%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU599^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 08:24:40 AM UTC 2026
% Result : Theorem 0.21s 0.32s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU599^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n011.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:56:31 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.21/0.27 Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p
% 0.21/0.32 % Version: 3.5.1-ho
% 0.21/0.32 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.21/0.32 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.32 % Starting ehoh_best5 with 300s (1) cores
% 0.21/0.32 % Starting almost_fo_3_lam with 300s (1) cores
% 0.21/0.32 % Starting new_bool_5 with 300s (1) cores
% 0.21/0.32 % Starting pre_casc_3 with 300s (1) cores
% 0.21/0.32 % Starting ho_unfolding_8 with 300s (1) cores
% 0.21/0.32 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.21/0.32 % Starting new_bool_3 with 300s (1) cores
% 0.21/0.32 % Starting new_ho_5 with 300s (1) cores
% 0.21/0.32 % ehoh_best5 with pid 133308 completed with status 0
% 0.21/0.32 % Result found by ehoh_best5
% 0.21/0.32 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.21/0.32 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.32 % Starting ehoh_best5 with 300s (1) cores
% 0.21/0.32 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.21/0.32 % No SInE strategy applied
% 0.21/0.32 % Search class: HGHSM-FSLM31-SHFMMSBN
% 0.21/0.32 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.32 % Starting SubtermCWHack with 31s (1) cores
% 0.21/0.32 % SubtermCWHack with pid 133322 completed with status 0
% 0.21/0.32 % Result found by SubtermCWHack
% 0.21/0.32 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.21/0.32 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.32 % Starting ehoh_best5 with 300s (1) cores
% 0.21/0.32 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.21/0.32 % No SInE strategy applied
% 0.21/0.32 % Search class: HGHSM-FSLM31-SHFMMSBN
% 0.21/0.32 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.32 % Starting SubtermCWHack with 31s (1) cores
% 0.21/0.32 % Preprocessing time : 0.003 s
% 0.21/0.32
% 0.21/0.32 % Proof found!
% 0.21/0.32 % SZS status Theorem
% 0.21/0.32 % SZS output start CNFRefutation
% 0.21/0.32 thf(decl_23, type, in: $i > $i > $o).
% 0.21/0.32 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.21/0.32 thf(decl_25, type, setextAx: $o).
% 0.21/0.32 thf(decl_26, type, emptyset: $i).
% 0.21/0.32 thf(decl_27, type, emptysetAx: $o).
% 0.21/0.32 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.21/0.32 thf(decl_29, type, setadjoinAx: $o).
% 0.21/0.32 thf(decl_30, type, powerset: $i > $i).
% 0.21/0.32 thf(decl_31, type, powersetAx: $o).
% 0.21/0.32 thf(decl_32, type, setunion: $i > $i).
% 0.21/0.32 thf(decl_33, type, setunionAx: $o).
% 0.21/0.32 thf(decl_34, type, omega: $i).
% 0.21/0.32 thf(decl_35, type, omega0Ax: $o).
% 0.21/0.32 thf(decl_36, type, omegaSAx: $o).
% 0.21/0.32 thf(decl_37, type, omegaIndAx: $o).
% 0.21/0.32 thf(decl_38, type, replAx: $o).
% 0.21/0.32 thf(decl_39, type, foundationAx: $o).
% 0.21/0.32 thf(decl_40, type, wellorderingAx: $o).
% 0.21/0.32 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.21/0.32 thf(decl_42, type, descrp: $o).
% 0.21/0.32 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.21/0.32 thf(decl_44, type, dsetconstrI: $o).
% 0.21/0.32 thf(decl_45, type, dsetconstrEL: $o).
% 0.21/0.32 thf(decl_46, type, dsetconstrER: $o).
% 0.21/0.32 thf(decl_47, type, exuE1: $o).
% 0.21/0.32 thf(decl_48, type, prop2set: $o > $i).
% 0.21/0.32 thf(decl_49, type, prop2setE: $o).
% 0.21/0.32 thf(decl_50, type, emptysetE: $o).
% 0.21/0.32 thf(decl_51, type, emptysetimpfalse: $o).
% 0.21/0.32 thf(decl_52, type, notinemptyset: $o).
% 0.21/0.32 thf(decl_53, type, exuE3e: $o).
% 0.21/0.32 thf(decl_54, type, setext: $o).
% 0.21/0.32 thf(decl_55, type, emptyI: $o).
% 0.21/0.32 thf(decl_56, type, noeltsimpempty: $o).
% 0.21/0.32 thf(decl_57, type, setbeta: $o).
% 0.21/0.32 thf(decl_58, type, nonempty: $i > $o).
% 0.21/0.32 thf(decl_59, type, nonemptyE1: $o).
% 0.21/0.32 thf(decl_60, type, nonemptyI: $o).
% 0.21/0.32 thf(decl_61, type, nonemptyI1: $o).
% 0.21/0.32 thf(decl_62, type, setadjoinIL: $o).
% 0.21/0.32 thf(decl_63, type, emptyinunitempty: $o).
% 0.21/0.32 thf(decl_64, type, setadjoinIR: $o).
% 0.21/0.32 thf(decl_65, type, setadjoinE: $o).
% 0.21/0.32 thf(decl_66, type, setadjoinOr: $o).
% 0.21/0.32 thf(decl_67, type, setoftrueEq: $o).
% 0.21/0.32 thf(decl_68, type, powersetI: $o).
% 0.21/0.32 thf(decl_69, type, emptyinPowerset: $o).
% 0.21/0.32 thf(decl_70, type, emptyInPowerset: $o).
% 0.21/0.32 thf(decl_71, type, powersetE: $o).
% 0.21/0.32 thf(decl_72, type, setunionI: $o).
% 0.21/0.32 thf(decl_73, type, setunionE: $o).
% 0.21/0.32 thf(decl_74, type, subPowSU: $o).
% 0.21/0.32 thf(decl_75, type, exuE2: $o).
% 0.21/0.32 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.21/0.32 thf(decl_77, type, uniqinunit: $o).
% 0.21/0.32 thf(decl_78, type, notinsingleton: $o).
% 0.21/0.32 thf(decl_79, type, eqinunit: $o).
% 0.21/0.32 thf(decl_80, type, singletonsswitch: $o).
% 0.21/0.32 thf(decl_81, type, upairsetE: $o).
% 0.21/0.32 thf(decl_82, type, upairsetIL: $o).
% 0.21/0.32 thf(decl_83, type, upairsetIR: $o).
% 0.21/0.32 thf(decl_84, type, emptyE1: $o).
% 0.21/0.32 thf(decl_85, type, vacuousDall: $o).
% 0.21/0.32 thf(decl_86, type, quantDeMorgan1: $o).
% 0.21/0.32 thf(decl_87, type, quantDeMorgan2: $o).
% 0.21/0.32 thf(decl_88, type, quantDeMorgan3: $o).
% 0.21/0.32 thf(decl_89, type, quantDeMorgan4: $o).
% 0.21/0.32 thf(decl_90, type, prop2setI: $o).
% 0.21/0.32 thf(decl_91, type, set2prop: $i > $o).
% 0.21/0.32 thf(decl_92, type, prop2set2propI: $o).
% 0.21/0.32 thf(decl_93, type, notdexE: $o).
% 0.21/0.32 thf(decl_94, type, notdallE: $o).
% 0.21/0.32 thf(decl_95, type, exuI1: $o).
% 0.21/0.32 thf(decl_96, type, exuI3: $o).
% 0.21/0.32 thf(decl_97, type, exuI2: $o).
% 0.21/0.32 thf(decl_98, type, inCongP: $o).
% 0.21/0.32 thf(decl_99, type, in__Cong: $o).
% 0.21/0.32 thf(decl_100, type, exuE3u: $o).
% 0.21/0.32 thf(decl_101, type, exu__Cong: $o).
% 0.21/0.32 thf(decl_102, type, emptyset__Cong: $o).
% 0.21/0.32 thf(decl_103, type, setadjoin__Cong: $o).
% 0.21/0.32 thf(decl_104, type, powerset__Cong: $o).
% 0.21/0.32 thf(decl_105, type, setunion__Cong: $o).
% 0.21/0.32 thf(decl_106, type, omega__Cong: $o).
% 0.21/0.32 thf(decl_107, type, exuEu: $o).
% 0.21/0.32 thf(decl_108, type, descr__Cong: $o).
% 0.21/0.32 thf(decl_109, type, dsetconstr__Cong: $o).
% 0.21/0.32 thf(decl_110, type, subset: $i > $i > $o).
% 0.21/0.32 thf(decl_113, type, subsetI1: $o).
% 0.21/0.32 thf(decl_114, type, eqimpsubset2: $o).
% 0.21/0.32 thf(decl_115, type, eqimpsubset1: $o).
% 0.21/0.32 thf(decl_116, type, subsetI2: $o).
% 0.21/0.32 thf(decl_117, type, emptysetsubset: $o).
% 0.21/0.32 thf(decl_118, type, subsetE: $o).
% 0.21/0.32 thf(decl_119, type, subsetE2: $o).
% 0.21/0.32 thf(decl_120, type, notsubsetI: $o).
% 0.21/0.32 thf(decl_121, type, notequalI1: $o).
% 0.21/0.32 thf(decl_122, type, notequalI2: $o).
% 0.21/0.32 thf(decl_123, type, subsetRefl: $o).
% 0.21/0.32 thf(decl_124, type, subsetTrans: $o).
% 0.21/0.32 thf(decl_125, type, setadjoinSub: $o).
% 0.21/0.32 thf(decl_126, type, setadjoinSub2: $o).
% 0.21/0.32 thf(decl_127, type, subset2powerset: $o).
% 0.21/0.32 thf(decl_128, type, setextsub: $o).
% 0.21/0.32 thf(decl_129, type, subsetemptysetimpeq: $o).
% 0.21/0.32 thf(decl_130, type, powersetI1: $o).
% 0.21/0.32 thf(decl_131, type, powersetE1: $o).
% 0.21/0.32 thf(decl_132, type, inPowerset: $o).
% 0.21/0.32 thf(decl_133, type, powersetsubset: $o).
% 0.21/0.32 thf(decl_134, type, sepInPowerset: $o).
% 0.21/0.32 thf(decl_135, type, sepSubset: $o).
% 0.21/0.32 thf(decl_136, type, binunion: $i > $i > $i).
% 0.21/0.32 thf(decl_137, type, binunionIL: $o).
% 0.21/0.32 thf(decl_138, type, upairset2IR: $o).
% 0.21/0.32 thf(decl_139, type, binunionIR: $o).
% 0.21/0.32 thf(decl_140, type, binunionEcases: $o).
% 0.21/0.32 thf(decl_141, type, binunionE: $o).
% 0.21/0.32 thf(decl_142, type, binunionLsub: $o).
% 0.21/0.32 thf(decl_143, type, binunionRsub: $o).
% 0.21/0.32 thf(decl_144, type, binintersect: $i > $i > $i).
% 0.21/0.32 thf(decl_145, type, binintersectI: $o).
% 0.21/0.32 thf(decl_146, type, binintersectSubset5: $o).
% 0.21/0.32 thf(decl_147, type, binintersectEL: $o).
% 0.21/0.32 thf(decl_148, type, binintersectLsub: $o).
% 0.21/0.32 thf(decl_149, type, binintersectSubset2: $o).
% 0.21/0.32 thf(decl_150, type, binintersectSubset3: $o).
% 0.21/0.32 thf(decl_151, type, binintersectER: $o).
% 0.21/0.32 thf(decl_152, type, disjointsetsI1: $o).
% 0.21/0.32 thf(decl_153, type, binintersectRsub: $o).
% 0.21/0.32 thf(decl_154, type, binintersectSubset4: $o).
% 0.21/0.32 thf(decl_155, type, epred1_0: $o).
% 0.21/0.32 thf(decl_156, type, esk1_2: $i > $i > $i).
% 0.21/0.32 thf(decl_157, type, esk2_2: $i > $i > $i).
% 0.21/0.32 thf(decl_158, type, esk3_2: $i > $i > $i).
% 0.21/0.32 thf(decl_159, type, esk4_1: $i > $i).
% 0.21/0.32 thf(decl_160, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.21/0.32 thf(decl_161, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.21/0.32 thf(decl_162, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.21/0.32 thf(decl_163, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.21/0.32 thf(decl_164, type, esk9_1: $i > $i).
% 0.21/0.32 thf(decl_165, type, esk10_2: ($i > $o) > $i > $i).
% 0.21/0.32 thf(decl_166, type, esk11_2: ($i > $o) > $i > $i).
% 0.21/0.32 thf(decl_167, type, esk12_1: ($i > $o) > $i).
% 0.21/0.32 thf(decl_168, type, esk13_2: ($i > $o) > $i > $i).
% 0.21/0.32 thf(decl_169, type, esk14_1: ($i > $o) > $i).
% 0.21/0.32 thf(decl_170, type, esk15_2: $i > $i > $i).
% 0.21/0.32 thf(decl_171, type, esk16_2: $i > $i > $i).
% 0.21/0.32 thf(decl_172, type, esk17_1: $i > $i).
% 0.21/0.32 thf(decl_173, type, esk18_1: $i > $i).
% 0.21/0.32 thf(decl_174, type, esk19_1: $i > $i).
% 0.21/0.32 thf(decl_175, type, esk20_2: $i > $i > $i).
% 0.21/0.32 thf(decl_176, type, esk21_3: $i > $i > $o > $i).
% 0.21/0.32 thf(decl_177, type, esk22_2: ($i > $o) > $i > $i).
% 0.21/0.32 thf(decl_178, type, esk23_1: ($i > $o) > $i).
% 0.21/0.32 thf(decl_179, type, esk24_1: $i > $i).
% 0.21/0.32 thf(decl_180, type, esk25_2: $i > ($i > $o) > $i).
% 0.21/0.32 thf(decl_181, type, esk26_2: $i > ($i > $o) > $i).
% 0.21/0.32 thf(decl_182, type, esk27_2: $i > ($i > $o) > $i).
% 0.21/0.32 thf(decl_183, type, esk28_2: $i > ($i > $o) > $i).
% 0.21/0.32 thf(decl_184, type, esk29_2: $i > ($i > $o) > $i).
% 0.21/0.32 thf(decl_185, type, esk30_2: $i > ($i > $o) > $i).
% 0.21/0.32 thf(decl_186, type, esk31_2: ($i > $o) > $i > $i).
% 0.21/0.32 thf(decl_187, type, esk32_1: ($i > $o) > $i).
% 0.21/0.32 thf(decl_188, type, esk33_1: ($i > $o) > $i).
% 0.21/0.32 thf(decl_189, type, esk34_1: ($i > $o) > $i).
% 0.21/0.32 thf(decl_190, type, esk35_1: ($i > $o) > $i).
% 0.21/0.32 thf(decl_191, type, esk36_2: ($i > $o) > $i > $i).
% 0.21/0.32 thf(decl_192, type, esk37_1: ($i > $o) > $i).
% 0.21/0.32 thf(decl_193, type, esk38_2: ($i > $o) > $i > $i).
% 0.21/0.32 thf(decl_194, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 0.21/0.32 thf(decl_195, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 0.21/0.32 thf(decl_196, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.21/0.32 thf(decl_197, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 0.21/0.32 thf(decl_198, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.21/0.32 thf(decl_199, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 0.21/0.32 thf(decl_200, type, esk45_2: ($i > $o) > $i > $i).
% 0.21/0.32 thf(decl_201, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 0.21/0.32 thf(decl_202, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 0.21/0.32 thf(decl_203, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.21/0.32 thf(decl_204, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.21/0.32 thf(decl_205, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.21/0.32 thf(decl_206, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.21/0.32 thf(decl_207, type, esk52_2: $i > $i > $i).
% 0.21/0.32 thf(decl_208, type, esk53_2: $i > $i > $i).
% 0.21/0.32 thf(decl_209, type, esk54_2: $i > $i > $i).
% 0.21/0.32 thf(decl_210, type, esk55_0: $i).
% 0.21/0.32 thf(decl_211, type, esk56_0: $i).
% 0.21/0.32 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', replAx)).
% 0.21/0.32 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', exu)).
% 0.21/0.32 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', descrp)).
% 0.21/0.32 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', exuE1)).
% 0.21/0.32 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', exuE3e)).
% 0.21/0.32 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', nonempty)).
% 0.21/0.32 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', nonemptyI)).
% 0.21/0.32 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', exuE2)).
% 0.21/0.32 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', exuI1)).
% 0.21/0.32 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', exuI3)).
% 0.21/0.32 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', exuI2)).
% 0.21/0.32 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', exuE3u)).
% 0.21/0.32 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', exu__Cong)).
% 0.21/0.32 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', exuEu)).
% 0.21/0.32 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', descr__Cong)).
% 0.21/0.32 thf(binintersectSubset1, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', binintersectSubset1)).
% 0.21/0.32 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', dsetconstrI)).
% 0.21/0.32 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', dsetconstrEL)).
% 0.21/0.32 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', dsetconstrER)).
% 0.21/0.32 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', setbeta)).
% 0.21/0.32 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', nonemptyE1)).
% 0.21/0.32 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', nonemptyI1)).
% 0.21/0.32 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', setoftrueEq)).
% 0.21/0.32 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', nonemptyImpWitness)).
% 0.21/0.32 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', emptyE1)).
% 0.21/0.32 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', dsetconstr__Cong)).
% 0.21/0.32 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', sepInPowerset)).
% 0.21/0.32 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', sepSubset)).
% 0.21/0.32 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', setextAx)).
% 0.21/0.32 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', emptysetAx)).
% 0.21/0.32 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', setadjoinAx)).
% 0.21/0.32 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', powersetAx)).
% 0.21/0.32 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', setunionAx)).
% 0.21/0.32 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', omega0Ax)).
% 0.21/0.32 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', omegaSAx)).
% 0.21/0.32 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', omegaIndAx)).
% 0.21/0.32 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', foundationAx)).
% 0.21/0.32 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', wellorderingAx)).
% 0.21/0.32 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', prop2setE)).
% 0.21/0.32 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', emptysetE)).
% 0.21/0.32 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', emptysetimpfalse)).
% 0.21/0.32 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', notinemptyset)).
% 0.21/0.32 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', setext)).
% 0.21/0.32 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', emptyI)).
% 0.21/0.32 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', noeltsimpempty)).
% 0.21/0.32 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', setadjoinIL)).
% 0.21/0.32 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', emptyinunitempty)).
% 0.21/0.32 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', setadjoinIR)).
% 0.21/0.32 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', setadjoinE)).
% 0.21/0.32 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', setadjoinOr)).
% 0.21/0.32 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', powersetI)).
% 0.21/0.32 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', emptyinPowerset)).
% 0.21/0.32 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', emptyInPowerset)).
% 0.21/0.32 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', powersetE)).
% 0.21/0.32 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', setunionI)).
% 0.21/0.32 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', setunionE)).
% 0.21/0.32 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', subPowSU)).
% 0.21/0.32 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', uniqinunit)).
% 0.21/0.32 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', notinsingleton)).
% 0.21/0.32 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', eqinunit)).
% 0.21/0.32 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', singletonsswitch)).
% 0.21/0.32 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', upairsetE)).
% 0.21/0.32 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', upairsetIL)).
% 0.21/0.32 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', upairsetIR)).
% 0.21/0.32 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', vacuousDall)).
% 0.21/0.32 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', quantDeMorgan1)).
% 0.21/0.32 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', quantDeMorgan2)).
% 0.21/0.32 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', quantDeMorgan3)).
% 0.21/0.32 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', quantDeMorgan4)).
% 0.21/0.32 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', prop2setI)).
% 0.21/0.32 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', prop2set2propI)).
% 0.21/0.32 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', notdexE)).
% 0.21/0.32 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', notdallE)).
% 0.21/0.32 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', inCongP)).
% 0.21/0.32 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', in__Cong)).
% 0.21/0.32 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', emptyset__Cong)).
% 0.21/0.32 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', setadjoin__Cong)).
% 0.21/0.32 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', powerset__Cong)).
% 0.21/0.32 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', setunion__Cong)).
% 0.21/0.32 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', omega__Cong)).
% 0.21/0.32 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', subsetI1)).
% 0.21/0.32 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', eqimpsubset2)).
% 0.21/0.32 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', eqimpsubset1)).
% 0.21/0.32 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', subsetI2)).
% 0.21/0.32 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', emptysetsubset)).
% 0.21/0.32 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', subsetE)).
% 0.21/0.32 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', subsetE2)).
% 0.21/0.32 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', notsubsetI)).
% 0.21/0.32 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', notequalI1)).
% 0.21/0.32 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', notequalI2)).
% 0.21/0.32 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', subsetRefl)).
% 0.21/0.32 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', subsetTrans)).
% 0.21/0.32 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', setadjoinSub)).
% 0.21/0.32 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', setadjoinSub2)).
% 0.21/0.32 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', subset2powerset)).
% 0.21/0.32 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', setextsub)).
% 0.21/0.32 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', subsetemptysetimpeq)).
% 0.21/0.32 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', powersetI1)).
% 0.21/0.32 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', powersetE1)).
% 0.21/0.32 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', inPowerset)).
% 0.21/0.32 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', powersetsubset)).
% 0.21/0.32 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', binunionIL)).
% 0.21/0.32 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', upairset2IR)).
% 0.21/0.32 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', binunionIR)).
% 0.21/0.32 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', binunionEcases)).
% 0.21/0.32 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', binunionE)).
% 0.21/0.32 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', binunionLsub)).
% 0.21/0.32 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', binunionRsub)).
% 0.21/0.32 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', binintersectI)).
% 0.21/0.32 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', binintersectSubset5)).
% 0.21/0.32 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', binintersectEL)).
% 0.21/0.32 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', binintersectLsub)).
% 0.21/0.32 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', binintersectSubset2)).
% 0.21/0.32 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', binintersectSubset3)).
% 0.21/0.32 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', binintersectER)).
% 0.21/0.32 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', disjointsetsI1)).
% 0.21/0.32 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', binintersectRsub)).
% 0.21/0.32 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.95iUwWXBAn/E---3.1_133270.p', binintersectSubset4)).
% 0.21/0.32 thf(c_0_118, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.21/0.32 thf(c_0_119, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.21/0.32 thf(c_0_120, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.21/0.32 thf(c_0_121, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.21/0.32 thf(c_0_122, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.21/0.32 thf(c_0_123, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.21/0.32 thf(c_0_124, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.21/0.32 thf(c_0_125, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.21/0.32 thf(c_0_126, 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])).
% 0.21/0.32 thf(c_0_127, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.21/0.32 thf(c_0_128, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.21/0.32 thf(c_0_129, 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])).
% 0.21/0.32 thf(c_0_130, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.21/0.32 thf(c_0_131, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 0.21/0.32 thf(c_0_132, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 0.21/0.32 thf(c_0_133, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[binintersectSubset1])).
% 0.21/0.32 thf(c_0_134, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X328:$i]:(((((X6 @ X2 @ X328)))&(![X329:$i]:(((((X6 @ X2 @ X329)))=>(((X328)=(X329)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_118, c_0_119])).
% 0.21/0.32 thf(c_0_135, plain, ((descrp)=(![X1:$i > $o]:((((?[X330:$i]:(((((X1 @ X330)))&(![X331:$i]:(((((X1 @ X331)))=>(((X330)=(X331))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_120, c_0_119])).
% 0.21/0.32 thf(c_0_136, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.21/0.32 thf(c_0_137, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.21/0.32 thf(c_0_138, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.21/0.32 thf(c_0_139, plain, ((exuE1)=(![X1:$i > $o]:((((?[X332:$i]:(((((X1 @ X332)))&(![X333:$i]:(((((X1 @ X333)))=>(((X332)=(X333))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_121, c_0_119])).
% 0.21/0.32 thf(c_0_140, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X334:$i]:(((((X1 @ X334)))&(![X335:$i]:(((((X1 @ X335)))=>(((X334)=(X335))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_122, c_0_119])).
% 0.21/0.32 thf(c_0_141, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.21/0.32 thf(c_0_142, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_123])).
% 0.21/0.32 thf(c_0_143, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_124, c_0_123])).
% 0.21/0.32 thf(c_0_144, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_123])).
% 0.21/0.32 thf(c_0_145, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.21/0.32 thf(c_0_146, plain, ((exuE2)=(![X1:$i > $o]:((((?[X336:$i]:(((((X1 @ X336)))&(![X337:$i]:(((((X1 @ X337)))=>(((X336)=(X337))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_125, c_0_119])).
% 0.21/0.32 thf(c_0_147, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_123])).
% 0.21/0.32 thf(c_0_148, 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])).
% 0.21/0.32 thf(c_0_149, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X338:$i]:(((((X1 @ X338)))&(![X339:$i]:(((((X1 @ X339)))=>(((X338)=(X339)))))))))))))), inference(apply_def,[status(thm)],[c_0_126, c_0_119])).
% 0.21/0.32 thf(c_0_150, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X340:$i]:(((((X1 @ X340)))&(![X341:$i]:(((((X1 @ X341)))=>(((X340)=(X341)))))))))))))))), inference(apply_def,[status(thm)],[c_0_127, c_0_119])).
% 0.21/0.32 thf(c_0_151, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X342:$i]:(((((X1 @ X342)))&(![X343:$i]:(((((X1 @ X343)))=>(((X342)=(X343)))))))))))))), inference(apply_def,[status(thm)],[c_0_128, c_0_119])).
% 0.21/0.32 thf(c_0_152, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X344:$i]:(((((X1 @ X344)))&(![X345:$i]:(((((X1 @ X345)))=>(((X344)=(X345))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_129, c_0_119])).
% 0.21/0.32 thf(c_0_153, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X346:$i]:(((((X1 @ X346)))&(![X347:$i]:(((((X1 @ X347)))=>(((X346)=(X347))))))))))<=>((?[X348:$i]:(((((X17 @ X348)))&(![X349:$i]:(((((X17 @ X349)))=>(((X348)=(X349)))))))))))))))), inference(apply_def,[status(thm)],[c_0_130, c_0_119])).
% 0.21/0.32 thf(c_0_154, plain, ((exuEu)=(![X1:$i > $o]:((((?[X350:$i]:(((((X1 @ X350)))&(![X351:$i]:(((((X1 @ X351)))=>(((X350)=(X351))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_131, c_0_119])).
% 0.21/0.32 thf(c_0_155, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X352:$i]:(((((X1 @ X352)))&(![X353:$i]:(((((X1 @ X353)))=>(((X352)=(X353))))))))))=>((((?[X354:$i]:(((((X17 @ X354)))&(![X355:$i]:(((((X17 @ X355)))=>(((X354)=(X355))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_132, c_0_119])).
% 0.21/0.32 thf(c_0_156, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 0.21/0.32 thf(c_0_157, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 0.21/0.32 thf(c_0_158, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 0.21/0.32 thf(c_0_159, plain, ((epred1_0)<=>![X385:$i]:(?[X386:$i]:((((![X387:$i]:(((in @ X387 @ X386)=>![X388:$i]:(((in @ X388 @ X387)=>(in @ X388 @ X385)))))&![X389:$i, X390:$i]:((((in @ X389 @ X385)&(in @ X390 @ X385))=>(![X391:$i]:(((in @ X391 @ X386)=>((in @ X389 @ X391)<=>(in @ X390 @ X391))))=>((X389)=(X390))))))&![X392:$i, X393:$i]:((((in @ X392 @ X386)&(in @ X393 @ X386))=>(![X394:$i]:(((in @ X394 @ X392)=>(in @ X394 @ X393)))|![X395:$i]:(((in @ X395 @ X393)=>(in @ X395 @ X392)))))))&![X396:$i]:(((![X397:$i]:(((in @ X397 @ X396)=>(in @ X397 @ X385)))&?[X398:$i]:((in @ X398 @ X396)))=>?[X399:$i, X400:$i]:(((((in @ X399 @ X386)&(in @ X400 @ X396))&~(?[X401:$i]:(((in @ X401 @ X399)&(in @ X401 @ X396)))))&![X402:$i]:(((in @ X402 @ X386)=>(![X403:$i]:(((in @ X403 @ X402)=>(in @ X403 @ X399)))|(in @ X400 @ X402)))))))))))), introduced(definition)).
% 0.21/0.32 thf(c_0_160, negated_conjecture, ~((![X356:$i, X357:$i]:((![X358:$i]:(((in @ X358 @ X356)<=>(in @ X358 @ X357)))=>((X356)=(X357))))=>(![X359:$i]:(~(in @ X359 @ emptyset))=>(![X360:$i, X361:$i, X362:$i]:(((in @ X362 @ (setadjoin @ X360 @ X361))<=>(((X362)=(X360))|(in @ X362 @ X361))))=>(![X363:$i, X364:$i]:(((in @ X364 @ (powerset @ X363))<=>![X365:$i]:(((in @ X365 @ X364)=>(in @ X365 @ X363)))))=>(![X366:$i, X367:$i]:(((in @ X367 @ (setunion @ X366))<=>?[X368:$i]:(((in @ X367 @ X368)&(in @ X368 @ X366)))))=>((in @ emptyset @ omega)=>(![X369:$i]:(((in @ X369 @ omega)=>(in @ (setadjoin @ X369 @ X369) @ omega)))=>(![X370:$i]:((((in @ emptyset @ X370)&![X371:$i]:((((in @ X371 @ omega)&(in @ X371 @ X370))=>(in @ (setadjoin @ X371 @ X371) @ X370))))=>![X372:$i]:(((in @ X372 @ omega)=>(in @ X372 @ X370)))))=>(![X373:$i > $i > $o, X374:$i]:((![X375:$i]:(((in @ X375 @ X374)=>?[X376:$i]:(((X373 @ X375 @ X376)&![X377:$i]:(((X373 @ X375 @ X377)=>((X376)=(X377))))))))=>?[X378:$i]:(![X379:$i]:(((in @ X379 @ X378)<=>?[X380:$i]:(((in @ X380 @ X374)&(X373 @ X380 @ X379))))))))=>(![X381:$i]:((?[X382:$i]:((in @ X382 @ X381))=>?[X383:$i]:(((in @ X383 @ X381)&~(?[X384:$i]:(((in @ X384 @ X383)&(in @ X384 @ X381))))))))=>((epred1_0)=>(![X404:$i > $o]:((?[X405:$i]:(((X404 @ X405)&![X406:$i]:(((X404 @ X406)=>((X405)=(X406))))))=>(X404 @ (descr @ (^[Z0:$i]:(X404 @ Z0))))))=>(![X407:$i, X408:$i > $o, X409:$i]:(((in @ X409 @ X407)=>((X408 @ X409)=>(in @ X409 @ (dsetconstr @ X407 @ X408)))))=>(![X410:$i, X411:$i > $o, X412:$i]:(((in @ X412 @ (dsetconstr @ X410 @ X411))=>(in @ X412 @ X410)))=>(![X413:$i, X414:$i > $o, X415:$i]:(((in @ X415 @ (dsetconstr @ X413 @ X414))=>(X414 @ X415)))=>(![X416:$i > $o]:((?[X417:$i]:(((X416 @ X417)&![X418:$i]:(((X416 @ X418)=>((X417)=(X418))))))=>?[X419:$i]:(((X416 @ X419)&![X420:$i]:(((X416 @ X420)=>((X419)=(X420))))))))=>(![X421:$o, X422:$i]:(((in @ X422 @ (prop2set @ ((X421))))=>(X421)))=>(![X423:$i]:(((in @ X423 @ emptyset)=>![X424:$o]:((X424))))=>(![X425:$i]:(((in @ X425 @ emptyset)=>~($true)))=>(![X426:$i]:(~(in @ X426 @ emptyset))=>(![X427:$i > $o]:((?[X428:$i]:(((X427 @ X428)&![X429:$i]:(((X427 @ X429)=>((X428)=(X429))))))=>?[X430:$i]:((X427 @ X430))))=>(![X431:$i, X432:$i]:((![X433:$i]:(((in @ X433 @ X431)=>(in @ X433 @ X432)))=>(![X434:$i]:(((in @ X434 @ X432)=>(in @ X434 @ X431)))=>((X431)=(X432)))))=>(![X435:$i]:((![X436:$i]:(~(in @ X436 @ X435))=>((X435)=(emptyset))))=>(![X437:$i]:((![X438:$i]:(~(in @ X438 @ X437))=>((X437)=(emptyset))))=>(![X439:$i, X440:$i > $o, X441:$i]:(((in @ X441 @ X439)=>((in @ X441 @ (dsetconstr @ X439 @ X440))<=>(X440 @ X441))))=>(![X442:$i]:((((X442)!=(emptyset))=>?[X443:$i]:((in @ X443 @ X442))))=>(![X444:$i, X445:$i > $o, X446:$i]:(((in @ X446 @ X444)=>((X445 @ X446)=>((dsetconstr @ X444 @ X445)!=(emptyset)))))=>(![X447:$i]:((?[X448:$i]:((in @ X448 @ X447))=>((X447)!=(emptyset))))=>(![X449:$i, X450:$i]:((in @ X449 @ (setadjoin @ X449 @ X450)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X451:$i, X452:$i, X453:$i]:(((in @ X453 @ X452)=>(in @ X453 @ (setadjoin @ X451 @ X452))))=>(![X454:$i, X455:$i, X456:$i]:(((in @ X456 @ (setadjoin @ X454 @ X455))=>![X457:$o]:(((((X456)=(X454))=>(X457))=>(((in @ X456 @ X455)=>(X457))=>(X457))))))=>(![X458:$i, X459:$i, X460:$i]:(((in @ X460 @ (setadjoin @ X458 @ X459))=>(((X460)=(X458))|(in @ X460 @ X459))))=>(![X461:$i]:(((dsetconstr @ X461 @ (^[Z0:$i]:($true)))=(X461)))=>(![X462:$i, X463:$i]:((![X464:$i]:(((in @ X464 @ X463)=>(in @ X464 @ X462)))=>(in @ X463 @ (powerset @ X462))))=>(![X465:$i]:((in @ emptyset @ (powerset @ X465)))=>(![X466:$i]:((in @ emptyset @ (powerset @ X466)))=>(![X467:$i, X468:$i, X469:$i]:(((in @ X468 @ (powerset @ X467))=>((in @ X469 @ X468)=>(in @ X469 @ X467))))=>(![X470:$i, X471:$i, X472:$i]:(((in @ X471 @ X472)=>((in @ X472 @ X470)=>(in @ X471 @ (setunion @ X470)))))=>(![X473:$i, X474:$i]:(((in @ X474 @ (setunion @ X473))=>![X475:$o]:((![X476:$i]:(((in @ X474 @ X476)=>((in @ X476 @ X473)=>(X475))))=>(X475)))))=>(![X477:$i, X478:$i]:(((in @ X478 @ X477)=>(in @ X478 @ (powerset @ (setunion @ X477)))))=>(![X479:$i > $o]:((?[X480:$i]:(((X479 @ X480)&![X481:$i]:(((X479 @ X481)=>((X480)=(X481))))))=>?[X482:$i]:(![X483:$i]:(((X479 @ X483)<=>((X483)=(X482)))))))=>(![X484:$i]:((((X484)!=(emptyset))=>?[X485:$i]:(((in @ X485 @ X484)&$true))))=>(![X486:$i, X487:$i]:(((in @ X486 @ (setadjoin @ X487 @ emptyset))=>((X486)=(X487))))=>(![X488:$i, X489:$i]:((((X488)!=(X489))=>~(in @ X489 @ (setadjoin @ X488 @ emptyset))))=>(![X490:$i, X491:$i]:((((X490)=(X491))=>(in @ X490 @ (setadjoin @ X491 @ emptyset))))=>(![X492:$i, X493:$i]:(((in @ X492 @ (setadjoin @ X493 @ emptyset))=>(in @ X493 @ (setadjoin @ X492 @ emptyset))))=>(![X494:$i, X495:$i, X496:$i]:(((in @ X496 @ (setadjoin @ X494 @ (setadjoin @ X495 @ emptyset)))=>(((X496)=(X494))|((X496)=(X495)))))=>(![X497:$i, X498:$i]:((in @ X497 @ (setadjoin @ X497 @ (setadjoin @ X498 @ emptyset))))=>(![X499:$i, X500:$i]:((in @ X500 @ (setadjoin @ X499 @ (setadjoin @ X500 @ emptyset))))=>(![X501:$i, X502:$i > $o]:((?[X503:$i]:(((in @ X503 @ X501)&(X502 @ X503)))=>(((dsetconstr @ X501 @ X502)=(emptyset))=>~($true))))=>(![X504:$i > $o, X505:$i]:(((in @ X505 @ emptyset)=>(X504 @ 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, X515:$i > $o]:((~(?[X516:$i]:(((in @ X516 @ X514)&(X515 @ X516))))=>![X517:$i]:(((in @ X517 @ X514)=>~((X515 @ X517))))))=>(![X518:$i, X519:$i > $o]:((?[X520:$i]:(((in @ X520 @ X518)&~((X519 @ X520))))=>~(![X521:$i]:(((in @ X521 @ X518)=>(X519 @ X521))))))=>(![X522:$o]:(((X522)=>(in @ emptyset @ (prop2set @ ((X522))))))=>(![X523:$o]:(((X523)=>(set2prop @ (prop2set @ ((X523))))))=>(![X524:$i, X525:$i > $o]:((~(?[X526:$i]:(((in @ X526 @ X524)&(X525 @ X526))))=>![X527:$i]:(((in @ X527 @ X524)=>~((X525 @ X527))))))=>(![X528:$i, X529:$i > $o]:((~(![X530:$i]:(((in @ X530 @ X528)=>(X529 @ X530))))=>?[X531:$i]:(((in @ X531 @ X528)&~((X529 @ X531))))))=>(![X532:$i > $o]:((?[X533:$i]:(((X532 @ X533)&![X534:$i]:(((X532 @ X534)=>((X533)=(X534))))))=>?[X535:$i]:(((X532 @ X535)&![X536:$i]:(((X532 @ X536)=>((X535)=(X536))))))))=>(![X537:$i > $o]:((?[X538:$i]:((X537 @ X538))=>(![X539:$i, X540:$i]:(((X537 @ X539)=>((X537 @ X540)=>((X539)=(X540)))))=>?[X541:$i]:(((X537 @ X541)&![X542:$i]:(((X537 @ X542)=>((X541)=(X542)))))))))=>(![X543:$i > $o]:((?[X544:$i]:(![X545:$i]:(((X543 @ X545)<=>((X545)=(X544)))))=>?[X546:$i]:(((X543 @ X546)&![X547:$i]:(((X543 @ X547)=>((X546)=(X547))))))))=>(![X548:$i, X549:$i]:((((X548)=(X549))=>![X550:$i, X551:$i]:((((X550)=(X551))=>((in @ X550 @ X548)=>(in @ X551 @ X549))))))=>(![X552:$i, X553:$i]:((((X552)=(X553))=>![X554:$i, X555:$i]:((((X554)=(X555))=>((in @ X554 @ X552)<=>(in @ X555 @ X553))))))=>(![X556:$i > $o]:((?[X557:$i]:(((X556 @ X557)&![X558:$i]:(((X556 @ X558)=>((X557)=(X558))))))=>![X559:$i, X560:$i]:(((X556 @ X559)=>((X556 @ X560)=>((X559)=(X560)))))))=>(![X561:$i > $o, X562:$i > $o]:((![X563:$i, X564:$i]:((((X563)=(X564))=>((X561 @ X563)<=>(X562 @ X564))))=>(?[X565:$i]:(((X561 @ X565)&![X566:$i]:(((X561 @ X566)=>((X565)=(X566))))))<=>?[X567:$i]:(((X562 @ X567)&![X568:$i]:(((X562 @ X568)=>((X567)=(X568)))))))))=>(((emptyset)=(emptyset))=>(![X569:$i, X570:$i]:((((X569)=(X570))=>![X571:$i, X572:$i]:((((X571)=(X572))=>((setadjoin @ X569 @ X571)=(setadjoin @ X570 @ X572))))))=>(![X573:$i, X574:$i]:((((X573)=(X574))=>((powerset @ X573)=(powerset @ X574))))=>(![X575:$i, X576:$i]:((((X575)=(X576))=>((setunion @ X575)=(setunion @ X576))))=>(((omega)=(omega))=>(![X577:$i > $o]:((?[X578:$i]:(((X577 @ X578)&![X579:$i]:(((X577 @ X579)=>((X578)=(X579))))))=>![X580:$i, X581:$i]:(((X577 @ X580)=>((X577 @ X581)=>((X580)=(X581)))))))=>(![X582:$i > $o, X583:$i > $o]:((![X584:$i, X585:$i]:((((X584)=(X585))=>((X582 @ X584)<=>(X583 @ X585))))=>(?[X586:$i]:(((X582 @ X586)&![X587:$i]:(((X582 @ X587)=>((X586)=(X587))))))=>(?[X588:$i]:(((X583 @ X588)&![X589:$i]:(((X583 @ X589)=>((X588)=(X589))))))=>((descr @ X582)=(descr @ X583))))))=>(![X590:$i, X591:$i]:((((X590)=(X591))=>![X592:$i > $o, X593:$i > $o]:((![X594:$i]:(((in @ X594 @ X590)=>![X595:$i]:(((in @ X595 @ X591)=>(((X594)=(X595))=>((X592 @ X594)<=>(X593 @ X595)))))))=>((dsetconstr @ X590 @ X592)=(dsetconstr @ X591 @ X593))))))=>(![X596:$i, X597:$i]:((![X598:$i]:(((in @ X598 @ X596)=>(in @ X598 @ X597)))=>(subset @ X596 @ X597)))=>(![X599:$i, X600:$i]:((((X599)=(X600))=>(subset @ X600 @ X599)))=>(![X601:$i, X602:$i]:((((X601)=(X602))=>(subset @ X601 @ X602)))=>(![X603:$i, X604:$i]:((![X605:$i]:(((in @ X605 @ X603)=>(in @ X605 @ X604)))=>(subset @ X603 @ X604)))=>(![X606:$i]:((subset @ emptyset @ X606))=>(![X607:$i, X608:$i, X609:$i]:(((subset @ X607 @ X608)=>((in @ X609 @ X607)=>(in @ X609 @ X608))))=>(![X610:$i, X611:$i, X612:$i]:(((subset @ X610 @ X611)=>(~(in @ X612 @ X611)=>~(in @ X612 @ X610))))=>(![X613:$i, X614:$i, X615:$i]:(((in @ X615 @ X613)=>(~(in @ X615 @ X614)=>~(subset @ X613 @ X614))))=>(![X616:$i, X617:$i]:((~(subset @ X616 @ X617)=>((X616)!=(X617))))=>(![X618:$i, X619:$i, X620:$i]:(((in @ X620 @ X618)=>(~(in @ X620 @ X619)=>((X618)!=(X619)))))=>(![X621:$i]:((subset @ X621 @ X621))=>(![X622:$i, X623:$i, X624:$i]:(((subset @ X622 @ X623)=>((subset @ X623 @ X624)=>(subset @ X622 @ X624))))=>(![X625:$i, X626:$i]:((subset @ X626 @ (setadjoin @ X625 @ X626)))=>(![X627:$i, X628:$i, X629:$i]:(((subset @ X627 @ X629)=>(subset @ X627 @ (setadjoin @ X628 @ X629))))=>(![X630:$i, X631:$i]:(((subset @ X630 @ X631)=>(in @ X630 @ (powerset @ X631))))=>(![X632:$i, X633:$i]:(((subset @ X632 @ X633)=>((subset @ X633 @ X632)=>((X632)=(X633)))))=>(![X634:$i]:(((subset @ X634 @ emptyset)=>((X634)=(emptyset))))=>(![X635:$i, X636:$i]:(((subset @ X636 @ X635)=>(in @ X636 @ (powerset @ X635))))=>(![X637:$i, X638:$i]:(((in @ X638 @ (powerset @ X637))=>(subset @ X638 @ X637)))=>(![X639:$i]:((in @ X639 @ (powerset @ X639)))=>(![X640:$i, X641:$i]:(((subset @ X640 @ X641)=>(subset @ (powerset @ X640) @ (powerset @ X641))))=>(![X642:$i, X643:$i > $o]:((in @ (dsetconstr @ X642 @ X643) @ (powerset @ X642)))=>(![X644:$i, X645:$i > $o]:((subset @ (dsetconstr @ X644 @ X645) @ X644))=>(![X646:$i, X647:$i, X648:$i]:(((in @ X648 @ X646)=>(in @ X648 @ (binunion @ X646 @ X647))))=>(![X649:$i, X650:$i]:((in @ X650 @ (setadjoin @ X649 @ (setadjoin @ X650 @ emptyset))))=>(![X651:$i, X652:$i, X653:$i]:(((in @ X653 @ X652)=>(in @ X653 @ (binunion @ X651 @ X652))))=>(![X654:$i, X655:$i, X656:$i, X657:$o]:(((in @ X656 @ (binunion @ X654 @ X655))=>(((in @ X656 @ X654)=>(X657))=>(((in @ X656 @ X655)=>(X657))=>(X657)))))=>(![X658:$i, X659:$i, X660:$i]:(((in @ X660 @ (binunion @ X658 @ X659))=>((in @ X660 @ X658)|(in @ X660 @ X659))))=>(![X661:$i, X662:$i]:((subset @ X661 @ (binunion @ X661 @ X662)))=>(![X663:$i, X664:$i]:((subset @ X664 @ (binunion @ X663 @ X664)))=>(![X665:$i, X666:$i, X667:$i]:(((in @ X667 @ X665)=>((in @ X667 @ X666)=>(in @ X667 @ (binintersect @ X665 @ X666)))))=>(![X668:$i, X669:$i, X670:$i]:(((subset @ X670 @ X668)=>((subset @ X670 @ X669)=>(subset @ X670 @ (binintersect @ X668 @ X669)))))=>(![X671:$i, X672:$i, X673:$i]:(((in @ X673 @ (binintersect @ X671 @ X672))=>(in @ X673 @ X671)))=>(![X674:$i, X675:$i]:((subset @ (binintersect @ X674 @ X675) @ X674))=>(![X676:$i, X677:$i]:(((subset @ X676 @ X677)=>((binintersect @ X676 @ X677)=(X676))))=>(![X678:$i, X679:$i]:((((binintersect @ X678 @ X679)=(X679))=>(subset @ X679 @ X678)))=>(![X680:$i, X681:$i, X682:$i]:(((in @ X682 @ (binintersect @ X680 @ X681))=>(in @ X682 @ X681)))=>(![X683:$i, X684:$i]:((~(?[X685:$i]:(((in @ X685 @ X683)&(in @ X685 @ X684))))=>((binintersect @ X683 @ X684)=(emptyset))))=>(![X686:$i, X687:$i]:((subset @ (binintersect @ X686 @ X687) @ X687))=>(![X688:$i, X689:$i]:(((subset @ X689 @ X688)=>((binintersect @ X688 @ X689)=(X689))))=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_133, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_134]), foundationAx]), wellorderingAx]), c_0_135]), c_0_136]), c_0_137]), c_0_138]), c_0_139]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_140]), setext]), emptyI]), noeltsimpempty]), c_0_141]), c_0_142]), c_0_143]), c_0_144]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_145]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_146]), c_0_147]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_148]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_149]), c_0_150]), c_0_151]), inCongP]), in__Cong]), c_0_152]), c_0_153]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_154]), c_0_155]), c_0_156]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_157]), c_0_158]), binunionIL]), upairset2IR]), binunionIR]), binunionEcases]), binunionE]), binunionLsub]), binunionRsub]), binintersectI]), binintersectSubset5]), binintersectEL]), binintersectLsub]), binintersectSubset2]), binintersectSubset3]), binintersectER]), disjointsetsI1]), binintersectRsub]), binintersectSubset4])])]), c_0_159])).
% 0.21/0.32 thf(c_0_161, negated_conjecture, ![X690:$i, X691:$i, X693:$i, X694:$i, X695:$i, X696:$i, X697:$i, X698:$i, X699:$i, X700:$i, X701:$i, X703:$i, X704:$i, X706:$i, X707:$i, X708:$i, X709:$i, X710:$i, X712:$i, X713:$i > $i > $o, X714:$i, X716:$i, X719:$i, X721:$i, X722:$i, X723:$i, X724:$i, X726:$i, X727:$i > $o, X728:$i, X730:$i, X731:$i > $o, X732:$i, X733:$i, X734:$i > $o, X735:$i, X736:$i, X737:$i > $o, X738:$i, X739:$i > $o, X740:$i, X743:$i, X744:$o, X745:$i, X746:$i, X747:$o, X748:$i, X749:$i, X750:$i > $o, X751:$i, X754:$i, X755:$i, X758:$i, X760:$i, X762:$i, X763:$i > $o, X764:$i, X765:$i, X767:$i, X768:$i > $o, X769:$i, X770:$i, X771:$i, X772:$i, X773:$i, X774:$i, X775:$i, X776:$i, X777:$i, X778:$i, X779:$i, X780:$o, X781:$i, X782:$i, X783:$i, X784:$i, X785:$i, X786:$i, X788:$i, X789:$i, X790:$i, X791:$i, X792:$i, X793:$i, X794:$i, X795:$i, X796:$i, X797:$i, X798:$o, X800:$i, X801:$i, X802:$i > $o, X803:$i, X806:$i, X807:$i, X808:$i, X810:$i, X811:$i, X812:$i, X813:$i, X814:$i, X815:$i, X816:$i, X817:$i, X818:$i, X819:$i, X820:$i, X821:$i, X822:$i, X823:$i, X824:$i, X825:$i, X826:$i > $o, X827:$i, X828:$i > $o, X829:$i, X830:$i, X831:$i > $o, X832:$i, X834:$i, X835:$i > $o, X837:$i, X838:$i, X839:$i > $o, X841:$i, X842:$i, X843:$i > $o, X844:$i, X846:$o, X847:$o, X848:$i, X849:$i > $o, X851:$i, X852:$i, X853:$i > $o, X854:$i, X856:$i > $o, X857:$i, X860:$i, X861:$i > $o, X862:$i, X866:$i, X867:$i > $o, X868:$i, X871:$i, X872:$i, X873:$i, X874:$i, X875:$i, X876:$i, X877:$i, X878:$i, X879:$i, X880:$i > $o, X881:$i, X883:$i, X884:$i, X885:$i > $o, X886:$i > $o, X889:$i, X892:$i, X893:$i, X896:$i, X897:$i, X898:$i, X899:$i, X900:$i, X901:$i, X902:$i, X903:$i, X904:$i, X905:$i > $o, X906:$i, X908:$i, X909:$i, X910:$i > $o, X911:$i > $o, X914:$i, X916:$i, X918:$i, X919:$i, X920:$i > $o, X921:$i > $o, X924:$i, X925:$i, X927:$i, X928:$i, X929:$i, X930:$i, X931:$i, X932:$i, X934:$i, X935:$i, X936:$i, X937:$i, X938:$i, X939:$i, X940:$i, X941:$i, X942:$i, X943:$i, X944:$i, X945:$i, X946:$i, X947:$i, X948:$i, X949:$i, X950:$i, X951:$i, X952:$i, X953:$i, X954:$i, X955:$i, X956:$i, X957:$i, X958:$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 > $o, X972:$i, X973:$i > $o, X974:$i, X975:$i, X976:$i, X977:$i, X978:$i, X979:$i, X980:$i, X981:$i, X982:$i, X983:$i, X984:$i, X985:$o, X986:$i, X987:$i, X988:$i, X989:$i, X990:$i, X991:$i, X992:$i, X993:$i, X994:$i, X995:$i, X996:$i, X997:$i, X998:$i, X999:$i, X1000:$i, X1001:$i, X1002:$i, X1003:$i, X1004:$i, X1005:$i, X1006:$i, X1007:$i, X1008:$i, X1009:$i, X1010:$i, X1011:$i, X1012:$i, X1014:$i, X1015:$i, X1016:$i, X1017:$i]:((((~(in @ (esk1_2 @ X690 @ X691) @ X690)|~(in @ (esk1_2 @ X690 @ X691) @ X691)|((X690)=(X691)))&((in @ (esk1_2 @ X690 @ X691) @ X690)|(in @ (esk1_2 @ X690 @ X691) @ X691)|((X690)=(X691))))&(~(in @ X693 @ emptyset)&(((~(in @ X696 @ (setadjoin @ X694 @ X695))|(((X696)=(X694))|(in @ X696 @ X695)))&((((X696)!=(X694))|(in @ X696 @ (setadjoin @ X694 @ X695)))&(~(in @ X696 @ X695)|(in @ X696 @ (setadjoin @ X694 @ X695)))))&(((~(in @ X698 @ (powerset @ X697))|(~(in @ X699 @ X698)|(in @ X699 @ X697)))&(((in @ (esk2_2 @ X700 @ X701) @ X701)|(in @ X701 @ (powerset @ X700)))&(~(in @ (esk2_2 @ X700 @ X701) @ X700)|(in @ X701 @ (powerset @ X700)))))&(((((in @ X704 @ (esk3_2 @ X703 @ X704))|~(in @ X704 @ (setunion @ X703)))&((in @ (esk3_2 @ X703 @ X704) @ X703)|~(in @ X704 @ (setunion @ X703))))&(~(in @ X707 @ X708)|~(in @ X708 @ X706)|(in @ X707 @ (setunion @ X706))))&((in @ emptyset @ omega)&((~(in @ X709 @ omega)|(in @ (setadjoin @ X709 @ X709) @ omega))&(((((in @ (esk4_1 @ X710) @ omega)|~(in @ emptyset @ X710)|(~(in @ X712 @ omega)|(in @ X712 @ X710)))&((in @ (esk4_1 @ X710) @ X710)|~(in @ emptyset @ X710)|(~(in @ X712 @ omega)|(in @ X712 @ X710))))&(~(in @ (setadjoin @ (esk4_1 @ X710) @ (esk4_1 @ X710)) @ X710)|~(in @ emptyset @ X710)|(~(in @ X712 @ omega)|(in @ X712 @ X710))))&((((((in @ (esk8_3 @ X713 @ X714 @ X719) @ X714)|~(in @ X719 @ (esk7_2 @ X713 @ X714))|(in @ (esk5_2 @ X713 @ X714) @ X714))&((X713 @ (esk8_3 @ X713 @ X714 @ X719) @ X719)|~(in @ X719 @ (esk7_2 @ X713 @ X714))|(in @ (esk5_2 @ X713 @ X714) @ X714)))&(~(in @ X722 @ X714)|~(X713 @ X722 @ X721)|(in @ X721 @ (esk7_2 @ X713 @ X714))|(in @ (esk5_2 @ X713 @ X714) @ X714)))&(((((in @ (esk8_3 @ X713 @ X714 @ X719) @ X714)|~(in @ X719 @ (esk7_2 @ X713 @ X714))|((X713 @ (esk5_2 @ X713 @ X714) @ (esk6_3 @ X713 @ X714 @ X716))|~(X713 @ (esk5_2 @ X713 @ X714) @ X716)))&((X713 @ (esk8_3 @ X713 @ X714 @ X719) @ X719)|~(in @ X719 @ (esk7_2 @ X713 @ X714))|((X713 @ (esk5_2 @ X713 @ X714) @ (esk6_3 @ X713 @ X714 @ X716))|~(X713 @ (esk5_2 @ X713 @ X714) @ X716))))&(~(in @ X722 @ X714)|~(X713 @ X722 @ X721)|(in @ X721 @ (esk7_2 @ X713 @ X714))|((X713 @ (esk5_2 @ X713 @ X714) @ (esk6_3 @ X713 @ X714 @ X716))|~(X713 @ (esk5_2 @ X713 @ X714) @ X716))))&((((in @ (esk8_3 @ X713 @ X714 @ X719) @ 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X909)|((X908)=(X909))))))&((((((X911 @ (esk49_3 @ X910 @ X911 @ X916))|~(X911 @ X916)|((descr @ X910)=(descr @ X911))|((X910 @ (esk48_3 @ X910 @ X911 @ X914))|~(X910 @ X914))|((esk46_2 @ X910 @ X911)=(esk47_2 @ X910 @ X911)))&(((X916)!=(esk49_3 @ X910 @ X911 @ X916))|~(X911 @ X916)|((descr @ X910)=(descr @ X911))|((X910 @ (esk48_3 @ X910 @ X911 @ X914))|~(X910 @ X914))|((esk46_2 @ X910 @ X911)=(esk47_2 @ X910 @ X911))))&(((X911 @ (esk49_3 @ X910 @ X911 @ X916))|~(X911 @ X916)|((descr @ X910)=(descr @ X911))|(((X914)!=(esk48_3 @ X910 @ X911 @ X914))|~(X910 @ X914))|((esk46_2 @ X910 @ X911)=(esk47_2 @ X910 @ X911)))&(((X916)!=(esk49_3 @ X910 @ X911 @ X916))|~(X911 @ X916)|((descr @ X910)=(descr @ X911))|(((X914)!=(esk48_3 @ X910 @ X911 @ X914))|~(X910 @ X914))|((esk46_2 @ X910 @ X911)=(esk47_2 @ X910 @ X911)))))&(((((X911 @ (esk49_3 @ X910 @ X911 @ X916))|~(X911 @ X916)|((descr @ X910)=(descr @ X911))|((X910 @ (esk48_3 @ X910 @ X911 @ X914))|~(X910 @ X914))|(~(X910 @ (esk46_2 @ X910 @ X911))|~(X911 @ (esk47_2 @ X910 @ X911))))&(((X916)!=(esk49_3 @ X910 @ X911 @ X916))|~(X911 @ X916)|((descr @ X910)=(descr @ X911))|((X910 @ (esk48_3 @ X910 @ X911 @ X914))|~(X910 @ X914))|(~(X910 @ (esk46_2 @ X910 @ X911))|~(X911 @ (esk47_2 @ X910 @ X911)))))&(((X911 @ (esk49_3 @ X910 @ X911 @ X916))|~(X911 @ X916)|((descr @ X910)=(descr @ X911))|(((X914)!=(esk48_3 @ X910 @ X911 @ X914))|~(X910 @ X914))|(~(X910 @ (esk46_2 @ X910 @ X911))|~(X911 @ (esk47_2 @ X910 @ X911))))&(((X916)!=(esk49_3 @ X910 @ X911 @ X916))|~(X911 @ X916)|((descr @ X910)=(descr @ X911))|(((X914)!=(esk48_3 @ X910 @ X911 @ X914))|~(X910 @ X914))|(~(X910 @ (esk46_2 @ X910 @ X911))|~(X911 @ (esk47_2 @ X910 @ X911))))))&((((X911 @ (esk49_3 @ X910 @ X911 @ X916))|~(X911 @ X916)|((descr @ X910)=(descr @ X911))|((X910 @ (esk48_3 @ X910 @ X911 @ X914))|~(X910 @ X914))|((X910 @ (esk46_2 @ X910 @ X911))|(X911 @ (esk47_2 @ X910 @ X911))))&(((X916)!=(esk49_3 @ X910 @ X911 @ X916))|~(X911 @ X916)|((descr @ X910)=(descr @ X911))|((X910 @ (esk48_3 @ X910 @ X911 @ X914))|~(X910 @ X914))|((X910 @ (esk46_2 @ X910 @ X911))|(X911 @ (esk47_2 @ X910 @ X911)))))&(((X911 @ (esk49_3 @ X910 @ X911 @ X916))|~(X911 @ X916)|((descr @ X910)=(descr @ X911))|(((X914)!=(esk48_3 @ X910 @ X911 @ X914))|~(X910 @ X914))|((X910 @ (esk46_2 @ X910 @ X911))|(X911 @ (esk47_2 @ X910 @ X911))))&(((X916)!=(esk49_3 @ X910 @ X911 @ X916))|~(X911 @ X916)|((descr @ X910)=(descr @ X911))|(((X914)!=(esk48_3 @ X910 @ X911 @ X914))|~(X910 @ X914))|((X910 @ (esk46_2 @ X910 @ X911))|(X911 @ (esk47_2 @ X910 @ X911))))))))&((((in @ (esk50_4 @ X918 @ X919 @ X920 @ X921) @ X918)|((dsetconstr @ X918 @ X920)=(dsetconstr @ X919 @ X921))|((X918)!=(X919)))&(((in @ (esk51_4 @ X918 @ X919 @ X920 @ X921) @ X919)|((dsetconstr @ X918 @ X920)=(dsetconstr @ X919 @ X921))|((X918)!=(X919)))&((((esk50_4 @ X918 @ X919 @ X920 @ X921)=(esk51_4 @ X918 @ X919 @ X920 @ X921))|((dsetconstr @ X918 @ X920)=(dsetconstr @ X919 @ X921))|((X918)!=(X919)))&((~(X920 @ (esk50_4 @ X918 @ X919 @ X920 @ X921))|~(X921 @ (esk51_4 @ X918 @ X919 @ X920 @ X921))|((dsetconstr @ X918 @ X920)=(dsetconstr @ X919 @ X921))|((X918)!=(X919)))&((X920 @ (esk50_4 @ X918 @ X919 @ X920 @ X921))|(X921 @ (esk51_4 @ X918 @ X919 @ X920 @ X921))|((dsetconstr @ X918 @ X920)=(dsetconstr @ X919 @ X921))|((X918)!=(X919)))))))&((((in @ (esk52_2 @ X924 @ X925) @ X924)|(subset @ X924 @ X925))&(~(in @ (esk52_2 @ X924 @ X925) @ X925)|(subset @ X924 @ X925)))&((((X927)!=(X928))|(subset @ X928 @ X927))&((((X929)!=(X930))|(subset @ X929 @ X930))&((((in @ (esk53_2 @ X931 @ X932) @ X931)|(subset @ X931 @ X932))&(~(in @ (esk53_2 @ X931 @ X932) @ X932)|(subset @ X931 @ X932)))&((subset @ emptyset @ X934)&((~(subset @ X935 @ X936)|(~(in @ X937 @ X935)|(in @ X937 @ X936)))&((~(subset @ X938 @ X939)|((in @ X940 @ X939)|~(in @ X940 @ X938)))&((~(in @ X943 @ X941)|((in @ X943 @ X942)|~(subset @ X941 @ X942)))&(((subset @ X944 @ X945)|((X944)!=(X945)))&((~(in @ X948 @ X946)|((in @ X948 @ X947)|((X946)!=(X947))))&((subset @ X949 @ X949)&((~(subset @ X950 @ X951)|(~(subset @ X951 @ X952)|(subset @ X950 @ X952)))&((subset @ X954 @ (setadjoin @ X953 @ X954))&((~(subset @ X955 @ X957)|(subset @ X955 @ (setadjoin @ X956 @ X957)))&((~(subset @ X958 @ X959)|(in @ X958 @ (powerset @ X959)))&((~(subset @ X960 @ X961)|(~(subset @ X961 @ X960)|((X960)=(X961))))&((~(subset @ X962 @ emptyset)|((X962)=(emptyset)))&((~(subset @ X964 @ X963)|(in @ X964 @ (powerset @ X963)))&((~(in @ X966 @ (powerset @ X965))|(subset @ X966 @ X965))&((in @ X967 @ (powerset @ X967))&((~(subset @ X968 @ X969)|(subset @ (powerset @ X968) @ (powerset @ X969)))&((in @ (dsetconstr @ X970 @ X971) @ (powerset @ X970))&((subset @ (dsetconstr @ X972 @ X973) @ X972)&((~(in @ X976 @ X974)|(in @ X976 @ (binunion @ X974 @ X975)))&((in @ X978 @ (setadjoin @ X977 @ (setadjoin @ X978 @ emptyset)))&((~(in @ X981 @ X980)|(in @ X981 @ (binunion @ X979 @ X980)))&(((((in @ X984 @ X983)|(X985)|(in @ X984 @ X982)|~(in @ X984 @ (binunion @ X982 @ X983)))&(~(X985)|(X985)|(in @ X984 @ X982)|~(in @ X984 @ (binunion @ X982 @ X983))))&(((in @ X984 @ X983)|(X985)|~(X985)|~(in @ X984 @ (binunion @ X982 @ X983)))&(~(X985)|(X985)|~(X985)|~(in @ X984 @ (binunion @ X982 @ X983)))))&((~(in @ X988 @ (binunion @ X986 @ X987))|((in @ X988 @ X986)|(in @ X988 @ X987)))&((subset @ X989 @ (binunion @ X989 @ X990))&((subset @ X992 @ (binunion @ X991 @ X992))&((~(in @ X995 @ X993)|(~(in @ X995 @ X994)|(in @ X995 @ (binintersect @ X993 @ X994))))&((~(subset @ X998 @ X996)|(~(subset @ X998 @ X997)|(subset @ X998 @ (binintersect @ X996 @ X997))))&((~(in @ X1001 @ (binintersect @ X999 @ X1000))|(in @ X1001 @ X999))&((subset @ (binintersect @ X1002 @ X1003) @ X1002)&((~(subset @ X1004 @ X1005)|((binintersect @ X1004 @ X1005)=(X1004)))&((((binintersect @ X1006 @ X1007)!=(X1007))|(subset @ X1007 @ X1006))&((~(in @ X1010 @ (binintersect @ X1008 @ X1009))|(in @ X1010 @ X1009))&((((in @ (esk54_2 @ X1011 @ X1012) @ X1011)|((binintersect @ X1011 @ X1012)=(emptyset)))&((in @ (esk54_2 @ X1011 @ X1012) @ X1012)|((binintersect @ X1011 @ X1012)=(emptyset))))&((subset @ (binintersect @ X1014 @ X1015) @ X1015)&((~(subset @ X1017 @ X1016)|((binintersect @ X1016 @ X1017)=(X1017)))&(((binintersect @ esk55_0 @ esk56_0)=(esk55_0))&~(subset @ esk55_0 @ esk56_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_160])])])])])])])).
% 0.21/0.32 thf(c_0_162, negated_conjecture, ![X2:$i, X3:$i]:((subset @ (binintersect @ X2 @ X3) @ X3)), inference(split_conjunct,[status(thm)],[c_0_161])).
% 0.21/0.32 thf(c_0_163, negated_conjecture, ((binintersect @ esk55_0 @ esk56_0)=(esk55_0)), inference(split_conjunct,[status(thm)],[c_0_161])).
% 0.21/0.32 thf(c_0_164, negated_conjecture, ~((subset @ esk55_0 @ esk56_0)), inference(split_conjunct,[status(thm)],[c_0_161])).
% 0.21/0.32 thf(c_0_165, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_162, c_0_163]), c_0_164]), ['proof']).
% 0.21/0.32 % SZS output end CNFRefutation
% 0.21/0.32 % Parsed axioms : 250
% 0.21/0.32 % Removed by relevancy pruning/SinE : 0
% 0.21/0.32 % Initial clauses : 365
% 0.21/0.32 % Removed in clause preprocessing : 150
% 0.21/0.32 % Initial clauses in saturation : 215
% 0.21/0.32 % Processed clauses : 27
% 0.21/0.32 % ...of these trivial : 1
% 0.21/0.32 % ...subsumed : 4
% 0.21/0.32 % ...remaining for further processing : 22
% 0.21/0.32 % Other redundant clauses eliminated : 1
% 0.21/0.32 % Clauses deleted for lack of memory : 0
% 0.21/0.32 % Backward-subsumed : 0
% 0.21/0.32 % Backward-rewritten : 1
% 0.21/0.32 % Generated clauses : 3
% 0.21/0.32 % ...of the previous two non-redundant : 0
% 0.21/0.32 % ...aggressively subsumed : 0
% 0.21/0.32 % Contextual simplify-reflections : 0
% 0.21/0.32 % Paramodulations : 2
% 0.21/0.32 % Factorizations : 0
% 0.21/0.32 % NegExts : 0
% 0.21/0.32 % Equation resolutions : 1
% 0.21/0.32 % Disequality decompositions : 0
% 0.21/0.32 % Total rewrite steps : 4
% 0.21/0.32 % ...of those cached : 1
% 0.21/0.32 % Propositional unsat checks : 0
% 0.21/0.32 % Propositional check models : 0
% 0.21/0.32 % Propositional check unsatisfiable : 0
% 0.21/0.32 % Propositional clauses : 0
% 0.21/0.32 % Propositional clauses after purity: 0
% 0.21/0.32 % Propositional unsat core size : 0
% 0.21/0.32 % Propositional preprocessing time : 0.000
% 0.21/0.32 % Propositional encoding time : 0.000
% 0.21/0.32 % Propositional solver time : 0.000
% 0.21/0.32 % Success case prop preproc time : 0.000
% 0.21/0.32 % Success case prop encoding time : 0.000
% 0.21/0.32 % Success case prop solver time : 0.000
% 0.21/0.32 % Current number of processed clauses : 20
% 0.21/0.32 % Positive orientable unit clauses : 17
% 0.21/0.32 % Positive unorientable unit clauses: 0
% 0.21/0.32 % Negative unit clauses : 3
% 0.21/0.32 % Non-unit-clauses : 0
% 0.21/0.32 % Current number of unprocessed clauses: 188
% 0.21/0.32 % ...number of literals in the above : 668
% 0.21/0.32 % Current number of archived formulas : 0
% 0.21/0.32 % Current number of archived clauses : 1
% 0.21/0.32 % Clause-clause subsumption calls (NU) : 0
% 0.21/0.32 % Rec. Clause-clause subsumption calls : 0
% 0.21/0.32 % Non-unit clause-clause subsumptions : 0
% 0.21/0.32 % Unit Clause-clause subsumption calls : 2
% 0.21/0.32 % Rewrite failures with RHS unbound : 0
% 0.21/0.32 % BW rewrite match attempts : 4
% 0.21/0.32 % BW rewrite match successes : 1
% 0.21/0.32 % Condensation attempts : 0
% 0.21/0.32 % Condensation successes : 0
% 0.21/0.32 % Termbank termtop insertions : 30248
% 0.21/0.32 % Search garbage collected termcells : 11685
% 0.21/0.32
% 0.21/0.32 % -------------------------------------------------
% 0.21/0.32 % User time : 0.025 s
% 0.21/0.32 % System time : 0.005 s
% 0.21/0.32 % Total time : 0.030 s
% 0.21/0.32 % Maximum resident set size: 6384 pages
% 0.21/0.32
% 0.21/0.32 % -------------------------------------------------
% 0.21/0.32 % User time : 0.034 s
% 0.21/0.32 % System time : 0.008 s
% 0.21/0.32 % Total time : 0.042 s
% 0.21/0.32 % Maximum resident set size: 5120 pages
% 0.21/0.32 % E exiting
%------------------------------------------------------------------------------