%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU616^1 : 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 : n007.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 08:24:44 AM UTC 2026
% Result : Theorem 0.23s 0.31s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU616^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n007.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 13:56:25 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.25 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.YgtZJrG1RR/E---3.1_3406372.p
% 0.23/0.31 % Version: 3.5.1-ho
% 0.23/0.31 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.23/0.31 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.31 % Starting ehoh_best5 with 300s (1) cores
% 0.23/0.31 % Starting almost_fo_3_lam with 300s (1) cores
% 0.23/0.31 % Starting new_bool_5 with 300s (1) cores
% 0.23/0.31 % Starting pre_casc_3 with 300s (1) cores
% 0.23/0.31 % Starting ho_unfolding_8 with 300s (1) cores
% 0.23/0.31 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.23/0.31 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.31 % Starting new_ho_5 with 300s (1) cores
% 0.23/0.31 % ehoh_best5 with pid 3406385 completed with status 0
% 0.23/0.31 % Result found by ehoh_best5
% 0.23/0.31 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.23/0.31 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.31 % Starting ehoh_best5 with 300s (1) cores
% 0.23/0.31 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.31 % No SInE strategy applied
% 0.23/0.31 % Search class: HGHSM-FSLS31-SHFMMSBN
% 0.23/0.31 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.31 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.31 % SubtermCWHack with pid 3406395 completed with status 0
% 0.23/0.31 % Result found by SubtermCWHack
% 0.23/0.31 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.23/0.31 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.31 % Starting ehoh_best5 with 300s (1) cores
% 0.23/0.31 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.31 % No SInE strategy applied
% 0.23/0.31 % Search class: HGHSM-FSLS31-SHFMMSBN
% 0.23/0.31 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.31 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.31 % Preprocessing time : 0.003 s
% 0.23/0.31
% 0.23/0.31 % Proof found!
% 0.23/0.31 % SZS status Theorem
% 0.23/0.31 % SZS output start CNFRefutation
% 0.23/0.31 thf(decl_23, type, in: $i > $i > $o).
% 0.23/0.31 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.23/0.31 thf(decl_25, type, setextAx: $o).
% 0.23/0.31 thf(decl_26, type, emptyset: $i).
% 0.23/0.31 thf(decl_27, type, emptysetAx: $o).
% 0.23/0.31 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.23/0.31 thf(decl_29, type, setadjoinAx: $o).
% 0.23/0.31 thf(decl_30, type, powerset: $i > $i).
% 0.23/0.31 thf(decl_31, type, powersetAx: $o).
% 0.23/0.31 thf(decl_32, type, setunion: $i > $i).
% 0.23/0.31 thf(decl_33, type, setunionAx: $o).
% 0.23/0.31 thf(decl_34, type, omega: $i).
% 0.23/0.31 thf(decl_35, type, omega0Ax: $o).
% 0.23/0.31 thf(decl_36, type, omegaSAx: $o).
% 0.23/0.31 thf(decl_37, type, omegaIndAx: $o).
% 0.23/0.31 thf(decl_38, type, replAx: $o).
% 0.23/0.31 thf(decl_39, type, foundationAx: $o).
% 0.23/0.31 thf(decl_40, type, wellorderingAx: $o).
% 0.23/0.31 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.23/0.31 thf(decl_42, type, descrp: $o).
% 0.23/0.31 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.23/0.31 thf(decl_44, type, dsetconstrI: $o).
% 0.23/0.31 thf(decl_45, type, dsetconstrEL: $o).
% 0.23/0.31 thf(decl_46, type, dsetconstrER: $o).
% 0.23/0.31 thf(decl_47, type, exuE1: $o).
% 0.23/0.31 thf(decl_48, type, prop2set: $o > $i).
% 0.23/0.31 thf(decl_49, type, prop2setE: $o).
% 0.23/0.31 thf(decl_50, type, emptysetE: $o).
% 0.23/0.31 thf(decl_51, type, emptysetimpfalse: $o).
% 0.23/0.31 thf(decl_52, type, notinemptyset: $o).
% 0.23/0.31 thf(decl_53, type, exuE3e: $o).
% 0.23/0.31 thf(decl_54, type, setext: $o).
% 0.23/0.31 thf(decl_55, type, emptyI: $o).
% 0.23/0.31 thf(decl_56, type, noeltsimpempty: $o).
% 0.23/0.31 thf(decl_57, type, setbeta: $o).
% 0.23/0.31 thf(decl_58, type, nonempty: $i > $o).
% 0.23/0.31 thf(decl_59, type, nonemptyE1: $o).
% 0.23/0.31 thf(decl_60, type, nonemptyI: $o).
% 0.23/0.31 thf(decl_61, type, nonemptyI1: $o).
% 0.23/0.31 thf(decl_62, type, setadjoinIL: $o).
% 0.23/0.31 thf(decl_63, type, emptyinunitempty: $o).
% 0.23/0.31 thf(decl_64, type, setadjoinIR: $o).
% 0.23/0.31 thf(decl_65, type, setadjoinE: $o).
% 0.23/0.31 thf(decl_66, type, setadjoinOr: $o).
% 0.23/0.31 thf(decl_67, type, setoftrueEq: $o).
% 0.23/0.31 thf(decl_68, type, powersetI: $o).
% 0.23/0.31 thf(decl_69, type, emptyinPowerset: $o).
% 0.23/0.31 thf(decl_70, type, emptyInPowerset: $o).
% 0.23/0.31 thf(decl_71, type, powersetE: $o).
% 0.23/0.31 thf(decl_72, type, setunionI: $o).
% 0.23/0.31 thf(decl_73, type, setunionE: $o).
% 0.23/0.31 thf(decl_74, type, subPowSU: $o).
% 0.23/0.31 thf(decl_75, type, exuE2: $o).
% 0.23/0.31 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.23/0.31 thf(decl_77, type, uniqinunit: $o).
% 0.23/0.31 thf(decl_78, type, notinsingleton: $o).
% 0.23/0.31 thf(decl_79, type, eqinunit: $o).
% 0.23/0.31 thf(decl_80, type, singletonsswitch: $o).
% 0.23/0.31 thf(decl_81, type, upairsetE: $o).
% 0.23/0.31 thf(decl_82, type, upairsetIL: $o).
% 0.23/0.31 thf(decl_83, type, upairsetIR: $o).
% 0.23/0.31 thf(decl_84, type, emptyE1: $o).
% 0.23/0.31 thf(decl_85, type, vacuousDall: $o).
% 0.23/0.31 thf(decl_86, type, quantDeMorgan1: $o).
% 0.23/0.31 thf(decl_87, type, quantDeMorgan2: $o).
% 0.23/0.31 thf(decl_88, type, quantDeMorgan3: $o).
% 0.23/0.31 thf(decl_89, type, quantDeMorgan4: $o).
% 0.23/0.31 thf(decl_90, type, prop2setI: $o).
% 0.23/0.31 thf(decl_91, type, set2prop: $i > $o).
% 0.23/0.31 thf(decl_92, type, prop2set2propI: $o).
% 0.23/0.31 thf(decl_93, type, notdexE: $o).
% 0.23/0.31 thf(decl_94, type, notdallE: $o).
% 0.23/0.31 thf(decl_95, type, exuI1: $o).
% 0.23/0.31 thf(decl_96, type, exuI3: $o).
% 0.23/0.31 thf(decl_97, type, exuI2: $o).
% 0.23/0.31 thf(decl_98, type, inCongP: $o).
% 0.23/0.31 thf(decl_99, type, in__Cong: $o).
% 0.23/0.31 thf(decl_100, type, exuE3u: $o).
% 0.23/0.31 thf(decl_101, type, exu__Cong: $o).
% 0.23/0.31 thf(decl_102, type, emptyset__Cong: $o).
% 0.23/0.31 thf(decl_103, type, setadjoin__Cong: $o).
% 0.23/0.31 thf(decl_104, type, powerset__Cong: $o).
% 0.23/0.31 thf(decl_105, type, setunion__Cong: $o).
% 0.23/0.31 thf(decl_106, type, omega__Cong: $o).
% 0.23/0.31 thf(decl_107, type, exuEu: $o).
% 0.23/0.31 thf(decl_108, type, descr__Cong: $o).
% 0.23/0.31 thf(decl_109, type, dsetconstr__Cong: $o).
% 0.23/0.31 thf(decl_110, type, subset: $i > $i > $o).
% 0.23/0.31 thf(decl_113, type, subsetI1: $o).
% 0.23/0.31 thf(decl_114, type, eqimpsubset2: $o).
% 0.23/0.31 thf(decl_115, type, eqimpsubset1: $o).
% 0.23/0.31 thf(decl_116, type, subsetI2: $o).
% 0.23/0.31 thf(decl_117, type, emptysetsubset: $o).
% 0.23/0.31 thf(decl_118, type, subsetE: $o).
% 0.23/0.31 thf(decl_119, type, subsetE2: $o).
% 0.23/0.31 thf(decl_120, type, notsubsetI: $o).
% 0.23/0.31 thf(decl_121, type, notequalI1: $o).
% 0.23/0.31 thf(decl_122, type, notequalI2: $o).
% 0.23/0.31 thf(decl_123, type, subsetRefl: $o).
% 0.23/0.31 thf(decl_124, type, subsetTrans: $o).
% 0.23/0.31 thf(decl_125, type, setadjoinSub: $o).
% 0.23/0.31 thf(decl_126, type, setadjoinSub2: $o).
% 0.23/0.31 thf(decl_127, type, subset2powerset: $o).
% 0.23/0.31 thf(decl_128, type, setextsub: $o).
% 0.23/0.31 thf(decl_129, type, subsetemptysetimpeq: $o).
% 0.23/0.31 thf(decl_130, type, powersetI1: $o).
% 0.23/0.31 thf(decl_131, type, powersetE1: $o).
% 0.23/0.31 thf(decl_132, type, inPowerset: $o).
% 0.23/0.31 thf(decl_133, type, powersetsubset: $o).
% 0.23/0.31 thf(decl_134, type, sepInPowerset: $o).
% 0.23/0.31 thf(decl_135, type, sepSubset: $o).
% 0.23/0.31 thf(decl_136, type, binunion: $i > $i > $i).
% 0.23/0.31 thf(decl_137, type, binunionIL: $o).
% 0.23/0.31 thf(decl_138, type, upairset2IR: $o).
% 0.23/0.31 thf(decl_139, type, binunionIR: $o).
% 0.23/0.31 thf(decl_140, type, binunionEcases: $o).
% 0.23/0.31 thf(decl_141, type, binunionE: $o).
% 0.23/0.31 thf(decl_142, type, binunionLsub: $o).
% 0.23/0.31 thf(decl_143, type, binunionRsub: $o).
% 0.23/0.31 thf(decl_144, type, binintersect: $i > $i > $i).
% 0.23/0.31 thf(decl_145, type, binintersectI: $o).
% 0.23/0.31 thf(decl_146, type, binintersectSubset5: $o).
% 0.23/0.31 thf(decl_147, type, binintersectEL: $o).
% 0.23/0.31 thf(decl_148, type, binintersectLsub: $o).
% 0.23/0.31 thf(decl_149, type, binintersectSubset2: $o).
% 0.23/0.31 thf(decl_150, type, binintersectSubset3: $o).
% 0.23/0.31 thf(decl_151, type, binintersectER: $o).
% 0.23/0.31 thf(decl_152, type, disjointsetsI1: $o).
% 0.23/0.31 thf(decl_153, type, binintersectRsub: $o).
% 0.23/0.31 thf(decl_154, type, binintersectSubset4: $o).
% 0.23/0.31 thf(decl_155, type, binintersectSubset1: $o).
% 0.23/0.31 thf(decl_156, type, bs114d: $o).
% 0.23/0.31 thf(decl_158, type, setminus: $i > $i > $i).
% 0.23/0.31 thf(decl_159, type, setminusI: $o).
% 0.23/0.31 thf(decl_160, type, setminusEL: $o).
% 0.23/0.31 thf(decl_161, type, setminusER: $o).
% 0.23/0.31 thf(decl_162, type, setminusSubset2: $o).
% 0.23/0.31 thf(decl_163, type, setminusERneg: $o).
% 0.23/0.31 thf(decl_164, type, setminusELneg: $o).
% 0.23/0.31 thf(decl_165, type, setminusILneg: $o).
% 0.23/0.31 thf(decl_166, type, setminusIRneg: $o).
% 0.23/0.31 thf(decl_167, type, setminusLsub: $o).
% 0.23/0.31 thf(decl_168, type, setminusSubset1: $o).
% 0.23/0.31 thf(decl_169, type, symdiff: $i > $i > $i).
% 0.23/0.31 thf(decl_170, type, symdiffE: $o).
% 0.23/0.31 thf(decl_171, type, symdiffI1: $o).
% 0.23/0.31 thf(decl_172, type, symdiffI2: $o).
% 0.23/0.31 thf(decl_173, type, symdiffIneg1: $o).
% 0.23/0.31 thf(decl_174, type, symdiffIneg2: $o).
% 0.23/0.31 thf(decl_176, type, epred1_0: $o).
% 0.23/0.31 thf(decl_177, type, esk1_2: $i > $i > $i).
% 0.23/0.31 thf(decl_178, type, esk2_2: $i > $i > $i).
% 0.23/0.31 thf(decl_179, type, esk3_2: $i > $i > $i).
% 0.23/0.31 thf(decl_180, type, esk4_1: $i > $i).
% 0.23/0.31 thf(decl_181, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.23/0.31 thf(decl_182, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.23/0.31 thf(decl_183, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.23/0.31 thf(decl_184, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.23/0.31 thf(decl_185, type, esk9_1: $i > $i).
% 0.23/0.31 thf(decl_186, type, esk10_2: ($i > $o) > $i > $i).
% 0.23/0.31 thf(decl_187, type, esk11_2: ($i > $o) > $i > $i).
% 0.23/0.31 thf(decl_188, type, esk12_1: ($i > $o) > $i).
% 0.23/0.31 thf(decl_189, type, esk13_2: ($i > $o) > $i > $i).
% 0.23/0.31 thf(decl_190, type, esk14_1: ($i > $o) > $i).
% 0.23/0.31 thf(decl_191, type, esk15_2: $i > $i > $i).
% 0.23/0.31 thf(decl_192, type, esk16_2: $i > $i > $i).
% 0.23/0.31 thf(decl_193, type, esk17_1: $i > $i).
% 0.23/0.31 thf(decl_194, type, esk18_1: $i > $i).
% 0.23/0.31 thf(decl_195, type, esk19_1: $i > $i).
% 0.23/0.31 thf(decl_196, type, esk20_2: $i > $i > $i).
% 0.23/0.31 thf(decl_197, type, esk21_3: $i > $i > $o > $i).
% 0.23/0.31 thf(decl_198, type, esk22_2: ($i > $o) > $i > $i).
% 0.23/0.31 thf(decl_199, type, esk23_1: ($i > $o) > $i).
% 0.23/0.31 thf(decl_200, type, esk24_1: $i > $i).
% 0.23/0.31 thf(decl_201, type, esk25_2: $i > ($i > $o) > $i).
% 0.23/0.31 thf(decl_202, type, esk26_2: $i > ($i > $o) > $i).
% 0.23/0.31 thf(decl_203, type, esk27_2: $i > ($i > $o) > $i).
% 0.23/0.31 thf(decl_204, type, esk28_2: $i > ($i > $o) > $i).
% 0.23/0.31 thf(decl_205, type, esk29_2: $i > ($i > $o) > $i).
% 0.23/0.31 thf(decl_206, type, esk30_2: $i > ($i > $o) > $i).
% 0.23/0.31 thf(decl_207, type, esk31_2: ($i > $o) > $i > $i).
% 0.23/0.31 thf(decl_208, type, esk32_1: ($i > $o) > $i).
% 0.23/0.31 thf(decl_209, type, esk33_1: ($i > $o) > $i).
% 0.23/0.31 thf(decl_210, type, esk34_1: ($i > $o) > $i).
% 0.23/0.31 thf(decl_211, type, esk35_1: ($i > $o) > $i).
% 0.23/0.31 thf(decl_212, type, esk36_2: ($i > $o) > $i > $i).
% 0.23/0.31 thf(decl_213, type, esk37_1: ($i > $o) > $i).
% 0.23/0.31 thf(decl_214, type, esk38_2: ($i > $o) > $i > $i).
% 0.23/0.31 thf(decl_215, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 0.23/0.31 thf(decl_216, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 0.23/0.31 thf(decl_217, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.23/0.31 thf(decl_218, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 0.23/0.31 thf(decl_219, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.23/0.31 thf(decl_220, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 0.23/0.31 thf(decl_221, type, esk45_2: ($i > $o) > $i > $i).
% 0.23/0.31 thf(decl_222, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 0.23/0.31 thf(decl_223, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 0.23/0.31 thf(decl_224, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.23/0.31 thf(decl_225, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.23/0.31 thf(decl_226, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.23/0.31 thf(decl_227, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.23/0.31 thf(decl_228, type, esk52_2: $i > $i > $i).
% 0.23/0.31 thf(decl_229, type, esk53_2: $i > $i > $i).
% 0.23/0.31 thf(decl_230, type, esk54_2: $i > $i > $i).
% 0.23/0.31 thf(decl_231, type, esk55_0: $i).
% 0.23/0.31 thf(decl_232, type, esk56_0: $i).
% 0.23/0.31 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', replAx)).
% 0.23/0.31 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', exu)).
% 0.23/0.31 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', descrp)).
% 0.23/0.31 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', exuE1)).
% 0.23/0.31 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', exuE3e)).
% 0.23/0.31 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', nonempty)).
% 0.23/0.31 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', nonemptyI)).
% 0.23/0.31 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', exuE2)).
% 0.23/0.31 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', exuI1)).
% 0.23/0.31 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', exuI3)).
% 0.23/0.31 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', exuI2)).
% 0.23/0.31 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', exuE3u)).
% 0.23/0.31 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', exu__Cong)).
% 0.23/0.31 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', exuEu)).
% 0.23/0.31 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', descr__Cong)).
% 0.23/0.31 thf(secondinupair, 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)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', secondinupair)).
% 0.23/0.31 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', dsetconstrI)).
% 0.23/0.31 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', dsetconstrEL)).
% 0.23/0.31 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', dsetconstrER)).
% 0.23/0.31 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', setbeta)).
% 0.23/0.31 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', nonemptyE1)).
% 0.23/0.31 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', nonemptyI1)).
% 0.23/0.31 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', setoftrueEq)).
% 0.23/0.31 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', nonemptyImpWitness)).
% 0.23/0.31 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', emptyE1)).
% 0.23/0.31 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', dsetconstr__Cong)).
% 0.23/0.31 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', sepInPowerset)).
% 0.23/0.31 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', sepSubset)).
% 0.23/0.31 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', setextAx)).
% 0.23/0.31 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', emptysetAx)).
% 0.23/0.31 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', setadjoinAx)).
% 0.23/0.31 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', powersetAx)).
% 0.23/0.31 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', setunionAx)).
% 0.23/0.31 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', omega0Ax)).
% 0.23/0.31 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', omegaSAx)).
% 0.23/0.31 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', omegaIndAx)).
% 0.23/0.31 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', foundationAx)).
% 0.23/0.31 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', wellorderingAx)).
% 0.23/0.31 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', prop2setE)).
% 0.23/0.31 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', emptysetE)).
% 0.23/0.31 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', emptysetimpfalse)).
% 0.23/0.31 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', notinemptyset)).
% 0.23/0.31 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', setext)).
% 0.23/0.31 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', emptyI)).
% 0.23/0.31 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', noeltsimpempty)).
% 0.23/0.31 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', setadjoinIL)).
% 0.23/0.31 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', emptyinunitempty)).
% 0.23/0.31 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', setadjoinIR)).
% 0.23/0.31 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', setadjoinE)).
% 0.23/0.31 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', setadjoinOr)).
% 0.23/0.31 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', powersetI)).
% 0.23/0.31 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', emptyinPowerset)).
% 0.23/0.31 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', emptyInPowerset)).
% 0.23/0.31 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', powersetE)).
% 0.23/0.31 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', setunionI)).
% 0.23/0.31 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', setunionE)).
% 0.23/0.31 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', subPowSU)).
% 0.23/0.31 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', uniqinunit)).
% 0.23/0.31 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', notinsingleton)).
% 0.23/0.31 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', eqinunit)).
% 0.23/0.31 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', singletonsswitch)).
% 0.23/0.31 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', upairsetE)).
% 0.23/0.31 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', upairsetIL)).
% 0.23/0.31 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', upairsetIR)).
% 0.23/0.31 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', vacuousDall)).
% 0.23/0.31 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', quantDeMorgan1)).
% 0.23/0.31 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', quantDeMorgan2)).
% 0.23/0.31 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', quantDeMorgan3)).
% 0.23/0.31 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', quantDeMorgan4)).
% 0.23/0.31 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', prop2setI)).
% 0.23/0.31 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', prop2set2propI)).
% 0.23/0.31 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', notdexE)).
% 0.23/0.31 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', notdallE)).
% 0.23/0.31 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', inCongP)).
% 0.23/0.31 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', in__Cong)).
% 0.23/0.31 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', emptyset__Cong)).
% 0.23/0.31 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', setadjoin__Cong)).
% 0.23/0.31 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', powerset__Cong)).
% 0.23/0.31 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', setunion__Cong)).
% 0.23/0.31 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', omega__Cong)).
% 0.23/0.31 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', subsetI1)).
% 0.23/0.31 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', eqimpsubset2)).
% 0.23/0.31 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', eqimpsubset1)).
% 0.23/0.31 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', subsetI2)).
% 0.23/0.31 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', emptysetsubset)).
% 0.23/0.31 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', subsetE)).
% 0.23/0.31 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', subsetE2)).
% 0.23/0.31 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', notsubsetI)).
% 0.23/0.31 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', notequalI1)).
% 0.23/0.31 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', notequalI2)).
% 0.23/0.31 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', subsetRefl)).
% 0.23/0.31 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', subsetTrans)).
% 0.23/0.31 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', setadjoinSub)).
% 0.23/0.31 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', setadjoinSub2)).
% 0.23/0.31 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', subset2powerset)).
% 0.23/0.31 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', setextsub)).
% 0.23/0.31 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', subsetemptysetimpeq)).
% 0.23/0.31 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', powersetI1)).
% 0.23/0.31 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', powersetE1)).
% 0.23/0.31 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', inPowerset)).
% 0.23/0.31 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', powersetsubset)).
% 0.23/0.31 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', binunionIL)).
% 0.23/0.31 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', upairset2IR)).
% 0.23/0.31 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', binunionIR)).
% 0.23/0.31 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', binunionEcases)).
% 0.23/0.31 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', binunionE)).
% 0.23/0.31 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', binunionLsub)).
% 0.23/0.31 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', binunionRsub)).
% 0.23/0.31 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', binintersectI)).
% 0.23/0.31 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', binintersectSubset5)).
% 0.23/0.31 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', binintersectEL)).
% 0.23/0.31 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', binintersectLsub)).
% 0.23/0.31 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', binintersectSubset2)).
% 0.23/0.31 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', binintersectSubset3)).
% 0.23/0.31 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', binintersectER)).
% 0.23/0.31 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', disjointsetsI1)).
% 0.23/0.31 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', binintersectRsub)).
% 0.23/0.31 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', binintersectSubset4)).
% 0.23/0.31 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', binintersectSubset1)).
% 0.23/0.31 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', bs114d)).
% 0.23/0.31 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', setminusI)).
% 0.23/0.31 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', setminusEL)).
% 0.23/0.31 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', setminusER)).
% 0.23/0.31 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', setminusSubset2)).
% 0.23/0.31 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', setminusERneg)).
% 0.23/0.31 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', setminusELneg)).
% 0.23/0.31 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', setminusILneg)).
% 0.23/0.31 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', setminusIRneg)).
% 0.23/0.31 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', setminusLsub)).
% 0.23/0.31 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', setminusSubset1)).
% 0.23/0.31 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', symdiffE)).
% 0.23/0.31 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', symdiffI1)).
% 0.23/0.31 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', symdiffI2)).
% 0.23/0.31 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', symdiffIneg1)).
% 0.23/0.31 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.YgtZJrG1RR/E---3.1_3406372.p', symdiffIneg2)).
% 0.23/0.31 thf(c_0_135, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.23/0.31 thf(c_0_136, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.23/0.31 thf(c_0_137, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.23/0.31 thf(c_0_138, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.23/0.31 thf(c_0_139, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.23/0.31 thf(c_0_140, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.23/0.31 thf(c_0_141, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.23/0.31 thf(c_0_142, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.23/0.31 thf(c_0_143, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 0.23/0.31 thf(c_0_144, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.23/0.31 thf(c_0_145, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.23/0.31 thf(c_0_146, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 0.23/0.31 thf(c_0_147, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.23/0.31 thf(c_0_148, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 0.23/0.31 thf(c_0_149, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))=>((exu @ (^[Z0:$i]:((X17 @ Z0))))=>((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 0.23/0.31 thf(c_0_150, 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)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[secondinupair])).
% 0.23/0.31 thf(c_0_151, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X377:$i]:(((((X6 @ X2 @ X377)))&(![X378:$i]:(((((X6 @ X2 @ X378)))=>(((X377)=(X378)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_135, c_0_136])).
% 0.23/0.31 thf(c_0_152, plain, ((descrp)=(![X1:$i > $o]:((((?[X379:$i]:(((((X1 @ X379)))&(![X380:$i]:(((((X1 @ X380)))=>(((X379)=(X380))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_137, c_0_136])).
% 0.23/0.31 thf(c_0_153, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.23/0.31 thf(c_0_154, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.23/0.31 thf(c_0_155, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.23/0.31 thf(c_0_156, plain, ((exuE1)=(![X1:$i > $o]:((((?[X381:$i]:(((((X1 @ X381)))&(![X382:$i]:(((((X1 @ X382)))=>(((X381)=(X382))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_138, c_0_136])).
% 0.23/0.31 thf(c_0_157, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X383:$i]:(((((X1 @ X383)))&(![X384:$i]:(((((X1 @ X384)))=>(((X383)=(X384))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_139, c_0_136])).
% 0.23/0.31 thf(c_0_158, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.23/0.31 thf(c_0_159, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_140])).
% 0.23/0.31 thf(c_0_160, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_141, c_0_140])).
% 0.23/0.31 thf(c_0_161, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_140])).
% 0.23/0.31 thf(c_0_162, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.23/0.31 thf(c_0_163, plain, ((exuE2)=(![X1:$i > $o]:((((?[X385:$i]:(((((X1 @ X385)))&(![X386:$i]:(((((X1 @ X386)))=>(((X385)=(X386))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_142, c_0_136])).
% 0.23/0.31 thf(c_0_164, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_140])).
% 0.23/0.31 thf(c_0_165, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
% 0.23/0.31 thf(c_0_166, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X387:$i]:(((((X1 @ X387)))&(![X388:$i]:(((((X1 @ X388)))=>(((X387)=(X388)))))))))))))), inference(apply_def,[status(thm)],[c_0_143, c_0_136])).
% 0.23/0.31 thf(c_0_167, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X389:$i]:(((((X1 @ X389)))&(![X390:$i]:(((((X1 @ X390)))=>(((X389)=(X390)))))))))))))))), inference(apply_def,[status(thm)],[c_0_144, c_0_136])).
% 0.23/0.31 thf(c_0_168, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X391:$i]:(((((X1 @ X391)))&(![X392:$i]:(((((X1 @ X392)))=>(((X391)=(X392)))))))))))))), inference(apply_def,[status(thm)],[c_0_145, c_0_136])).
% 0.23/0.31 thf(c_0_169, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X393:$i]:(((((X1 @ X393)))&(![X394:$i]:(((((X1 @ X394)))=>(((X393)=(X394))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_146, c_0_136])).
% 0.23/0.31 thf(c_0_170, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X395:$i]:(((((X1 @ X395)))&(![X396:$i]:(((((X1 @ X396)))=>(((X395)=(X396))))))))))<=>((?[X397:$i]:(((((X17 @ X397)))&(![X398:$i]:(((((X17 @ X398)))=>(((X397)=(X398)))))))))))))))), inference(apply_def,[status(thm)],[c_0_147, c_0_136])).
% 0.23/0.31 thf(c_0_171, plain, ((exuEu)=(![X1:$i > $o]:((((?[X399:$i]:(((((X1 @ X399)))&(![X400:$i]:(((((X1 @ X400)))=>(((X399)=(X400))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_148, c_0_136])).
% 0.23/0.31 thf(c_0_172, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X401:$i]:(((((X1 @ X401)))&(![X402:$i]:(((((X1 @ X402)))=>(((X401)=(X402))))))))))=>((((?[X403:$i]:(((((X17 @ X403)))&(![X404:$i]:(((((X17 @ X404)))=>(((X403)=(X404))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_149, c_0_136])).
% 0.23/0.31 thf(c_0_173, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 0.23/0.31 thf(c_0_174, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 0.23/0.31 thf(c_0_175, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 0.23/0.31 thf(c_0_176, plain, ((epred1_0)<=>![X434:$i]:(?[X435:$i]:((((![X436:$i]:(((in @ X436 @ X435)=>![X437:$i]:(((in @ X437 @ X436)=>(in @ X437 @ X434)))))&![X438:$i, X439:$i]:((((in @ X438 @ X434)&(in @ X439 @ X434))=>(![X440:$i]:(((in @ X440 @ X435)=>((in @ X438 @ X440)<=>(in @ X439 @ X440))))=>((X438)=(X439))))))&![X441:$i, X442:$i]:((((in @ X441 @ X435)&(in @ X442 @ X435))=>(![X443:$i]:(((in @ X443 @ X441)=>(in @ X443 @ X442)))|![X444:$i]:(((in @ X444 @ X442)=>(in @ X444 @ X441)))))))&![X445:$i]:(((![X446:$i]:(((in @ X446 @ X445)=>(in @ X446 @ X434)))&?[X447:$i]:((in @ X447 @ X445)))=>?[X448:$i, X449:$i]:(((((in @ X448 @ X435)&(in @ X449 @ X445))&~(?[X450:$i]:(((in @ X450 @ X448)&(in @ X450 @ X445)))))&![X451:$i]:(((in @ X451 @ X435)=>(![X452:$i]:(((in @ X452 @ X451)=>(in @ X452 @ X448)))|(in @ X449 @ X451)))))))))))), introduced(definition)).
% 0.23/0.31 thf(c_0_177, negated_conjecture, ~((![X405:$i, X406:$i]:((![X407:$i]:(((in @ X407 @ X405)<=>(in @ X407 @ X406)))=>((X405)=(X406))))=>(![X408:$i]:(~(in @ X408 @ emptyset))=>(![X409:$i, X410:$i, X411:$i]:(((in @ X411 @ (setadjoin @ X409 @ X410))<=>(((X411)=(X409))|(in @ X411 @ X410))))=>(![X412:$i, X413:$i]:(((in @ X413 @ (powerset @ X412))<=>![X414:$i]:(((in @ X414 @ X413)=>(in @ X414 @ X412)))))=>(![X415:$i, X416:$i]:(((in @ X416 @ (setunion @ X415))<=>?[X417:$i]:(((in @ X416 @ X417)&(in @ X417 @ X415)))))=>((in @ emptyset @ omega)=>(![X418:$i]:(((in @ X418 @ omega)=>(in @ (setadjoin @ X418 @ X418) @ omega)))=>(![X419:$i]:((((in @ emptyset @ X419)&![X420:$i]:((((in @ X420 @ omega)&(in @ X420 @ X419))=>(in @ (setadjoin @ X420 @ X420) @ X419))))=>![X421:$i]:(((in @ X421 @ omega)=>(in @ X421 @ X419)))))=>(![X422:$i > $i > $o, X423:$i]:((![X424:$i]:(((in @ X424 @ X423)=>?[X425:$i]:(((X422 @ X424 @ X425)&![X426:$i]:(((X422 @ X424 @ X426)=>((X425)=(X426))))))))=>?[X427:$i]:(![X428:$i]:(((in @ X428 @ X427)<=>?[X429:$i]:(((in @ X429 @ X423)&(X422 @ X429 @ X428))))))))=>(![X430:$i]:((?[X431:$i]:((in @ X431 @ X430))=>?[X432:$i]:(((in @ X432 @ X430)&~(?[X433:$i]:(((in @ X433 @ X432)&(in @ X433 @ X430))))))))=>((epred1_0)=>(![X453:$i > $o]:((?[X454:$i]:(((X453 @ X454)&![X455:$i]:(((X453 @ X455)=>((X454)=(X455))))))=>(X453 @ (descr @ (^[Z0:$i]:(X453 @ Z0))))))=>(![X456:$i, X457:$i > $o, X458:$i]:(((in @ X458 @ X456)=>((X457 @ X458)=>(in @ X458 @ (dsetconstr @ X456 @ X457)))))=>(![X459:$i, X460:$i > $o, X461:$i]:(((in @ X461 @ (dsetconstr @ X459 @ X460))=>(in @ X461 @ X459)))=>(![X462:$i, X463:$i > $o, X464:$i]:(((in @ X464 @ (dsetconstr @ X462 @ X463))=>(X463 @ X464)))=>(![X465:$i > $o]:((?[X466:$i]:(((X465 @ X466)&![X467:$i]:(((X465 @ X467)=>((X466)=(X467))))))=>?[X468:$i]:(((X465 @ X468)&![X469:$i]:(((X465 @ X469)=>((X468)=(X469))))))))=>(![X470:$o, X471:$i]:(((in @ X471 @ (prop2set @ ((X470))))=>(X470)))=>(![X472:$i]:(((in @ X472 @ emptyset)=>![X473:$o]:((X473))))=>(![X474:$i]:(((in @ X474 @ emptyset)=>~($true)))=>(![X475:$i]:(~(in @ X475 @ emptyset))=>(![X476:$i > $o]:((?[X477:$i]:(((X476 @ X477)&![X478:$i]:(((X476 @ X478)=>((X477)=(X478))))))=>?[X479:$i]:((X476 @ X479))))=>(![X480:$i, X481:$i]:((![X482:$i]:(((in @ X482 @ X480)=>(in @ X482 @ X481)))=>(![X483:$i]:(((in @ X483 @ X481)=>(in @ X483 @ X480)))=>((X480)=(X481)))))=>(![X484:$i]:((![X485:$i]:(~(in @ X485 @ X484))=>((X484)=(emptyset))))=>(![X486:$i]:((![X487:$i]:(~(in @ X487 @ X486))=>((X486)=(emptyset))))=>(![X488:$i, X489:$i > $o, X490:$i]:(((in @ X490 @ X488)=>((in @ X490 @ (dsetconstr @ X488 @ X489))<=>(X489 @ X490))))=>(![X491:$i]:((((X491)!=(emptyset))=>?[X492:$i]:((in @ X492 @ X491))))=>(![X493:$i, X494:$i > $o, X495:$i]:(((in @ X495 @ X493)=>((X494 @ X495)=>((dsetconstr @ X493 @ X494)!=(emptyset)))))=>(![X496:$i]:((?[X497:$i]:((in @ X497 @ X496))=>((X496)!=(emptyset))))=>(![X498:$i, X499:$i]:((in @ X498 @ (setadjoin @ X498 @ X499)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X500:$i, X501:$i, X502:$i]:(((in @ X502 @ X501)=>(in @ X502 @ (setadjoin @ X500 @ X501))))=>(![X503:$i, X504:$i, X505:$i]:(((in @ X505 @ (setadjoin @ X503 @ X504))=>![X506:$o]:(((((X505)=(X503))=>(X506))=>(((in @ X505 @ X504)=>(X506))=>(X506))))))=>(![X507:$i, X508:$i, X509:$i]:(((in @ X509 @ (setadjoin @ X507 @ X508))=>(((X509)=(X507))|(in @ X509 @ X508))))=>(![X510:$i]:(((dsetconstr @ X510 @ (^[Z0:$i]:($true)))=(X510)))=>(![X511:$i, X512:$i]:((![X513:$i]:(((in @ X513 @ X512)=>(in @ X513 @ X511)))=>(in @ X512 @ (powerset @ X511))))=>(![X514:$i]:((in @ emptyset @ (powerset @ X514)))=>(![X515:$i]:((in @ emptyset @ (powerset @ X515)))=>(![X516:$i, X517:$i, X518:$i]:(((in @ X517 @ (powerset @ X516))=>((in @ X518 @ X517)=>(in @ X518 @ X516))))=>(![X519:$i, X520:$i, X521:$i]:(((in @ X520 @ X521)=>((in @ X521 @ X519)=>(in @ X520 @ (setunion @ X519)))))=>(![X522:$i, X523:$i]:(((in @ X523 @ (setunion @ X522))=>![X524:$o]:((![X525:$i]:(((in @ X523 @ X525)=>((in @ X525 @ X522)=>(X524))))=>(X524)))))=>(![X526:$i, X527:$i]:(((in @ X527 @ X526)=>(in @ X527 @ (powerset @ (setunion @ X526)))))=>(![X528:$i > $o]:((?[X529:$i]:(((X528 @ X529)&![X530:$i]:(((X528 @ X530)=>((X529)=(X530))))))=>?[X531:$i]:(![X532:$i]:(((X528 @ X532)<=>((X532)=(X531)))))))=>(![X533:$i]:((((X533)!=(emptyset))=>?[X534:$i]:(((in @ X534 @ X533)&$true))))=>(![X535:$i, X536:$i]:(((in @ X535 @ (setadjoin @ X536 @ emptyset))=>((X535)=(X536))))=>(![X537:$i, X538:$i]:((((X537)!=(X538))=>~(in @ X538 @ (setadjoin @ X537 @ emptyset))))=>(![X539:$i, X540:$i]:((((X539)=(X540))=>(in @ X539 @ (setadjoin @ X540 @ emptyset))))=>(![X541:$i, X542:$i]:(((in @ X541 @ (setadjoin @ X542 @ emptyset))=>(in @ X542 @ (setadjoin @ X541 @ emptyset))))=>(![X543:$i, X544:$i, X545:$i]:(((in @ X545 @ (setadjoin @ X543 @ (setadjoin @ X544 @ emptyset)))=>(((X545)=(X543))|((X545)=(X544)))))=>(![X546:$i, X547:$i]:((in @ X546 @ (setadjoin @ X546 @ (setadjoin @ X547 @ emptyset))))=>(![X548:$i, X549:$i]:((in @ X549 @ (setadjoin @ X548 @ (setadjoin @ X549 @ emptyset))))=>(![X550:$i, X551:$i > $o]:((?[X552:$i]:(((in @ X552 @ X550)&(X551 @ X552)))=>(((dsetconstr @ X550 @ X551)=(emptyset))=>~($true))))=>(![X553:$i > $o, X554:$i]:(((in @ X554 @ emptyset)=>(X553 @ X554)))=>(![X555:$i, X556:$i > $o]:((~(![X557:$i]:(((in @ X557 @ X555)=>(X556 @ X557))))=>?[X558:$i]:(((in @ X558 @ X555)&~((X556 @ X558))))))=>(![X559:$i, X560:$i > $o]:((![X561:$i]:(((in @ X561 @ X559)=>~((X560 @ X561))))=>~(?[X562:$i]:(((in @ X562 @ X559)&(X560 @ X562))))))=>(![X563:$i, X564:$i > $o]:((~(?[X565:$i]:(((in @ X565 @ X563)&(X564 @ X565))))=>![X566:$i]:(((in @ X566 @ X563)=>~((X564 @ X566))))))=>(![X567:$i, X568:$i > $o]:((?[X569:$i]:(((in @ X569 @ X567)&~((X568 @ X569))))=>~(![X570:$i]:(((in @ X570 @ X567)=>(X568 @ X570))))))=>(![X571:$o]:(((X571)=>(in @ emptyset @ (prop2set @ ((X571))))))=>(![X572:$o]:(((X572)=>(set2prop @ (prop2set @ ((X572))))))=>(![X573:$i, X574:$i > $o]:((~(?[X575:$i]:(((in @ X575 @ X573)&(X574 @ X575))))=>![X576:$i]:(((in @ X576 @ X573)=>~((X574 @ X576))))))=>(![X577:$i, X578:$i > $o]:((~(![X579:$i]:(((in @ X579 @ X577)=>(X578 @ X579))))=>?[X580:$i]:(((in @ X580 @ X577)&~((X578 @ X580))))))=>(![X581:$i > $o]:((?[X582:$i]:(((X581 @ X582)&![X583:$i]:(((X581 @ X583)=>((X582)=(X583))))))=>?[X584:$i]:(((X581 @ X584)&![X585:$i]:(((X581 @ X585)=>((X584)=(X585))))))))=>(![X586:$i > $o]:((?[X587:$i]:((X586 @ X587))=>(![X588:$i, X589:$i]:(((X586 @ X588)=>((X586 @ X589)=>((X588)=(X589)))))=>?[X590:$i]:(((X586 @ X590)&![X591:$i]:(((X586 @ X591)=>((X590)=(X591)))))))))=>(![X592:$i > $o]:((?[X593:$i]:(![X594:$i]:(((X592 @ X594)<=>((X594)=(X593)))))=>?[X595:$i]:(((X592 @ X595)&![X596:$i]:(((X592 @ X596)=>((X595)=(X596))))))))=>(![X597:$i, X598:$i]:((((X597)=(X598))=>![X599:$i, X600:$i]:((((X599)=(X600))=>((in @ X599 @ X597)=>(in @ X600 @ X598))))))=>(![X601:$i, X602:$i]:((((X601)=(X602))=>![X603:$i, X604:$i]:((((X603)=(X604))=>((in @ X603 @ X601)<=>(in @ X604 @ X602))))))=>(![X605:$i > $o]:((?[X606:$i]:(((X605 @ X606)&![X607:$i]:(((X605 @ X607)=>((X606)=(X607))))))=>![X608:$i, X609:$i]:(((X605 @ X608)=>((X605 @ X609)=>((X608)=(X609)))))))=>(![X610:$i > $o, X611:$i > $o]:((![X612:$i, X613:$i]:((((X612)=(X613))=>((X610 @ X612)<=>(X611 @ X613))))=>(?[X614:$i]:(((X610 @ X614)&![X615:$i]:(((X610 @ X615)=>((X614)=(X615))))))<=>?[X616:$i]:(((X611 @ X616)&![X617:$i]:(((X611 @ X617)=>((X616)=(X617)))))))))=>(((emptyset)=(emptyset))=>(![X618:$i, X619:$i]:((((X618)=(X619))=>![X620:$i, X621:$i]:((((X620)=(X621))=>((setadjoin @ X618 @ X620)=(setadjoin @ X619 @ X621))))))=>(![X622:$i, X623:$i]:((((X622)=(X623))=>((powerset @ X622)=(powerset @ X623))))=>(![X624:$i, X625:$i]:((((X624)=(X625))=>((setunion @ X624)=(setunion @ X625))))=>(((omega)=(omega))=>(![X626:$i > $o]:((?[X627:$i]:(((X626 @ X627)&![X628:$i]:(((X626 @ X628)=>((X627)=(X628))))))=>![X629:$i, X630:$i]:(((X626 @ X629)=>((X626 @ X630)=>((X629)=(X630)))))))=>(![X631:$i > $o, X632:$i > $o]:((![X633:$i, X634:$i]:((((X633)=(X634))=>((X631 @ X633)<=>(X632 @ X634))))=>(?[X635:$i]:(((X631 @ X635)&![X636:$i]:(((X631 @ X636)=>((X635)=(X636))))))=>(?[X637:$i]:(((X632 @ X637)&![X638:$i]:(((X632 @ X638)=>((X637)=(X638))))))=>((descr @ X631)=(descr @ X632))))))=>(![X639:$i, X640:$i]:((((X639)=(X640))=>![X641:$i > $o, X642:$i > $o]:((![X643:$i]:(((in @ X643 @ X639)=>![X644:$i]:(((in @ X644 @ X640)=>(((X643)=(X644))=>((X641 @ X643)<=>(X642 @ X644)))))))=>((dsetconstr @ X639 @ X641)=(dsetconstr @ X640 @ X642))))))=>(![X645:$i, X646:$i]:((![X647:$i]:(((in @ X647 @ X645)=>(in @ X647 @ X646)))=>(subset @ X645 @ X646)))=>(![X648:$i, X649:$i]:((((X648)=(X649))=>(subset @ X649 @ X648)))=>(![X650:$i, X651:$i]:((((X650)=(X651))=>(subset @ X650 @ X651)))=>(![X652:$i, X653:$i]:((![X654:$i]:(((in @ X654 @ X652)=>(in @ X654 @ X653)))=>(subset @ X652 @ X653)))=>(![X655:$i]:((subset @ emptyset @ X655))=>(![X656:$i, X657:$i, X658:$i]:(((subset @ X656 @ X657)=>((in @ X658 @ X656)=>(in @ X658 @ X657))))=>(![X659:$i, X660:$i, X661:$i]:(((subset @ X659 @ X660)=>(~(in @ X661 @ X660)=>~(in @ X661 @ X659))))=>(![X662:$i, X663:$i, X664:$i]:(((in @ X664 @ X662)=>(~(in @ X664 @ X663)=>~(subset @ X662 @ X663))))=>(![X665:$i, X666:$i]:((~(subset @ X665 @ X666)=>((X665)!=(X666))))=>(![X667:$i, X668:$i, X669:$i]:(((in @ X669 @ X667)=>(~(in @ X669 @ X668)=>((X667)!=(X668)))))=>(![X670:$i]:((subset @ X670 @ X670))=>(![X671:$i, X672:$i, X673:$i]:(((subset @ X671 @ X672)=>((subset @ X672 @ X673)=>(subset @ X671 @ X673))))=>(![X674:$i, X675:$i]:((subset @ X675 @ (setadjoin @ X674 @ X675)))=>(![X676:$i, X677:$i, X678:$i]:(((subset @ X676 @ X678)=>(subset @ X676 @ (setadjoin @ X677 @ X678))))=>(![X679:$i, X680:$i]:(((subset @ X679 @ X680)=>(in @ X679 @ (powerset @ X680))))=>(![X681:$i, X682:$i]:(((subset @ X681 @ X682)=>((subset @ X682 @ X681)=>((X681)=(X682)))))=>(![X683:$i]:(((subset @ X683 @ emptyset)=>((X683)=(emptyset))))=>(![X684:$i, X685:$i]:(((subset @ X685 @ X684)=>(in @ X685 @ (powerset @ X684))))=>(![X686:$i, X687:$i]:(((in @ X687 @ (powerset @ X686))=>(subset @ X687 @ X686)))=>(![X688:$i]:((in @ X688 @ (powerset @ X688)))=>(![X689:$i, X690:$i]:(((subset @ X689 @ X690)=>(subset @ (powerset @ X689) @ (powerset @ X690))))=>(![X691:$i, X692:$i > $o]:((in @ (dsetconstr @ X691 @ X692) @ (powerset @ X691)))=>(![X693:$i, X694:$i > $o]:((subset @ (dsetconstr @ X693 @ X694) @ X693))=>(![X695:$i, X696:$i, X697:$i]:(((in @ X697 @ X695)=>(in @ X697 @ (binunion @ X695 @ X696))))=>(![X698:$i, X699:$i]:((in @ X699 @ (setadjoin @ X698 @ (setadjoin @ X699 @ emptyset))))=>(![X700:$i, X701:$i, X702:$i]:(((in @ X702 @ X701)=>(in @ X702 @ (binunion @ X700 @ X701))))=>(![X703:$i, X704:$i, X705:$i, X706:$o]:(((in @ X705 @ (binunion @ X703 @ X704))=>(((in @ X705 @ X703)=>(X706))=>(((in @ X705 @ X704)=>(X706))=>(X706)))))=>(![X707:$i, X708:$i, X709:$i]:(((in @ X709 @ (binunion @ X707 @ X708))=>((in @ X709 @ X707)|(in @ X709 @ X708))))=>(![X710:$i, X711:$i]:((subset @ X710 @ (binunion @ X710 @ X711)))=>(![X712:$i, X713:$i]:((subset @ X713 @ (binunion @ X712 @ X713)))=>(![X714:$i, X715:$i, X716:$i]:(((in @ X716 @ X714)=>((in @ X716 @ X715)=>(in @ X716 @ (binintersect @ X714 @ X715)))))=>(![X717:$i, X718:$i, X719:$i]:(((subset @ X719 @ X717)=>((subset @ X719 @ X718)=>(subset @ X719 @ (binintersect @ X717 @ X718)))))=>(![X720:$i, X721:$i, X722:$i]:(((in @ X722 @ (binintersect @ X720 @ X721))=>(in @ X722 @ X720)))=>(![X723:$i, X724:$i]:((subset @ (binintersect @ X723 @ X724) @ X723))=>(![X725:$i, X726:$i]:(((subset @ X725 @ X726)=>((binintersect @ X725 @ X726)=(X725))))=>(![X727:$i, X728:$i]:((((binintersect @ X727 @ X728)=(X728))=>(subset @ X728 @ X727)))=>(![X729:$i, X730:$i, X731:$i]:(((in @ X731 @ (binintersect @ X729 @ X730))=>(in @ X731 @ X730)))=>(![X732:$i, X733:$i]:((~(?[X734:$i]:(((in @ X734 @ X732)&(in @ X734 @ X733))))=>((binintersect @ X732 @ X733)=(emptyset))))=>(![X735:$i, X736:$i]:((subset @ (binintersect @ X735 @ X736) @ X736))=>(![X737:$i, X738:$i]:(((subset @ X738 @ X737)=>((binintersect @ X737 @ X738)=(X738))))=>(![X739:$i, X740:$i]:((((binintersect @ X739 @ X740)=(X739))=>(subset @ X739 @ X740)))=>(![X741:$i, X742:$i, X743:$i]:(((binintersect @ X741 @ (binunion @ X742 @ X743))=(binunion @ (binintersect @ X741 @ X742) @ (binintersect @ X741 @ X743))))=>(![X744:$i, X745:$i, X746:$i]:(((in @ X746 @ X744)=>(~(in @ X746 @ X745)=>(in @ X746 @ (setminus @ X744 @ X745)))))=>(![X747:$i, X748:$i, X749:$i]:(((in @ X749 @ (setminus @ X747 @ X748))=>(in @ X749 @ X747)))=>(![X750:$i, X751:$i, X752:$i]:(((in @ X752 @ (setminus @ X750 @ X751))=>~(in @ X752 @ X751)))=>(![X753:$i, X754:$i]:(((subset @ X753 @ X754)=>((setminus @ X753 @ X754)=(emptyset))))=>(![X755:$i, X756:$i, X757:$i]:((~(in @ X757 @ (setminus @ X755 @ X756))=>((in @ X757 @ X755)=>(in @ X757 @ X756))))=>(![X758:$i, X759:$i, X760:$i]:((~(in @ X760 @ (setminus @ X758 @ X759))=>(~(in @ X760 @ X759)=>~(in @ X760 @ X758))))=>(![X761:$i, X762:$i, X763:$i]:((~(in @ X763 @ X761)=>~(in @ X763 @ (setminus @ X761 @ X762))))=>(![X764:$i, X765:$i, X766:$i]:(((in @ X766 @ X765)=>~(in @ X766 @ (setminus @ X764 @ X765))))=>(![X767:$i, X768:$i]:((subset @ (setminus @ X767 @ X768) @ X767))=>(![X769:$i, X770:$i]:((((setminus @ X769 @ X770)=(emptyset))=>(subset @ X769 @ X770)))=>(![X771:$i, X772:$i, X773:$i]:(((in @ X773 @ (symdiff @ X771 @ X772))=>![X774:$o]:((((in @ X773 @ X771)=>(~(in @ X773 @ X772)=>(X774)))=>((~(in @ X773 @ X771)=>((in @ X773 @ X772)=>(X774)))=>(X774))))))=>(![X775:$i, X776:$i, X777:$i]:(((in @ X777 @ X775)=>(~(in @ X777 @ X776)=>(in @ X777 @ (symdiff @ X775 @ X776)))))=>(![X778:$i, X779:$i, X780:$i]:((~(in @ X780 @ X778)=>((in @ X780 @ X779)=>(in @ X780 @ (symdiff @ X778 @ X779)))))=>(![X781:$i, X782:$i, X783:$i]:(((in @ X783 @ X781)=>((in @ X783 @ X782)=>~(in @ X783 @ (symdiff @ X781 @ X782)))))=>(![X784:$i, X785:$i, X786:$i]:((~(in @ X786 @ X784)=>(~(in @ X786 @ X785)=>~(in @ X786 @ (symdiff @ X784 @ X785)))))=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(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_150, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_151]), foundationAx]), wellorderingAx]), c_0_152]), c_0_153]), c_0_154]), c_0_155]), c_0_156]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_157]), setext]), emptyI]), noeltsimpempty]), c_0_158]), c_0_159]), c_0_160]), c_0_161]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_162]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_163]), c_0_164]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_165]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_166]), c_0_167]), c_0_168]), inCongP]), in__Cong]), c_0_169]), c_0_170]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_171]), c_0_172]), c_0_173]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_174]), c_0_175]), binunionIL]), upairset2IR]), binunionIR]), binunionEcases]), binunionE]), binunionLsub]), binunionRsub]), binintersectI]), binintersectSubset5]), binintersectEL]), binintersectLsub]), binintersectSubset2]), binintersectSubset3]), binintersectER]), disjointsetsI1]), binintersectRsub]), binintersectSubset4]), binintersectSubset1]), bs114d]), setminusI]), setminusEL]), setminusER]), setminusSubset2]), setminusERneg]), setminusELneg]), setminusILneg]), setminusIRneg]), setminusLsub]), setminusSubset1]), symdiffE]), symdiffI1]), symdiffI2]), symdiffIneg1]), symdiffIneg2])])]), c_0_176])).
% 0.23/0.31 thf(c_0_178, negated_conjecture, ![X787:$i, X788:$i, X790:$i, X791:$i, X792:$i, X793:$i, X794:$i, X795:$i, X796:$i, X797:$i, X798:$i, X800:$i, X801:$i, X803:$i, X804:$i, X805:$i, X806:$i, X807:$i, X809:$i, X810:$i > $i > $o, X811:$i, X813:$i, X816:$i, X818:$i, X819:$i, X820:$i, X821:$i, X823:$i, X824:$i > $o, X825:$i, X827:$i, X828:$i > $o, X829:$i, X830:$i, X831:$i > $o, X832:$i, X833:$i, X834:$i > $o, X835:$i, X836:$i > $o, X837:$i, X840:$i, X841:$o, X842:$i, X843:$i, X844:$o, X845:$i, X846:$i, X847:$i > $o, X848:$i, X851:$i, X852:$i, X855:$i, X857:$i, X859:$i, X860:$i > $o, X861:$i, X862:$i, X864:$i, X865:$i > $o, X866:$i, X867:$i, X868:$i, X869:$i, X870:$i, X871:$i, X872:$i, X873:$i, X874:$i, X875:$i, X876:$i, X877:$o, X878:$i, X879:$i, X880:$i, X881:$i, X882:$i, X883:$i, X885:$i, X886:$i, X887:$i, X888:$i, X889:$i, X890:$i, X891:$i, X892:$i, X893:$i, X894:$i, X895:$o, X897:$i, X898:$i, X899:$i > $o, X900:$i, X903:$i, X904:$i, X905:$i, X907:$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 > $o, X924:$i, X925:$i > $o, X926:$i, X927:$i, X928:$i > $o, X929:$i, X931:$i, X932:$i > $o, X934:$i, X935:$i, X936:$i > $o, X938:$i, X939:$i, X940:$i > $o, X941:$i, X943:$o, X944:$o, X945:$i, X946:$i > $o, X948:$i, X949:$i, X950:$i > $o, X951:$i, X953:$i > $o, X954:$i, X957:$i, X958:$i > $o, X959:$i, X963:$i, X964:$i > $o, X965:$i, X968:$i, X969:$i, X970:$i, X971:$i, X972:$i, X973:$i, X974:$i, X975:$i, X976:$i, X977:$i > $o, X978:$i, X980:$i, X981:$i, X982:$i > $o, X983:$i > $o, X986:$i, X989:$i, X990:$i, X993:$i, X994:$i, X995:$i, X996:$i, X997:$i, X998:$i, X999:$i, X1000:$i, X1001:$i, X1002:$i > $o, X1003:$i, X1005:$i, X1006:$i, X1007:$i > $o, X1008:$i > $o, X1011:$i, X1013:$i, X1015:$i, X1016:$i, X1017:$i > $o, X1018:$i > $o, X1021:$i, X1022:$i, X1024:$i, X1025:$i, X1026:$i, X1027:$i, X1028:$i, X1029:$i, X1031:$i, X1032:$i, X1033:$i, X1034:$i, X1035:$i, X1036:$i, X1037:$i, X1038:$i, X1039:$i, X1040:$i, X1041:$i, X1042:$i, X1043:$i, X1044:$i, X1045:$i, X1046:$i, X1047:$i, X1048:$i, X1049:$i, X1050:$i, X1051:$i, X1052:$i, X1053:$i, X1054:$i, X1055:$i, X1056:$i, X1057:$i, X1058:$i, X1059:$i, X1060:$i, X1061:$i, X1062:$i, X1063:$i, X1064:$i, X1065:$i, X1066:$i, X1067:$i, X1068:$i > $o, X1069:$i, X1070:$i > $o, X1071:$i, X1072:$i, X1073:$i, X1074:$i, X1075:$i, X1076:$i, X1077:$i, X1078:$i, X1079:$i, X1080:$i, X1081:$i, X1082:$o, X1083:$i, X1084:$i, X1085:$i, X1086:$i, X1087:$i, X1088:$i, X1089:$i, X1090:$i, X1091:$i, X1092:$i, X1093:$i, X1094:$i, X1095:$i, X1096:$i, X1097:$i, X1098:$i, X1099:$i, X1100:$i, X1101:$i, X1102:$i, X1103:$i, X1104:$i, X1105:$i, X1106:$i, X1107:$i, X1108:$i, X1109:$i, X1111:$i, X1112:$i, X1113:$i, X1114:$i, X1115:$i, X1116:$i, X1117:$i, X1118:$i, X1119:$i, X1120:$i, X1121:$i, X1122:$i, X1123:$i, X1124:$i, X1125:$i, X1126:$i, X1127:$i, X1128:$i, X1129:$i, X1130:$i, X1131:$i, X1132:$i, X1133:$i, X1134:$i, X1135:$i, X1136:$i, X1137:$i, X1138:$i, X1139:$i, X1140:$i, X1141:$i, X1142:$i, X1143:$i, X1144:$i, X1145:$i, X1146:$i, X1147:$i, X1148:$i, X1149:$i, X1150:$o, X1151:$i, X1152:$i, X1153:$i, X1154:$i, X1155:$i, X1156:$i, X1157:$i, X1158:$i, X1159:$i, X1160:$i, X1161:$i, X1162:$i]:((((~(in @ (esk1_2 @ X787 @ X788) @ X787)|~(in @ (esk1_2 @ X787 @ X788) @ X788)|((X787)=(X788)))&((in @ (esk1_2 @ X787 @ X788) @ X787)|(in @ (esk1_2 @ X787 @ X788) @ X788)|((X787)=(X788))))&(~(in @ X790 @ emptyset)&(((~(in @ X793 @ (setadjoin @ X791 @ X792))|(((X793)=(X791))|(in @ X793 @ X792)))&((((X793)!=(X791))|(in @ X793 @ (setadjoin @ X791 @ X792)))&(~(in @ X793 @ X792)|(in @ X793 @ (setadjoin @ X791 @ X792)))))&(((~(in @ X795 @ (powerset @ X794))|(~(in @ X796 @ X795)|(in @ X796 @ X794)))&(((in @ (esk2_2 @ X797 @ X798) @ X798)|(in @ X798 @ (powerset @ X797)))&(~(in @ (esk2_2 @ X797 @ X798) @ X797)|(in @ X798 @ (powerset @ X797)))))&(((((in @ X801 @ (esk3_2 @ X800 @ X801))|~(in @ X801 @ (setunion @ X800)))&((in @ (esk3_2 @ X800 @ X801) @ X800)|~(in @ X801 @ (setunion @ X800))))&(~(in @ X804 @ X805)|~(in @ X805 @ X803)|(in @ X804 @ (setunion @ X803))))&((in @ emptyset @ omega)&((~(in @ X806 @ omega)|(in @ (setadjoin @ X806 @ X806) @ omega))&(((((in @ (esk4_1 @ X807) @ omega)|~(in @ emptyset @ X807)|(~(in @ X809 @ omega)|(in @ X809 @ X807)))&((in @ (esk4_1 @ X807) @ X807)|~(in @ emptyset @ X807)|(~(in @ X809 @ omega)|(in @ X809 @ X807))))&(~(in @ (setadjoin @ (esk4_1 @ X807) @ (esk4_1 @ X807)) @ X807)|~(in @ emptyset @ X807)|(~(in @ X809 @ omega)|(in @ X809 @ X807))))&((((((in @ (esk8_3 @ X810 @ X811 @ X816) @ X811)|~(in @ X816 @ (esk7_2 @ X810 @ X811))|(in @ (esk5_2 @ X810 @ X811) @ X811))&((X810 @ (esk8_3 @ X810 @ X811 @ X816) @ X816)|~(in @ X816 @ (esk7_2 @ X810 @ X811))|(in @ (esk5_2 @ X810 @ X811) @ X811)))&(~(in @ X819 @ X811)|~(X810 @ X819 @ X818)|(in @ X818 @ (esk7_2 @ X810 @ X811))|(in @ (esk5_2 @ X810 @ X811) @ X811)))&(((((in @ (esk8_3 @ X810 @ X811 @ X816) @ X811)|~(in @ X816 @ (esk7_2 @ X810 @ X811))|((X810 @ (esk5_2 @ X810 @ X811) @ (esk6_3 @ X810 @ X811 @ X813))|~(X810 @ (esk5_2 @ X810 @ X811) @ X813)))&((X810 @ (esk8_3 @ X810 @ X811 @ X816) @ X816)|~(in @ X816 @ (esk7_2 @ X810 @ X811))|((X810 @ (esk5_2 @ X810 @ X811) @ (esk6_3 @ X810 @ X811 @ X813))|~(X810 @ (esk5_2 @ X810 @ X811) @ X813))))&(~(in @ X819 @ X811)|~(X810 @ X819 @ X818)|(in @ X818 @ (esk7_2 @ X810 @ X811))|((X810 @ (esk5_2 @ X810 @ X811) @ (esk6_3 @ X810 @ X811 @ X813))|~(X810 @ (esk5_2 @ X810 @ X811) @ X813))))&((((in @ (esk8_3 @ X810 @ X811 @ X816) @ X811)|~(in @ X816 @ (esk7_2 @ X810 @ X811))|(((X813)!=(esk6_3 @ X810 @ X811 @ X813))|~(X810 @ (esk5_2 @ X810 @ X811) @ X813)))&((X810 @ (esk8_3 @ X810 @ X811 @ X816) @ X816)|~(in @ X816 @ (esk7_2 @ X810 @ X811))|(((X813)!=(esk6_3 @ X810 @ X811 @ X813))|~(X810 @ (esk5_2 @ X810 @ X811) @ X813))))&(~(in @ X819 @ X811)|~(X810 @ X819 @ X818)|(in @ X818 @ (esk7_2 @ X810 @ X811))|(((X813)!=(esk6_3 @ X810 @ X811 @ X813))|~(X810 @ (esk5_2 @ X810 @ X811) @ X813))))))&((((in @ (esk9_1 @ X820) @ X820)|~(in @ X821 @ X820))&(~(in @ X823 @ (esk9_1 @ X820))|~(in @ X823 @ X820)|~(in @ X821 @ X820)))&((epred1_0)&((((X824 @ (esk10_2 @ X824 @ X825))|~(X824 @ X825)|(X824 @ (descr @ X824)))&(((X825)!=(esk10_2 @ X824 @ X825))|~(X824 @ X825)|(X824 @ (descr @ X824))))&((~(in @ X829 @ X827)|(~(X828 @ X829)|(in @ X829 @ (dsetconstr @ X827 @ X828))))&((~(in @ X832 @ (dsetconstr @ X830 @ X831))|(in @ X832 @ X830))&((~(in @ X835 @ (dsetconstr @ X833 @ X834))|(X834 @ X835))&(((((X836 @ (esk12_1 @ X836))|((X836 @ (esk11_2 @ X836 @ X837))|~(X836 @ X837)))&(~(X836 @ X840)|((esk12_1 @ X836)=(X840))|((X836 @ (esk11_2 @ X836 @ X837))|~(X836 @ X837))))&(((X836 @ (esk12_1 @ X836))|(((X837)!=(esk11_2 @ X836 @ X837))|~(X836 @ X837)))&(~(X836 @ X840)|((esk12_1 @ X836)=(X840))|(((X837)!=(esk11_2 @ X836 @ X837))|~(X836 @ X837)))))&((~(in @ X842 @ (prop2set @ ((X841))))|(X841))&((~(in @ X843 @ emptyset)|(X844))&((~(in @ X845 @ emptyset)|~($true))&(~(in @ X846 @ emptyset)&((((X847 @ (esk13_2 @ X847 @ X848))|~(X847 @ X848)|(X847 @ (esk14_1 @ X847)))&(((X848)!=(esk13_2 @ X847 @ X848))|~(X847 @ X848)|(X847 @ (esk14_1 @ X847))))&(((((in @ (esk16_2 @ X851 @ X852) @ X852)|((X851)=(X852))|(in @ (esk15_2 @ X851 @ X852) @ X851))&(~(in @ (esk16_2 @ X851 @ X852) @ X851)|((X851)=(X852))|(in @ (esk15_2 @ X851 @ X852) @ X851)))&(((in @ (esk16_2 @ X851 @ X852) @ X852)|((X851)=(X852))|~(in @ (esk15_2 @ X851 @ X852) @ X852))&(~(in @ (esk16_2 @ X851 @ X852) @ X851)|((X851)=(X852))|~(in @ (esk15_2 @ X851 @ X852) @ X852))))&(((in @ (esk17_1 @ X855) @ X855)|((X855)=(emptyset)))&(((in @ (esk18_1 @ X857) @ X857)|((X857)=(emptyset)))&(((~(in @ X861 @ (dsetconstr @ X859 @ X860))|(X860 @ X861)|~(in @ X861 @ X859))&(~(X860 @ X861)|(in @ X861 @ (dsetconstr @ X859 @ X860))|~(in @ X861 @ X859)))&((((X862)=(emptyset))|(in @ (esk19_1 @ X862) @ X862))&((~(in @ X866 @ X864)|(~(X865 @ X866)|((dsetconstr @ X864 @ X865)!=(emptyset))))&((~(in @ X868 @ 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X1049)|(subset @ X1047 @ X1049)))&((subset @ X1051 @ (setadjoin @ X1050 @ X1051))&((~(subset @ X1052 @ X1054)|(subset @ X1052 @ (setadjoin @ X1053 @ X1054)))&((~(subset @ X1055 @ X1056)|(in @ X1055 @ (powerset @ X1056)))&((~(subset @ X1057 @ X1058)|(~(subset @ X1058 @ X1057)|((X1057)=(X1058))))&((~(subset @ X1059 @ emptyset)|((X1059)=(emptyset)))&((~(subset @ X1061 @ X1060)|(in @ X1061 @ (powerset @ X1060)))&((~(in @ X1063 @ (powerset @ X1062))|(subset @ X1063 @ X1062))&((in @ X1064 @ (powerset @ X1064))&((~(subset @ X1065 @ X1066)|(subset @ (powerset @ X1065) @ (powerset @ X1066)))&((in @ (dsetconstr @ X1067 @ X1068) @ (powerset @ X1067))&((subset @ (dsetconstr @ X1069 @ X1070) @ X1069)&((~(in @ X1073 @ X1071)|(in @ X1073 @ (binunion @ X1071 @ X1072)))&((in @ X1075 @ (setadjoin @ X1074 @ (setadjoin @ X1075 @ emptyset)))&((~(in @ X1078 @ X1077)|(in @ X1078 @ (binunion @ X1076 @ X1077)))&(((((in @ X1081 @ X1080)|(X1082)|(in @ X1081 @ X1079)|~(in @ X1081 @ (binunion @ X1079 @ X1080)))&(~(X1082)|(X1082)|(in @ X1081 @ X1079)|~(in @ X1081 @ (binunion @ X1079 @ X1080))))&(((in @ X1081 @ X1080)|(X1082)|~(X1082)|~(in @ X1081 @ (binunion @ X1079 @ X1080)))&(~(X1082)|(X1082)|~(X1082)|~(in @ X1081 @ (binunion @ X1079 @ X1080)))))&((~(in @ X1085 @ (binunion @ X1083 @ X1084))|((in @ X1085 @ X1083)|(in @ X1085 @ X1084)))&((subset @ X1086 @ (binunion @ X1086 @ X1087))&((subset @ X1089 @ (binunion @ X1088 @ X1089))&((~(in @ X1092 @ X1090)|(~(in @ X1092 @ X1091)|(in @ X1092 @ (binintersect @ X1090 @ X1091))))&((~(subset @ X1095 @ X1093)|(~(subset @ X1095 @ X1094)|(subset @ X1095 @ (binintersect @ X1093 @ X1094))))&((~(in @ X1098 @ (binintersect @ X1096 @ X1097))|(in @ X1098 @ X1096))&((subset @ (binintersect @ X1099 @ X1100) @ X1099)&((~(subset @ X1101 @ X1102)|((binintersect @ X1101 @ X1102)=(X1101)))&((((binintersect @ X1103 @ X1104)!=(X1104))|(subset @ X1104 @ X1103))&((~(in @ X1107 @ (binintersect @ X1105 @ X1106))|(in @ X1107 @ X1106))&((((in @ (esk54_2 @ X1108 @ X1109) @ X1108)|((binintersect @ X1108 @ X1109)=(emptyset)))&((in @ (esk54_2 @ X1108 @ X1109) @ X1109)|((binintersect @ X1108 @ X1109)=(emptyset))))&((subset @ (binintersect @ X1111 @ X1112) @ X1112)&((~(subset @ X1114 @ X1113)|((binintersect @ X1113 @ X1114)=(X1114)))&((((binintersect @ X1115 @ X1116)!=(X1115))|(subset @ X1115 @ X1116))&(((binintersect @ X1117 @ (binunion @ X1118 @ X1119))=(binunion @ (binintersect @ X1117 @ X1118) @ (binintersect @ X1117 @ X1119)))&((~(in @ X1122 @ X1120)|((in @ X1122 @ X1121)|(in @ X1122 @ (setminus @ X1120 @ X1121))))&((~(in @ X1125 @ (setminus @ X1123 @ X1124))|(in @ X1125 @ X1123))&((~(in @ X1128 @ (setminus @ X1126 @ X1127))|~(in @ X1128 @ X1127))&((~(subset @ X1129 @ X1130)|((setminus @ X1129 @ X1130)=(emptyset)))&(((in @ X1133 @ (setminus @ X1131 @ X1132))|(~(in @ X1133 @ X1131)|(in @ X1133 @ X1132)))&(((in @ X1136 @ (setminus @ X1134 @ X1135))|((in @ X1136 @ X1135)|~(in @ X1136 @ X1134)))&(((in @ X1139 @ X1137)|~(in @ X1139 @ (setminus @ X1137 @ X1138)))&((~(in @ X1142 @ X1141)|~(in @ X1142 @ (setminus @ X1140 @ X1141)))&((subset @ (setminus @ X1143 @ X1144) @ X1143)&((((setminus @ X1145 @ X1146)!=(emptyset))|(subset @ X1145 @ X1146))&((((~(in @ X1149 @ X1147)|(X1150)|(in @ X1149 @ X1147)|~(in @ X1149 @ (symdiff @ X1147 @ X1148)))&(((in @ X1149 @ X1148)|(X1150)|(in @ X1149 @ X1147)|~(in @ X1149 @ (symdiff @ X1147 @ X1148)))&(~(X1150)|(X1150)|(in @ X1149 @ X1147)|~(in @ X1149 @ (symdiff @ X1147 @ X1148)))))&(((~(in @ X1149 @ X1147)|(X1150)|~(in @ X1149 @ X1148)|~(in @ X1149 @ (symdiff @ X1147 @ X1148)))&(((in @ X1149 @ X1148)|(X1150)|~(in @ X1149 @ X1148)|~(in @ X1149 @ (symdiff @ X1147 @ X1148)))&(~(X1150)|(X1150)|~(in @ X1149 @ X1148)|~(in @ X1149 @ (symdiff @ X1147 @ X1148)))))&((~(in @ X1149 @ X1147)|(X1150)|~(X1150)|~(in @ X1149 @ (symdiff @ X1147 @ X1148)))&(((in @ X1149 @ X1148)|(X1150)|~(X1150)|~(in @ X1149 @ (symdiff @ X1147 @ X1148)))&(~(X1150)|(X1150)|~(X1150)|~(in @ X1149 @ (symdiff @ X1147 @ X1148)))))))&((~(in @ X1153 @ X1151)|((in @ X1153 @ X1152)|(in @ X1153 @ (symdiff @ X1151 @ X1152))))&(((in @ X1156 @ X1154)|(~(in @ X1156 @ X1155)|(in @ X1156 @ (symdiff @ X1154 @ X1155))))&((~(in @ X1159 @ X1157)|(~(in @ X1159 @ X1158)|~(in @ X1159 @ (symdiff @ X1157 @ X1158))))&(((in @ X1162 @ X1160)|((in @ X1162 @ X1161)|~(in @ X1162 @ (symdiff @ X1160 @ X1161))))&~(in @ esk56_0 @ (setadjoin @ esk55_0 @ (setadjoin @ esk56_0 @ emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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_177])])])])])])])).
% 0.23/0.31 thf(c_0_179, negated_conjecture, ~((in @ esk56_0 @ (setadjoin @ esk55_0 @ (setadjoin @ esk56_0 @ emptyset)))), inference(split_conjunct,[status(thm)],[c_0_178])).
% 0.23/0.31 thf(c_0_180, negated_conjecture, ![X3:$i, X2:$i]:((in @ X2 @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset)))), inference(split_conjunct,[status(thm)],[c_0_178])).
% 0.23/0.31 thf(c_0_181, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_179, c_0_180])]), ['proof']).
% 0.23/0.31 % SZS output end CNFRefutation
% 0.23/0.31 % Parsed axioms : 289
% 0.23/0.31 % Removed by relevancy pruning/SinE : 0
% 0.23/0.31 % Initial clauses : 410
% 0.23/0.31 % Removed in clause preprocessing : 178
% 0.23/0.31 % Initial clauses in saturation : 232
% 0.23/0.31 % Processed clauses : 62
% 0.23/0.31 % ...of these trivial : 5
% 0.23/0.31 % ...subsumed : 8
% 0.23/0.31 % ...remaining for further processing : 48
% 0.23/0.31 % Other redundant clauses eliminated : 4
% 0.23/0.31 % Clauses deleted for lack of memory : 0
% 0.23/0.31 % Backward-subsumed : 0
% 0.23/0.31 % Backward-rewritten : 2
% 0.23/0.31 % Generated clauses : 54
% 0.23/0.31 % ...of the previous two non-redundant : 30
% 0.23/0.31 % ...aggressively subsumed : 0
% 0.23/0.31 % Contextual simplify-reflections : 0
% 0.23/0.31 % Paramodulations : 50
% 0.23/0.31 % Factorizations : 0
% 0.23/0.31 % NegExts : 0
% 0.23/0.31 % Equation resolutions : 4
% 0.23/0.31 % Disequality decompositions : 0
% 0.23/0.31 % Total rewrite steps : 31
% 0.23/0.31 % ...of those cached : 15
% 0.23/0.31 % Propositional unsat checks : 0
% 0.23/0.31 % Propositional check models : 0
% 0.23/0.31 % Propositional check unsatisfiable : 0
% 0.23/0.31 % Propositional clauses : 0
% 0.23/0.31 % Propositional clauses after purity: 0
% 0.23/0.31 % Propositional unsat core size : 0
% 0.23/0.31 % Propositional preprocessing time : 0.000
% 0.23/0.31 % Propositional encoding time : 0.000
% 0.23/0.31 % Propositional solver time : 0.000
% 0.23/0.31 % Success case prop preproc time : 0.000
% 0.23/0.31 % Success case prop encoding time : 0.000
% 0.23/0.31 % Success case prop solver time : 0.000
% 0.23/0.31 % Current number of processed clauses : 42
% 0.23/0.31 % Positive orientable unit clauses : 30
% 0.23/0.31 % Positive unorientable unit clauses: 0
% 0.23/0.31 % Negative unit clauses : 1
% 0.23/0.31 % Non-unit-clauses : 11
% 0.23/0.31 % Current number of unprocessed clauses: 200
% 0.23/0.31 % ...number of literals in the above : 703
% 0.23/0.31 % Current number of archived formulas : 0
% 0.23/0.31 % Current number of archived clauses : 2
% 0.23/0.31 % Clause-clause subsumption calls (NU) : 2
% 0.23/0.31 % Rec. Clause-clause subsumption calls : 1
% 0.23/0.31 % Non-unit clause-clause subsumptions : 1
% 0.23/0.31 % Unit Clause-clause subsumption calls : 3
% 0.23/0.31 % Rewrite failures with RHS unbound : 0
% 0.23/0.31 % BW rewrite match attempts : 6
% 0.23/0.31 % BW rewrite match successes : 2
% 0.23/0.31 % Condensation attempts : 0
% 0.23/0.31 % Condensation successes : 0
% 0.23/0.31 % Termbank termtop insertions : 34426
% 0.23/0.31 % Search garbage collected termcells : 13093
% 0.23/0.31
% 0.23/0.31 % -------------------------------------------------
% 0.23/0.31 % User time : 0.027 s
% 0.23/0.31 % System time : 0.008 s
% 0.23/0.31 % Total time : 0.035 s
% 0.23/0.31 % Maximum resident set size: 6480 pages
% 0.23/0.31
% 0.23/0.31 % -------------------------------------------------
% 0.23/0.31 % User time : 0.034 s
% 0.23/0.31 % System time : 0.015 s
% 0.23/0.31 % Total time : 0.049 s
% 0.23/0.31 % Maximum resident set size: 5120 pages
% 0.23/0.31 % E exiting
%------------------------------------------------------------------------------