%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU706^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:25:17 AM UTC 2026
% Result : Theorem 0.80s 0.42s
% Output : CNFRefutation 0.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU706^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n009.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 14:13:00 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.25 Running higher-order theorem proving
% 0.23/0.30 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p
% 0.80/0.42 % Version: 3.5.1-ho
% 0.80/0.42 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.80/0.42 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.80/0.42 % Starting ehoh_best5 with 300s (1) cores
% 0.80/0.42 % Starting almost_fo_3_lam with 300s (1) cores
% 0.80/0.42 % Starting new_bool_5 with 300s (1) cores
% 0.80/0.42 % Starting pre_casc_3 with 300s (1) cores
% 0.80/0.42 % Starting ho_unfolding_8 with 300s (1) cores
% 0.80/0.42 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.80/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.80/0.42 % Starting new_ho_5 with 300s (1) cores
% 0.80/0.42 % almost_fo_3_lam with pid 4065194 completed with status 0
% 0.80/0.42 % Result found by almost_fo_3_lam
% 0.80/0.42 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.80/0.42 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.80/0.42 % Starting ehoh_best5 with 300s (1) cores
% 0.80/0.42 % Starting almost_fo_3_lam with 300s (1) cores
% 0.80/0.42 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.80/0.42 % No SInE strategy applied
% 0.80/0.42 % Search class: HGHSM-FSLM32-DHFMMSBN
% 0.80/0.42 % partial match(1): HGHSM-FSLM32-MHFMMSBN
% 0.80/0.42 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.80/0.42 % Starting SubtermCWHack with 28s (1) cores
% 0.80/0.42 % SubtermCWHack with pid 4065225 completed with status 0
% 0.80/0.42 % Result found by SubtermCWHack
% 0.80/0.42 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.80/0.42 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.80/0.42 % Starting ehoh_best5 with 300s (1) cores
% 0.80/0.42 % Starting almost_fo_3_lam with 300s (1) cores
% 0.80/0.42 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.80/0.42 % No SInE strategy applied
% 0.80/0.42 % Search class: HGHSM-FSLM32-DHFMMSBN
% 0.80/0.42 % partial match(1): HGHSM-FSLM32-MHFMMSBN
% 0.80/0.42 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.80/0.42 % Starting SubtermCWHack with 28s (1) cores
% 0.80/0.42 % Preprocessing time : 0.004 s
% 0.80/0.42
% 0.80/0.42 % Proof found!
% 0.80/0.42 % SZS status Theorem
% 0.80/0.42 % SZS output start CNFRefutation
% 0.80/0.42 thf(decl_23, type, in: $i > $i > $o).
% 0.80/0.42 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.80/0.42 thf(decl_25, type, setextAx: $o).
% 0.80/0.42 thf(decl_26, type, emptyset: $i).
% 0.80/0.42 thf(decl_27, type, emptysetAx: $o).
% 0.80/0.42 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.80/0.42 thf(decl_29, type, setadjoinAx: $o).
% 0.80/0.42 thf(decl_30, type, powerset: $i > $i).
% 0.80/0.42 thf(decl_31, type, powersetAx: $o).
% 0.80/0.42 thf(decl_32, type, setunion: $i > $i).
% 0.80/0.42 thf(decl_33, type, setunionAx: $o).
% 0.80/0.42 thf(decl_34, type, omega: $i).
% 0.80/0.42 thf(decl_35, type, omega0Ax: $o).
% 0.80/0.42 thf(decl_36, type, omegaSAx: $o).
% 0.80/0.42 thf(decl_37, type, omegaIndAx: $o).
% 0.80/0.42 thf(decl_38, type, replAx: $o).
% 0.80/0.42 thf(decl_39, type, foundationAx: $o).
% 0.80/0.42 thf(decl_40, type, wellorderingAx: $o).
% 0.80/0.42 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.80/0.42 thf(decl_42, type, descrp: $o).
% 0.80/0.42 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.80/0.42 thf(decl_44, type, dsetconstrI: $o).
% 0.80/0.42 thf(decl_45, type, dsetconstrEL: $o).
% 0.80/0.42 thf(decl_46, type, dsetconstrER: $o).
% 0.80/0.42 thf(decl_47, type, exuE1: $o).
% 0.80/0.42 thf(decl_48, type, prop2set: $o > $i).
% 0.80/0.42 thf(decl_49, type, prop2setE: $o).
% 0.80/0.42 thf(decl_50, type, emptysetE: $o).
% 0.80/0.42 thf(decl_51, type, emptysetimpfalse: $o).
% 0.80/0.42 thf(decl_52, type, notinemptyset: $o).
% 0.80/0.42 thf(decl_53, type, exuE3e: $o).
% 0.80/0.42 thf(decl_54, type, setext: $o).
% 0.80/0.42 thf(decl_55, type, emptyI: $o).
% 0.80/0.42 thf(decl_56, type, noeltsimpempty: $o).
% 0.80/0.42 thf(decl_57, type, setbeta: $o).
% 0.80/0.42 thf(decl_58, type, nonempty: $i > $o).
% 0.80/0.42 thf(decl_59, type, nonemptyE1: $o).
% 0.80/0.42 thf(decl_60, type, nonemptyI: $o).
% 0.80/0.42 thf(decl_61, type, nonemptyI1: $o).
% 0.80/0.42 thf(decl_62, type, setadjoinIL: $o).
% 0.80/0.42 thf(decl_63, type, emptyinunitempty: $o).
% 0.80/0.42 thf(decl_64, type, setadjoinIR: $o).
% 0.80/0.42 thf(decl_65, type, setadjoinE: $o).
% 0.80/0.42 thf(decl_66, type, setadjoinOr: $o).
% 0.80/0.42 thf(decl_67, type, setoftrueEq: $o).
% 0.80/0.42 thf(decl_68, type, powersetI: $o).
% 0.80/0.42 thf(decl_69, type, emptyinPowerset: $o).
% 0.80/0.42 thf(decl_70, type, emptyInPowerset: $o).
% 0.80/0.42 thf(decl_71, type, powersetE: $o).
% 0.80/0.42 thf(decl_72, type, setunionI: $o).
% 0.80/0.42 thf(decl_73, type, setunionE: $o).
% 0.80/0.42 thf(decl_74, type, subPowSU: $o).
% 0.80/0.42 thf(decl_75, type, exuE2: $o).
% 0.80/0.42 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.80/0.42 thf(decl_77, type, uniqinunit: $o).
% 0.80/0.42 thf(decl_78, type, notinsingleton: $o).
% 0.80/0.42 thf(decl_79, type, eqinunit: $o).
% 0.80/0.42 thf(decl_80, type, singletonsswitch: $o).
% 0.80/0.42 thf(decl_81, type, upairsetE: $o).
% 0.80/0.42 thf(decl_82, type, upairsetIL: $o).
% 0.80/0.42 thf(decl_83, type, upairsetIR: $o).
% 0.80/0.42 thf(decl_84, type, emptyE1: $o).
% 0.80/0.42 thf(decl_85, type, vacuousDall: $o).
% 0.80/0.42 thf(decl_86, type, quantDeMorgan1: $o).
% 0.80/0.42 thf(decl_87, type, quantDeMorgan2: $o).
% 0.80/0.42 thf(decl_88, type, quantDeMorgan3: $o).
% 0.80/0.42 thf(decl_89, type, quantDeMorgan4: $o).
% 0.80/0.42 thf(decl_90, type, prop2setI: $o).
% 0.80/0.42 thf(decl_91, type, set2prop: $i > $o).
% 0.80/0.42 thf(decl_92, type, prop2set2propI: $o).
% 0.80/0.42 thf(decl_93, type, notdexE: $o).
% 0.80/0.42 thf(decl_94, type, notdallE: $o).
% 0.80/0.42 thf(decl_95, type, exuI1: $o).
% 0.80/0.42 thf(decl_96, type, exuI3: $o).
% 0.80/0.42 thf(decl_97, type, exuI2: $o).
% 0.80/0.42 thf(decl_98, type, inCongP: $o).
% 0.80/0.42 thf(decl_99, type, in__Cong: $o).
% 0.80/0.42 thf(decl_100, type, exuE3u: $o).
% 0.80/0.42 thf(decl_101, type, exu__Cong: $o).
% 0.80/0.42 thf(decl_102, type, emptyset__Cong: $o).
% 0.80/0.42 thf(decl_103, type, setadjoin__Cong: $o).
% 0.80/0.42 thf(decl_104, type, powerset__Cong: $o).
% 0.80/0.42 thf(decl_105, type, setunion__Cong: $o).
% 0.80/0.42 thf(decl_106, type, omega__Cong: $o).
% 0.80/0.42 thf(decl_107, type, exuEu: $o).
% 0.80/0.42 thf(decl_108, type, descr__Cong: $o).
% 0.80/0.42 thf(decl_109, type, dsetconstr__Cong: $o).
% 0.80/0.42 thf(decl_110, type, subset: $i > $i > $o).
% 0.80/0.42 thf(decl_113, type, subsetI1: $o).
% 0.80/0.42 thf(decl_114, type, eqimpsubset2: $o).
% 0.80/0.42 thf(decl_115, type, eqimpsubset1: $o).
% 0.80/0.42 thf(decl_116, type, subsetI2: $o).
% 0.80/0.42 thf(decl_117, type, emptysetsubset: $o).
% 0.80/0.42 thf(decl_118, type, subsetE: $o).
% 0.80/0.42 thf(decl_119, type, subsetE2: $o).
% 0.80/0.42 thf(decl_120, type, notsubsetI: $o).
% 0.80/0.42 thf(decl_121, type, notequalI1: $o).
% 0.80/0.42 thf(decl_122, type, notequalI2: $o).
% 0.80/0.42 thf(decl_123, type, subsetRefl: $o).
% 0.80/0.42 thf(decl_124, type, subsetTrans: $o).
% 0.80/0.42 thf(decl_125, type, setadjoinSub: $o).
% 0.80/0.42 thf(decl_126, type, setadjoinSub2: $o).
% 0.80/0.42 thf(decl_127, type, subset2powerset: $o).
% 0.80/0.42 thf(decl_128, type, setextsub: $o).
% 0.80/0.42 thf(decl_129, type, subsetemptysetimpeq: $o).
% 0.80/0.42 thf(decl_130, type, powersetI1: $o).
% 0.80/0.42 thf(decl_131, type, powersetE1: $o).
% 0.80/0.42 thf(decl_132, type, inPowerset: $o).
% 0.80/0.42 thf(decl_133, type, powersetsubset: $o).
% 0.80/0.42 thf(decl_134, type, sepInPowerset: $o).
% 0.80/0.42 thf(decl_135, type, sepSubset: $o).
% 0.80/0.42 thf(decl_136, type, binunion: $i > $i > $i).
% 0.80/0.42 thf(decl_137, type, binunionIL: $o).
% 0.80/0.42 thf(decl_138, type, upairset2IR: $o).
% 0.80/0.42 thf(decl_139, type, binunionIR: $o).
% 0.80/0.42 thf(decl_140, type, binunionEcases: $o).
% 0.80/0.42 thf(decl_141, type, binunionE: $o).
% 0.80/0.42 thf(decl_142, type, binunionLsub: $o).
% 0.80/0.42 thf(decl_143, type, binunionRsub: $o).
% 0.80/0.42 thf(decl_144, type, binintersect: $i > $i > $i).
% 0.80/0.42 thf(decl_145, type, binintersectI: $o).
% 0.80/0.42 thf(decl_146, type, binintersectSubset5: $o).
% 0.80/0.42 thf(decl_147, type, binintersectEL: $o).
% 0.80/0.42 thf(decl_148, type, binintersectLsub: $o).
% 0.80/0.42 thf(decl_149, type, binintersectSubset2: $o).
% 0.80/0.42 thf(decl_150, type, binintersectSubset3: $o).
% 0.80/0.42 thf(decl_151, type, binintersectER: $o).
% 0.80/0.42 thf(decl_152, type, disjointsetsI1: $o).
% 0.80/0.42 thf(decl_153, type, binintersectRsub: $o).
% 0.80/0.42 thf(decl_154, type, binintersectSubset4: $o).
% 0.80/0.42 thf(decl_155, type, binintersectSubset1: $o).
% 0.80/0.42 thf(decl_156, type, bs114d: $o).
% 0.80/0.42 thf(decl_158, type, setminus: $i > $i > $i).
% 0.80/0.42 thf(decl_159, type, setminusI: $o).
% 0.80/0.42 thf(decl_160, type, setminusEL: $o).
% 0.80/0.42 thf(decl_161, type, setminusER: $o).
% 0.80/0.42 thf(decl_162, type, setminusSubset2: $o).
% 0.80/0.42 thf(decl_163, type, setminusERneg: $o).
% 0.80/0.42 thf(decl_164, type, setminusELneg: $o).
% 0.80/0.42 thf(decl_165, type, setminusILneg: $o).
% 0.80/0.42 thf(decl_166, type, setminusIRneg: $o).
% 0.80/0.42 thf(decl_167, type, setminusLsub: $o).
% 0.80/0.42 thf(decl_168, type, setminusSubset1: $o).
% 0.80/0.42 thf(decl_169, type, symdiff: $i > $i > $i).
% 0.80/0.42 thf(decl_170, type, symdiffE: $o).
% 0.80/0.42 thf(decl_171, type, symdiffI1: $o).
% 0.80/0.42 thf(decl_172, type, symdiffI2: $o).
% 0.80/0.42 thf(decl_173, type, symdiffIneg1: $o).
% 0.80/0.42 thf(decl_174, type, symdiffIneg2: $o).
% 0.80/0.42 thf(decl_175, type, iskpair: $i > $o).
% 0.80/0.42 thf(decl_176, type, secondinupair: $o).
% 0.80/0.42 thf(decl_177, type, setukpairIL: $o).
% 0.80/0.42 thf(decl_178, type, setukpairIR: $o).
% 0.80/0.42 thf(decl_179, type, kpairiskpair: $o).
% 0.80/0.42 thf(decl_180, type, kpair: $i > $i > $i).
% 0.80/0.42 thf(decl_181, type, kpairp: $o).
% 0.80/0.42 thf(decl_182, type, cartprod: $i > $i > $i).
% 0.80/0.42 thf(decl_183, type, singletonsubset: $o).
% 0.80/0.42 thf(decl_184, type, singletoninpowerset: $o).
% 0.80/0.42 thf(decl_185, type, singletoninpowunion: $o).
% 0.80/0.42 thf(decl_186, type, upairset2E: $o).
% 0.80/0.42 thf(decl_187, type, upairsubunion: $o).
% 0.80/0.42 thf(decl_188, type, upairinpowunion: $o).
% 0.80/0.42 thf(decl_189, type, ubforcartprodlem1: $o).
% 0.80/0.42 thf(decl_190, type, ubforcartprodlem2: $o).
% 0.80/0.42 thf(decl_191, type, ubforcartprodlem3: $o).
% 0.80/0.42 thf(decl_192, type, cartprodpairin: $o).
% 0.80/0.42 thf(decl_193, type, cartprodmempair1: $o).
% 0.80/0.42 thf(decl_194, type, cartprodmempair: $o).
% 0.80/0.42 thf(decl_195, type, setunionE2: $o).
% 0.80/0.42 thf(decl_196, type, setunionsingleton1: $o).
% 0.80/0.42 thf(decl_197, type, setunionsingleton2: $o).
% 0.80/0.42 thf(decl_198, type, setunionsingleton: $o).
% 0.80/0.42 thf(decl_199, type, singleton: $i > $o).
% 0.80/0.42 thf(decl_200, type, singletonprop: $o).
% 0.80/0.42 thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 0.80/0.42 thf(decl_202, type, ex1E1: $o).
% 0.80/0.42 thf(decl_203, type, ex1I: $o).
% 0.80/0.42 thf(decl_204, type, ex1I2: $o).
% 0.80/0.42 thf(decl_205, type, singletonsuniq: $o).
% 0.80/0.42 thf(decl_210, type, setukpairinjL1: $o).
% 0.80/0.42 thf(decl_211, type, kfstsingleton: $o).
% 0.80/0.42 thf(decl_212, type, theprop: $o).
% 0.80/0.42 thf(decl_213, type, kfst: $i > $i).
% 0.80/0.42 thf(decl_214, type, kfstpairEq: $o).
% 0.80/0.42 thf(decl_215, type, cartprodfstin: $o).
% 0.80/0.42 thf(decl_216, type, setukpairinjL2: $o).
% 0.80/0.42 thf(decl_217, type, setukpairinjL: $o).
% 0.80/0.42 thf(decl_218, type, setukpairinjR11: $o).
% 0.80/0.42 thf(decl_219, type, setukpairinjR12: $o).
% 0.80/0.42 thf(decl_220, type, setukpairinjR1: $o).
% 0.80/0.42 thf(decl_221, type, upairequniteq: $o).
% 0.80/0.42 thf(decl_222, type, setukpairinjR2: $o).
% 0.80/0.42 thf(decl_223, type, setukpairinjR: $o).
% 0.80/0.42 thf(decl_224, type, ksndsingleton: $o).
% 0.80/0.42 thf(decl_225, type, ksnd: $i > $i).
% 0.80/0.42 thf(decl_226, type, ksndpairEq: $o).
% 0.80/0.42 thf(decl_227, type, kpairsurjEq: $o).
% 0.80/0.42 thf(decl_228, type, cartprodsndin: $o).
% 0.80/0.42 thf(decl_229, type, cartprodpairmemEL: $o).
% 0.80/0.42 thf(decl_230, type, cartprodpairmemER: $o).
% 0.80/0.42 thf(decl_231, type, cartprodmempaircEq: $o).
% 0.80/0.42 thf(decl_232, type, cartprodfstpairEq: $o).
% 0.80/0.42 thf(decl_233, type, cartprodsndpairEq: $o).
% 0.80/0.42 thf(decl_234, type, cartprodpairsurjEq: $o).
% 0.80/0.42 thf(decl_235, type, breln: $i > $i > $i > $o).
% 0.80/0.42 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 0.80/0.42 thf(decl_237, type, dpsetconstrI: $o).
% 0.80/0.42 thf(decl_238, type, dpsetconstrSub: $o).
% 0.80/0.42 thf(decl_239, type, setOfPairsIsBReln: $o).
% 0.80/0.42 thf(decl_240, type, dpsetconstrERa: $o).
% 0.80/0.42 thf(decl_241, type, dpsetconstrEL1: $o).
% 0.80/0.42 thf(decl_242, type, dpsetconstrEL2: $o).
% 0.80/0.42 thf(decl_243, type, dpsetconstrER: $o).
% 0.80/0.42 thf(decl_244, type, func: $i > $i > $i > $o).
% 0.80/0.42 thf(decl_245, type, funcSet: $i > $i > $i).
% 0.80/0.42 thf(decl_246, type, funcImageSingleton: $o).
% 0.80/0.42 thf(decl_247, type, apProp: $o).
% 0.80/0.42 thf(decl_248, type, ap: $i > $i > $i > $i > $i).
% 0.80/0.42 thf(decl_249, type, app: $o).
% 0.80/0.42 thf(decl_250, type, infuncsetfunc: $o).
% 0.80/0.42 thf(decl_251, type, ap2p: $o).
% 0.80/0.42 thf(decl_252, type, funcinfuncset: $o).
% 0.80/0.42 thf(decl_253, type, lamProp: $o).
% 0.80/0.42 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
% 0.80/0.42 thf(decl_255, type, lamp: $o).
% 0.80/0.42 thf(decl_256, type, lam2p: $o).
% 0.80/0.42 thf(decl_257, type, brelnall1: $o).
% 0.80/0.42 thf(decl_258, type, brelnall2: $o).
% 0.80/0.42 thf(decl_259, type, ex1E2: $o).
% 0.80/0.42 thf(decl_260, type, funcGraphProp1: $o).
% 0.80/0.42 thf(decl_261, type, funcGraphProp3: $o).
% 0.80/0.42 thf(decl_262, type, funcGraphProp2: $o).
% 0.80/0.42 thf(decl_263, type, funcextLem: $o).
% 0.80/0.42 thf(decl_264, type, funcGraphProp4: $o).
% 0.80/0.42 thf(decl_265, type, subbreln: $o).
% 0.80/0.42 thf(decl_266, type, eqbreln: $o).
% 0.80/0.42 thf(decl_267, type, funcext: $o).
% 0.80/0.42 thf(decl_268, type, funcext2: $o).
% 0.80/0.42 thf(decl_269, type, ap2apEq1: $o).
% 0.80/0.42 thf(decl_270, type, ap2apEq2: $o).
% 0.80/0.42 thf(decl_271, type, beta1: $o).
% 0.80/0.42 thf(decl_272, type, eta1: $o).
% 0.80/0.42 thf(decl_273, type, lam2lamEq: $o).
% 0.80/0.42 thf(decl_274, type, beta2: $o).
% 0.80/0.42 thf(decl_275, type, eta2: $o).
% 0.80/0.42 thf(decl_276, type, iffalseProp1: $o).
% 0.80/0.42 thf(decl_277, type, iffalseProp2: $o).
% 0.80/0.42 thf(decl_278, type, iftrueProp1: $o).
% 0.80/0.42 thf(decl_279, type, iftrueProp2: $o).
% 0.80/0.42 thf(decl_280, type, ifSingleton: $o).
% 0.80/0.42 thf(decl_281, type, if: $i > $o > $i > $i > $i).
% 0.80/0.42 thf(decl_282, type, ifp: $o).
% 0.80/0.42 thf(decl_283, type, epred1_0: $o).
% 0.80/0.42 thf(decl_284, type, esk1_2: $i > $i > $i).
% 0.80/0.42 thf(decl_285, type, esk2_2: $i > $i > $i).
% 0.80/0.42 thf(decl_286, type, esk3_2: $i > $i > $i).
% 0.80/0.42 thf(decl_287, type, esk4_1: $i > $i).
% 0.80/0.42 thf(decl_288, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.80/0.42 thf(decl_289, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.80/0.42 thf(decl_290, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.80/0.42 thf(decl_291, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.80/0.42 thf(decl_292, type, esk9_1: $i > $i).
% 0.80/0.42 thf(decl_293, type, esk10_2: ($i > $o) > $i > $i).
% 0.80/0.42 thf(decl_294, type, esk11_2: ($i > $o) > $i > $i).
% 0.80/0.42 thf(decl_295, type, esk12_1: ($i > $o) > $i).
% 0.80/0.42 thf(decl_296, type, esk13_2: ($i > $o) > $i > $i).
% 0.80/0.42 thf(decl_297, type, esk14_1: ($i > $o) > $i).
% 0.80/0.42 thf(decl_298, type, esk15_2: $i > $i > $i).
% 0.80/0.42 thf(decl_299, type, esk16_2: $i > $i > $i).
% 0.80/0.42 thf(decl_300, type, esk17_1: $i > $i).
% 0.80/0.42 thf(decl_301, type, esk18_1: $i > $i).
% 0.80/0.42 thf(decl_302, type, esk19_1: $i > $i).
% 0.80/0.42 thf(decl_303, type, esk20_2: $i > $i > $i).
% 0.80/0.42 thf(decl_304, type, esk21_3: $i > $i > $o > $i).
% 0.80/0.42 thf(decl_305, type, esk22_2: ($i > $o) > $i > $i).
% 0.80/0.42 thf(decl_306, type, esk23_1: ($i > $o) > $i).
% 0.80/0.42 thf(decl_307, type, esk24_1: $i > $i).
% 0.80/0.42 thf(decl_308, type, esk25_2: $i > ($i > $o) > $i).
% 0.80/0.42 thf(decl_309, type, esk26_2: $i > ($i > $o) > $i).
% 0.80/0.42 thf(decl_310, type, esk27_2: $i > ($i > $o) > $i).
% 0.80/0.42 thf(decl_311, type, esk28_2: $i > ($i > $o) > $i).
% 0.80/0.42 thf(decl_312, type, esk29_2: $i > ($i > $o) > $i).
% 0.80/0.42 thf(decl_313, type, esk30_2: $i > ($i > $o) > $i).
% 0.80/0.42 thf(decl_314, type, esk31_2: ($i > $o) > $i > $i).
% 0.80/0.42 thf(decl_315, type, esk32_1: ($i > $o) > $i).
% 0.80/0.42 thf(decl_316, type, esk33_1: ($i > $o) > $i).
% 0.80/0.42 thf(decl_317, type, esk34_1: ($i > $o) > $i).
% 0.80/0.42 thf(decl_318, type, esk35_1: ($i > $o) > $i).
% 0.80/0.42 thf(decl_319, type, esk36_2: ($i > $o) > $i > $i).
% 0.80/0.42 thf(decl_320, type, esk37_1: ($i > $o) > $i).
% 0.80/0.42 thf(decl_321, type, esk38_2: ($i > $o) > $i > $i).
% 0.80/0.42 thf(decl_322, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 0.80/0.42 thf(decl_323, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 0.80/0.42 thf(decl_324, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.80/0.42 thf(decl_325, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 0.80/0.42 thf(decl_326, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.80/0.42 thf(decl_327, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 0.80/0.42 thf(decl_328, type, esk45_2: ($i > $o) > $i > $i).
% 0.80/0.42 thf(decl_329, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 0.80/0.42 thf(decl_330, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 0.80/0.42 thf(decl_331, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.80/0.42 thf(decl_332, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.80/0.42 thf(decl_333, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.80/0.42 thf(decl_334, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.80/0.42 thf(decl_335, type, esk52_2: $i > $i > $i).
% 0.80/0.42 thf(decl_336, type, esk53_2: $i > $i > $i).
% 0.80/0.42 thf(decl_337, type, esk54_2: $i > $i > $i).
% 0.80/0.42 thf(decl_338, type, esk55_3: $i > $i > $i > $i).
% 0.80/0.42 thf(decl_339, type, esk56_3: $i > $i > $i > $i).
% 0.80/0.42 thf(decl_340, type, esk57_2: $i > $i > $i).
% 0.80/0.42 thf(decl_341, type, esk58_2: $i > ($i > $o) > $i).
% 0.80/0.42 thf(decl_342, type, esk59_2: $i > ($i > $o) > $i).
% 0.80/0.42 thf(decl_343, type, esk60_2: $i > ($i > $o) > $i).
% 0.80/0.42 thf(decl_344, type, esk61_2: $i > ($i > $o) > $i).
% 0.80/0.42 thf(decl_345, type, esk62_3: $i > ($i > $o) > $i > $i).
% 0.80/0.42 thf(decl_346, type, esk63_3: $i > ($i > $o) > $i > $i).
% 0.80/0.42 thf(decl_347, type, esk64_2: $i > ($i > $o) > $i).
% 0.80/0.42 thf(decl_348, type, esk65_2: $i > ($i > $o) > $i).
% 0.80/0.42 thf(decl_349, type, esk66_2: $i > ($i > $o) > $i).
% 0.80/0.42 thf(decl_350, type, esk67_1: $i > $i).
% 0.80/0.42 thf(decl_351, type, esk68_1: $i > $i).
% 0.80/0.42 thf(decl_352, type, esk69_4: $i > $i > $i > $i > $i).
% 0.80/0.42 thf(decl_353, type, esk70_3: $i > $i > ($i > $i) > $i).
% 0.80/0.42 thf(decl_354, type, esk71_3: $i > $i > ($i > $i) > $i).
% 0.80/0.42 thf(decl_355, type, esk72_3: $i > $i > ($i > $i) > $i).
% 0.80/0.42 thf(decl_356, type, esk73_4: $i > $i > $i > ($i > $o) > $i).
% 0.80/0.42 thf(decl_357, type, esk74_4: $i > $i > $i > ($i > $o) > $i).
% 0.80/0.42 thf(decl_358, type, esk75_4: $i > $i > $i > ($i > $o) > $i).
% 0.80/0.42 thf(decl_359, type, esk76_4: $i > $i > $i > ($i > $o) > $i).
% 0.80/0.42 thf(decl_360, type, esk77_4: $i > $i > $i > $i > $i).
% 0.80/0.42 thf(decl_361, type, esk78_4: $i > $i > $i > $i > $i).
% 0.80/0.42 thf(decl_362, type, esk79_4: $i > $i > $i > $i > $i).
% 0.80/0.42 thf(decl_363, type, esk80_4: $i > $i > $i > $i > $i).
% 0.80/0.42 thf(decl_364, type, esk81_4: $i > $i > $i > $i > $i).
% 0.80/0.42 thf(decl_365, type, esk82_4: $i > $i > $i > $i > $i).
% 0.80/0.42 thf(decl_366, type, esk83_4: $i > $i > $i > $i > $i).
% 0.80/0.42 thf(decl_367, type, esk84_4: $i > $i > $i > $i > $i).
% 0.80/0.42 thf(decl_368, type, esk85_4: $i > $i > $i > $i > $i).
% 0.80/0.42 thf(decl_369, type, esk86_3: $i > $i > ($i > $i) > $i).
% 0.80/0.42 thf(decl_370, type, esk87_3: $i > $i > ($i > $i) > $i).
% 0.80/0.42 thf(decl_371, type, esk88_3: $i > $i > ($i > $i) > $i).
% 0.80/0.42 thf(decl_372, type, esk89_4: $i > $o > $i > $i > $i).
% 0.80/0.42 thf(decl_373, type, esk90_0: $i).
% 0.80/0.42 thf(decl_374, type, esk91_0: $i).
% 0.80/0.42 thf(decl_375, type, esk92_0: $i).
% 0.80/0.42 thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', ex1)).
% 0.80/0.42 thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:((((in @ X2 @ X4))&(((X4)=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', singleton)).
% 0.80/0.42 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', replAx)).
% 0.80/0.42 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', exu)).
% 0.80/0.42 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', descrp)).
% 0.80/0.42 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', exuE1)).
% 0.80/0.42 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', exuE3e)).
% 0.80/0.42 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', nonempty)).
% 0.80/0.42 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', nonemptyI)).
% 0.80/0.42 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', exuE2)).
% 0.80/0.42 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.UhgPT125N9/E---3.1_4065180.p', exuI1)).
% 0.80/0.42 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', exuI3)).
% 0.80/0.42 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', exuI2)).
% 0.80/0.42 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.UhgPT125N9/E---3.1_4065180.p', exuE3u)).
% 0.80/0.42 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', exu__Cong)).
% 0.80/0.42 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', exuEu)).
% 0.80/0.42 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', descr__Cong)).
% 0.80/0.42 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', singletonprop)).
% 0.80/0.42 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', ex1E1)).
% 0.80/0.42 thf(ex1I, axiom, ((ex1I)<=>![X4:$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.UhgPT125N9/E---3.1_4065180.p', ex1I)).
% 0.80/0.42 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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', ex1I2)).
% 0.80/0.42 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', kfstsingleton)).
% 0.80/0.42 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', ksndsingleton)).
% 0.80/0.42 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', setOfPairsIsBReln)).
% 0.80/0.42 thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', breln)).
% 0.80/0.42 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', funcImageSingleton)).
% 0.80/0.42 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', ex1E2)).
% 0.80/0.42 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X43))&(((X14)=(X2)))))|(((~((X43)))&(((X14)=(X3))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', ifSingleton)).
% 0.80/0.42 thf(theeq, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>((subbreln)=>((eqbreln)=>((funcext)=>((funcext2)=>((ap2apEq1)=>((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>((beta2)=>((eta2)=>((iffalseProp1)=>((iffalseProp2)=>((iftrueProp1)=>((iftrueProp2)=>((ifSingleton)=>((ifp)=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', theeq)).
% 0.80/0.42 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', dsetconstrI)).
% 0.80/0.42 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', dsetconstrEL)).
% 0.80/0.42 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', dsetconstrER)).
% 0.80/0.42 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', setbeta)).
% 0.80/0.42 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', nonemptyE1)).
% 0.80/0.42 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', nonemptyI1)).
% 0.80/0.42 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', setoftrueEq)).
% 0.80/0.42 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', nonemptyImpWitness)).
% 0.80/0.42 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.UhgPT125N9/E---3.1_4065180.p', emptyE1)).
% 0.80/0.42 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', dsetconstr__Cong)).
% 0.80/0.42 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', sepInPowerset)).
% 0.80/0.42 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', sepSubset)).
% 0.80/0.42 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', theprop)).
% 0.80/0.42 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', dpsetconstrI)).
% 0.80/0.42 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', dpsetconstrSub)).
% 0.80/0.42 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', dpsetconstrERa)).
% 0.80/0.42 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', dpsetconstrEL1)).
% 0.80/0.42 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', dpsetconstrEL2)).
% 0.80/0.42 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', dpsetconstrER)).
% 0.80/0.42 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', apProp)).
% 0.80/0.42 thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X30 @ X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', lamProp)).
% 0.80/0.42 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', lamp)).
% 0.80/0.42 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', lam2p)).
% 0.80/0.42 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', brelnall1)).
% 0.80/0.42 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', brelnall2)).
% 0.80/0.42 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', subbreln)).
% 0.80/0.42 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', eqbreln)).
% 0.80/0.42 thf(beta1, axiom, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X36 @ X3))) @ X2)=(X36 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', beta1)).
% 0.80/0.42 thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', eta1)).
% 0.80/0.42 thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', lam2lamEq)).
% 0.80/0.42 thf(beta2, axiom, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X38 @ X3))) @ X2)=(X38 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', beta2)).
% 0.80/0.42 thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', eta2)).
% 0.80/0.42 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X39))&(((X14)=(X2)))))|(((~((X39)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', iffalseProp1)).
% 0.80/0.42 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X40))&(((X14)=(X2)))))|(((~((X40)))&(((X14)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', iffalseProp2)).
% 0.80/0.42 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X41))&(((X14)=(X2)))))|(((~((X41)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', iftrueProp1)).
% 0.80/0.42 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X42))&(((X14)=(X2)))))|(((~((X42)))&(((X14)=(X3)))))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', iftrueProp2)).
% 0.80/0.42 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', setextAx)).
% 0.80/0.42 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', emptysetAx)).
% 0.80/0.42 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', setadjoinAx)).
% 0.80/0.42 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', powersetAx)).
% 0.80/0.42 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', setunionAx)).
% 0.80/0.42 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', omega0Ax)).
% 0.80/0.42 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', omegaSAx)).
% 0.80/0.42 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', omegaIndAx)).
% 0.80/0.42 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', foundationAx)).
% 0.80/0.42 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.UhgPT125N9/E---3.1_4065180.p', wellorderingAx)).
% 0.80/0.42 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', prop2setE)).
% 0.80/0.42 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', emptysetE)).
% 0.80/0.42 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', emptysetimpfalse)).
% 0.80/0.42 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', notinemptyset)).
% 0.80/0.42 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', setext)).
% 0.80/0.42 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', emptyI)).
% 0.80/0.42 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', noeltsimpempty)).
% 0.80/0.42 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', setadjoinIL)).
% 0.80/0.42 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', emptyinunitempty)).
% 0.80/0.42 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', setadjoinIR)).
% 0.80/0.42 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.UhgPT125N9/E---3.1_4065180.p', setadjoinE)).
% 0.80/0.42 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', setadjoinOr)).
% 0.80/0.42 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', powersetI)).
% 0.80/0.42 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', emptyinPowerset)).
% 0.80/0.42 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', emptyInPowerset)).
% 0.80/0.42 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', powersetE)).
% 0.80/0.42 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', setunionI)).
% 0.80/0.42 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.UhgPT125N9/E---3.1_4065180.p', setunionE)).
% 0.80/0.42 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', subPowSU)).
% 0.80/0.42 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', uniqinunit)).
% 0.80/0.42 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', notinsingleton)).
% 0.80/0.42 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', eqinunit)).
% 0.80/0.42 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', singletonsswitch)).
% 0.80/0.42 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', upairsetE)).
% 0.80/0.42 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', upairsetIL)).
% 0.80/0.42 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', upairsetIR)).
% 0.80/0.42 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', vacuousDall)).
% 0.80/0.42 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', quantDeMorgan1)).
% 0.80/0.42 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', quantDeMorgan2)).
% 0.80/0.42 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', quantDeMorgan3)).
% 0.80/0.42 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', quantDeMorgan4)).
% 0.80/0.42 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', prop2setI)).
% 0.80/0.42 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', prop2set2propI)).
% 0.80/0.42 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', notdexE)).
% 0.80/0.42 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', notdallE)).
% 0.80/0.42 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', inCongP)).
% 0.80/0.42 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', in__Cong)).
% 0.80/0.42 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', emptyset__Cong)).
% 0.80/0.42 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', setadjoin__Cong)).
% 0.80/0.42 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', powerset__Cong)).
% 0.80/0.42 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', setunion__Cong)).
% 0.80/0.42 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', omega__Cong)).
% 0.80/0.42 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', subsetI1)).
% 0.80/0.42 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', eqimpsubset2)).
% 0.80/0.42 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', eqimpsubset1)).
% 0.80/0.42 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', subsetI2)).
% 0.80/0.42 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', emptysetsubset)).
% 0.80/0.42 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', subsetE)).
% 0.80/0.42 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', subsetE2)).
% 0.80/0.42 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', notsubsetI)).
% 0.80/0.42 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', notequalI1)).
% 0.80/0.42 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', notequalI2)).
% 0.80/0.42 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', subsetRefl)).
% 0.80/0.42 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', subsetTrans)).
% 0.80/0.42 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', setadjoinSub)).
% 0.80/0.42 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', setadjoinSub2)).
% 0.80/0.42 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', subset2powerset)).
% 0.80/0.42 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', setextsub)).
% 0.80/0.42 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', subsetemptysetimpeq)).
% 0.80/0.42 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', powersetI1)).
% 0.80/0.42 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', powersetE1)).
% 0.80/0.42 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', inPowerset)).
% 0.80/0.42 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', powersetsubset)).
% 0.80/0.42 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', binunionIL)).
% 0.80/0.42 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', upairset2IR)).
% 0.80/0.42 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', binunionIR)).
% 0.80/0.42 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', binunionEcases)).
% 0.80/0.42 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', binunionE)).
% 0.80/0.42 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', binunionLsub)).
% 0.80/0.42 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', binunionRsub)).
% 0.80/0.42 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', binintersectI)).
% 0.80/0.42 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', binintersectSubset5)).
% 0.80/0.42 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', binintersectEL)).
% 0.80/0.42 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', binintersectLsub)).
% 0.80/0.42 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', binintersectSubset2)).
% 0.80/0.42 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', binintersectSubset3)).
% 0.80/0.42 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', binintersectER)).
% 0.80/0.42 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', disjointsetsI1)).
% 0.80/0.42 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', binintersectRsub)).
% 0.80/0.42 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', binintersectSubset4)).
% 0.80/0.42 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', binintersectSubset1)).
% 0.80/0.42 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', bs114d)).
% 0.80/0.42 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', setminusI)).
% 0.80/0.42 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', setminusEL)).
% 0.80/0.42 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', setminusER)).
% 0.80/0.42 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', setminusSubset2)).
% 0.80/0.42 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', setminusERneg)).
% 0.80/0.42 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', setminusELneg)).
% 0.80/0.42 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', setminusILneg)).
% 0.80/0.42 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', setminusIRneg)).
% 0.80/0.42 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', setminusLsub)).
% 0.80/0.42 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', setminusSubset1)).
% 0.80/0.42 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', symdiffE)).
% 0.80/0.42 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', symdiffI1)).
% 0.80/0.42 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', symdiffI2)).
% 0.80/0.42 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', symdiffIneg1)).
% 0.80/0.42 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', symdiffIneg2)).
% 0.80/0.42 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', secondinupair)).
% 0.80/0.42 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', setukpairIL)).
% 0.80/0.42 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', setukpairIR)).
% 0.80/0.42 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', kpairiskpair)).
% 0.80/0.42 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', kpairp)).
% 0.80/0.42 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', singletonsubset)).
% 0.80/0.42 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', singletoninpowerset)).
% 0.80/0.42 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', singletoninpowunion)).
% 0.80/0.42 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', upairset2E)).
% 0.80/0.42 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', upairsubunion)).
% 0.80/0.42 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', upairinpowunion)).
% 0.80/0.42 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', ubforcartprodlem1)).
% 0.80/0.42 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', ubforcartprodlem2)).
% 0.80/0.42 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', ubforcartprodlem3)).
% 0.80/0.42 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', cartprodpairin)).
% 0.80/0.42 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.UhgPT125N9/E---3.1_4065180.p', cartprodmempair1)).
% 0.80/0.42 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', cartprodmempair)).
% 0.80/0.42 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', setunionE2)).
% 0.80/0.42 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', setunionsingleton1)).
% 0.80/0.42 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', setunionsingleton2)).
% 0.80/0.42 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', setunionsingleton)).
% 0.80/0.42 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', singletonsuniq)).
% 0.80/0.42 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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.UhgPT125N9/E---3.1_4065180.p', setukpairinjL1)).
% 0.80/0.42 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', kfstpairEq)).
% 0.80/0.42 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', cartprodfstin)).
% 0.80/0.42 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', setukpairinjL2)).
% 0.80/0.42 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', setukpairinjL)).
% 0.80/0.42 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', setukpairinjR11)).
% 0.80/0.42 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', setukpairinjR12)).
% 0.80/0.42 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', setukpairinjR1)).
% 0.80/0.42 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', upairequniteq)).
% 0.80/0.42 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.UhgPT125N9/E---3.1_4065180.p', setukpairinjR2)).
% 0.80/0.42 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.UhgPT125N9/E---3.1_4065180.p', setukpairinjR)).
% 0.80/0.42 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', ksndpairEq)).
% 0.80/0.42 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', kpairsurjEq)).
% 0.80/0.42 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', cartprodsndin)).
% 0.80/0.42 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.UhgPT125N9/E---3.1_4065180.p', cartprodpairmemEL)).
% 0.80/0.42 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.UhgPT125N9/E---3.1_4065180.p', cartprodpairmemER)).
% 0.80/0.42 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.UhgPT125N9/E---3.1_4065180.p', cartprodmempaircEq)).
% 0.80/0.42 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.UhgPT125N9/E---3.1_4065180.p', cartprodfstpairEq)).
% 0.80/0.42 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.UhgPT125N9/E---3.1_4065180.p', cartprodsndpairEq)).
% 0.80/0.42 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', cartprodpairsurjEq)).
% 0.80/0.42 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', app)).
% 0.80/0.42 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', infuncsetfunc)).
% 0.80/0.42 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', ap2p)).
% 0.80/0.42 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', funcinfuncset)).
% 0.80/0.42 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', funcGraphProp1)).
% 0.80/0.42 thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', funcGraphProp3)).
% 0.80/0.42 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', funcGraphProp2)).
% 0.80/0.42 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', funcextLem)).
% 0.80/0.42 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', funcGraphProp4)).
% 0.80/0.42 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', funcext)).
% 0.80/0.42 thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', funcext2)).
% 0.80/0.42 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', ap2apEq1)).
% 0.80/0.42 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', ap2apEq2)).
% 0.80/0.42 thf(ifp, axiom, ((ifp)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X45)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.UhgPT125N9/E---3.1_4065180.p', ifp)).
% 0.80/0.42 thf(c_0_228, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((?[X759:$i]:((((in @ X759 @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))))&(((dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))=(setadjoin @ X759 @ emptyset))))))))), inference(fof_simplification,[status(thm)],[ex1])).
% 0.80/0.42 thf(c_0_229, plain, ((singleton)=(^[Z0:$i]:(?[X2:$i]:((((in @ X2 @ Z0))&(((Z0)=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[singleton])).
% 0.80/0.42 thf(c_0_230, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.80/0.42 thf(c_0_231, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.80/0.42 thf(c_0_232, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.80/0.42 thf(c_0_233, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.80/0.42 thf(c_0_234, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.80/0.42 thf(c_0_235, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.80/0.42 thf(c_0_236, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.80/0.42 thf(c_0_237, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.80/0.42 thf(c_0_238, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 0.80/0.42 thf(c_0_239, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.80/0.42 thf(c_0_240, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.80/0.42 thf(c_0_241, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 0.80/0.42 thf(c_0_242, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.80/0.42 thf(c_0_243, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 0.80/0.42 thf(c_0_244, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))=>((exu @ (^[Z0:$i]:((X17 @ Z0))))=>((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 0.80/0.42 thf(c_0_245, plain, ((singletonprop)<=>![X4:$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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 0.80/0.42 thf(c_0_246, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 0.80/0.42 thf(c_0_247, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((?[X759:$i]:((((in @ X759 @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))))&(((dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))=(setadjoin @ X759 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_228, c_0_229])).
% 0.80/0.42 thf(c_0_248, 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])).
% 0.80/0.42 thf(c_0_249, 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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 0.80/0.42 thf(c_0_250, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 0.80/0.42 thf(c_0_251, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 0.80/0.42 thf(c_0_252, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 0.80/0.42 thf(c_0_253, plain, ((breln)=(^[Z0:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
% 0.80/0.42 thf(c_0_254, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
% 0.80/0.42 thf(c_0_255, plain, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[ex1E2])).
% 0.80/0.42 thf(c_0_256, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X43))&(((Z0)=(X2)))))|(((~((X43)))&(((Z0)=(X3))))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
% 0.80/0.42 thf(c_0_257, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>((subbreln)=>((eqbreln)=>((funcext)=>((funcext2)=>((ap2apEq1)=>((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>((beta2)=>((eta2)=>((iffalseProp1)=>((iffalseProp2)=>((iftrueProp1)=>((iftrueProp2)=>((ifSingleton)=>((ifp)=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[theeq])).
% 0.80/0.42 thf(c_0_258, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X730:$i]:(((((X6 @ X2 @ X730)))&(![X731:$i]:(((((X6 @ X2 @ X731)))=>(((X730)=(X731)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_230, c_0_231])).
% 0.80/0.42 thf(c_0_259, plain, ((descrp)=(![X1:$i > $o]:((((?[X732:$i]:(((((X1 @ X732)))&(![X733:$i]:(((((X1 @ X733)))=>(((X732)=(X733))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_232, c_0_231])).
% 0.80/0.42 thf(c_0_260, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.80/0.42 thf(c_0_261, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.80/0.42 thf(c_0_262, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.80/0.42 thf(c_0_263, plain, ((exuE1)=(![X1:$i > $o]:((((?[X734:$i]:(((((X1 @ X734)))&(![X735:$i]:(((((X1 @ X735)))=>(((X734)=(X735))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_233, c_0_231])).
% 0.80/0.42 thf(c_0_264, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X736:$i]:(((((X1 @ X736)))&(![X737:$i]:(((((X1 @ X737)))=>(((X736)=(X737))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_234, c_0_231])).
% 0.80/0.42 thf(c_0_265, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.80/0.42 thf(c_0_266, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_235])).
% 0.80/0.42 thf(c_0_267, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_236, c_0_235])).
% 0.80/0.42 thf(c_0_268, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_235])).
% 0.80/0.42 thf(c_0_269, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.80/0.42 thf(c_0_270, plain, ((exuE2)=(![X1:$i > $o]:((((?[X738:$i]:(((((X1 @ X738)))&(![X739:$i]:(((((X1 @ X739)))=>(((X738)=(X739))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_237, c_0_231])).
% 0.80/0.42 thf(c_0_271, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_235])).
% 0.80/0.42 thf(c_0_272, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
% 0.80/0.42 thf(c_0_273, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X740:$i]:(((((X1 @ X740)))&(![X741:$i]:(((((X1 @ X741)))=>(((X740)=(X741)))))))))))))), inference(apply_def,[status(thm)],[c_0_238, c_0_231])).
% 0.80/0.42 thf(c_0_274, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X742:$i]:(((((X1 @ X742)))&(![X743:$i]:(((((X1 @ X743)))=>(((X742)=(X743)))))))))))))))), inference(apply_def,[status(thm)],[c_0_239, c_0_231])).
% 0.80/0.42 thf(c_0_275, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X744:$i]:(((((X1 @ X744)))&(![X745:$i]:(((((X1 @ X745)))=>(((X744)=(X745)))))))))))))), inference(apply_def,[status(thm)],[c_0_240, c_0_231])).
% 0.80/0.42 thf(c_0_276, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X746:$i]:(((((X1 @ X746)))&(![X747:$i]:(((((X1 @ X747)))=>(((X746)=(X747))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_241, c_0_231])).
% 0.80/0.42 thf(c_0_277, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X748:$i]:(((((X1 @ X748)))&(![X749:$i]:(((((X1 @ X749)))=>(((X748)=(X749))))))))))<=>((?[X750:$i]:(((((X17 @ X750)))&(![X751:$i]:(((((X17 @ X751)))=>(((X750)=(X751)))))))))))))))), inference(apply_def,[status(thm)],[c_0_242, c_0_231])).
% 0.80/0.42 thf(c_0_278, plain, ((exuEu)=(![X1:$i > $o]:((((?[X752:$i]:(((((X1 @ X752)))&(![X753:$i]:(((((X1 @ X753)))=>(((X752)=(X753))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_243, c_0_231])).
% 0.80/0.42 thf(c_0_279, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X754:$i]:(((((X1 @ X754)))&(![X755:$i]:(((((X1 @ X755)))=>(((X754)=(X755))))))))))=>((((?[X756:$i]:(((((X17 @ X756)))&(![X757:$i]:(((((X17 @ X757)))=>(((X756)=(X757))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_244, c_0_231])).
% 0.80/0.42 thf(c_0_280, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 0.80/0.42 thf(c_0_281, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 0.80/0.42 thf(c_0_282, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 0.80/0.42 thf(c_0_283, 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)))))=>((?[X758:$i]:((((in @ X758 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(setadjoin @ X758 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_245, c_0_229])).
% 0.80/0.42 thf(c_0_284, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:((((?[X760:$i]:((((in @ X760 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X760 @ emptyset)))))))=>(?[X2:$i]:((((in @ X2 @ X4))&((X1 @ X2))))))))), inference(apply_def,[status(thm)],[c_0_246, c_0_247])).
% 0.80/0.42 thf(c_0_285, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>(((![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X3))=>(((X3)=(X2))))))))=>((?[X761:$i]:((((in @ X761 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X761 @ emptyset))))))))))))))), inference(apply_def,[status(thm)],[c_0_248, c_0_247])).
% 0.80/0.42 thf(c_0_286, 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)))))=>((?[X762:$i]:((((in @ X762 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X762 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_249, c_0_247])).
% 0.80/0.42 thf(c_0_287, plain, ((kfstsingleton)=(![X18:$i]:((((iskpair @ X18))=>((?[X763:$i]:((((in @ X763 @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))))&(((dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))=(setadjoin @ X763 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_250, c_0_229])).
% 0.80/0.42 thf(c_0_288, axiom, ((theprop)=(![X21:$i]:((((?[X764:$i]:((((in @ X764 @ X21))&(((X21)=(setadjoin @ X764 @ emptyset)))))))=>((in @ (setunion @ X21) @ X21)))))), inference(apply_def,[status(thm)],[theprop, c_0_229])).
% 0.80/0.42 thf(c_0_289, plain, ((ksndsingleton)=(![X18:$i]:((((iskpair @ X18))=>((?[X765:$i]:((((in @ X765 @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))))&(((dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))=(setadjoin @ X765 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_251, c_0_229])).
% 0.80/0.42 thf(c_0_290, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 0.80/0.42 thf(c_0_291, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 0.80/0.42 thf(c_0_292, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_252, c_0_253])).
% 0.80/0.42 thf(c_0_293, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 0.80/0.42 thf(c_0_294, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 0.80/0.42 thf(c_0_295, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 0.80/0.42 thf(c_0_296, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 0.80/0.42 thf(c_0_297, plain, ((funcImageSingleton)=(![X4:$i, X5:$i, X29:$i]:((((func @ X4 @ X5 @ X29))=>(![X2:$i]:((((in @ X2 @ X4))=>((?[X766:$i]:((((in @ X766 @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))=(setadjoin @ X766 @ emptyset)))))))))))))), inference(apply_def,[status(thm)],[c_0_254, c_0_229])).
% 0.80/0.42 thf(c_0_298, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
% 0.80/0.42 thf(c_0_299, plain, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:(((X30 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])).
% 0.80/0.42 thf(c_0_300, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
% 0.80/0.42 thf(c_0_301, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
% 0.80/0.42 thf(c_0_302, axiom, ((brelnall1)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((X1 @ (kpair @ X2 @ X3)))))))))))=>(![X2:$i]:((((in @ X2 @ X33))=>((X1 @ X2)))))))))))), inference(apply_def,[status(thm)],[brelnall1, c_0_253])).
% 0.80/0.42 thf(c_0_303, axiom, ((brelnall2)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((X1 @ (kpair @ X2 @ X3)))))))))))=>(![X2:$i]:((((in @ X2 @ X33))=>((X1 @ X2)))))))))))), inference(apply_def,[status(thm)],[brelnall2, c_0_253])).
% 0.80/0.42 thf(c_0_304, plain, ((ex1E2)=(![X4:$i, X1:$i > $o]:((((?[X767:$i]:((((in @ X767 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X767 @ emptyset)))))))=>(![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))))))))))), inference(apply_def,[status(thm)],[c_0_255, c_0_247])).
% 0.80/0.42 thf(c_0_305, axiom, ((subbreln)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X35:$i]:(((((subset @ X35 @ (cartprod @ X4 @ X5))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((in @ (kpair @ X2 @ X3) @ X35))))))))))=>((subset @ X33 @ X35))))))))))), inference(apply_def,[status(thm)],[subbreln, c_0_253])).
% 0.80/0.42 thf(c_0_306, axiom, ((eqbreln)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X35:$i]:(((((subset @ X35 @ (cartprod @ X4 @ X5))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((in @ (kpair @ X2 @ X3) @ X35))))))))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X35))=>((in @ (kpair @ X2 @ X3) @ X33))))))))))=>(((X33)=(X35)))))))))))))), inference(apply_def,[status(thm)],[eqbreln, c_0_253])).
% 0.80/0.42 thf(c_0_307, plain, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X36 @ Z0))) @ X2)=(X36 @ X2))))))), inference(fof_simplification,[status(thm)],[beta1])).
% 0.80/0.42 thf(c_0_308, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])).
% 0.80/0.42 thf(c_0_309, plain, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[Z0:$i]:(X37 @ Z0)))=(lam @ X4 @ X5 @ (^[Z0:$i]:(X37 @ Z0))))))), inference(fof_simplification,[status(thm)],[lam2lamEq])).
% 0.80/0.42 thf(c_0_310, plain, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X38 @ Z0))) @ X2)=(X38 @ X2))))))), inference(fof_simplification,[status(thm)],[beta2])).
% 0.80/0.42 thf(c_0_311, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])).
% 0.80/0.42 thf(c_0_312, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X39))&(((Z0)=(X2)))))|(((~((X39)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
% 0.80/0.42 thf(c_0_313, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X40))&(((Z0)=(X2)))))|(((~((X40)))&(((Z0)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])).
% 0.80/0.42 thf(c_0_314, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X41))&(((Z0)=(X2)))))|(((~((X41)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
% 0.80/0.42 thf(c_0_315, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X42))&(((Z0)=(X2)))))|(((~((X42)))&(((Z0)=(X3)))))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])).
% 0.80/0.42 thf(c_0_316, plain, ((ifSingleton)=(![X4:$i, X43:$o, X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X4))=>((?[X768:$i]:((((in @ X768 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X43))&(((Z0)=(X2)))))|(((~((X43)))&(((Z0)=(X3)))))))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:((((((X43))&(((Z0)=(X2)))))|(((~((X43)))&(((Z0)=(X3)))))))))=(setadjoin @ X768 @ emptyset)))))))))))))), inference(apply_def,[status(thm)],[c_0_256, c_0_229])).
% 0.80/0.42 thf(c_0_317, plain, ((epred1_0)<=>![X798:$i]:(?[X799:$i]:((((![X800:$i]:(((in @ X800 @ X799)=>![X801:$i]:(((in @ X801 @ X800)=>(in @ X801 @ X798)))))&![X802:$i, X803:$i]:((((in @ X802 @ X798)&(in @ X803 @ X798))=>(![X804:$i]:(((in @ X804 @ X799)=>((in @ X802 @ X804)<=>(in @ X803 @ X804))))=>((X802)=(X803))))))&![X805:$i, X806:$i]:((((in @ X805 @ X799)&(in @ X806 @ X799))=>(![X807:$i]:(((in @ X807 @ X805)=>(in @ X807 @ X806)))|![X808:$i]:(((in @ X808 @ X806)=>(in @ X808 @ X805)))))))&![X809:$i]:(((![X810:$i]:(((in @ X810 @ X809)=>(in @ X810 @ X798)))&?[X811:$i]:((in @ X811 @ X809)))=>?[X812:$i, X813:$i]:(((((in @ X812 @ X799)&(in @ X813 @ X809))&~(?[X814:$i]:(((in @ X814 @ X812)&(in @ X814 @ X809)))))&![X815:$i]:(((in @ X815 @ X799)=>(![X816:$i]:(((in @ X816 @ X815)=>(in @ X816 @ X812)))|(in @ X813 @ X815)))))))))))), introduced(definition)).
% 0.80/0.42 thf(c_0_318, negated_conjecture, ~((![X769:$i, X770:$i]:((![X771:$i]:(((in @ X771 @ X769)<=>(in @ X771 @ X770)))=>((X769)=(X770))))=>(![X772:$i]:(~(in @ X772 @ emptyset))=>(![X773:$i, X774:$i, X775:$i]:(((in @ X775 @ (setadjoin @ X773 @ X774))<=>(((X775)=(X773))|(in @ X775 @ X774))))=>(![X776:$i, X777:$i]:(((in @ X777 @ (powerset @ X776))<=>![X778:$i]:(((in @ X778 @ X777)=>(in @ X778 @ X776)))))=>(![X779:$i, X780:$i]:(((in @ X780 @ (setunion @ X779))<=>?[X781:$i]:(((in @ X780 @ X781)&(in @ X781 @ X779)))))=>((in @ emptyset @ omega)=>(![X782:$i]:(((in @ X782 @ omega)=>(in @ (setadjoin @ X782 @ X782) @ omega)))=>(![X783:$i]:((((in @ emptyset @ X783)&![X784:$i]:((((in @ X784 @ omega)&(in @ X784 @ X783))=>(in @ (setadjoin @ X784 @ X784) @ X783))))=>![X785:$i]:(((in @ X785 @ omega)=>(in @ X785 @ X783)))))=>(![X786:$i > $i > $o, X787:$i]:((![X788:$i]:(((in @ X788 @ X787)=>?[X789:$i]:(((X786 @ X788 @ X789)&![X790:$i]:(((X786 @ X788 @ X790)=>((X789)=(X790))))))))=>?[X791:$i]:(![X792:$i]:(((in @ X792 @ X791)<=>?[X793:$i]:(((in @ X793 @ X787)&(X786 @ X793 @ X792))))))))=>(![X794:$i]:((?[X795:$i]:((in @ X795 @ X794))=>?[X796:$i]:(((in @ X796 @ X794)&~(?[X797:$i]:(((in @ X797 @ X796)&(in @ X797 @ X794))))))))=>((epred1_0)=>(![X817:$i > $o]:((?[X818:$i]:(((X817 @ X818)&![X819:$i]:(((X817 @ X819)=>((X818)=(X819))))))=>(X817 @ (descr @ (^[Z0:$i]:(X817 @ Z0))))))=>(![X820:$i, X821:$i > $o, X822:$i]:(((in @ X822 @ X820)=>((X821 @ X822)=>(in @ X822 @ (dsetconstr @ X820 @ X821)))))=>(![X823:$i, X824:$i > $o, X825:$i]:(((in @ X825 @ (dsetconstr @ X823 @ X824))=>(in @ X825 @ X823)))=>(![X826:$i, X827:$i > $o, X828:$i]:(((in @ X828 @ (dsetconstr @ X826 @ X827))=>(X827 @ X828)))=>(![X829:$i > $o]:((?[X830:$i]:(((X829 @ X830)&![X831:$i]:(((X829 @ X831)=>((X830)=(X831))))))=>?[X832:$i]:(((X829 @ X832)&![X833:$i]:(((X829 @ X833)=>((X832)=(X833))))))))=>(![X834:$o, X835:$i]:(((in @ X835 @ (prop2set @ ((X834))))=>(X834)))=>(![X836:$i]:(((in @ X836 @ emptyset)=>![X837:$o]:((X837))))=>(![X838:$i]:(((in @ X838 @ emptyset)=>~($true)))=>(![X839:$i]:(~(in @ X839 @ emptyset))=>(![X840:$i > $o]:((?[X841:$i]:(((X840 @ X841)&![X842:$i]:(((X840 @ X842)=>((X841)=(X842))))))=>?[X843:$i]:((X840 @ X843))))=>(![X844:$i, X845:$i]:((![X846:$i]:(((in @ X846 @ X844)=>(in @ X846 @ X845)))=>(![X847:$i]:(((in @ X847 @ X845)=>(in @ X847 @ X844)))=>((X844)=(X845)))))=>(![X848:$i]:((![X849:$i]:(~(in @ X849 @ X848))=>((X848)=(emptyset))))=>(![X850:$i]:((![X851:$i]:(~(in @ X851 @ X850))=>((X850)=(emptyset))))=>(![X852:$i, X853:$i > $o, X854:$i]:(((in @ X854 @ X852)=>((in @ X854 @ (dsetconstr @ X852 @ X853))<=>(X853 @ X854))))=>(![X855:$i]:((((X855)!=(emptyset))=>?[X856:$i]:((in @ X856 @ X855))))=>(![X857:$i, X858:$i > $o, X859:$i]:(((in @ X859 @ X857)=>((X858 @ X859)=>((dsetconstr @ X857 @ X858)!=(emptyset)))))=>(![X860:$i]:((?[X861:$i]:((in @ X861 @ X860))=>((X860)!=(emptyset))))=>(![X862:$i, X863:$i]:((in @ X862 @ (setadjoin @ X862 @ X863)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X864:$i, X865:$i, X866:$i]:(((in @ X866 @ X865)=>(in @ X866 @ (setadjoin @ X864 @ X865))))=>(![X867:$i, X868:$i, X869:$i]:(((in @ X869 @ (setadjoin @ X867 @ X868))=>![X870:$o]:(((((X869)=(X867))=>(X870))=>(((in @ X869 @ X868)=>(X870))=>(X870))))))=>(![X871:$i, X872:$i, X873:$i]:(((in @ X873 @ (setadjoin @ X871 @ X872))=>(((X873)=(X871))|(in @ X873 @ X872))))=>(![X874:$i]:(((dsetconstr @ X874 @ (^[Z0:$i]:($true)))=(X874)))=>(![X875:$i, X876:$i]:((![X877:$i]:(((in @ X877 @ X876)=>(in @ X877 @ X875)))=>(in @ X876 @ (powerset @ X875))))=>(![X878:$i]:((in @ emptyset @ (powerset @ X878)))=>(![X879:$i]:((in @ emptyset @ (powerset @ X879)))=>(![X880:$i, X881:$i, X882:$i]:(((in @ X881 @ (powerset @ X880))=>((in @ X882 @ X881)=>(in @ X882 @ X880))))=>(![X883:$i, X884:$i, X885:$i]:(((in @ X884 @ X885)=>((in @ X885 @ X883)=>(in @ X884 @ (setunion @ X883)))))=>(![X886:$i, X887:$i]:(((in @ X887 @ (setunion @ X886))=>![X888:$o]:((![X889:$i]:(((in @ X887 @ X889)=>((in @ X889 @ X886)=>(X888))))=>(X888)))))=>(![X890:$i, X891:$i]:(((in @ X891 @ X890)=>(in @ X891 @ (powerset @ (setunion @ X890)))))=>(![X892:$i > $o]:((?[X893:$i]:(((X892 @ X893)&![X894:$i]:(((X892 @ X894)=>((X893)=(X894))))))=>?[X895:$i]:(![X896:$i]:(((X892 @ X896)<=>((X896)=(X895)))))))=>(![X897:$i]:((((X897)!=(emptyset))=>?[X898:$i]:(((in @ X898 @ X897)&$true))))=>(![X899:$i, X900:$i]:(((in @ X899 @ (setadjoin @ X900 @ emptyset))=>((X899)=(X900))))=>(![X901:$i, X902:$i]:((((X901)!=(X902))=>~(in @ X902 @ (setadjoin @ X901 @ emptyset))))=>(![X903:$i, X904:$i]:((((X903)=(X904))=>(in @ X903 @ (setadjoin @ X904 @ emptyset))))=>(![X905:$i, X906:$i]:(((in @ X905 @ (setadjoin @ X906 @ emptyset))=>(in @ X906 @ (setadjoin @ X905 @ emptyset))))=>(![X907:$i, X908:$i, X909:$i]:(((in @ X909 @ (setadjoin @ X907 @ (setadjoin @ X908 @ emptyset)))=>(((X909)=(X907))|((X909)=(X908)))))=>(![X910:$i, X911:$i]:((in @ X910 @ (setadjoin @ X910 @ (setadjoin @ X911 @ emptyset))))=>(![X912:$i, X913:$i]:((in @ X913 @ (setadjoin @ X912 @ (setadjoin @ X913 @ emptyset))))=>(![X914:$i, X915:$i > $o]:((?[X916:$i]:(((in @ X916 @ X914)&(X915 @ X916)))=>(((dsetconstr @ X914 @ X915)=(emptyset))=>~($true))))=>(![X917:$i > $o, X918:$i]:(((in @ X918 @ emptyset)=>(X917 @ X918)))=>(![X919:$i, X920:$i > $o]:((~(![X921:$i]:(((in @ X921 @ X919)=>(X920 @ X921))))=>?[X922:$i]:(((in @ X922 @ X919)&~((X920 @ X922))))))=>(![X923:$i, X924:$i > $o]:((![X925:$i]:(((in @ X925 @ X923)=>~((X924 @ X925))))=>~(?[X926:$i]:(((in @ X926 @ X923)&(X924 @ X926))))))=>(![X927:$i, X928:$i > $o]:((~(?[X929:$i]:(((in @ X929 @ X927)&(X928 @ X929))))=>![X930:$i]:(((in @ X930 @ X927)=>~((X928 @ X930))))))=>(![X931:$i, X932:$i > $o]:((?[X933:$i]:(((in @ X933 @ X931)&~((X932 @ X933))))=>~(![X934:$i]:(((in @ X934 @ X931)=>(X932 @ X934))))))=>(![X935:$o]:(((X935)=>(in @ emptyset @ (prop2set @ ((X935))))))=>(![X936:$o]:(((X936)=>(set2prop @ (prop2set @ ((X936))))))=>(![X937:$i, X938:$i > $o]:((~(?[X939:$i]:(((in @ X939 @ X937)&(X938 @ X939))))=>![X940:$i]:(((in @ X940 @ X937)=>~((X938 @ X940))))))=>(![X941:$i, X942:$i > $o]:((~(![X943:$i]:(((in @ X943 @ X941)=>(X942 @ X943))))=>?[X944:$i]:(((in @ X944 @ X941)&~((X942 @ X944))))))=>(![X945:$i > $o]:((?[X946:$i]:(((X945 @ X946)&![X947:$i]:(((X945 @ X947)=>((X946)=(X947))))))=>?[X948:$i]:(((X945 @ X948)&![X949:$i]:(((X945 @ X949)=>((X948)=(X949))))))))=>(![X950:$i > $o]:((?[X951:$i]:((X950 @ X951))=>(![X952:$i, X953:$i]:(((X950 @ X952)=>((X950 @ X953)=>((X952)=(X953)))))=>?[X954:$i]:(((X950 @ X954)&![X955:$i]:(((X950 @ X955)=>((X954)=(X955)))))))))=>(![X956:$i > $o]:((?[X957:$i]:(![X958:$i]:(((X956 @ X958)<=>((X958)=(X957)))))=>?[X959:$i]:(((X956 @ X959)&![X960:$i]:(((X956 @ X960)=>((X959)=(X960))))))))=>(![X961:$i, X962:$i]:((((X961)=(X962))=>![X963:$i, X964:$i]:((((X963)=(X964))=>((in @ X963 @ X961)=>(in @ X964 @ X962))))))=>(![X965:$i, X966:$i]:((((X965)=(X966))=>![X967:$i, X968:$i]:((((X967)=(X968))=>((in @ X967 @ X965)<=>(in @ X968 @ X966))))))=>(![X969:$i > $o]:((?[X970:$i]:(((X969 @ X970)&![X971:$i]:(((X969 @ X971)=>((X970)=(X971))))))=>![X972:$i, X973:$i]:(((X969 @ X972)=>((X969 @ X973)=>((X972)=(X973)))))))=>(![X974:$i > $o, X975:$i > $o]:((![X976:$i, X977:$i]:((((X976)=(X977))=>((X974 @ X976)<=>(X975 @ X977))))=>(?[X978:$i]:(((X974 @ X978)&![X979:$i]:(((X974 @ X979)=>((X978)=(X979))))))<=>?[X980:$i]:(((X975 @ X980)&![X981:$i]:(((X975 @ X981)=>((X980)=(X981)))))))))=>(((emptyset)=(emptyset))=>(![X982:$i, X983:$i]:((((X982)=(X983))=>![X984:$i, X985:$i]:((((X984)=(X985))=>((setadjoin @ X982 @ X984)=(setadjoin @ X983 @ X985))))))=>(![X986:$i, X987:$i]:((((X986)=(X987))=>((powerset @ X986)=(powerset @ X987))))=>(![X988:$i, X989:$i]:((((X988)=(X989))=>((setunion @ X988)=(setunion @ X989))))=>(((omega)=(omega))=>(![X990:$i > $o]:((?[X991:$i]:(((X990 @ X991)&![X992:$i]:(((X990 @ X992)=>((X991)=(X992))))))=>![X993:$i, X994:$i]:(((X990 @ X993)=>((X990 @ X994)=>((X993)=(X994)))))))=>(![X995:$i 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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(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_257, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_258]), foundationAx]), wellorderingAx]), c_0_259]), c_0_260]), c_0_261]), c_0_262]), c_0_263]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_264]), setext]), emptyI]), noeltsimpempty]), c_0_265]), c_0_266]), c_0_267]), c_0_268]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_269]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_270]), c_0_271]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_272]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_273]), c_0_274]), c_0_275]), inCongP]), in__Cong]), c_0_276]), c_0_277]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_278]), c_0_279]), c_0_280]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_281]), c_0_282]), 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_229]), c_0_283]), c_0_284]), c_0_285]), c_0_286]), singletonsuniq]), setukpairinjL1]), c_0_287]), c_0_288]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_289]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_290]), c_0_291]), c_0_292]), c_0_293]), c_0_294]), c_0_295]), c_0_296]), c_0_297]), c_0_298]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_299]), c_0_300]), c_0_301]), c_0_302]), c_0_303]), c_0_304]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), c_0_305]), c_0_306]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_307]), c_0_308]), c_0_309]), c_0_310]), c_0_311]), c_0_312]), c_0_313]), c_0_314]), c_0_315]), c_0_316]), ifp])])]), c_0_317])).
% 0.80/0.42 thf(c_0_319, negated_conjecture, ![X1498:$i, X1499:$i, X1501:$i, X1502:$i, X1503:$i, X1504:$i, X1505:$i, X1506:$i, X1507:$i, X1508:$i, X1509:$i, X1511:$i, X1512:$i, X1514:$i, X1515:$i, X1516:$i, X1517:$i, X1518:$i, X1520:$i, X1521:$i > $i > $o, X1522:$i, X1524:$i, X1527:$i, X1529:$i, X1530:$i, X1531:$i, X1532:$i, X1534:$i, X1535:$i > $o, X1536:$i, X1538:$i, X1539:$i > $o, X1540:$i, X1541:$i, X1542:$i > $o, X1543:$i, X1544:$i, X1545:$i > $o, X1546:$i, X1547:$i > $o, X1548:$i, X1551:$i, X1552:$o, X1553:$i, X1554:$i, X1555:$o, X1556:$i, X1557:$i, X1558:$i > $o, X1559:$i, X1562:$i, X1563:$i, X1566:$i, X1568:$i, X1570:$i, X1571:$i > $o, X1572:$i, X1573:$i, X1575:$i, X1576:$i > $o, X1577:$i, X1578:$i, X1579:$i, X1580:$i, X1581:$i, X1582:$i, X1583:$i, X1584:$i, X1585:$i, X1586:$i, X1587:$i, X1588:$o, X1589:$i, X1590:$i, X1591:$i, X1592:$i, X1593:$i, X1594:$i, X1596:$i, X1597:$i, X1598:$i, X1599:$i, X1600:$i, X1601:$i, X1602:$i, X1603:$i, X1604:$i, X1605:$i, X1606:$o, X1608:$i, X1609:$i, X1610:$i > $o, X1611:$i, X1614:$i, X1615:$i, X1616:$i, X1618:$i, X1619:$i, X1620:$i, X1621:$i, X1622:$i, X1623:$i, X1624:$i, X1625:$i, X1626:$i, X1627:$i, X1628:$i, X1629:$i, X1630:$i, X1631:$i, X1632:$i, X1633:$i, X1634:$i > $o, X1635:$i, X1636:$i > $o, X1637:$i, X1638:$i, X1639:$i > $o, X1640:$i, X1642:$i, X1643:$i > $o, X1645:$i, X1646:$i, X1647:$i > $o, X1649:$i, X1650:$i, X1651:$i > $o, X1652:$i, X1654:$o, X1655:$o, X1656:$i, X1657:$i > $o, X1659:$i, X1660:$i, X1661:$i > $o, X1662:$i, X1664:$i > $o, X1665:$i, X1668:$i, X1669:$i > $o, X1670:$i, X1674:$i, X1675:$i > $o, X1676:$i, X1679:$i, X1680:$i, X1681:$i, X1682:$i, X1683:$i, X1684:$i, X1685:$i, X1686:$i, X1687:$i, X1688:$i > $o, X1689:$i, X1691:$i, X1692:$i, X1693:$i > $o, X1694:$i > $o, X1697:$i, X1700:$i, X1701:$i, X1704:$i, X1705:$i, X1706:$i, X1707:$i, X1708:$i, X1709:$i, X1710:$i, X1711:$i, X1712:$i, X1713:$i > $o, X1714:$i, X1716:$i, X1717:$i, X1718:$i > $o, X1719:$i > $o, X1722:$i, X1724:$i, X1726:$i, X1727:$i, X1728:$i > $o, X1729:$i > $o, X1732:$i, X1733:$i, X1735:$i, X1736:$i, X1737:$i, X1738:$i, X1739:$i, X1740:$i, X1742:$i, X1743:$i, X1744:$i, X1745:$i, X1746:$i, X1747:$i, X1748:$i, X1749:$i, X1750:$i, X1751:$i, X1752:$i, X1753:$i, X1754:$i, X1755:$i, X1756:$i, X1757:$i, X1758:$i, X1759:$i, X1760:$i, X1761:$i, X1762:$i, X1763:$i, X1764:$i, X1765:$i, X1766:$i, X1767:$i, X1768:$i, X1769:$i, X1770:$i, X1771:$i, X1772:$i, X1773:$i, X1774:$i, X1775:$i, X1776:$i, X1777:$i, X1778:$i, X1779:$i > $o, X1780:$i, X1781:$i > $o, X1782:$i, X1783:$i, X1784:$i, X1785:$i, X1786:$i, X1787:$i, X1788:$i, X1789:$i, X1790:$i, X1791:$i, X1792:$i, X1793:$o, X1794:$i, X1795:$i, X1796:$i, X1797:$i, X1798:$i, X1799:$i, X1800:$i, X1801:$i, X1802:$i, X1803:$i, X1804:$i, X1805:$i, X1806:$i, X1807:$i, X1808:$i, X1809:$i, X1810:$i, X1811:$i, X1812:$i, X1813:$i, X1814:$i, X1815:$i, X1816:$i, X1817:$i, X1818:$i, X1819:$i, X1820:$i, X1822:$i, X1823:$i, X1824:$i, X1825:$i, X1826:$i, X1827:$i, X1828:$i, X1829:$i, X1830:$i, X1831:$i, X1832:$i, X1833:$i, X1834:$i, X1835:$i, X1836:$i, X1837:$i, X1838:$i, X1839:$i, X1840:$i, X1841:$i, X1842:$i, X1843:$i, X1844:$i, X1845:$i, X1846:$i, X1847:$i, X1848:$i, X1849:$i, X1850:$i, X1851:$i, X1852:$i, X1853:$i, X1854:$i, X1855:$i, X1856:$i, X1857:$i, X1858:$i, X1859:$i, X1860:$i, X1861:$o, X1862:$i, X1863:$i, X1864:$i, X1865:$i, X1866:$i, X1867:$i, X1868:$i, X1869:$i, X1870:$i, X1871:$i, X1872:$i, X1873:$i, X1874:$i, X1875:$i, X1876:$i, X1877:$i, X1878:$i, X1879:$i, X1880:$i, X1881:$i, X1882:$i, X1883:$i, X1884:$i, X1885:$i, X1886:$i, X1887:$i, X1888:$i, X1889:$i, X1890:$i, X1891:$i, X1892:$i, X1893:$i, X1894:$i, X1895:$i, X1896:$i, X1897:$i, X1898:$i, X1899:$i, X1900:$i, X1901:$i, X1902:$i, X1903:$i, X1904:$i, X1905:$i, X1906:$i, X1907:$i, X1908:$i, X1909:$i, X1910:$i, X1911:$i, X1912:$i, X1913:$i, X1914:$i, X1915:$i, X1916:$i, X1917:$i, X1918:$i, X1919:$i, X1920:$i, X1923:$i, X1924:$i, X1925:$i, X1926:$i, X1927:$i, X1929:$i, X1930:$i, X1931:$i, X1932:$i, X1933:$i > $o, X1936:$i, X1938:$i, X1939:$i > $o, X1940:$i, X1942:$i, X1943:$i > $o, X1944:$i, X1947:$i, X1948:$i > $o, X1951:$i, X1953:$i, X1954:$i, X1955:$i, X1956:$i, X1957:$i, X1958:$i, X1960:$i, X1961:$i, X1962:$i, X1963:$i, X1964:$i, X1965:$i, X1966:$i, X1967:$i, X1968:$i, X1969:$i, X1970:$i, X1971:$i, X1972:$i, X1973:$i, X1974:$i, X1975:$i, X1976:$i, X1977:$i, X1978:$i, X1979:$i, X1980:$i, X1981:$i, X1982:$i, X1983:$i, X1984:$i, X1985:$i, X1986:$i, X1987:$i, X1988:$i, X1989:$i, X1990:$i, X1991:$i, X1992:$i, X1993:$i, X1994:$i, X1996:$i, X1997:$i, X1998:$i, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$i, X2004:$i, X2005:$i, X2006:$i, X2007:$i, X2008:$i, X2009:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2015:$i, X2016:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$i, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2025:$i, X2026:$i, X2027:$i > $i > $o, X2028:$i, X2029:$i, X2030:$i, X2031:$i, X2032:$i > $i > $o, X2033:$i, X2034:$i, X2035:$i > $i > $o, X2036:$i, X2037:$i, X2038:$i > $i > $o, X2039:$i, X2040:$i, X2041:$i, X2042:$i, X2043:$i > $i > $o, X2044:$i, X2045:$i, X2046:$i, X2047:$i, X2048:$i > $i > $o, X2049:$i, X2050:$i, X2051:$i, X2052:$i, X2053:$i > $i > $o, X2054:$i, X2055:$i, X2056:$i, X2057:$i, X2058:$i, X2059:$i, X2061:$i, X2062:$i, X2063:$i, X2064:$i, X2065:$i, X2066:$i, X2067:$i, X2068:$i, X2069:$i, X2070:$i, X2071:$i, X2072:$i, X2073:$i, X2074:$i, X2075:$i, X2076:$i, X2077:$i, X2078:$i, X2079:$i, X2080:$i, X2081:$i > $i, X2083:$i, X2084:$i, X2085:$i > $i, X2087:$i, X2088:$i, X2089:$i > $i, X2091:$i, X2092:$i, X2093:$i, X2094:$i > $o, X2097:$i, X2098:$i, X2099:$i, X2100:$i, X2101:$i > $o, X2104:$i, X2105:$i, X2106:$i > $o, X2107:$i, X2108:$i, X2109:$i, X2110:$i, X2111:$i, X2112:$i, X2113:$i, X2114:$i, X2115:$i, X2116:$i, X2117:$i, X2118:$i, X2119:$i, X2120:$i, X2121:$i, X2122:$i, X2123:$i, X2124:$i, X2125:$i, X2126:$i, X2128:$i, X2129:$i, X2130:$i, X2131:$i, X2132:$i, X2133:$i, X2134:$i, X2135:$i, X2136:$i, X2137:$i, X2138:$i, X2141:$i, X2142:$i, X2143:$i, X2144:$i, X2149:$i, X2150:$i, X2151:$i, X2152:$i, X2154:$i, X2155:$i, X2156:$i, X2157:$i, X2159:$i, X2160:$i, X2161:$i, X2162:$i, X2163:$i, X2164:$i, X2165:$i, X2166:$i, X2167:$i, X2168:$i, X2169:$i > $i, X2171:$i, X2172:$i, X2173:$i, X2174:$i, X2175:$i, X2176:$i, X2177:$i > $i, X2179:$i, X2180:$i, X2181:$i > $i, X2183:$i, X2184:$i, X2185:$i, X2186:$i, X2187:$i, X2188:$o, X2189:$i, X2190:$i, X2191:$i, X2192:$o, X2193:$i, X2194:$i, X2195:$i, X2196:$o, X2197:$i, X2198:$i, X2199:$i, X2200:$o, X2201:$i, X2202:$i, X2203:$i, X2204:$o, X2205:$i, X2206:$i, X2208:$i, X2209:$o, X2210:$i, X2211:$i]:((((~(in @ (esk1_2 @ X1498 @ X1499) @ X1498)|~(in @ (esk1_2 @ X1498 @ X1499) @ X1499)|((X1498)=(X1499)))&((in @ (esk1_2 @ X1498 @ X1499) @ X1498)|(in @ (esk1_2 @ X1498 @ X1499) @ X1499)|((X1498)=(X1499))))&(~(in @ X1501 @ emptyset)&(((~(in @ X1504 @ (setadjoin @ X1502 @ X1503))|(((X1504)=(X1502))|(in @ X1504 @ X1503)))&((((X1504)!=(X1502))|(in @ X1504 @ (setadjoin @ X1502 @ X1503)))&(~(in @ X1504 @ 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@ X2142))|~(subset @ X2143 @ (cartprod @ X2141 @ X2142)))&(((in @ (kpair @ (esk82_4 @ X2141 @ X2142 @ X2143 @ X2144) @ (esk83_4 @ X2141 @ X2142 @ X2143 @ X2144)) @ X2144)|((X2143)=(X2144))|(in @ (kpair @ (esk80_4 @ X2141 @ X2142 @ X2143 @ X2144) @ (esk81_4 @ X2141 @ X2142 @ X2143 @ X2144)) @ X2143)|~(subset @ X2144 @ (cartprod @ X2141 @ X2142))|~(subset @ X2143 @ (cartprod @ X2141 @ X2142)))&(~(in @ (kpair @ (esk82_4 @ X2141 @ X2142 @ X2143 @ X2144) @ (esk83_4 @ X2141 @ X2142 @ X2143 @ X2144)) @ X2143)|((X2143)=(X2144))|(in @ (kpair @ (esk80_4 @ X2141 @ X2142 @ X2143 @ X2144) @ (esk81_4 @ X2141 @ X2142 @ X2143 @ X2144)) @ X2143)|~(subset @ X2144 @ (cartprod @ X2141 @ X2142))|~(subset @ X2143 @ (cartprod @ X2141 @ X2142))))))&(((in @ (esk82_4 @ X2141 @ X2142 @ X2143 @ X2144) @ X2141)|((X2143)=(X2144))|~(in @ (kpair @ (esk80_4 @ X2141 @ X2142 @ X2143 @ X2144) @ (esk81_4 @ X2141 @ X2142 @ X2143 @ X2144)) @ X2144)|~(subset @ X2144 @ (cartprod @ X2141 @ X2142))|~(subset @ X2143 @ (cartprod @ X2141 @ X2142)))&(((in @ (esk83_4 @ X2141 @ X2142 @ X2143 @ X2144) @ X2142)|((X2143)=(X2144))|~(in @ (kpair @ (esk80_4 @ X2141 @ X2142 @ X2143 @ X2144) @ (esk81_4 @ X2141 @ X2142 @ X2143 @ X2144)) @ X2144)|~(subset @ X2144 @ (cartprod @ X2141 @ X2142))|~(subset @ X2143 @ (cartprod @ X2141 @ X2142)))&(((in @ (kpair @ (esk82_4 @ X2141 @ X2142 @ X2143 @ X2144) @ (esk83_4 @ X2141 @ X2142 @ X2143 @ X2144)) @ X2144)|((X2143)=(X2144))|~(in @ (kpair @ (esk80_4 @ X2141 @ X2142 @ X2143 @ X2144) @ (esk81_4 @ X2141 @ X2142 @ X2143 @ X2144)) @ X2144)|~(subset @ X2144 @ (cartprod @ X2141 @ X2142))|~(subset @ X2143 @ (cartprod @ X2141 @ X2142)))&(~(in @ (kpair @ (esk82_4 @ X2141 @ X2142 @ X2143 @ X2144) @ (esk83_4 @ X2141 @ X2142 @ X2143 @ X2144)) @ X2143)|((X2143)=(X2144))|~(in @ (kpair @ (esk80_4 @ X2141 @ X2142 @ X2143 @ X2144) @ (esk81_4 @ X2141 @ X2142 @ X2143 @ X2144)) @ X2144)|~(subset @ X2144 @ (cartprod @ X2141 @ X2142))|~(subset @ X2143 @ (cartprod @ X2141 @ X2142)))))))))&((((in @ (esk84_4 @ X2149 @ X2150 @ X2151 @ X2152) @ X2149)|((X2151)=(X2152))|~(func @ X2149 @ X2150 @ X2152)|~(func @ X2149 @ X2150 @ X2151))&(((ap @ X2149 @ X2150 @ X2151 @ (esk84_4 @ X2149 @ X2150 @ X2151 @ X2152))!=(ap @ X2149 @ X2150 @ X2152 @ (esk84_4 @ X2149 @ X2150 @ X2151 @ X2152)))|((X2151)=(X2152))|~(func @ X2149 @ X2150 @ X2152)|~(func @ X2149 @ X2150 @ X2151)))&((((in @ (esk85_4 @ X2154 @ X2155 @ X2156 @ X2157) @ X2154)|((X2156)=(X2157))|~(in @ X2157 @ (funcSet @ X2154 @ X2155))|~(in @ X2156 @ (funcSet @ X2154 @ X2155)))&(((ap @ X2154 @ X2155 @ X2156 @ (esk85_4 @ X2154 @ X2155 @ X2156 @ X2157))!=(ap @ X2154 @ X2155 @ X2157 @ (esk85_4 @ X2154 @ X2155 @ X2156 @ X2157)))|((X2156)=(X2157))|~(in @ X2157 @ (funcSet @ X2154 @ X2155))|~(in @ X2156 @ (funcSet @ X2154 @ X2155))))&((~(in @ X2161 @ (funcSet @ X2159 @ X2160))|(~(in @ X2162 @ X2159)|((ap @ X2159 @ X2160 @ X2161 @ X2162)=(ap @ X2159 @ X2160 @ X2161 @ X2162))))&((~(func @ X2163 @ X2164 @ X2165)|(~(in @ X2166 @ X2163)|((ap @ X2163 @ X2164 @ X2165 @ X2166)=(ap @ X2163 @ X2164 @ X2165 @ X2166))))&((((in @ (esk86_3 @ X2167 @ X2168 @ X2169) @ X2167)|(~(in @ X2171 @ X2167)|((ap @ X2167 @ X2168 @ (lam @ X2167 @ X2168 @ X2169) @ X2171)=(X2169 @ X2171))))&(~(in @ (X2169 @ (esk86_3 @ X2167 @ X2168 @ X2169)) @ X2168)|(~(in @ X2171 @ X2167)|((ap @ X2167 @ X2168 @ (lam @ X2167 @ X2168 @ X2169) @ X2171)=(X2169 @ X2171)))))&((~(func @ X2172 @ X2173 @ X2174)|((lam @ X2172 @ X2173 @ (ap @ X2172 @ X2173 @ X2174))=(X2174)))&((((in @ (esk87_3 @ X2175 @ X2176 @ X2177) @ X2175)|((lam @ X2175 @ X2176 @ X2177)=(lam @ X2175 @ X2176 @ X2177)))&(~(in @ (X2177 @ (esk87_3 @ X2175 @ X2176 @ X2177)) @ X2176)|((lam @ X2175 @ X2176 @ X2177)=(lam @ X2175 @ X2176 @ X2177))))&((((in @ (esk88_3 @ X2179 @ X2180 @ X2181) @ X2179)|(~(in @ X2183 @ X2179)|((ap @ X2179 @ X2180 @ (lam @ X2179 @ X2180 @ X2181) @ X2183)=(X2181 @ X2183))))&(~(in @ (X2181 @ (esk88_3 @ X2179 @ X2180 @ X2181)) @ X2180)|(~(in @ X2183 @ X2179)|((ap @ X2179 @ X2180 @ (lam @ X2179 @ X2180 @ X2181) @ X2183)=(X2181 @ X2183)))))&((~(in @ X2186 @ (funcSet @ X2184 @ X2185))|((lam @ X2184 @ X2185 @ (ap @ X2184 @ X2185 @ X2186))=(X2186)))&((~(in @ X2189 @ X2187)|(~(in @ X2190 @ X2187)|((X2188)|(in @ X2190 @ (dsetconstr @ X2187 @ (^[Z0:$i]:((((((X2188))&(((Z0)=(X2189)))))|(((~((X2188)))&(((Z0)=(X2190)))))))))))))&((~(in @ X2193 @ X2191)|(~(in @ X2194 @ X2191)|((X2192)|((dsetconstr @ X2191 @ (^[Z0:$i]:((((((X2192))&(((Z0)=(X2193)))))|(((~((X2192)))&(((Z0)=(X2194)))))))))=(setadjoin @ X2194 @ emptyset)))))&((~(in @ X2197 @ X2195)|(~(in @ X2198 @ X2195)|(~(X2196)|(in @ X2197 @ (dsetconstr @ X2195 @ (^[Z0:$i]:((((((X2196))&(((Z0)=(X2197)))))|(((~((X2196)))&(((Z0)=(X2198)))))))))))))&((~(in @ X2201 @ X2199)|(~(in @ X2202 @ X2199)|(~(X2200)|((dsetconstr @ X2199 @ (^[Z0:$i]:((((((X2200))&(((Z0)=(X2201)))))|(((~((X2200)))&(((Z0)=(X2202)))))))))=(setadjoin @ X2201 @ emptyset)))))&((((in @ (esk89_4 @ X2203 @ X2204 @ X2205 @ X2206) @ (dsetconstr @ X2203 @ (^[Z0:$i]:((((((X2204))&(((Z0)=(X2205)))))|(((~((X2204)))&(((Z0)=(X2206))))))))))|~(in @ X2206 @ X2203)|~(in @ X2205 @ X2203))&(((dsetconstr @ X2203 @ (^[Z0:$i]:((((((X2204))&(((Z0)=(X2205)))))|(((~((X2204)))&(((Z0)=(X2206)))))))))=(setadjoin @ (esk89_4 @ X2203 @ X2204 @ X2205 @ X2206) @ emptyset))|~(in @ X2206 @ X2203)|~(in @ X2205 @ X2203)))&((~(in @ X2210 @ X2208)|(~(in @ X2211 @ X2208)|(in @ (if @ X2208 @ ((X2209)) @ X2210 @ X2211) @ X2208)))&(((in @ esk91_0 @ esk90_0)&((esk90_0)=(setadjoin @ esk91_0 @ emptyset)))&((in @ esk92_0 @ esk90_0)&((setunion @ esk90_0)!=(esk92_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_318])])])])])])])).
% 0.80/0.42 thf(c_0_320, negated_conjecture, ![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2))), inference(split_conjunct,[status(thm)],[c_0_319])).
% 0.80/0.42 thf(c_0_321, negated_conjecture, ((esk90_0)=(setadjoin @ esk91_0 @ emptyset)), inference(split_conjunct,[status(thm)],[c_0_319])).
% 0.80/0.42 thf(c_0_322, negated_conjecture, ![X3:$i, X2:$i]:((((X2)=(X3))|~((in @ X3 @ (setadjoin @ X2 @ emptyset))))), inference(split_conjunct,[status(thm)],[c_0_319])).
% 0.80/0.42 thf(c_0_323, negated_conjecture, ((setunion @ esk90_0)!=(esk92_0)), inference(split_conjunct,[status(thm)],[c_0_319])).
% 0.80/0.42 thf(c_0_324, negated_conjecture, ((setunion @ esk90_0)=(esk91_0)), inference(spm,[status(thm)],[c_0_320, c_0_321])).
% 0.80/0.42 thf(c_0_325, negated_conjecture, ![X2:$i]:((((esk91_0)=(X2))|~((in @ X2 @ esk90_0)))), inference(spm,[status(thm)],[c_0_322, c_0_321])).
% 0.80/0.42 thf(c_0_326, negated_conjecture, (in @ esk92_0 @ esk90_0), inference(split_conjunct,[status(thm)],[c_0_319])).
% 0.80/0.42 thf(c_0_327, negated_conjecture, ((esk92_0)!=(esk91_0)), inference(rw,[status(thm)],[c_0_323, c_0_324])).
% 0.80/0.42 thf(c_0_328, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_325, c_0_326]), c_0_327]), ['proof']).
% 0.80/0.42 % SZS output end CNFRefutation
% 0.80/0.42 % Parsed axioms : 489
% 0.80/0.42 % Removed by relevancy pruning/SinE : 0
% 0.80/0.42 % Initial clauses : 673
% 0.80/0.42 % Removed in clause preprocessing : 289
% 0.80/0.42 % Initial clauses in saturation : 384
% 0.80/0.42 % Processed clauses : 109
% 0.80/0.42 % ...of these trivial : 9
% 0.80/0.42 % ...subsumed : 18
% 0.80/0.42 % ...remaining for further processing : 82
% 0.80/0.42 % Other redundant clauses eliminated : 10
% 0.80/0.42 % Clauses deleted for lack of memory : 0
% 0.80/0.42 % Backward-subsumed : 0
% 0.80/0.42 % Backward-rewritten : 3
% 0.80/0.42 % Generated clauses : 144
% 0.80/0.42 % ...of the previous two non-redundant : 77
% 0.80/0.42 % ...aggressively subsumed : 0
% 0.80/0.42 % Contextual simplify-reflections : 0
% 0.80/0.42 % Paramodulations : 133
% 0.80/0.42 % Factorizations : 0
% 0.80/0.42 % NegExts : 0
% 0.80/0.42 % Equation resolutions : 11
% 0.80/0.42 % Disequality decompositions : 0
% 0.80/0.42 % Total rewrite steps : 65
% 0.80/0.42 % ...of those cached : 37
% 0.80/0.42 % Propositional unsat checks : 0
% 0.80/0.42 % Propositional check models : 0
% 0.80/0.42 % Propositional check unsatisfiable : 0
% 0.80/0.42 % Propositional clauses : 0
% 0.80/0.42 % Propositional clauses after purity: 0
% 0.80/0.42 % Propositional unsat core size : 0
% 0.80/0.42 % Propositional preprocessing time : 0.000
% 0.80/0.42 % Propositional encoding time : 0.000
% 0.80/0.42 % Propositional solver time : 0.000
% 0.80/0.42 % Success case prop preproc time : 0.000
% 0.80/0.42 % Success case prop encoding time : 0.000
% 0.80/0.42 % Success case prop solver time : 0.000
% 0.80/0.42 % Current number of processed clauses : 73
% 0.80/0.42 % Positive orientable unit clauses : 39
% 0.80/0.42 % Positive unorientable unit clauses: 0
% 0.80/0.42 % Negative unit clauses : 2
% 0.80/0.42 % Non-unit-clauses : 32
% 0.80/0.42 % Current number of unprocessed clauses: 352
% 0.80/0.42 % ...number of literals in the above : 1189
% 0.80/0.42 % Current number of archived formulas : 0
% 0.80/0.42 % Current number of archived clauses : 3
% 0.80/0.42 % Clause-clause subsumption calls (NU) : 112
% 0.80/0.42 % Rec. Clause-clause subsumption calls : 98
% 0.80/0.42 % Non-unit clause-clause subsumptions : 10
% 0.80/0.42 % Unit Clause-clause subsumption calls : 27
% 0.80/0.42 % Rewrite failures with RHS unbound : 0
% 0.80/0.42 % BW rewrite match attempts : 7
% 0.80/0.42 % BW rewrite match successes : 3
% 0.80/0.42 % Condensation attempts : 0
% 0.80/0.42 % Condensation successes : 0
% 0.80/0.42 % Termbank termtop insertions : 62253
% 0.80/0.42 % Search garbage collected termcells : 23156
% 0.80/0.42
% 0.80/0.42 % -------------------------------------------------
% 0.80/0.42 % User time : 0.068 s
% 0.80/0.42 % System time : 0.009 s
% 0.80/0.42 % Total time : 0.077 s
% 0.80/0.42 % Maximum resident set size: 9024 pages
% 0.80/0.42
% 0.80/0.42 % -------------------------------------------------
% 0.80/0.42 % User time : 0.080 s
% 0.80/0.42 % System time : 0.018 s
% 0.80/0.42 % Total time : 0.098 s
% 0.80/0.42 % Maximum resident set size: 5632 pages
% 0.80/0.42 % E exiting
%------------------------------------------------------------------------------