0.00/0.04	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.07	% Command  : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM
0.17/0.43	% Computer : n016.cluster.edu
0.17/0.43	% Model    : x86_64 x86_64
0.17/0.43	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.17/0.43	% Memory   : 8046.5625MB
0.17/0.43	% OS       : Linux 6.8.0-71-generic
0.17/0.43	% CPULimit : 1440
0.17/0.43	% WCLimit  : 180
0.17/0.43	% DateTime : Mon Jul 27 13:08:07 UTC 2026
0.17/0.43	% CPUTime  : 
0.17/0.43	Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM
0.17/0.49	Running higher-order theorem proving
0.25/0.53	Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=180 /export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p
3.51/1.14	% Version: 3.5.1-ho
3.51/1.14	% Preprocessing class: HSLMSLSSLLLCHSA.
3.51/1.14	% Scheduled 5 strats onto 8 cores with 180 seconds (1440 total)
3.51/1.14	% Starting ho_unfolding_5 with 720s (4) cores
3.51/1.14	% Starting pre_casc_3 with 180s (1) cores
3.51/1.14	% Starting new_ho_10_cnf2 with 180s (1) cores
3.51/1.14	% Starting full_lambda_10 with 180s (1) cores
3.51/1.14	% Starting ehoh_best_nonlift_rwall with 180s (1) cores
3.51/1.14	% ho_unfolding_5 with pid 1366153 completed with status 0
3.51/1.14	% Result found by ho_unfolding_5
3.51/1.14	% Preprocessing class: HSLMSLSSLLLCHSA.
3.51/1.14	% Scheduled 5 strats onto 8 cores with 180 seconds (1440 total)
3.51/1.14	% Starting ho_unfolding_5 with 720s (4) cores
3.51/1.14	% (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
3.51/1.14	% No SInE strategy applied
3.51/1.14	% Search class: HGHSM-FSLM31-MHSMMSBN
3.51/1.14	% Scheduled 7 strats onto 4 cores with 720 seconds (720 total)
3.51/1.14	% Starting SubtermCWHack with 65s (1) cores
3.51/1.14	% Starting ho_unfolding_5 with 73s (1) cores
3.51/1.14	% Starting pre_casc_3 with 103s (1) cores
3.51/1.14	% Starting new_bool_3 with 65s (1) cores
3.51/1.14	% ho_unfolding_5 with pid 1366160 completed with status 0
3.51/1.14	% Result found by ho_unfolding_5
3.51/1.14	% Preprocessing class: HSLMSLSSLLLCHSA.
3.51/1.14	% Scheduled 5 strats onto 8 cores with 180 seconds (1440 total)
3.51/1.14	% Starting ho_unfolding_5 with 720s (4) cores
3.51/1.14	% (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
3.51/1.14	% No SInE strategy applied
3.51/1.14	% Search class: HGHSM-FSLM31-MHSMMSBN
3.51/1.14	% Scheduled 7 strats onto 4 cores with 720 seconds (720 total)
3.51/1.14	% Starting SubtermCWHack with 65s (1) cores
3.51/1.14	% Starting ho_unfolding_5 with 73s (1) cores
3.51/1.14	% Preprocessing time       : 0.009 s
3.51/1.14	% Presaturation interreduction done
3.51/1.14	
3.51/1.14	% Proof found!
3.51/1.14	% SZS status Theorem
3.51/1.14	% SZS output start CNFRefutation
3.51/1.14	thf(decl_23, type, in: $i > $i > $o).
3.51/1.14	thf(decl_24, type, exu: ($i > $o) > $o).
3.51/1.14	thf(decl_25, type, setextAx: $o).
3.51/1.14	thf(decl_26, type, emptyset: $i).
3.51/1.14	thf(decl_27, type, emptysetAx: $o).
3.51/1.14	thf(decl_28, type, setadjoin: $i > $i > $i).
3.51/1.14	thf(decl_29, type, setadjoinAx: $o).
3.51/1.14	thf(decl_30, type, powerset: $i > $i).
3.51/1.14	thf(decl_31, type, powersetAx: $o).
3.51/1.14	thf(decl_32, type, setunion: $i > $i).
3.51/1.14	thf(decl_33, type, setunionAx: $o).
3.51/1.14	thf(decl_34, type, omega: $i).
3.51/1.14	thf(decl_35, type, omega0Ax: $o).
3.51/1.14	thf(decl_36, type, omegaSAx: $o).
3.51/1.14	thf(decl_37, type, omegaIndAx: $o).
3.51/1.14	thf(decl_38, type, replAx: $o).
3.51/1.14	thf(decl_39, type, foundationAx: $o).
3.51/1.14	thf(decl_40, type, wellorderingAx: $o).
3.51/1.14	thf(decl_41, type, descr: ($i > $o) > $i).
3.51/1.14	thf(decl_42, type, descrp: $o).
3.51/1.14	thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
3.51/1.14	thf(decl_44, type, dsetconstrI: $o).
3.51/1.14	thf(decl_45, type, dsetconstrEL: $o).
3.51/1.14	thf(decl_46, type, dsetconstrER: $o).
3.51/1.14	thf(decl_47, type, exuE1: $o).
3.51/1.14	thf(decl_48, type, prop2set: $o > $i).
3.51/1.14	thf(decl_49, type, prop2setE: $o).
3.51/1.14	thf(decl_50, type, emptysetE: $o).
3.51/1.14	thf(decl_51, type, emptysetimpfalse: $o).
3.51/1.14	thf(decl_52, type, notinemptyset: $o).
3.51/1.14	thf(decl_53, type, exuE3e: $o).
3.51/1.14	thf(decl_54, type, setext: $o).
3.51/1.14	thf(decl_55, type, emptyI: $o).
3.51/1.14	thf(decl_56, type, noeltsimpempty: $o).
3.51/1.14	thf(decl_57, type, setbeta: $o).
3.51/1.14	thf(decl_58, type, nonempty: $i > $o).
3.51/1.14	thf(decl_59, type, nonemptyE1: $o).
3.51/1.14	thf(decl_60, type, nonemptyI: $o).
3.51/1.14	thf(decl_61, type, nonemptyI1: $o).
3.51/1.15	thf(decl_62, type, setadjoinIL: $o).
3.51/1.15	thf(decl_63, type, emptyinunitempty: $o).
3.51/1.15	thf(decl_64, type, setadjoinIR: $o).
3.51/1.15	thf(decl_65, type, setadjoinE: $o).
3.51/1.15	thf(decl_66, type, setadjoinOr: $o).
3.51/1.15	thf(decl_67, type, setoftrueEq: $o).
3.51/1.15	thf(decl_68, type, powersetI: $o).
3.51/1.15	thf(decl_69, type, emptyinPowerset: $o).
3.51/1.15	thf(decl_70, type, emptyInPowerset: $o).
3.51/1.15	thf(decl_71, type, powersetE: $o).
3.51/1.15	thf(decl_72, type, setunionI: $o).
3.51/1.15	thf(decl_73, type, setunionE: $o).
3.51/1.15	thf(decl_74, type, subPowSU: $o).
3.51/1.15	thf(decl_75, type, exuE2: $o).
3.51/1.15	thf(decl_76, type, nonemptyImpWitness: $o).
3.51/1.15	thf(decl_77, type, uniqinunit: $o).
3.51/1.15	thf(decl_78, type, notinsingleton: $o).
3.51/1.15	thf(decl_79, type, eqinunit: $o).
3.51/1.15	thf(decl_80, type, singletonsswitch: $o).
3.51/1.15	thf(decl_81, type, upairsetE: $o).
3.51/1.15	thf(decl_82, type, upairsetIL: $o).
3.51/1.15	thf(decl_83, type, upairsetIR: $o).
3.51/1.15	thf(decl_84, type, emptyE1: $o).
3.51/1.15	thf(decl_85, type, vacuousDall: $o).
3.51/1.15	thf(decl_86, type, quantDeMorgan1: $o).
3.51/1.15	thf(decl_87, type, quantDeMorgan2: $o).
3.51/1.15	thf(decl_88, type, quantDeMorgan3: $o).
3.51/1.15	thf(decl_89, type, quantDeMorgan4: $o).
3.51/1.15	thf(decl_90, type, prop2setI: $o).
3.51/1.15	thf(decl_91, type, set2prop: $i > $o).
3.51/1.15	thf(decl_92, type, prop2set2propI: $o).
3.51/1.15	thf(decl_93, type, notdexE: $o).
3.51/1.15	thf(decl_94, type, notdallE: $o).
3.51/1.15	thf(decl_95, type, exuI1: $o).
3.51/1.15	thf(decl_96, type, exuI3: $o).
3.51/1.15	thf(decl_97, type, exuI2: $o).
3.51/1.15	thf(decl_98, type, inCongP: $o).
3.51/1.15	thf(decl_99, type, in__Cong: $o).
3.51/1.15	thf(decl_100, type, exuE3u: $o).
3.51/1.15	thf(decl_101, type, exu__Cong: $o).
3.51/1.15	thf(decl_102, type, emptyset__Cong: $o).
3.51/1.15	thf(decl_103, type, setadjoin__Cong: $o).
3.51/1.15	thf(decl_104, type, powerset__Cong: $o).
3.51/1.15	thf(decl_105, type, setunion__Cong: $o).
3.51/1.15	thf(decl_106, type, omega__Cong: $o).
3.51/1.15	thf(decl_107, type, exuEu: $o).
3.51/1.15	thf(decl_108, type, descr__Cong: $o).
3.51/1.15	thf(decl_109, type, dsetconstr__Cong: $o).
3.51/1.15	thf(decl_110, type, subset: $i > $i > $o).
3.51/1.15	thf(decl_113, type, subsetI1: $o).
3.51/1.15	thf(decl_114, type, eqimpsubset2: $o).
3.51/1.15	thf(decl_115, type, eqimpsubset1: $o).
3.51/1.15	thf(decl_116, type, subsetI2: $o).
3.51/1.15	thf(decl_117, type, emptysetsubset: $o).
3.51/1.15	thf(decl_118, type, subsetE: $o).
3.51/1.15	thf(decl_119, type, subsetE2: $o).
3.51/1.15	thf(decl_120, type, notsubsetI: $o).
3.51/1.15	thf(decl_121, type, notequalI1: $o).
3.51/1.15	thf(decl_122, type, notequalI2: $o).
3.51/1.15	thf(decl_123, type, subsetRefl: $o).
3.51/1.15	thf(decl_124, type, subsetTrans: $o).
3.51/1.15	thf(decl_125, type, setadjoinSub: $o).
3.51/1.15	thf(decl_126, type, setadjoinSub2: $o).
3.51/1.15	thf(decl_127, type, subset2powerset: $o).
3.51/1.15	thf(decl_128, type, setextsub: $o).
3.51/1.15	thf(decl_129, type, subsetemptysetimpeq: $o).
3.51/1.15	thf(decl_130, type, powersetI1: $o).
3.51/1.15	thf(decl_131, type, powersetE1: $o).
3.51/1.15	thf(decl_132, type, inPowerset: $o).
3.51/1.15	thf(decl_133, type, powersetsubset: $o).
3.51/1.15	thf(decl_134, type, sepInPowerset: $o).
3.51/1.15	thf(decl_135, type, sepSubset: $o).
3.51/1.15	thf(decl_136, type, binunion: $i > $i > $i).
3.51/1.15	thf(decl_137, type, binunionIL: $o).
3.51/1.15	thf(decl_138, type, upairset2IR: $o).
3.51/1.15	thf(decl_139, type, binunionIR: $o).
3.51/1.15	thf(decl_140, type, binunionEcases: $o).
3.51/1.15	thf(decl_141, type, binunionE: $o).
3.51/1.15	thf(decl_142, type, binunionLsub: $o).
3.51/1.15	thf(decl_143, type, binunionRsub: $o).
3.51/1.15	thf(decl_144, type, binintersect: $i > $i > $i).
3.51/1.15	thf(decl_145, type, binintersectI: $o).
3.51/1.15	thf(decl_146, type, binintersectSubset5: $o).
3.51/1.15	thf(decl_147, type, binintersectEL: $o).
3.51/1.15	thf(decl_148, type, binintersectLsub: $o).
3.51/1.15	thf(decl_149, type, binintersectSubset2: $o).
3.51/1.15	thf(decl_150, type, binintersectSubset3: $o).
3.51/1.15	thf(decl_151, type, binintersectER: $o).
3.51/1.15	thf(decl_152, type, disjointsetsI1: $o).
3.51/1.15	thf(decl_153, type, binintersectRsub: $o).
3.51/1.15	thf(decl_154, type, binintersectSubset4: $o).
3.51/1.15	thf(decl_155, type, binintersectSubset1: $o).
3.51/1.15	thf(decl_156, type, bs114d: $o).
3.51/1.15	thf(decl_158, type, setminus: $i > $i > $i).
3.51/1.15	thf(decl_159, type, setminusI: $o).
3.51/1.15	thf(decl_160, type, setminusEL: $o).
3.51/1.15	thf(decl_161, type, setminusER: $o).
3.51/1.15	thf(decl_162, type, setminusSubset2: $o).
3.51/1.15	thf(decl_163, type, setminusERneg: $o).
3.51/1.15	thf(decl_164, type, setminusELneg: $o).
3.51/1.15	thf(decl_165, type, setminusILneg: $o).
3.51/1.15	thf(decl_166, type, setminusIRneg: $o).
3.51/1.15	thf(decl_167, type, setminusLsub: $o).
3.51/1.15	thf(decl_168, type, setminusSubset1: $o).
3.51/1.15	thf(decl_169, type, symdiff: $i > $i > $i).
3.51/1.15	thf(decl_170, type, symdiffE: $o).
3.51/1.15	thf(decl_171, type, symdiffI1: $o).
3.51/1.15	thf(decl_172, type, symdiffI2: $o).
3.51/1.15	thf(decl_173, type, symdiffIneg1: $o).
3.51/1.15	thf(decl_174, type, symdiffIneg2: $o).
3.51/1.15	thf(decl_175, type, iskpair: $i > $o).
3.51/1.15	thf(decl_176, type, secondinupair: $o).
3.51/1.15	thf(decl_177, type, setukpairIL: $o).
3.51/1.15	thf(decl_178, type, setukpairIR: $o).
3.51/1.15	thf(decl_179, type, kpairiskpair: $o).
3.51/1.15	thf(decl_180, type, kpair: $i > $i > $i).
3.51/1.15	thf(decl_181, type, kpairp: $o).
3.51/1.15	thf(decl_182, type, cartprod: $i > $i > $i).
3.51/1.15	thf(decl_183, type, singletonsubset: $o).
3.51/1.15	thf(decl_184, type, singletoninpowerset: $o).
3.51/1.15	thf(decl_185, type, singletoninpowunion: $o).
3.51/1.15	thf(decl_186, type, upairset2E: $o).
3.51/1.15	thf(decl_187, type, upairsubunion: $o).
3.51/1.15	thf(decl_188, type, upairinpowunion: $o).
3.51/1.15	thf(decl_189, type, ubforcartprodlem1: $o).
3.51/1.15	thf(decl_190, type, ubforcartprodlem2: $o).
3.51/1.15	thf(decl_191, type, ubforcartprodlem3: $o).
3.51/1.15	thf(decl_192, type, cartprodpairin: $o).
3.51/1.15	thf(decl_193, type, cartprodmempair1: $o).
3.51/1.15	thf(decl_194, type, cartprodmempair: $o).
3.51/1.15	thf(decl_195, type, setunionE2: $o).
3.51/1.15	thf(decl_196, type, setunionsingleton1: $o).
3.51/1.15	thf(decl_197, type, setunionsingleton2: $o).
3.51/1.15	thf(decl_198, type, setunionsingleton: $o).
3.51/1.15	thf(decl_199, type, singleton: $i > $o).
3.51/1.15	thf(decl_200, type, singletonprop: $o).
3.51/1.15	thf(decl_201, type, ex1: $i > ($i > $o) > $o).
3.51/1.15	thf(decl_202, type, ex1E1: $o).
3.51/1.15	thf(decl_203, type, ex1I: $o).
3.51/1.15	thf(decl_204, type, ex1I2: $o).
3.51/1.15	thf(decl_205, type, singletonsuniq: $o).
3.51/1.15	thf(decl_210, type, setukpairinjL1: $o).
3.51/1.15	thf(decl_211, type, kfstsingleton: $o).
3.51/1.15	thf(decl_212, type, theprop: $o).
3.51/1.15	thf(decl_213, type, kfst: $i > $i).
3.51/1.15	thf(decl_214, type, kfstpairEq: $o).
3.51/1.15	thf(decl_215, type, cartprodfstin: $o).
3.51/1.15	thf(decl_216, type, setukpairinjL2: $o).
3.51/1.15	thf(decl_217, type, setukpairinjL: $o).
3.51/1.15	thf(decl_218, type, setukpairinjR11: $o).
3.51/1.15	thf(decl_219, type, setukpairinjR12: $o).
3.51/1.15	thf(decl_220, type, setukpairinjR1: $o).
3.51/1.15	thf(decl_221, type, upairequniteq: $o).
3.51/1.15	thf(decl_222, type, setukpairinjR2: $o).
3.51/1.15	thf(decl_223, type, setukpairinjR: $o).
3.51/1.15	thf(decl_224, type, ksndsingleton: $o).
3.51/1.15	thf(decl_225, type, ksnd: $i > $i).
3.51/1.15	thf(decl_226, type, ksndpairEq: $o).
3.51/1.15	thf(decl_227, type, kpairsurjEq: $o).
3.51/1.15	thf(decl_228, type, cartprodsndin: $o).
3.51/1.15	thf(decl_229, type, cartprodpairmemEL: $o).
3.51/1.15	thf(decl_230, type, cartprodpairmemER: $o).
3.51/1.15	thf(decl_231, type, cartprodmempaircEq: $o).
3.51/1.15	thf(decl_232, type, cartprodfstpairEq: $o).
3.51/1.15	thf(decl_233, type, cartprodsndpairEq: $o).
3.51/1.15	thf(decl_234, type, cartprodpairsurjEq: $o).
3.51/1.15	thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
3.51/1.15	thf(decl_237, type, epred1_0: $o).
3.51/1.15	thf(decl_238, type, esk1_2: $i > $i > $i).
3.51/1.15	thf(decl_239, type, esk2_2: $i > $i > $i).
3.51/1.15	thf(decl_240, type, esk3_2: $i > $i > $i).
3.51/1.15	thf(decl_241, type, esk4_1: $i > $i).
3.51/1.15	thf(decl_242, type, esk5_2: ($i > $i > $o) > $i > $i).
3.51/1.15	thf(decl_243, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
3.51/1.15	thf(decl_244, type, esk7_2: ($i > $i > $o) > $i > $i).
3.51/1.15	thf(decl_245, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
3.51/1.15	thf(decl_246, type, esk9_1: $i > $i).
3.51/1.15	thf(decl_247, type, esk10_2: ($i > $o) > $i > $i).
3.51/1.15	thf(decl_248, type, esk11_2: ($i > $o) > $i > $i).
3.51/1.15	thf(decl_249, type, esk12_1: ($i > $o) > $i).
3.51/1.15	thf(decl_250, type, esk13_2: ($i > $o) > $i > $i).
3.51/1.15	thf(decl_251, type, esk14_1: ($i > $o) > $i).
3.51/1.15	thf(decl_252, type, esk15_2: $i > $i > $i).
3.51/1.15	thf(decl_253, type, esk16_2: $i > $i > $i).
3.51/1.15	thf(decl_254, type, esk17_1: $i > $i).
3.51/1.15	thf(decl_255, type, esk18_1: $i > $i).
3.51/1.15	thf(decl_256, type, esk19_1: $i > $i).
3.51/1.15	thf(decl_257, type, esk20_2: $i > $i > $i).
3.51/1.15	thf(decl_258, type, esk21_3: $i > $i > $o > $i).
3.51/1.15	thf(decl_259, type, esk22_2: ($i > $o) > $i > $i).
3.51/1.15	thf(decl_260, type, esk23_1: ($i > $o) > $i).
3.51/1.15	thf(decl_261, type, esk24_1: $i > $i).
3.51/1.15	thf(decl_262, type, esk25_2: $i > ($i > $o) > $i).
3.51/1.15	thf(decl_263, type, esk26_2: $i > ($i > $o) > $i).
3.51/1.15	thf(decl_264, type, esk27_2: $i > ($i > $o) > $i).
3.51/1.15	thf(decl_265, type, esk28_2: $i > ($i > $o) > $i).
3.51/1.15	thf(decl_266, type, esk29_2: $i > ($i > $o) > $i).
3.51/1.15	thf(decl_267, type, esk30_2: $i > ($i > $o) > $i).
3.51/1.15	thf(decl_268, type, esk31_2: ($i > $o) > $i > $i).
3.51/1.15	thf(decl_269, type, esk32_1: ($i > $o) > $i).
3.51/1.15	thf(decl_270, type, esk33_1: ($i > $o) > $i).
3.51/1.15	thf(decl_271, type, esk34_1: ($i > $o) > $i).
3.51/1.15	thf(decl_272, type, esk35_1: ($i > $o) > $i).
3.51/1.15	thf(decl_273, type, esk36_2: ($i > $o) > $i > $i).
3.51/1.15	thf(decl_274, type, esk37_1: ($i > $o) > $i).
3.51/1.15	thf(decl_275, type, esk38_2: ($i > $o) > $i > $i).
3.51/1.15	thf(decl_276, type, esk39_2: ($i > $o) > ($i > $o) > $i).
3.51/1.15	thf(decl_277, type, esk40_2: ($i > $o) > ($i > $o) > $i).
3.51/1.15	thf(decl_278, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
3.51/1.15	thf(decl_279, type, esk42_2: ($i > $o) > ($i > $o) > $i).
3.51/1.15	thf(decl_280, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
3.51/1.15	thf(decl_281, type, esk44_2: ($i > $o) > ($i > $o) > $i).
3.51/1.15	thf(decl_282, type, esk45_2: ($i > $o) > $i > $i).
3.51/1.15	thf(decl_283, type, esk46_2: ($i > $o) > ($i > $o) > $i).
3.51/1.15	thf(decl_284, type, esk47_2: ($i > $o) > ($i > $o) > $i).
3.51/1.15	thf(decl_285, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
3.51/1.15	thf(decl_286, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
3.51/1.15	thf(decl_287, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
3.51/1.15	thf(decl_288, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
3.51/1.15	thf(decl_289, type, esk52_2: $i > $i > $i).
3.51/1.15	thf(decl_290, type, esk53_2: $i > $i > $i).
3.51/1.15	thf(decl_291, type, esk54_2: $i > $i > $i).
3.51/1.15	thf(decl_292, type, esk55_3: $i > $i > $i > $i).
3.51/1.15	thf(decl_293, type, esk56_3: $i > $i > $i > $i).
3.51/1.15	thf(decl_294, type, esk57_2: $i > $i > $i).
3.51/1.15	thf(decl_295, type, esk58_2: $i > ($i > $o) > $i).
3.51/1.15	thf(decl_296, type, esk59_2: $i > ($i > $o) > $i).
3.51/1.15	thf(decl_297, type, esk60_2: $i > ($i > $o) > $i).
3.51/1.15	thf(decl_298, type, esk61_2: $i > ($i > $o) > $i).
3.51/1.15	thf(decl_299, type, esk62_3: $i > ($i > $o) > $i > $i).
3.51/1.15	thf(decl_300, type, esk63_3: $i > ($i > $o) > $i > $i).
3.51/1.15	thf(decl_301, type, esk64_2: $i > ($i > $o) > $i).
3.51/1.15	thf(decl_302, type, esk65_2: $i > ($i > $o) > $i).
3.51/1.15	thf(decl_303, type, esk66_2: $i > ($i > $o) > $i).
3.51/1.15	thf(decl_304, type, esk67_1: $i > $i).
3.51/1.15	thf(decl_305, type, esk68_1: $i > $i).
3.51/1.15	thf(decl_306, type, esk69_0: $i).
3.51/1.15	thf(decl_307, type, esk70_0: $i).
3.51/1.15	thf(decl_308, type, epred2_0: $i > $i > $o).
3.51/1.15	thf(decl_309, type, esk71_0: $i).
3.51/1.15	thf(decl_310, type, esk72_0: $i).
3.51/1.15	thf(decl_316, type, epred3_3: ($i > $i > $o) > $i > $i > $i > $o).
3.51/1.15	thf(decl_320, type, esk78_4: $i > $i > $i > ($i > $i > $o) > $i).
3.51/1.15	thf(decl_321, type, esk79_4: $i > $i > $i > ($i > $i > $o) > $i).
3.51/1.15	thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', ex1)).
3.51/1.15	thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:((((in @ X2 @ X4))&(((X4)=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', singleton)).
3.51/1.15	thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', replAx)).
3.51/1.15	thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', exu)).
3.51/1.15	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', descrp)).
3.51/1.15	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', exuE1)).
3.51/1.15	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', exuE3e)).
3.51/1.15	thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', nonempty)).
3.51/1.15	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', nonemptyI)).
3.51/1.15	thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', exuE2)).
3.51/1.15	thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', exuI1)).
3.51/1.15	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', exuI3)).
3.51/1.15	thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', exuI2)).
3.51/1.15	thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', exuE3u)).
3.51/1.15	thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', exu__Cong)).
3.51/1.15	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', exuEu)).
3.51/1.15	thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', descr__Cong)).
3.51/1.15	thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', singletonprop)).
3.51/1.15	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', ex1E1)).
3.51/1.15	thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', ex1I)).
3.51/1.15	thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', ex1I2)).
3.51/1.15	thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', kfstsingleton)).
3.51/1.15	thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', ksndsingleton)).
3.51/1.15	thf(dpsetconstrI, conjecture, (((emptysetAx)=>((((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>(((wellorderingAx)=>(((dsetconstrI)=>((((((emptysetE)=>((((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>(((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>(((((setadjoinOr)=>((((emptyinPowerset)=>((emptyInPowerset)=>(((setunionI)=>((((exuE2)=>(((uniqinunit)=>((notinsingleton)=>(((singletonsswitch)=>((((((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((((((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>(((exu__Cong)=>(((setadjoin__Cong)=>((((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>(((eqimpsubset2)=>(((subsetI2)=>(((subsetE)=>(((notsubsetI)=>(((((subsetTrans)=>(((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>(((inPowerset)=>((((sepSubset)=>((binunionIL)=>((upairset2IR)=>((((binunionE)=>(((binunionRsub)=>(((((binintersectLsub)=>(((binintersectSubset3)=>(((disjointsetsI1)=>(((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>(((setminusER)=>((setminusSubset2)=>(((((setminusIRneg)=>((setminusLsub)=>(((((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>(((setukpairIL)=>((setukpairIR)=>((((singletonsubset)=>((singletoninpowerset)=>((((((ubforcartprodlem1)=>(((ubforcartprodlem3)=>(((cartprodmempair1)=>(((setunionE2)=>((((((ex1E1)=>((((singletonsuniq)=>(((kfstsingleton)=>((((cartprodfstin)=>((setukpairinjL2)=>(((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((((setukpairinjR)=>(((ksndpairEq)=>((kpairsurjEq)=>(((((((cartprodsndpairEq)=>(![X4:$i, X5:$i, X23:$i > $i > $o, X2:$i]:((![X3:$i]:((((X23 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X23 @ X14 @ X18))))))<=(in @ X3 @ X5)))<=(in @ X2 @ X4)))<=(cartprodpairsurjEq)))<=(cartprodfstpairEq))<=(cartprodmempaircEq))<=(cartprodpairmemER))<=(cartprodpairmemEL))<=(cartprodsndin))))<=(ksndsingleton)))<=(setukpairinjR2))<=(upairequniteq)))))<=(setukpairinjL))))<=(kfstpairEq))<=(theprop)))<=(setukpairinjL1)))<=(ex1I2))<=(ex1I)))<=(singletonprop))<=(setunionsingleton))<=(setunionsingleton2))<=(setunionsingleton1)))<=(cartprodmempair)))<=(cartprodpairin)))<=(ubforcartprodlem2)))<=(upairinpowunion))<=(upairsubunion))<=(upairset2E))<=(singletoninpowunion))))<=(kpairp))<=(kpairiskpair))))<=(secondinupair)))))<=(symdiffI1))<=(symdiffE))<=(setminusSubset1))))<=(setminusILneg))<=(setminusELneg))<=(setminusERneg))))<=(setminusEL))))))<=(binintersectRsub)))<=(binintersectER)))<=(binintersectSubset2)))<=(binintersectEL))<=(binintersectSubset5))<=(binintersectI)))<=(binunionLsub)))<=(binunionEcases))<=(binunionIR)))))<=(sepInPowerset))<=(powersetsubset)))<=(powersetE1)))))))<=(setadjoinSub)))<=(subsetRefl))<=(notequalI2))<=(notequalI1)))<=(subsetE2)))<=(emptysetsubset)))<=(eqimpsubset1)))<=(subsetI1))))))<=(setunion__Cong))<=(powerset__Cong)))<=(emptyset__Cong)))<=(exuE3u))))))))<=(notdexE))<=(prop2set2propI))<=(prop2setI))<=(quantDeMorgan4))))))<=(emptyE1))<=(upairsetIR))<=(upairsetIL))<=(upairsetE)))<=(eqinunit))))<=(nonemptyImpWitness)))<=(subPowSU))<=(setunionE)))<=(powersetE))))<=(powersetI))<=(setoftrueEq)))<=(setadjoinE))<=(setadjoinIR))<=(emptyinunitempty)))))<=(nonemptyE1)))))))<=(notinemptyset))<=(emptysetimpfalse)))<=(prop2setE))<=(exuE1))<=(dsetconstrER))<=(dsetconstrEL)))<=(descrp)))<=(foundationAx)))))))<=(powersetAx))<=(setadjoinAx)))<=(setextAx)), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', dpsetconstrI)).
3.51/1.15	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', dsetconstrI)).
3.51/1.15	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', dsetconstrEL)).
3.51/1.15	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', dsetconstrER)).
3.51/1.15	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setbeta)).
3.51/1.15	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', nonemptyE1)).
3.51/1.15	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', nonemptyI1)).
3.51/1.15	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setoftrueEq)).
3.51/1.15	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', nonemptyImpWitness)).
3.51/1.15	thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', emptyE1)).
3.51/1.15	thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', dsetconstr__Cong)).
3.51/1.15	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', sepInPowerset)).
3.51/1.15	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', sepSubset)).
3.51/1.15	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', theprop)).
3.51/1.15	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setextAx)).
3.51/1.15	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', emptysetAx)).
3.51/1.15	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setadjoinAx)).
3.51/1.15	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', powersetAx)).
3.51/1.15	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setunionAx)).
3.51/1.15	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', omega0Ax)).
3.51/1.15	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', omegaSAx)).
3.51/1.15	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', omegaIndAx)).
3.51/1.15	thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', foundationAx)).
3.51/1.15	thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', wellorderingAx)).
3.51/1.15	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', prop2setE)).
3.51/1.15	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', emptysetE)).
3.51/1.15	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', emptysetimpfalse)).
3.51/1.15	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', notinemptyset)).
3.51/1.15	thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setext)).
3.51/1.15	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', emptyI)).
3.51/1.15	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', noeltsimpempty)).
3.51/1.15	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setadjoinIL)).
3.51/1.15	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', emptyinunitempty)).
3.51/1.15	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setadjoinIR)).
3.51/1.15	thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setadjoinE)).
3.51/1.15	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setadjoinOr)).
3.51/1.15	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', powersetI)).
3.51/1.15	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', emptyinPowerset)).
3.51/1.15	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', emptyInPowerset)).
3.51/1.15	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', powersetE)).
3.51/1.15	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setunionI)).
3.51/1.15	thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setunionE)).
3.51/1.15	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', subPowSU)).
3.51/1.15	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', uniqinunit)).
3.51/1.15	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', notinsingleton)).
3.51/1.15	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', eqinunit)).
3.51/1.15	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', singletonsswitch)).
3.51/1.15	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', upairsetE)).
3.51/1.15	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', upairsetIL)).
3.51/1.15	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', upairsetIR)).
3.51/1.15	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', vacuousDall)).
3.51/1.15	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', quantDeMorgan1)).
3.51/1.15	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', quantDeMorgan2)).
3.51/1.15	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', quantDeMorgan3)).
3.51/1.15	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', quantDeMorgan4)).
3.51/1.15	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', prop2setI)).
3.51/1.15	thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', prop2set2propI)).
3.51/1.15	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', notdexE)).
3.51/1.15	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', notdallE)).
3.51/1.15	thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', inCongP)).
3.51/1.15	thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', in__Cong)).
3.51/1.15	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', emptyset__Cong)).
3.51/1.15	thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setadjoin__Cong)).
3.51/1.15	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', powerset__Cong)).
3.51/1.15	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setunion__Cong)).
3.51/1.15	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', omega__Cong)).
3.51/1.15	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', subsetI1)).
3.51/1.15	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', eqimpsubset2)).
3.51/1.15	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', eqimpsubset1)).
3.51/1.15	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', subsetI2)).
3.51/1.15	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', emptysetsubset)).
3.51/1.15	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', subsetE)).
3.51/1.15	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', subsetE2)).
3.51/1.15	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', notsubsetI)).
3.51/1.15	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', notequalI1)).
3.51/1.15	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', notequalI2)).
3.51/1.15	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', subsetRefl)).
3.51/1.15	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', subsetTrans)).
3.51/1.15	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setadjoinSub)).
3.51/1.15	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setadjoinSub2)).
3.51/1.15	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', subset2powerset)).
3.51/1.15	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setextsub)).
3.51/1.15	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', subsetemptysetimpeq)).
3.51/1.15	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', powersetI1)).
3.51/1.15	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', powersetE1)).
3.51/1.15	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', inPowerset)).
3.51/1.15	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', powersetsubset)).
3.51/1.15	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', binunionIL)).
3.51/1.15	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', upairset2IR)).
3.51/1.15	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', binunionIR)).
3.51/1.15	thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', binunionEcases)).
3.51/1.15	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', binunionE)).
3.51/1.15	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', binunionLsub)).
3.51/1.15	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', binunionRsub)).
3.51/1.15	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', binintersectI)).
3.51/1.15	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', binintersectSubset5)).
3.51/1.15	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', binintersectEL)).
3.51/1.15	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', binintersectLsub)).
3.51/1.15	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', binintersectSubset2)).
3.51/1.15	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', binintersectSubset3)).
3.51/1.15	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', binintersectER)).
3.51/1.15	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', disjointsetsI1)).
3.51/1.15	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', binintersectRsub)).
3.51/1.15	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', binintersectSubset4)).
3.51/1.15	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', binintersectSubset1)).
3.51/1.15	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', bs114d)).
3.51/1.15	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setminusI)).
3.51/1.15	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setminusEL)).
3.51/1.15	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setminusER)).
3.51/1.15	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setminusSubset2)).
3.51/1.15	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setminusERneg)).
3.51/1.15	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setminusELneg)).
3.51/1.15	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setminusILneg)).
3.51/1.15	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setminusIRneg)).
3.51/1.15	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setminusLsub)).
3.51/1.15	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setminusSubset1)).
3.51/1.15	thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', symdiffE)).
3.51/1.15	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', symdiffI1)).
3.51/1.15	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', symdiffI2)).
3.51/1.15	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', symdiffIneg1)).
3.51/1.15	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', symdiffIneg2)).
3.51/1.15	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', secondinupair)).
3.51/1.15	thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setukpairIL)).
3.51/1.15	thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setukpairIR)).
3.51/1.15	thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', kpairiskpair)).
3.51/1.15	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', kpairp)).
3.51/1.15	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', singletonsubset)).
3.51/1.15	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', singletoninpowerset)).
3.51/1.15	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', singletoninpowunion)).
3.51/1.15	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', upairset2E)).
3.51/1.15	thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', upairsubunion)).
3.51/1.15	thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', upairinpowunion)).
3.51/1.15	thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', ubforcartprodlem1)).
3.51/1.15	thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', ubforcartprodlem2)).
3.51/1.15	thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', ubforcartprodlem3)).
3.51/1.15	thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', cartprodpairin)).
3.51/1.15	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', cartprodmempair1)).
3.51/1.15	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', cartprodmempair)).
3.51/1.15	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setunionE2)).
3.51/1.15	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setunionsingleton1)).
3.51/1.15	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setunionsingleton2)).
3.51/1.15	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setunionsingleton)).
3.51/1.15	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', singletonsuniq)).
3.51/1.15	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setukpairinjL1)).
3.51/1.15	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', kfstpairEq)).
3.51/1.15	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', cartprodfstin)).
3.51/1.15	thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setukpairinjL2)).
3.51/1.15	thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setukpairinjL)).
3.51/1.15	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setukpairinjR11)).
3.51/1.15	thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setukpairinjR12)).
3.51/1.15	thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setukpairinjR1)).
3.51/1.15	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', upairequniteq)).
3.51/1.15	thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setukpairinjR2)).
3.51/1.15	thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', setukpairinjR)).
3.51/1.15	thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', ksndpairEq)).
3.51/1.15	thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', kpairsurjEq)).
3.51/1.15	thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', cartprodsndin)).
3.51/1.15	thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', cartprodpairmemEL)).
3.51/1.15	thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', cartprodpairmemER)).
3.51/1.15	thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', cartprodmempaircEq)).
3.51/1.15	thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', cartprodfstpairEq)).
3.51/1.15	thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', cartprodsndpairEq)).
3.51/1.15	thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', cartprodpairsurjEq)).
3.51/1.15	thf(dpsetconstr, axiom, ((dpsetconstr)=(^[X4:$i, X5:$i, X22:$i > $i > $o]:(dsetconstr @ (cartprod @ X4 @ X5) @ (^[X18:$i]:(?[X2:$i]:((((in @ X2 @ X4))&(?[X3:$i]:((((((in @ X3 @ X5))&((X22 @ X2 @ X3))))&(((X18)=(kpair @ X2 @ X3))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.UZ5rcplGOz/E---3.1_1366140.p', dpsetconstr)).
3.51/1.15	thf(c_0_187, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((?[X556:$i]:((((in @ X556 @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))))&(((dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))=(setadjoin @ X556 @ emptyset))))))))), inference(fof_simplification,[status(thm)],[ex1])).
3.51/1.15	thf(c_0_188, plain, ((singleton)=(^[Z0:$i]:(?[X2:$i]:((((in @ X2 @ Z0))&(((Z0)=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[singleton])).
3.51/1.15	thf(c_0_189, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
3.51/1.15	thf(c_0_190, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
3.51/1.15	thf(c_0_191, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
3.51/1.15	thf(c_0_192, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
3.51/1.15	thf(c_0_193, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
3.51/1.15	thf(c_0_194, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
3.51/1.15	thf(c_0_195, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
3.51/1.15	thf(c_0_196, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
3.51/1.15	thf(c_0_197, 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])).
3.51/1.15	thf(c_0_198, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
3.51/1.15	thf(c_0_199, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
3.51/1.15	thf(c_0_200, 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])).
3.51/1.15	thf(c_0_201, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
3.51/1.15	thf(c_0_202, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
3.51/1.15	thf(c_0_203, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
3.51/1.15	thf(c_0_204, plain, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
3.51/1.15	thf(c_0_205, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
3.51/1.15	thf(c_0_206, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((?[X556:$i]:((((in @ X556 @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))))&(((dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))=(setadjoin @ X556 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_187, c_0_188])).
3.51/1.15	thf(c_0_207, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])).
3.51/1.15	thf(c_0_208, plain, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
3.51/1.15	thf(c_0_209, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
3.51/1.15	thf(c_0_210, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
3.51/1.15	thf(c_0_211, negated_conjecture, ~((((emptysetAx)=>((((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>(((wellorderingAx)=>(((dsetconstrI)=>((((((emptysetE)=>((((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>(((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>(((((setadjoinOr)=>((((emptyinPowerset)=>((emptyInPowerset)=>(((setunionI)=>((((exuE2)=>(((uniqinunit)=>((notinsingleton)=>(((singletonsswitch)=>((((((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((((((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>(((exu__Cong)=>(((setadjoin__Cong)=>((((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>(((eqimpsubset2)=>(((subsetI2)=>(((subsetE)=>(((notsubsetI)=>(((((subsetTrans)=>(((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>(((inPowerset)=>((((sepSubset)=>((binunionIL)=>((upairset2IR)=>((((binunionE)=>(((binunionRsub)=>(((((binintersectLsub)=>(((binintersectSubset3)=>(((disjointsetsI1)=>(((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>(((setminusER)=>((setminusSubset2)=>(((((setminusIRneg)=>((setminusLsub)=>(((((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>(((setukpairIL)=>((setukpairIR)=>((((singletonsubset)=>((singletoninpowerset)=>((((((ubforcartprodlem1)=>(((ubforcartprodlem3)=>(((cartprodmempair1)=>(((setunionE2)=>((((((ex1E1)=>((((singletonsuniq)=>(((kfstsingleton)=>((((cartprodfstin)=>((setukpairinjL2)=>(((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((((setukpairinjR)=>(((ksndpairEq)=>((kpairsurjEq)=>(((((((cartprodsndpairEq)=>(![X4:$i, X5:$i, X23:$i > $i > $o, X2:$i]:((![X3:$i]:((((X23 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X23 @ X14 @ X18))))))<=(in @ X3 @ X5)))<=(in @ X2 @ X4)))<=(cartprodpairsurjEq)))<=(cartprodfstpairEq))<=(cartprodmempaircEq))<=(cartprodpairmemER))<=(cartprodpairmemEL))<=(cartprodsndin))))<=(ksndsingleton)))<=(setukpairinjR2))<=(upairequniteq)))))<=(setukpairinjL))))<=(kfstpairEq))<=(theprop)))<=(setukpairinjL1)))<=(ex1I2))<=(ex1I)))<=(singletonprop))<=(setunionsingleton))<=(setunionsingleton2))<=(setunionsingleton1)))<=(cartprodmempair)))<=(cartprodpairin)))<=(ubforcartprodlem2)))<=(upairinpowunion))<=(upairsubunion))<=(upairset2E))<=(singletoninpowunion))))<=(kpairp))<=(kpairiskpair))))<=(secondinupair)))))<=(symdiffI1))<=(symdiffE))<=(setminusSubset1))))<=(setminusILneg))<=(setminusELneg))<=(setminusERneg))))<=(setminusEL))))))<=(binintersectRsub)))<=(binintersectER)))<=(binintersectSubset2)))<=(binintersectEL))<=(binintersectSubset5))<=(binintersectI)))<=(binunionLsub)))<=(binunionEcases))<=(binunionIR)))))<=(sepInPowerset))<=(powersetsubset)))<=(powersetE1)))))))<=(setadjoinSub)))<=(subsetRefl))<=(notequalI2))<=(notequalI1)))<=(subsetE2)))<=(emptysetsubset)))<=(eqimpsubset1)))<=(subsetI1))))))<=(setunion__Cong))<=(powerset__Cong)))<=(emptyset__Cong)))<=(exuE3u))))))))<=(notdexE))<=(prop2set2propI))<=(prop2setI))<=(quantDeMorgan4))))))<=(emptyE1))<=(upairsetIR))<=(upairsetIL))<=(upairsetE)))<=(eqinunit))))<=(nonemptyImpWitness)))<=(subPowSU))<=(setunionE)))<=(powersetE))))<=(powersetI))<=(setoftrueEq)))<=(setadjoinE))<=(setadjoinIR))<=(emptyinunitempty)))))<=(nonemptyE1)))))))<=(notinemptyset))<=(emptysetimpfalse)))<=(prop2setE))<=(exuE1))<=(dsetconstrER))<=(dsetconstrEL)))<=(descrp)))<=(foundationAx)))))))<=(powersetAx))<=(setadjoinAx)))<=(setextAx))), inference(assume_negation,[status(cth)],[dpsetconstrI])).
3.51/1.15	thf(c_0_212, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X527:$i]:(((((X6 @ X2 @ X527)))&(![X528:$i]:(((((X6 @ X2 @ X528)))=>(((X527)=(X528)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_189, c_0_190])).
3.51/1.15	thf(c_0_213, plain, ((descrp)=(![X1:$i > $o]:((((?[X529:$i]:(((((X1 @ X529)))&(![X530:$i]:(((((X1 @ X530)))=>(((X529)=(X530))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_191, c_0_190])).
3.51/1.15	thf(c_0_214, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
3.51/1.15	thf(c_0_215, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
3.51/1.15	thf(c_0_216, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
3.51/1.15	thf(c_0_217, plain, ((exuE1)=(![X1:$i > $o]:((((?[X531:$i]:(((((X1 @ X531)))&(![X532:$i]:(((((X1 @ X532)))=>(((X531)=(X532))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_192, c_0_190])).
3.51/1.15	thf(c_0_218, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X533:$i]:(((((X1 @ X533)))&(![X534:$i]:(((((X1 @ X534)))=>(((X533)=(X534))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_193, c_0_190])).
3.51/1.15	thf(c_0_219, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
3.51/1.15	thf(c_0_220, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_194])).
3.51/1.15	thf(c_0_221, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_195, c_0_194])).
3.51/1.15	thf(c_0_222, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_194])).
3.51/1.15	thf(c_0_223, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
3.51/1.15	thf(c_0_224, plain, ((exuE2)=(![X1:$i > $o]:((((?[X535:$i]:(((((X1 @ X535)))&(![X536:$i]:(((((X1 @ X536)))=>(((X535)=(X536))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_196, c_0_190])).
3.51/1.15	thf(c_0_225, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_194])).
3.51/1.15	thf(c_0_226, 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])).
3.51/1.15	thf(c_0_227, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X537:$i]:(((((X1 @ X537)))&(![X538:$i]:(((((X1 @ X538)))=>(((X537)=(X538)))))))))))))), inference(apply_def,[status(thm)],[c_0_197, c_0_190])).
3.51/1.15	thf(c_0_228, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X539:$i]:(((((X1 @ X539)))&(![X540:$i]:(((((X1 @ X540)))=>(((X539)=(X540)))))))))))))))), inference(apply_def,[status(thm)],[c_0_198, c_0_190])).
3.51/1.15	thf(c_0_229, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X541:$i]:(((((X1 @ X541)))&(![X542:$i]:(((((X1 @ X542)))=>(((X541)=(X542)))))))))))))), inference(apply_def,[status(thm)],[c_0_199, c_0_190])).
3.51/1.15	thf(c_0_230, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X543:$i]:(((((X1 @ X543)))&(![X544:$i]:(((((X1 @ X544)))=>(((X543)=(X544))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_200, c_0_190])).
3.51/1.15	thf(c_0_231, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X545:$i]:(((((X1 @ X545)))&(![X546:$i]:(((((X1 @ X546)))=>(((X545)=(X546))))))))))<=>((?[X547:$i]:(((((X17 @ X547)))&(![X548:$i]:(((((X17 @ X548)))=>(((X547)=(X548)))))))))))))))), inference(apply_def,[status(thm)],[c_0_201, c_0_190])).
3.51/1.15	thf(c_0_232, plain, ((exuEu)=(![X1:$i > $o]:((((?[X549:$i]:(((((X1 @ X549)))&(![X550:$i]:(((((X1 @ X550)))=>(((X549)=(X550))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_202, c_0_190])).
3.51/1.15	thf(c_0_233, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X551:$i]:(((((X1 @ X551)))&(![X552:$i]:(((((X1 @ X552)))=>(((X551)=(X552))))))))))=>((((?[X553:$i]:(((((X17 @ X553)))&(![X554:$i]:(((((X17 @ X554)))=>(((X553)=(X554))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_203, c_0_190])).
3.51/1.15	thf(c_0_234, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
3.51/1.15	thf(c_0_235, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
3.51/1.15	thf(c_0_236, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
3.51/1.15	thf(c_0_237, plain, ((singletonprop)=(![X4:$i, X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))))=>(((?[X2:$i]:((((in @ X2 @ X4))&((X1 @ X2)))))=>((?[X555:$i]:((((in @ X555 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(setadjoin @ X555 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_204, c_0_188])).
3.51/1.15	thf(c_0_238, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:((((?[X557:$i]:((((in @ X557 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X557 @ emptyset)))))))=>(?[X2:$i]:((((in @ X2 @ X4))&((X1 @ X2))))))))), inference(apply_def,[status(thm)],[c_0_205, c_0_206])).
3.51/1.15	thf(c_0_239, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>(((![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X3))=>(((X3)=(X2))))))))=>((?[X558:$i]:((((in @ X558 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X558 @ emptyset))))))))))))))), inference(apply_def,[status(thm)],[c_0_207, c_0_206])).
3.51/1.15	thf(c_0_240, plain, ((ex1I2)=(![X4:$i, X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))))=>(((?[X2:$i]:((((in @ X2 @ X4))&((X1 @ X2)))))=>((?[X559:$i]:((((in @ X559 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X559 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_208, c_0_206])).
3.51/1.15	thf(c_0_241, plain, ((kfstsingleton)=(![X18:$i]:((((iskpair @ X18))=>((?[X560:$i]:((((in @ X560 @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))))&(((dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))=(setadjoin @ X560 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_209, c_0_188])).
3.51/1.15	thf(c_0_242, axiom, ((theprop)=(![X21:$i]:((((?[X561:$i]:((((in @ X561 @ X21))&(((X21)=(setadjoin @ X561 @ emptyset)))))))=>((in @ (setunion @ X21) @ X21)))))), inference(apply_def,[status(thm)],[theprop, c_0_188])).
3.51/1.15	thf(c_0_243, plain, ((ksndsingleton)=(![X18:$i]:((((iskpair @ X18))=>((?[X562:$i]:((((in @ X562 @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))))&(((dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))=(setadjoin @ X562 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_210, c_0_188])).
3.51/1.15	thf(c_0_244, plain, ((epred1_0)<=>![X579:$i]:(?[X580:$i]:((((![X581:$i]:(((in @ X581 @ X580)=>![X582:$i]:(((in @ X582 @ X581)=>(in @ X582 @ X579)))))&![X583:$i, X584:$i]:((((in @ X583 @ X579)&(in @ X584 @ X579))=>(![X585:$i]:(((in @ X585 @ X580)=>((in @ X583 @ X585)<=>(in @ X584 @ X585))))=>((X583)=(X584))))))&![X586:$i, X587:$i]:((((in @ X586 @ X580)&(in @ X587 @ X580))=>(![X588:$i]:(((in @ X588 @ X586)=>(in @ X588 @ X587)))|![X589:$i]:(((in @ X589 @ X587)=>(in @ X589 @ X586)))))))&![X590:$i]:(((![X591:$i]:(((in @ X591 @ X590)=>(in @ X591 @ X579)))&?[X592:$i]:((in @ X592 @ X590)))=>?[X593:$i, X594:$i]:(((((in @ X593 @ X580)&(in @ X594 @ X590))&~(?[X595:$i]:(((in @ X595 @ X593)&(in @ X595 @ X590)))))&![X596:$i]:(((in @ X596 @ X580)=>(![X597:$i]:(((in @ X597 @ X596)=>(in @ X597 @ X593)))|(in @ X594 @ X596)))))))))))), introduced(definition)).
3.51/1.15	thf(c_0_245, negated_conjecture, ~((![X1093:$i, X1094:$i]:((![X1095:$i]:(((in @ X1095 @ X1093)<=>(in @ X1095 @ X1094)))=>((X1093)=(X1094))))=>(![X563:$i]:(~(in @ X563 @ emptyset))=>(![X1090:$i, X1091:$i, X1092:$i]:(((in @ X1092 @ (setadjoin @ X1090 @ X1091))<=>(((X1092)=(X1090))|(in @ X1092 @ X1091))))=>(![X1087:$i, X1088:$i]:(((in @ X1088 @ (powerset @ X1087))<=>![X1089:$i]:(((in @ X1089 @ X1088)=>(in @ X1089 @ X1087)))))=>(![X564:$i, X565:$i]:(((in @ X565 @ (setunion @ X564))<=>?[X566:$i]:(((in @ X565 @ X566)&(in @ X566 @ X564)))))=>((in @ emptyset @ omega)=>(![X567:$i]:(((in @ X567 @ omega)=>(in @ (setadjoin @ X567 @ X567) @ omega)))=>(![X568:$i]:((((in @ emptyset @ X568)&![X569:$i]:((((in @ X569 @ omega)&(in @ X569 @ X568))=>(in @ (setadjoin @ X569 @ X569) @ X568))))=>![X570:$i]:(((in @ X570 @ omega)=>(in @ X570 @ X568)))))=>(![X571:$i > $i > $o, X572:$i]:((![X573:$i]:(((in @ X573 @ X572)=>?[X574:$i]:(((X571 @ X573 @ X574)&![X575:$i]:(((X571 @ X573 @ X575)=>((X574)=(X575))))))))=>?[X576:$i]:(![X577:$i]:(((in @ X577 @ X576)<=>?[X578:$i]:(((in @ X578 @ X572)&(X571 @ X578 @ X577))))))))=>(![X1083:$i]:((?[X1084:$i]:((in @ X1084 @ X1083))=>?[X1085:$i]:(((in @ X1085 @ X1083)&~(?[X1086:$i]:(((in @ X1086 @ X1085)&(in @ X1086 @ X1083))))))))=>((epred1_0)=>(![X1080:$i > $o]:((?[X1081:$i]:(((X1080 @ X1081)&![X1082:$i]:(((X1080 @ X1082)=>((X1081)=(X1082))))))=>(X1080 @ (descr @ (^[Z0:$i]:(X1080 @ Z0))))))=>(![X598:$i, X599:$i > $o, X600:$i]:(((in @ X600 @ X598)=>((X599 @ X600)=>(in @ X600 @ (dsetconstr @ X598 @ X599)))))=>(![X1077:$i, X1078:$i > $o, X1079:$i]:(((in @ X1079 @ (dsetconstr @ X1077 @ X1078))=>(in @ X1079 @ X1077)))=>(![X1074:$i, X1075:$i > $o, X1076:$i]:(((in @ X1076 @ (dsetconstr @ X1074 @ X1075))=>(X1075 @ X1076)))=>(![X1069:$i > $o]:((?[X1070:$i]:(((X1069 @ X1070)&![X1071:$i]:(((X1069 @ X1071)=>((X1070)=(X1071))))))=>?[X1072:$i]:(((X1069 @ X1072)&![X1073:$i]:(((X1069 @ X1073)=>((X1072)=(X1073))))))))=>(![X1067:$o, X1068:$i]:(((in @ X1068 @ (prop2set @ ((X1067))))=>(X1067)))=>(![X601:$i]:(((in @ X601 @ emptyset)=>![X602:$o]:((X602))))=>(![X1066:$i]:(((in @ X1066 @ emptyset)=>~($true)))=>(![X1065:$i]:(~(in @ X1065 @ emptyset))=>(![X603:$i > $o]:((?[X604:$i]:(((X603 @ X604)&![X605:$i]:(((X603 @ X605)=>((X604)=(X605))))))=>?[X606:$i]:((X603 @ X606))))=>(![X607:$i, X608:$i]:((![X609:$i]:(((in @ X609 @ X607)=>(in @ X609 @ X608)))=>(![X610:$i]:(((in @ X610 @ X608)=>(in @ X610 @ X607)))=>((X607)=(X608)))))=>(![X611:$i]:((![X612:$i]:(~(in @ X612 @ X611))=>((X611)=(emptyset))))=>(![X613:$i]:((![X614:$i]:(~(in @ X614 @ X613))=>((X613)=(emptyset))))=>(![X615:$i, X616:$i > $o, X617:$i]:(((in @ X617 @ X615)=>((in @ X617 @ (dsetconstr @ X615 @ X616))<=>(X616 @ X617))))=>(![X1063:$i]:((((X1063)!=(emptyset))=>?[X1064:$i]:((in @ X1064 @ X1063))))=>(![X618:$i, X619:$i > $o, X620:$i]:(((in @ X620 @ X618)=>((X619 @ X620)=>((dsetconstr @ X618 @ X619)!=(emptyset)))))=>(![X621:$i]:((?[X622:$i]:((in @ X622 @ X621))=>((X621)!=(emptyset))))=>(![X623:$i, X624:$i]:((in @ X623 @ (setadjoin @ X623 @ X624)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1060:$i, X1061:$i, X1062:$i]:(((in @ X1062 @ X1061)=>(in @ X1062 @ (setadjoin @ X1060 @ X1061))))=>(![X1056:$i, X1057:$i, X1058:$i]:(((in @ X1058 @ (setadjoin @ X1056 @ X1057))=>![X1059:$o]:(((((X1058)=(X1056))=>(X1059))=>(((in @ X1058 @ X1057)=>(X1059))=>(X1059))))))=>(![X625:$i, X626:$i, X627:$i]:(((in @ X627 @ (setadjoin @ X625 @ X626))=>(((X627)=(X625))|(in @ X627 @ X626))))=>(![X1055:$i]:(((dsetconstr @ X1055 @ (^[Z0:$i]:($true)))=(X1055)))=>(![X1052:$i, X1053:$i]:((![X1054:$i]:(((in @ X1054 @ X1053)=>(in @ X1054 @ X1052)))=>(in @ X1053 @ (powerset @ X1052))))=>(![X628:$i]:((in @ emptyset @ (powerset @ X628)))=>(![X629:$i]:((in @ emptyset @ (powerset @ X629)))=>(![X1049:$i, X1050:$i, X1051:$i]:(((in @ X1050 @ (powerset @ X1049))=>((in @ X1051 @ X1050)=>(in @ X1051 @ X1049))))=>(![X630:$i, X631:$i, X632:$i]:(((in @ X631 @ X632)=>((in @ X632 @ X630)=>(in @ X631 @ (setunion @ X630)))))=>(![X1045:$i, X1046:$i]:(((in @ X1046 @ (setunion @ X1045))=>![X1047:$o]:((![X1048:$i]:(((in @ X1046 @ X1048)=>((in @ X1048 @ X1045)=>(X1047))))=>(X1047)))))=>(![X1043:$i, X1044:$i]:(((in @ X1044 @ X1043)=>(in @ X1044 @ (powerset @ (setunion @ X1043)))))=>(![X633:$i > $o]:((?[X634:$i]:(((X633 @ X634)&![X635:$i]:(((X633 @ X635)=>((X634)=(X635))))))=>?[X636:$i]:(![X637:$i]:(((X633 @ X637)<=>((X637)=(X636)))))))=>(![X1041:$i]:((((X1041)!=(emptyset))=>?[X1042:$i]:(((in @ X1042 @ X1041)&$true))))=>(![X638:$i, X639:$i]:(((in @ X638 @ (setadjoin @ X639 @ emptyset))=>((X638)=(X639))))=>(![X640:$i, X641:$i]:((((X640)!=(X641))=>~(in @ X641 @ (setadjoin @ X640 @ emptyset))))=>(![X1039:$i, X1040:$i]:((((X1039)=(X1040))=>(in @ X1039 @ (setadjoin @ X1040 @ emptyset))))=>(![X642:$i, X643:$i]:(((in @ X642 @ (setadjoin @ X643 @ emptyset))=>(in @ X643 @ (setadjoin @ X642 @ emptyset))))=>(![X1036:$i, X1037:$i, X1038:$i]:(((in @ X1038 @ (setadjoin @ X1036 @ (setadjoin @ X1037 @ emptyset)))=>(((X1038)=(X1036))|((X1038)=(X1037)))))=>(![X1034:$i, X1035:$i]:((in @ X1034 @ (setadjoin @ X1034 @ (setadjoin @ X1035 @ emptyset))))=>(![X1032:$i, X1033:$i]:((in @ X1033 @ (setadjoin @ X1032 @ (setadjoin @ X1033 @ emptyset))))=>(![X1029:$i, X1030:$i > $o]:((?[X1031:$i]:(((in @ X1031 @ X1029)&(X1030 @ X1031)))=>(((dsetconstr @ X1029 @ X1030)=(emptyset))=>~($true))))=>(![X644:$i > $o, X645:$i]:(((in @ X645 @ emptyset)=>(X644 @ X645)))=>(![X646:$i, X647:$i > $o]:((~(![X648:$i]:(((in @ X648 @ X646)=>(X647 @ X648))))=>?[X649:$i]:(((in @ X649 @ X646)&~((X647 @ X649))))))=>(![X650:$i, X651:$i > $o]:((![X652:$i]:(((in @ X652 @ X650)=>~((X651 @ X652))))=>~(?[X653:$i]:(((in @ X653 @ X650)&(X651 @ X653))))))=>(![X654:$i, X655:$i > $o]:((~(?[X656:$i]:(((in @ X656 @ X654)&(X655 @ X656))))=>![X657:$i]:(((in @ X657 @ X654)=>~((X655 @ X657))))))=>(![X1025:$i, X1026:$i > $o]:((?[X1027:$i]:(((in @ X1027 @ X1025)&~((X1026 @ X1027))))=>~(![X1028:$i]:(((in @ X1028 @ X1025)=>(X1026 @ X1028))))))=>(![X1024:$o]:(((X1024)=>(in @ emptyset @ (prop2set @ ((X1024))))))=>(![X1023:$o]:(((X1023)=>(set2prop @ (prop2set @ ((X1023))))))=>(![X1019:$i, X1020:$i > $o]:((~(?[X1021:$i]:(((in @ X1021 @ X1019)&(X1020 @ X1021))))=>![X1022:$i]:(((in @ X1022 @ X1019)=>~((X1020 @ X1022))))))=>(![X658:$i, X659:$i > $o]:((~(![X660:$i]:(((in @ X660 @ X658)=>(X659 @ X660))))=>?[X661:$i]:(((in @ X661 @ X658)&~((X659 @ X661))))))=>(![X662:$i > $o]:((?[X663:$i]:(((X662 @ X663)&![X664:$i]:(((X662 @ X664)=>((X663)=(X664))))))=>?[X665:$i]:(((X662 @ X665)&![X666:$i]:(((X662 @ X666)=>((X665)=(X666))))))))=>(![X667:$i > $o]:((?[X668:$i]:((X667 @ X668))=>(![X669:$i, X670:$i]:(((X667 @ X669)=>((X667 @ X670)=>((X669)=(X670)))))=>?[X671:$i]:(((X667 @ X671)&![X672:$i]:(((X667 @ X672)=>((X671)=(X672)))))))))=>(![X673:$i > $o]:((?[X674:$i]:(![X675:$i]:(((X673 @ X675)<=>((X675)=(X674)))))=>?[X676:$i]:(((X673 @ X676)&![X677:$i]:(((X673 @ X677)=>((X676)=(X677))))))))=>(![X678:$i, X679:$i]:((((X678)=(X679))=>![X680:$i, X681:$i]:((((X680)=(X681))=>((in @ X680 @ X678)=>(in @ X681 @ X679))))))=>(![X682:$i, X683:$i]:((((X682)=(X683))=>![X684:$i, X685:$i]:((((X684)=(X685))=>((in @ X684 @ X682)<=>(in @ X685 @ X683))))))=>(![X1014:$i > $o]:((?[X1015:$i]:(((X1014 @ X1015)&![X1016:$i]:(((X1014 @ X1016)=>((X1015)=(X1016))))))=>![X1017:$i, X1018:$i]:(((X1014 @ X1017)=>((X1014 @ X1018)=>((X1017)=(X1018)))))))=>(![X686:$i > $o, X687:$i > $o]:((![X688:$i, X689:$i]:((((X688)=(X689))=>((X686 @ X688)<=>(X687 @ X689))))=>(?[X690:$i]:(((X686 @ X690)&![X691:$i]:(((X686 @ X691)=>((X690)=(X691))))))<=>?[X692:$i]:(((X687 @ X692)&![X693:$i]:(((X687 @ X693)=>((X692)=(X693)))))))))=>(((emptyset)=(emptyset))=>(![X694:$i, X695:$i]:((((X694)=(X695))=>![X696:$i, X697:$i]:((((X696)=(X697))=>((setadjoin @ X694 @ X696)=(setadjoin @ X695 @ X697))))))=>(![X1012:$i, X1013:$i]:((((X1012)=(X1013))=>((powerset @ X1012)=(powerset @ X1013))))=>(![X1010:$i, 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X844)=>![X847:$i]:(((in @ X847 @ X845)=>((ksnd @ (kpair @ X846 @ X847))=(X847))))))=>(![X848:$i, X849:$i, X850:$i]:(((in @ X850 @ (cartprod @ X848 @ X849))=>((kpair @ (kfst @ X850) @ (ksnd @ X850))=(X850))))=>![X4:$i, X5:$i, X23:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X23 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ X23))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_211]), setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_212]), foundationAx]), wellorderingAx]), c_0_213]), c_0_214]), c_0_215]), c_0_216]), c_0_217]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_218]), setext]), emptyI]), noeltsimpempty]), c_0_219]), c_0_220]), c_0_221]), c_0_222]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_223]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_224]), c_0_225]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_226]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_227]), c_0_228]), c_0_229]), inCongP]), in__Cong]), c_0_230]), c_0_231]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_232]), c_0_233]), c_0_234]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_235]), c_0_236]), 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]), secondinupair]), setukpairIL]), setukpairIR]), kpairiskpair]), kpairp]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1]), cartprodmempair]), setunionE2]), setunionsingleton1]), setunionsingleton2]), setunionsingleton]), c_0_237]), c_0_238]), c_0_239]), c_0_240]), singletonsuniq]), setukpairinjL1]), c_0_241]), c_0_242]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_243]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq])])]), c_0_244])).
3.51/1.15	thf(c_0_246, plain, ![X1096:$i, X1097:$i, X1098:$i > $i > $o]:(((dpsetconstr @ X1096 @ X1097 @ X1098)=(dsetconstr @ (cartprod @ X1096 @ X1097) @ (^[Z0:$i]:(?[X2:$i]:((((in @ X2 @ X1096))&(?[X3:$i]:((((((in @ X3 @ X1097))&(X1098 @ X2 @ X3)))&(((Z0)=(kpair @ X2 @ X3))))))))))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[dpsetconstr])])).
3.51/1.15	thf(c_0_247, negated_conjecture, ![X1102:$i, X1103:$i, X1105:$i, X1106:$i, X1107:$i, X1108:$i, X1109:$i, X1110:$i, X1111:$i, X1112:$i, X1113:$i, X1115:$i, X1116:$i, X1118:$i, X1119:$i, X1120:$i, X1121:$i, X1122:$i, X1124:$i, X1125:$i > $i > $o, X1126:$i, X1128:$i, X1131:$i, X1133:$i, X1134:$i, X1135:$i, X1136:$i, X1138:$i, X1139:$i > $o, X1140:$i, X1142:$i, X1143:$i > $o, X1144:$i, X1145:$i, X1146:$i > $o, X1147:$i, X1148:$i, X1149:$i > $o, X1150:$i, X1151:$i > $o, X1152:$i, X1155:$i, X1156:$o, X1157:$i, X1158:$i, X1159:$o, X1160:$i, X1161:$i, X1162:$i > $o, X1163:$i, X1166:$i, X1167:$i, X1170:$i, X1172:$i, X1174:$i, X1175:$i > $o, X1176:$i, X1177:$i, X1179:$i, X1180:$i > $o, X1181:$i, X1182:$i, X1183:$i, X1184:$i, X1185:$i, X1186:$i, X1187:$i, X1188:$i, X1189:$i, X1190:$i, X1191:$i, X1192:$o, X1193:$i, X1194:$i, X1195:$i, X1196:$i, X1197:$i, X1198:$i, X1200:$i, X1201:$i, X1202:$i, X1203:$i, X1204:$i, X1205:$i, X1206:$i, X1207:$i, X1208:$i, X1209:$i, X1210:$o, X1212:$i, X1213:$i, X1214:$i > $o, X1215:$i, X1218:$i, X1219:$i, X1220:$i, X1222:$i, X1223:$i, X1224:$i, X1225:$i, X1226:$i, X1227:$i, X1228:$i, X1229:$i, X1230:$i, X1231:$i, X1232:$i, X1233:$i, X1234:$i, X1235:$i, X1236:$i, X1237:$i, X1238:$i > $o, X1239:$i, X1240:$i > $o, X1241:$i, X1242:$i, X1243:$i > $o, X1244:$i, X1246:$i, X1247:$i > $o, X1249:$i, X1250:$i, X1251:$i > $o, X1253:$i, X1254:$i, X1255:$i > $o, X1256:$i, X1258:$o, X1259:$o, X1260:$i, X1261:$i > $o, X1263:$i, X1264:$i, X1265:$i > $o, X1266:$i, X1268:$i > $o, X1269:$i, X1272:$i, X1273:$i > $o, X1274:$i, X1278:$i, X1279:$i > $o, X1280:$i, X1283:$i, X1284:$i, X1285:$i, X1286:$i, X1287:$i, X1288:$i, X1289:$i, X1290:$i, X1291:$i, X1292:$i > $o, X1293:$i, X1295:$i, X1296:$i, X1297:$i > $o, X1298:$i > $o, X1301:$i, X1304:$i, X1305:$i, X1308:$i, X1309:$i, X1310:$i, X1311:$i, X1312:$i, X1313:$i, X1314:$i, X1315:$i, X1316:$i, X1317:$i > $o, X1318:$i, X1320:$i, X1321:$i, X1322:$i > $o, X1323:$i > $o, X1326:$i, X1328:$i, X1330:$i, X1331:$i, X1332:$i > $o, X1333:$i > $o, X1336:$i, X1337:$i, X1339:$i, X1340:$i, X1341:$i, X1342:$i, X1343:$i, X1344:$i, X1346:$i, X1347:$i, X1348:$i, X1349:$i, X1350:$i, X1351:$i, X1352:$i, X1353:$i, X1354:$i, X1355:$i, X1356:$i, X1357:$i, X1358:$i, X1359:$i, X1360:$i, X1361:$i, X1362:$i, X1363:$i, X1364:$i, X1365:$i, X1366:$i, X1367:$i, X1368:$i, X1369:$i, X1370:$i, X1371:$i, X1372:$i, X1373:$i, X1374:$i, X1375:$i, X1376:$i, X1377:$i, X1378:$i, X1379:$i, X1380:$i, X1381:$i, X1382:$i, X1383:$i > $o, X1384:$i, X1385:$i > $o, X1386:$i, X1387:$i, X1388:$i, X1389:$i, X1390:$i, X1391:$i, X1392:$i, X1393:$i, X1394:$i, X1395:$i, X1396:$i, X1397:$o, X1398:$i, X1399:$i, X1400:$i, X1401:$i, X1402:$i, X1403:$i, X1404:$i, X1405:$i, X1406:$i, X1407:$i, X1408:$i, X1409:$i, X1410:$i, X1411:$i, X1412:$i, X1413:$i, X1414:$i, X1415:$i, X1416:$i, X1417:$i, X1418:$i, X1419:$i, X1420:$i, X1421:$i, X1422:$i, X1423:$i, X1424:$i, X1426:$i, X1427:$i, X1428:$i, X1429:$i, X1430:$i, X1431:$i, X1432:$i, X1433:$i, X1434:$i, X1435:$i, X1436:$i, X1437:$i, X1438:$i, X1439:$i, X1440:$i, X1441:$i, X1442:$i, X1443:$i, X1444:$i, X1445:$i, X1446:$i, X1447:$i, X1448:$i, X1449:$i, X1450:$i, X1451:$i, X1452:$i, X1453:$i, X1454:$i, X1455:$i, X1456:$i, X1457:$i, X1458:$i, X1459:$i, X1460:$i, X1461:$i, X1462:$i, X1463:$i, X1464:$i, X1465:$o, X1466:$i, X1467:$i, X1468:$i, X1469:$i, X1470:$i, X1471:$i, X1472:$i, X1473:$i, X1474:$i, X1475:$i, X1476:$i, X1477:$i, X1478:$i, X1479:$i, X1480:$i, X1481:$i, X1482:$i, X1483:$i, X1484:$i, X1485:$i, X1486:$i, X1487:$i, X1488:$i, X1489:$i, X1490:$i, X1491:$i, X1492:$i, X1493:$i, X1494:$i, X1495:$i, X1496:$i, X1497:$i, X1498:$i, X1499:$i, X1500:$i, X1501:$i, X1502:$i, X1503:$i, X1504:$i, X1505:$i, X1506:$i, X1507:$i, X1508:$i, X1509:$i, X1510:$i, X1511:$i, X1512:$i, X1513:$i, X1514:$i, X1515:$i, X1516:$i, X1517:$i, X1518:$i, X1519:$i, X1520:$i, X1521:$i, X1522:$i, X1523:$i, X1524:$i, X1527:$i, X1528:$i, X1529:$i, X1530:$i, X1531:$i, X1533:$i, X1534:$i, X1535:$i, X1536:$i, X1537:$i > $o, X1540:$i, X1542:$i, X1543:$i > $o, X1544:$i, X1546:$i, X1547:$i > $o, X1548:$i, X1551:$i, X1552:$i > $o, X1555:$i, X1557:$i, X1558:$i, X1559:$i, X1560:$i, X1561:$i, X1562:$i, X1564:$i, X1565:$i, X1566:$i, X1567:$i, X1568:$i, X1569:$i, X1570:$i, X1571:$i, X1572:$i, X1573:$i, X1574:$i, X1575:$i, X1576:$i, X1577:$i, X1578:$i, X1579:$i, X1580:$i, X1581:$i, X1582:$i, X1583:$i, X1584:$i, X1585:$i, X1586:$i, X1587:$i, X1588:$i, X1589:$i, X1590:$i, X1591:$i, X1592:$i, X1593:$i, X1594:$i, X1595:$i, X1596:$i, X1597:$i, X1598:$i, X1600:$i, X1601:$i, X1602:$i, X1603:$i, X1604:$i, X1605:$i, X1606:$i, X1607:$i, X1608:$i, X1609:$i, X1610:$i, X1611:$i, X1612:$i, X1613:$i, X1614:$i, X1615:$i, X1616:$i, X1617:$i, X1618:$i, X1619:$i, X1620:$i, X1621:$i, X1622:$i, X1623:$i, X1624:$i, X1625:$i, X1626:$i, X1627:$i, X1628:$i]:((((~(in @ (esk1_2 @ X1102 @ X1103) @ X1102)|~(in @ (esk1_2 @ X1102 @ X1103) @ X1103)|((X1102)=(X1103)))&((in @ (esk1_2 @ X1102 @ X1103) @ X1102)|(in @ (esk1_2 @ X1102 @ X1103) @ X1103)|((X1102)=(X1103))))&(~(in @ X1105 @ emptyset)&(((~(in @ X1108 @ (setadjoin @ X1106 @ X1107))|(((X1108)=(X1106))|(in @ X1108 @ X1107)))&((((X1108)!=(X1106))|(in @ X1108 @ (setadjoin @ X1106 @ X1107)))&(~(in @ X1108 @ X1107)|(in @ X1108 @ (setadjoin @ X1106 @ X1107)))))&(((~(in @ X1110 @ (powerset @ X1109))|(~(in @ X1111 @ X1110)|(in @ X1111 @ X1109)))&(((in @ (esk2_2 @ X1112 @ X1113) @ X1113)|(in @ X1113 @ (powerset @ X1112)))&(~(in @ (esk2_2 @ X1112 @ X1113) @ X1112)|(in @ X1113 @ (powerset @ X1112)))))&(((((in @ X1116 @ (esk3_2 @ X1115 @ X1116))|~(in @ X1116 @ (setunion @ X1115)))&((in @ (esk3_2 @ X1115 @ X1116) @ X1115)|~(in @ X1116 @ (setunion @ X1115))))&(~(in @ X1119 @ X1120)|~(in @ X1120 @ X1118)|(in @ X1119 @ (setunion @ X1118))))&((in @ emptyset @ omega)&((~(in @ X1121 @ omega)|(in @ (setadjoin @ X1121 @ X1121) @ omega))&(((((in @ (esk4_1 @ X1122) @ omega)|~(in @ emptyset @ X1122)|(~(in @ X1124 @ omega)|(in @ X1124 @ X1122)))&((in @ (esk4_1 @ X1122) @ X1122)|~(in @ emptyset @ X1122)|(~(in @ X1124 @ omega)|(in @ X1124 @ X1122))))&(~(in @ (setadjoin @ (esk4_1 @ X1122) @ (esk4_1 @ X1122)) @ X1122)|~(in @ emptyset @ X1122)|(~(in @ X1124 @ omega)|(in @ X1124 @ X1122))))&((((((in @ (esk8_3 @ X1125 @ X1126 @ X1131) @ X1126)|~(in @ X1131 @ (esk7_2 @ X1125 @ X1126))|(in @ (esk5_2 @ X1125 @ X1126) @ X1126))&((X1125 @ (esk8_3 @ X1125 @ X1126 @ X1131) @ X1131)|~(in @ X1131 @ (esk7_2 @ X1125 @ X1126))|(in @ (esk5_2 @ X1125 @ X1126) @ X1126)))&(~(in @ X1134 @ X1126)|~(X1125 @ X1134 @ X1133)|(in @ X1133 @ (esk7_2 @ X1125 @ X1126))|(in @ (esk5_2 @ X1125 @ X1126) @ X1126)))&(((((in @ (esk8_3 @ X1125 @ X1126 @ X1131) @ X1126)|~(in @ X1131 @ (esk7_2 @ X1125 @ X1126))|((X1125 @ (esk5_2 @ X1125 @ X1126) @ (esk6_3 @ X1125 @ X1126 @ X1128))|~(X1125 @ (esk5_2 @ X1125 @ X1126) @ X1128)))&((X1125 @ (esk8_3 @ X1125 @ X1126 @ X1131) @ X1131)|~(in @ X1131 @ (esk7_2 @ X1125 @ X1126))|((X1125 @ (esk5_2 @ X1125 @ X1126) @ (esk6_3 @ X1125 @ X1126 @ X1128))|~(X1125 @ (esk5_2 @ 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X1547 @ X1548) @ emptyset))|(in @ (esk62_3 @ X1546 @ X1547 @ X1548) @ X1546)|~(X1547 @ X1548)|~(in @ X1548 @ X1546)))&((((in @ (esk63_3 @ X1546 @ X1547 @ X1548) @ (dsetconstr @ X1546 @ X1547))|(X1547 @ (esk62_3 @ X1546 @ X1547 @ X1548))|~(X1547 @ X1548)|~(in @ X1548 @ X1546))&(((dsetconstr @ X1546 @ X1547)=(setadjoin @ (esk63_3 @ X1546 @ X1547 @ X1548) @ emptyset))|(X1547 @ (esk62_3 @ X1546 @ X1547 @ X1548))|~(X1547 @ X1548)|~(in @ X1548 @ X1546)))&(((in @ (esk63_3 @ X1546 @ X1547 @ X1548) @ (dsetconstr @ X1546 @ X1547))|((esk62_3 @ X1546 @ X1547 @ X1548)!=(X1548))|~(X1547 @ X1548)|~(in @ X1548 @ X1546))&(((dsetconstr @ X1546 @ X1547)=(setadjoin @ (esk63_3 @ X1546 @ X1547 @ X1548) @ emptyset))|((esk62_3 @ X1546 @ X1547 @ X1548)!=(X1548))|~(X1547 @ X1548)|~(in @ X1548 @ X1546)))))&(((((in @ (esk66_2 @ X1551 @ X1552) @ (dsetconstr @ X1551 @ X1552))|(~(in @ X1555 @ X1551)|~(X1552 @ X1555))|(in @ (esk64_2 @ X1551 @ X1552) @ X1551))&(((dsetconstr @ X1551 @ X1552)=(setadjoin @ (esk66_2 @ X1551 @ X1552) @ emptyset))|(~(in @ X1555 @ X1551)|~(X1552 @ X1555))|(in @ (esk64_2 @ X1551 @ X1552) @ X1551)))&((((in @ (esk66_2 @ X1551 @ X1552) @ (dsetconstr @ X1551 @ X1552))|(~(in @ X1555 @ X1551)|~(X1552 @ X1555))|(in @ (esk65_2 @ X1551 @ X1552) @ X1551))&(((dsetconstr @ X1551 @ X1552)=(setadjoin @ (esk66_2 @ X1551 @ X1552) @ emptyset))|(~(in @ X1555 @ X1551)|~(X1552 @ X1555))|(in @ (esk65_2 @ X1551 @ X1552) @ X1551)))&((((in @ (esk66_2 @ X1551 @ X1552) @ (dsetconstr @ X1551 @ X1552))|(~(in @ X1555 @ X1551)|~(X1552 @ X1555))|(X1552 @ (esk64_2 @ X1551 @ X1552)))&(((dsetconstr @ X1551 @ X1552)=(setadjoin @ (esk66_2 @ X1551 @ X1552) @ emptyset))|(~(in @ X1555 @ X1551)|~(X1552 @ X1555))|(X1552 @ (esk64_2 @ X1551 @ X1552))))&((((in @ (esk66_2 @ X1551 @ X1552) @ (dsetconstr @ X1551 @ X1552))|(~(in @ X1555 @ X1551)|~(X1552 @ X1555))|(X1552 @ (esk65_2 @ X1551 @ X1552)))&(((dsetconstr @ X1551 @ X1552)=(setadjoin @ (esk66_2 @ X1551 @ X1552) @ emptyset))|(~(in @ X1555 @ X1551)|~(X1552 @ X1555))|(X1552 @ (esk65_2 @ X1551 @ X1552))))&(((in @ (esk66_2 @ X1551 @ X1552) @ (dsetconstr @ X1551 @ X1552))|(~(in @ X1555 @ X1551)|~(X1552 @ X1555))|((esk64_2 @ X1551 @ X1552)!=(esk65_2 @ X1551 @ X1552)))&(((dsetconstr @ X1551 @ X1552)=(setadjoin @ (esk66_2 @ X1551 @ X1552) @ emptyset))|(~(in @ X1555 @ X1551)|~(X1552 @ X1555))|((esk64_2 @ X1551 @ X1552)!=(esk65_2 @ X1551 @ X1552))))))))&((((setadjoin @ X1557 @ emptyset)!=(setadjoin @ X1558 @ emptyset))|((X1557)=(X1558)))&((~(in @ (setadjoin @ X1561 @ emptyset) @ (setadjoin @ (setadjoin @ X1559 @ emptyset) @ (setadjoin @ (setadjoin @ X1559 @ (setadjoin @ X1560 @ emptyset)) @ emptyset)))|((X1559)=(X1561)))&((((in @ (esk67_1 @ X1562) @ (dsetconstr @ (setunion @ X1562) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1562)))))|~(iskpair @ X1562))&(((dsetconstr @ (setunion @ X1562) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1562))))=(setadjoin @ (esk67_1 @ X1562) @ emptyset))|~(iskpair @ X1562)))&((~(in @ X1565 @ X1564)|((X1564)!=(setadjoin @ X1565 @ emptyset))|(in @ (setunion @ X1564) @ X1564))&(((kfst @ (kpair @ X1566 @ X1567))=(X1566))&((~(in @ X1570 @ (cartprod @ X1568 @ X1569))|(in @ (kfst @ X1570) @ X1568))&((((setadjoin @ (setadjoin @ X1571 @ emptyset) @ (setadjoin @ (setadjoin @ X1571 @ (setadjoin @ X1572 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1573 @ emptyset) @ (setadjoin @ (setadjoin @ X1573 @ (setadjoin @ X1574 @ emptyset)) @ emptyset)))|((X1571)=(X1573)))&((((kpair @ X1575 @ X1576)!=(kpair @ X1577 @ X1578))|((X1575)=(X1577)))&((((X1579)!=(X1580))|((setadjoin @ X1579 @ (setadjoin @ X1580 @ emptyset))=(setadjoin @ X1579 @ emptyset)))&((((X1581)!=(X1582))|((setadjoin @ (setadjoin @ X1581 @ emptyset) @ (setadjoin @ (setadjoin @ X1581 @ (setadjoin @ X1582 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X1581 @ emptyset) @ emptyset)))&((((setadjoin @ (setadjoin @ X1583 @ emptyset) @ (setadjoin @ (setadjoin @ X1583 @ (setadjoin @ X1584 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1585 @ emptyset) @ (setadjoin @ (setadjoin @ X1585 @ (setadjoin @ X1586 @ emptyset)) @ emptyset)))|(((X1585)!=(X1586))|((X1584)=(X1586))))&((((setadjoin @ X1587 @ (setadjoin @ X1588 @ emptyset))!=(setadjoin @ X1589 @ emptyset))|((X1587)=(X1588)))&((((setadjoin @ (setadjoin @ X1590 @ emptyset) @ (setadjoin @ (setadjoin @ X1590 @ (setadjoin @ X1591 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1592 @ emptyset) @ (setadjoin @ (setadjoin @ X1592 @ (setadjoin @ X1593 @ emptyset)) @ emptyset)))|((X1591)=(X1593)))&((((kpair @ X1594 @ X1595)!=(kpair @ X1596 @ X1597))|((X1595)=(X1597)))&((((in @ (esk68_1 @ X1598) @ (dsetconstr @ (setunion @ X1598) @ (^[Z0:$i]:(((X1598)=(kpair @ (kfst @ X1598) @ Z0))))))|~(iskpair @ X1598))&(((dsetconstr @ (setunion @ X1598) @ (^[Z0:$i]:(((X1598)=(kpair @ (kfst @ X1598) @ Z0)))))=(setadjoin @ (esk68_1 @ X1598) @ emptyset))|~(iskpair @ X1598)))&(((ksnd @ (kpair @ X1600 @ X1601))=(X1601))&((~(iskpair @ X1602)|((kpair @ (kfst @ X1602) @ (ksnd @ X1602))=(X1602)))&((~(in @ X1605 @ (cartprod @ X1603 @ X1604))|(in @ (ksnd @ X1605) @ X1604))&((~(in @ (kpair @ X1608 @ X1609) @ (cartprod @ X1606 @ X1607))|(in @ X1608 @ X1606))&((~(in @ (kpair @ X1612 @ X1613) @ (cartprod @ X1610 @ X1611))|(in @ X1613 @ X1611))&((~(in @ X1616 @ X1614)|(~(in @ X1617 @ X1615)|((kpair @ X1616 @ X1617)=(kpair @ X1616 @ X1617))))&((~(in @ X1620 @ X1618)|(~(in @ X1621 @ X1619)|((kfst @ (kpair @ X1620 @ X1621))=(X1620))))&((~(in @ X1624 @ X1622)|(~(in @ X1625 @ X1623)|((ksnd @ (kpair @ X1624 @ X1625))=(X1625))))&((~(in @ X1628 @ (cartprod @ X1626 @ X1627))|((kpair @ (kfst @ X1628) @ (ksnd @ X1628))=(X1628)))&((in @ esk71_0 @ esk69_0)&((in @ esk72_0 @ esk70_0)&((epred2_0 @ esk71_0 @ esk72_0)&~(in @ (kpair @ esk71_0 @ esk72_0) @ (dpsetconstr @ esk69_0 @ esk70_0 @ epred2_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_245])])])])])])])).
3.51/1.15	thf(c_0_248, plain, ![X1099:$i, X1100:$i, X1101:$i > $i > $o]:(((dpsetconstr @ X1099 @ X1100 @ X1101)=(dsetconstr @ (cartprod @ X1099 @ X1100) @ (^[Z0:$i]:(?[X2:$i]:((((in @ X2 @ X1099))&(?[X3:$i]:((((((in @ X3 @ X1100))&(X1101 @ X2 @ X3)))&(((Z0)=(kpair @ X2 @ X3))))))))))))), inference(variable_rename,[status(thm)],[c_0_246])).
3.51/1.15	thf(c_0_249, plain, ![X1655:$i, X2:$i, X3:$i, X6:$i > $i > $o]:(((epred3_3 @ X6 @ X3 @ X2 @ X1655)<=>?[X1653:$i]:(((in @ X1653 @ X2)&?[X1654:$i]:((((in @ X1654 @ X3)&(X6 @ X1653 @ X1654))&((X1655)=(kpair @ X1653 @ X1654)))))))), introduced(definition)).
3.51/1.15	thf(c_0_250, negated_conjecture, ~((in @ (kpair @ esk71_0 @ esk72_0) @ (dpsetconstr @ esk69_0 @ esk70_0 @ epred2_0))), inference(split_conjunct,[status(thm)],[c_0_247])).
3.51/1.15	thf(c_0_251, plain, ![X6:$i > $i > $o, X3:$i, X2:$i]:(((dpsetconstr @ X2 @ X3 @ X6)=(dsetconstr @ (cartprod @ X2 @ X3) @ (epred3_3 @ X6 @ X3 @ X2)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_248]), c_0_249])).
3.51/1.15	thf(c_0_252, plain, ![X1661:$i, X1662:$i, X1663:$i, X1664:$i > $i > $o, X1667:$i, X1668:$i]:(((((in @ (esk78_4 @ X1661 @ X1662 @ X1663 @ X1664) @ X1662)|~(epred3_3 @ X1664 @ X1663 @ X1662 @ X1661))&((((in @ (esk79_4 @ X1661 @ X1662 @ X1663 @ X1664) @ X1663)|~(epred3_3 @ X1664 @ X1663 @ X1662 @ X1661))&((X1664 @ (esk78_4 @ X1661 @ X1662 @ X1663 @ X1664) @ (esk79_4 @ X1661 @ X1662 @ X1663 @ X1664))|~(epred3_3 @ X1664 @ X1663 @ X1662 @ X1661)))&(((X1661)=(kpair @ (esk78_4 @ X1661 @ X1662 @ X1663 @ X1664) @ (esk79_4 @ X1661 @ X1662 @ X1663 @ X1664)))|~(epred3_3 @ X1664 @ X1663 @ X1662 @ X1661))))&(~(in @ X1667 @ X1662)|(~(in @ X1668 @ X1663)|~(X1664 @ X1667 @ X1668)|((X1661)!=(kpair @ X1667 @ X1668)))|(epred3_3 @ X1664 @ X1663 @ X1662 @ X1661)))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])])])])])).
3.51/1.15	thf(c_0_253, negated_conjecture, ~((in @ (kpair @ esk71_0 @ esk72_0) @ (dsetconstr @ (cartprod @ esk69_0 @ esk70_0) @ (epred3_3 @ epred2_0 @ esk70_0 @ esk69_0)))), inference(rw,[status(thm)],[c_0_250, c_0_251])).
3.51/1.15	thf(c_0_254, negated_conjecture, ![X1:$i > $o, X2:$i, X3:$i]:(((in @ X2 @ (dsetconstr @ X3 @ X1))|~((X1 @ X2))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_247])).
3.51/1.15	thf(c_0_255, plain, ![X7:$i, X3:$i, X2:$i, X6:$i > $i > $o, X5:$i, X4:$i]:(((epred3_3 @ X6 @ X5 @ X3 @ X7)|~((in @ X2 @ X3))|~((in @ X4 @ X5))|~((X6 @ X2 @ X4))|((X7)!=(kpair @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_252])).
3.51/1.15	thf(c_0_256, negated_conjecture, (~((in @ (kpair @ esk71_0 @ esk72_0) @ (cartprod @ esk69_0 @ esk70_0)))|~((epred3_3 @ epred2_0 @ esk70_0 @ esk69_0 @ (kpair @ esk71_0 @ esk72_0)))), inference(spm,[status(thm)],[c_0_253, c_0_254])).
3.51/1.15	thf(c_0_257, plain, ![X2:$i, X3:$i, X4:$i, X6:$i > $i > $o, X5:$i]:(((epred3_3 @ X6 @ X2 @ X3 @ (kpair @ X4 @ X5))|~((in @ X5 @ X2))|~((in @ X4 @ X3))|~((X6 @ X4 @ X5)))), inference(er,[status(thm)],[c_0_255])).
3.51/1.15	thf(c_0_258, negated_conjecture, (in @ esk72_0 @ esk70_0), inference(split_conjunct,[status(thm)],[c_0_247])).
3.51/1.15	thf(c_0_259, negated_conjecture, (in @ esk71_0 @ esk69_0), inference(split_conjunct,[status(thm)],[c_0_247])).
3.51/1.15	thf(c_0_260, negated_conjecture, (epred2_0 @ esk71_0 @ esk72_0), inference(split_conjunct,[status(thm)],[c_0_247])).
3.51/1.15	thf(c_0_261, negated_conjecture, ~((in @ (kpair @ esk71_0 @ esk72_0) @ (cartprod @ esk69_0 @ esk70_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_256, c_0_257]), c_0_258]), c_0_259]), c_0_260])])).
3.51/1.15	thf(c_0_262, negated_conjecture, ![X2:$i, X3:$i, X4:$i, X5:$i]:(((in @ (kpair @ X2 @ X4) @ (cartprod @ X3 @ X5))|~((in @ X2 @ X3))|~((in @ X4 @ X5)))), inference(split_conjunct,[status(thm)],[c_0_247])).
3.51/1.15	thf(c_0_263, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_261, c_0_262]), c_0_258]), c_0_259])]), ['proof']).
3.51/1.15	% SZS output end CNFRefutation
3.51/1.15	% Parsed axioms                        : 402
3.51/1.15	% Removed by relevancy pruning/SinE    : 0
3.51/1.15	% Initial clauses                      : 562
3.51/1.15	% Removed in clause preprocessing      : 242
3.51/1.15	% Initial clauses in saturation        : 320
3.51/1.15	% Processed clauses                    : 1343
3.51/1.15	% ...of these trivial                  : 52
3.51/1.15	% ...subsumed                          : 435
3.51/1.15	% ...remaining for further processing  : 856
3.51/1.15	% Other redundant clauses eliminated   : 47
3.51/1.15	% Clauses deleted for lack of memory   : 0
3.51/1.15	% Backward-subsumed                    : 35
3.51/1.15	% Backward-rewritten                   : 5
3.51/1.15	% Generated clauses                    : 7923
3.51/1.15	% ...of the previous two non-redundant : 7545
3.51/1.15	% ...aggressively subsumed             : 0
3.51/1.15	% Contextual simplify-reflections      : 2
3.51/1.15	% Paramodulations                      : 7842
3.51/1.15	% Factorizations                       : 2
3.51/1.15	% NegExts                              : 4
3.51/1.15	% Equation resolutions                 : 52
3.51/1.15	% Disequality decompositions           : 0
3.51/1.15	% Total rewrite steps                  : 669
3.51/1.15	% ...of those cached                   : 557
3.51/1.15	% Propositional unsat checks           : 0
3.51/1.15	%    Propositional check models        : 0
3.51/1.15	%    Propositional check unsatisfiable : 0
3.51/1.15	%    Propositional clauses             : 0
3.51/1.15	%    Propositional clauses after purity: 0
3.51/1.15	%    Propositional unsat core size     : 0
3.51/1.15	%    Propositional preprocessing time  : 0.000
3.51/1.15	%    Propositional encoding time       : 0.000
3.51/1.15	%    Propositional solver time         : 0.000
3.51/1.15	%    Success case prop preproc time    : 0.000
3.51/1.15	%    Success case prop encoding time   : 0.000
3.51/1.15	%    Success case prop solver time     : 0.000
3.51/1.15	% Current number of processed clauses  : 521
3.51/1.15	%    Positive orientable unit clauses  : 63
3.51/1.15	%    Positive unorientable unit clauses: 0
3.51/1.15	%    Negative unit clauses             : 15
3.51/1.15	%    Non-unit-clauses                  : 443
3.51/1.15	% Current number of unprocessed clauses: 6674
3.51/1.15	% ...number of literals in the above   : 21667
3.51/1.15	% Current number of archived formulas  : 0
3.51/1.15	% Current number of archived clauses   : 320
3.51/1.15	% Clause-clause subsumption calls (NU) : 32890
3.51/1.15	% Rec. Clause-clause subsumption calls : 20932
3.51/1.15	% Non-unit clause-clause subsumptions  : 300
3.51/1.15	% Unit Clause-clause subsumption calls : 680
3.51/1.15	% Rewrite failures with RHS unbound    : 0
3.51/1.15	% BW rewrite match attempts            : 18
3.51/1.15	% BW rewrite match successes           : 5
3.51/1.15	% Condensation attempts                : 0
3.51/1.15	% Condensation successes               : 0
3.51/1.15	% Termbank termtop insertions          : 169651
3.51/1.15	% Search garbage collected termcells   : 18112
3.51/1.15	
3.51/1.15	% -------------------------------------------------
3.51/1.15	% User time                : 0.398 s
3.51/1.15	% System time              : 0.033 s
3.51/1.15	% Total time               : 0.431 s
3.51/1.15	% Maximum resident set size: 7104 pages
3.51/1.15	
3.51/1.15	% -------------------------------------------------
3.51/1.15	% User time                : 1.508 s
3.51/1.15	% System time              : 0.103 s
3.51/1.15	% Total time               : 1.611 s
3.51/1.15	% Maximum resident set size: 5376 pages
3.51/1.15	% E exiting
3.51/1.15	EOF