|(in @ X668 @ X667)))&((((X668)!=(X666))|(in @ X668 @ (setadjoin @ X666 @ X667)))&(~(in @ X668 @ X667)|(in @ X668 @ (setadjoin @ X666 @ X667)))))&(((~(in @ X670 @ (powerset @ X669))|(~(in @ X671 @ X670)|(in @ X671 @ X669)))&(((in @ (esk2_2 @ X672 @ X673) @ X673)|(in @ X673 @ (powerset @ X672)))&(~(in @ (esk2_2 @ X672 @ X673) @ X672)|(in @ X673 @ (powerset @ X672)))))&(((((in @ X676 @ (esk3_2 @ X675 @ X676))|~(in @ X676 @ (setunion @ X675)))&((in @ (esk3_2 @ X675 @ X676) @ X675)|~(in @ X676 @ (setunion @ X675))))&(~(in @ X679 @ X680)|~(in @ X680 @ X678)|(in @ X679 @ (setunion @ X678))))&((in @ emptyset @ omega)&((~(in @ X681 @ omega)|(in @ (setadjoin @ X681 @ X681) @ omega))&(((((in @ (esk4_1 @ X682) @ omega)|~(in @ emptyset @ X682)|(~(in @ X684 @ omega)|(in @ X684 @ X682)))&((in @ (esk4_1 @ X682) @ X682)|~(in @ emptyset @ X682)|(~(in @ X684 @ omega)|(in @ X684 @ X682))))&(~(in @ (setadjoin @ (esk4_1 @ X682) @ (esk4_1 @ X682)) @ X682)|~(in @ emptyset @ X682)|(~(in @ X684 @ omega)|(in @ X684 @ X682))))&((((((in @ (esk8_3 @ X685 @ X686 @ X691) @ X686)|~(in @ X691 @ (esk7_2 @ X685 @ X686))|(in @ (esk5_2 @ X685 @ X686) @ X686))&((X685 @ (esk8_3 @ X685 @ X686 @ X691) @ X691)|~(in @ X691 @ (esk7_2 @ X685 @ X686))|(in @ (esk5_2 @ X685 @ X686) @ X686)))&(~(in @ X694 @ X686)|~(X685 @ X694 @ X693)|(in @ X693 @ (esk7_2 @ X685 @ X686))|(in @ (esk5_2 @ X685 @ X686) @ X686)))&(((((in @ (esk8_3 @ X685 @ X686 @ X691) @ X686)|~(in @ X691 @ (esk7_2 @ X685 @ X686))|((X685 @ (esk5_2 @ X685 @ X686) @ (esk6_3 @ X685 @ X686 @ X688))|~(X685 @ (esk5_2 @ X685 @ X686) @ X688)))&((X685 @ (esk8_3 @ X685 @ X686 @ X691) @ X691)|~(in @ X691 @ (esk7_2 @ X685 @ X686))|((X685 @ (esk5_2 @ X685 @ X686) @ (esk6_3 @ X685 @ X686 @ X688))|~(X685 @ (esk5_2 @ X685 @ X686) @ X688))))&(~(in @ X694 @ X686)|~(X685 @ X694 @ X693)|(in @ X693 @ (esk7_2 @ X685 @ X686))|((X685 @ (esk5_2 @ X685 @ X686) @ (esk6_3 @ X685 @ X686 @ X688))|~(X685 @ (esk5_2 @ X685 @ X686) @ X688))))&((((in @ (esk8_3 @ X685 @ X686 @ X691) @ X686)|~(in @ X691 @ (esk7_2 @ X685 @ X686))|(((X688)!=(esk6_3 @ X685 @ X686 @ X688))|~(X685 @ (esk5_2 @ X685 @ X686) @ X688)))&((X685 @ (esk8_3 @ X685 @ X686 @ X691) @ 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X883)))))&(((X883 @ (esk49_3 @ X882 @ X883 @ X888))|~(X883 @ X888)|((descr @ X882)=(descr @ X883))|(((X886)!=(esk48_3 @ X882 @ X883 @ X886))|~(X882 @ X886))|((X882 @ (esk46_2 @ X882 @ X883))|(X883 @ (esk47_2 @ X882 @ X883))))&(((X888)!=(esk49_3 @ X882 @ X883 @ X888))|~(X883 @ X888)|((descr @ X882)=(descr @ X883))|(((X886)!=(esk48_3 @ X882 @ X883 @ X886))|~(X882 @ X886))|((X882 @ (esk46_2 @ X882 @ X883))|(X883 @ (esk47_2 @ X882 @ X883))))))))&((((in @ (esk50_4 @ X890 @ X891 @ X892 @ X893) @ X890)|((dsetconstr @ X890 @ X892)=(dsetconstr @ X891 @ X893))|((X890)!=(X891)))&(((in @ (esk51_4 @ X890 @ X891 @ X892 @ X893) @ X891)|((dsetconstr @ X890 @ X892)=(dsetconstr @ X891 @ X893))|((X890)!=(X891)))&((((esk50_4 @ X890 @ X891 @ X892 @ X893)=(esk51_4 @ X890 @ X891 @ X892 @ X893))|((dsetconstr @ X890 @ X892)=(dsetconstr @ X891 @ X893))|((X890)!=(X891)))&((~(X892 @ (esk50_4 @ X890 @ X891 @ X892 @ X893))|~(X893 @ (esk51_4 @ X890 @ X891 @ X892 @ X893))|((dsetconstr @ X890 @ X892)=(dsetconstr @ X891 @ X893))|((X890)!=(X891)))&((X892 @ (esk50_4 @ X890 @ X891 @ X892 @ X893))|(X893 @ (esk51_4 @ X890 @ X891 @ X892 @ X893))|((dsetconstr @ X890 @ X892)=(dsetconstr @ X891 @ X893))|((X890)!=(X891)))))))&((((in @ (esk52_2 @ X896 @ X897) @ X896)|(subset @ X896 @ X897))&(~(in @ (esk52_2 @ X896 @ X897) @ X897)|(subset @ X896 @ X897)))&((((X899)!=(X900))|(subset @ X900 @ X899))&((((X901)!=(X902))|(subset @ X901 @ X902))&((((in @ (esk53_2 @ X903 @ X904) @ X903)|(subset @ X903 @ X904))&(~(in @ (esk53_2 @ X903 @ X904) @ X904)|(subset @ X903 @ X904)))&((subset @ emptyset @ X906)&((~(subset @ X907 @ X908)|(~(in @ X909 @ X907)|(in @ X909 @ X908)))&((~(subset @ X910 @ X911)|((in @ X912 @ X911)|~(in @ X912 @ X910)))&((~(in @ X915 @ X913)|((in @ X915 @ X914)|~(subset @ X913 @ X914)))&(((subset @ X916 @ X917)|((X916)!=(X917)))&((~(in @ X920 @ X918)|((in @ X920 @ X919)|((X918)!=(X919))))&((subset @ X921 @ X921)&((~(subset @ X922 @ X923)|(~(subset @ X923 @ X924)|(subset @ X922 @ X924)))&((subset @ X926 @ (setadjoin @ X925 @ X926))&((~(subset @ X927 @ X929)|(subset @ X927 @ (setadjoin @ X928 @ X929)))&((~(subset @ X930 @ X931)|(in @ X930 @ (powerset @ X931)))&((~(subset @ X932 @ X933)|(~(subset @ X933 @ X932)|((X932)=(X933))))&((~(subset @ X934 @ emptyset)|((X934)=(emptyset)))&((~(subset @ X936 @ X935)|(in @ X936 @ (powerset @ X935)))&((~(in @ X938 @ (powerset @ X937))|(subset @ X938 @ X937))&((in @ X939 @ (powerset @ X939))&((~(subset @ X940 @ X941)|(subset @ (powerset @ X940) @ (powerset @ X941)))&((in @ (dsetconstr @ X942 @ X943) @ (powerset @ X942))&((subset @ (dsetconstr @ X944 @ X945) @ X944)&((~(in @ X948 @ X946)|(in @ X948 @ (binunion @ X946 @ X947)))&((in @ X950 @ (setadjoin @ X949 @ (setadjoin @ X950 @ emptyset)))&((~(in @ X953 @ X952)|(in @ X953 @ (binunion @ X951 @ X952)))&(((((in @ X956 @ X955)|(X957)|(in @ X956 @ X954)|~(in @ X956 @ (binunion @ X954 @ X955)))&(~(X957)|(X957)|(in @ X956 @ X954)|~(in @ X956 @ (binunion @ X954 @ X955))))&(((in @ X956 @ X955)|(X957)|~(X957)|~(in @ X956 @ (binunion @ X954 @ X955)))&(~(X957)|(X957)|~(X957)|~(in @ X956 @ (binunion @ X954 @ X955)))))&((~(in @ X960 @ (binunion @ X958 @ X959))|((in @ X960 @ X958)|(in @ X960 @ X959)))&((subset @ X961 @ (binunion @ X961 @ X962))&((subset @ X964 @ (binunion @ X963 @ X964))&((~(in @ X967 @ X965)|(~(in @ X967 @ X966)|(in @ X967 @ (binintersect @ X965 @ X966))))&((~(subset @ X970 @ X968)|(~(subset @ X970 @ X969)|(subset @ X970 @ (binintersect @ X968 @ X969))))&((~(in @ X973 @ (binintersect @ X971 @ X972))|(in @ X973 @ X971))&~(subset @ (binintersect @ esk54_0 @ esk55_0) @ esk54_0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_154])])])])])])])).
% 0.33/0.46 thf(c_0_157, plain, ![X660:$i, X661:$i]:(((binintersect @ X660 @ X661)=(dsetconstr @ X660 @ (^[Z0:$i]:((in @ Z0 @ X661)))))), inference(variable_rename,[status(thm)],[c_0_155])).
% 0.33/0.46 thf(c_0_158, plain, ![X995:$i, X3:$i]:(((epred2_1 @ X3 @ X995)<=>(in @ X995 @ X3))), introduced(definition)).
% 0.33/0.46 thf(c_0_159, negated_conjecture, ![X1:$i > $o, X2:$i]:((subset @ (dsetconstr @ X2 @ X1) @ X2)), inference(split_conjunct,[status(thm)],[c_0_156])).
% 0.33/0.46 thf(c_0_160, plain, ![X2:$i, X3:$i]:(((binintersect @ X2 @ X3)=(dsetconstr @ X2 @ (epred2_1 @ X3)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_157]), c_0_158])).
% 0.33/0.46 thf(c_0_161, negated_conjecture, ~((subset @ (binintersect @ esk54_0 @ esk55_0) @ esk54_0)), inference(split_conjunct,[status(thm)],[c_0_156])).
% 0.33/0.46 thf(c_0_162, negated_conjecture, ![X3:$i, X2:$i]:((subset @ (binintersect @ X2 @ X3) @ X2)), inference(spm,[status(thm)],[c_0_159, c_0_160])).
% 0.33/0.46 thf(c_0_163, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_161, c_0_162])]), ['proof']).
% 0.33/0.46 % SZS output end CNFRefutation
% 0.33/0.46 % Parsed axioms : 237
% 0.33/0.46 % Removed by relevancy pruning/SinE : 0
% 0.33/0.46 % Initial clauses : 352
% 0.33/0.46 % Removed in clause preprocessing : 143
% 0.33/0.46 % Initial clauses in saturation : 209
% 0.33/0.46 % Processed clauses : 47
% 0.33/0.46 % ...of these trivial : 1
% 0.33/0.46 % ...subsumed : 7
% 0.33/0.46 % ...remaining for further processing : 39
% 0.33/0.46 % Other redundant clauses eliminated : 4
% 0.33/0.46 % Clauses deleted for lack of memory : 0
% 0.33/0.46 % Backward-subsumed : 0
% 0.33/0.46 % Backward-rewritten : 3
% 0.33/0.46 % Generated clauses : 28
% 0.33/0.46 % ...of the previous two non-redundant : 18
% 0.33/0.46 % ...aggressively subsumed : 0
% 0.33/0.46 % Contextual simplify-reflections : 0
% 0.33/0.46 % Paramodulations : 24
% 0.33/0.46 % Factorizations : 0
% 0.33/0.46 % NegExts : 0
% 0.33/0.46 % Equation resolutions : 4
% 0.33/0.46 % Disequality decompositions : 0
% 0.33/0.46 % Total rewrite steps : 12
% 0.33/0.46 % ...of those cached : 3
% 0.33/0.46 % Propositional unsat checks : 0
% 0.33/0.46 % Propositional check models : 0
% 0.33/0.46 % Propositional check unsatisfiable : 0
% 0.33/0.46 % Propositional clauses : 0
% 0.33/0.46 % Propositional clauses after purity: 0
% 0.33/0.46 % Propositional unsat core size : 0
% 0.33/0.46 % Propositional preprocessing time : 0.000
% 0.33/0.46 % Propositional encoding time : 0.000
% 0.33/0.46 % Propositional solver time : 0.000
% 0.33/0.46 % Success case prop preproc time : 0.000
% 0.33/0.46 % Success case prop encoding time : 0.000
% 0.33/0.46 % Success case prop solver time : 0.000
% 0.33/0.46 % Current number of processed clauses : 32
% 0.33/0.46 % Positive orientable unit clauses : 22
% 0.33/0.46 % Positive unorientable unit clauses: 0
% 0.33/0.46 % Negative unit clauses : 1
% 0.33/0.46 % Non-unit-clauses : 9
% 0.33/0.46 % Current number of unprocessed clauses: 180
% 0.33/0.46 % ...number of literals in the above : 648
% 0.33/0.46 % Current number of archived formulas : 0
% 0.33/0.46 % Current number of archived clauses : 3
% 0.33/0.46 % Clause-clause subsumption calls (NU) : 11
% 0.33/0.46 % Rec. Clause-clause subsumption calls : 11
% 0.33/0.46 % Non-unit clause-clause subsumptions : 1
% 0.33/0.46 % Unit Clause-clause subsumption calls : 7
% 0.33/0.46 % Rewrite failures with RHS unbound : 0
% 0.33/0.46 % BW rewrite match attempts : 6
% 0.33/0.46 % BW rewrite match successes : 3
% 0.33/0.46 % Condensation attempts : 0
% 0.33/0.46 % Condensation successes : 0
% 0.33/0.46 % Termbank termtop insertions : 29589
% 0.33/0.46 % Search garbage collected termcells : 11319
% 0.33/0.46
% 0.33/0.46 % -------------------------------------------------
% 0.33/0.46 % User time : 0.034 s
% 0.33/0.46 % System time : 0.007 s
% 0.33/0.46 % Total time : 0.040 s
% 0.33/0.46 % Maximum resident set size: 6680 pages
% 0.33/0.46
% 0.33/0.46 % -------------------------------------------------
% 0.33/0.46 % User time : 0.043 s
% 0.33/0.46 % System time : 0.016 s
% 0.33/0.46 % Total time : 0.059 s
% 0.33/0.46 % Maximum resident set size: 4864 pages
% 0.33/0.46 % E exiting
%------------------------------------------------------------------------------