%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU709^1 : 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 : n010.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 08:25:18 AM UTC 2026
% Result : Theorem 4.65s 0.99s
% Output : CNFRefutation 4.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU709^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n010.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 14:13:33 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.20/0.27 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.ulj0i2I61i/E---3.1_2918013.p
% 4.65/0.99 % Version: 3.5.1-ho
% 4.65/0.99 % Preprocessing class: HSLMSLSSLLLCHFA.
% 4.65/0.99 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 4.65/0.99 % Starting ehoh_best5 with 300s (1) cores
% 4.65/0.99 % Starting almost_fo_3_lam with 300s (1) cores
% 4.65/0.99 % Starting new_bool_5 with 300s (1) cores
% 4.65/0.99 % Starting pre_casc_3 with 300s (1) cores
% 4.65/0.99 % Starting ho_unfolding_8 with 300s (1) cores
% 4.65/0.99 % Starting new_ho_10_cnf2 with 300s (1) cores
% 4.65/0.99 % Starting new_bool_3 with 300s (1) cores
% 4.65/0.99 % Starting new_ho_5 with 300s (1) cores
% 4.65/0.99 % new_bool_5 with pid 2918055 completed with status 0
% 4.65/0.99 % Result found by new_bool_5
% 4.65/0.99 % Preprocessing class: HSLMSLSSLLLCHFA.
% 4.65/0.99 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 4.65/0.99 % Starting ehoh_best5 with 300s (1) cores
% 4.65/0.99 % Starting almost_fo_3_lam with 300s (1) cores
% 4.65/0.99 % Starting new_bool_5 with 300s (1) cores
% 4.65/0.99 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 4.65/0.99 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 4.65/0.99 % Search class: HGHSM-FSLM32-MHFMMSBN
% 4.65/0.99 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 4.65/0.99 % Starting SubtermCWHack with 28s (1) cores
% 4.65/0.99 % SubtermCWHack with pid 2918076 completed with status 0
% 4.65/0.99 % Result found by SubtermCWHack
% 4.65/0.99 % Preprocessing class: HSLMSLSSLLLCHFA.
% 4.65/0.99 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 4.65/0.99 % Starting ehoh_best5 with 300s (1) cores
% 4.65/0.99 % Starting almost_fo_3_lam with 300s (1) cores
% 4.65/0.99 % Starting new_bool_5 with 300s (1) cores
% 4.65/0.99 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 4.65/0.99 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 4.65/0.99 % Search class: HGHSM-FSLM32-MHFMMSBN
% 4.65/0.99 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 4.65/0.99 % Starting SubtermCWHack with 28s (1) cores
% 4.65/0.99 % Preprocessing time : 0.007 s
% 4.65/0.99
% 4.65/0.99 % Proof found!
% 4.65/0.99 % SZS status Theorem
% 4.65/0.99 % SZS output start CNFRefutation
% 4.65/0.99 thf(decl_23, type, in: $i > $i > $o).
% 4.65/0.99 thf(decl_24, type, exu: ($i > $o) > $o).
% 4.65/0.99 thf(decl_25, type, setextAx: $o).
% 4.65/0.99 thf(decl_26, type, emptyset: $i).
% 4.65/0.99 thf(decl_27, type, emptysetAx: $o).
% 4.65/0.99 thf(decl_28, type, setadjoin: $i > $i > $i).
% 4.65/0.99 thf(decl_29, type, setadjoinAx: $o).
% 4.65/0.99 thf(decl_30, type, powerset: $i > $i).
% 4.65/0.99 thf(decl_31, type, powersetAx: $o).
% 4.65/0.99 thf(decl_32, type, setunion: $i > $i).
% 4.65/0.99 thf(decl_33, type, setunionAx: $o).
% 4.65/0.99 thf(decl_34, type, omega: $i).
% 4.65/0.99 thf(decl_35, type, omega0Ax: $o).
% 4.65/0.99 thf(decl_36, type, omegaSAx: $o).
% 4.65/0.99 thf(decl_37, type, omegaIndAx: $o).
% 4.65/0.99 thf(decl_38, type, replAx: $o).
% 4.65/0.99 thf(decl_39, type, foundationAx: $o).
% 4.65/0.99 thf(decl_40, type, wellorderingAx: $o).
% 4.65/0.99 thf(decl_41, type, descr: ($i > $o) > $i).
% 4.65/0.99 thf(decl_42, type, descrp: $o).
% 4.65/0.99 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 4.65/0.99 thf(decl_44, type, dsetconstrI: $o).
% 4.65/0.99 thf(decl_45, type, dsetconstrEL: $o).
% 4.65/0.99 thf(decl_46, type, dsetconstrER: $o).
% 4.65/0.99 thf(decl_47, type, exuE1: $o).
% 4.65/0.99 thf(decl_48, type, prop2set: $o > $i).
% 4.65/0.99 thf(decl_49, type, prop2setE: $o).
% 4.65/0.99 thf(decl_50, type, emptysetE: $o).
% 4.65/0.99 thf(decl_51, type, emptysetimpfalse: $o).
% 4.65/0.99 thf(decl_52, type, notinemptyset: $o).
% 4.65/0.99 thf(decl_53, type, exuE3e: $o).
% 4.65/0.99 thf(decl_54, type, setext: $o).
% 4.65/0.99 thf(decl_55, type, emptyI: $o).
% 4.65/0.99 thf(decl_56, type, noeltsimpempty: $o).
% 4.65/0.99 thf(decl_57, type, setbeta: $o).
% 4.65/0.99 thf(decl_58, type, nonempty: $i > $o).
% 4.65/0.99 thf(decl_59, type, nonemptyE1: $o).
% 4.65/0.99 thf(decl_60, type, nonemptyI: $o).
% 4.65/0.99 thf(decl_61, type, nonemptyI1: $o).
% 4.65/0.99 thf(decl_62, type, setadjoinIL: $o).
% 4.65/0.99 thf(decl_63, type, emptyinunitempty: $o).
% 4.65/0.99 thf(decl_64, type, setadjoinIR: $o).
% 4.65/0.99 thf(decl_65, type, setadjoinE: $o).
% 4.65/0.99 thf(decl_66, type, setadjoinOr: $o).
% 4.65/0.99 thf(decl_67, type, setoftrueEq: $o).
% 4.65/0.99 thf(decl_68, type, powersetI: $o).
% 4.65/0.99 thf(decl_69, type, emptyinPowerset: $o).
% 4.65/0.99 thf(decl_70, type, emptyInPowerset: $o).
% 4.65/0.99 thf(decl_71, type, powersetE: $o).
% 4.65/0.99 thf(decl_72, type, setunionI: $o).
% 4.65/0.99 thf(decl_73, type, setunionE: $o).
% 4.65/0.99 thf(decl_74, type, subPowSU: $o).
% 4.65/0.99 thf(decl_75, type, exuE2: $o).
% 4.65/0.99 thf(decl_76, type, nonemptyImpWitness: $o).
% 4.65/0.99 thf(decl_77, type, uniqinunit: $o).
% 4.65/0.99 thf(decl_78, type, notinsingleton: $o).
% 4.65/0.99 thf(decl_79, type, eqinunit: $o).
% 4.65/0.99 thf(decl_80, type, singletonsswitch: $o).
% 4.65/0.99 thf(decl_81, type, upairsetE: $o).
% 4.65/0.99 thf(decl_82, type, upairsetIL: $o).
% 4.65/0.99 thf(decl_83, type, upairsetIR: $o).
% 4.65/0.99 thf(decl_84, type, emptyE1: $o).
% 4.65/0.99 thf(decl_85, type, vacuousDall: $o).
% 4.65/0.99 thf(decl_86, type, quantDeMorgan1: $o).
% 4.65/0.99 thf(decl_87, type, quantDeMorgan2: $o).
% 4.65/0.99 thf(decl_88, type, quantDeMorgan3: $o).
% 4.65/0.99 thf(decl_89, type, quantDeMorgan4: $o).
% 4.65/0.99 thf(decl_90, type, prop2setI: $o).
% 4.65/0.99 thf(decl_92, type, prop2set2propI: $o).
% 4.65/0.99 thf(decl_93, type, notdexE: $o).
% 4.65/0.99 thf(decl_94, type, notdallE: $o).
% 4.65/0.99 thf(decl_95, type, exuI1: $o).
% 4.65/0.99 thf(decl_96, type, exuI3: $o).
% 4.65/0.99 thf(decl_97, type, exuI2: $o).
% 4.65/0.99 thf(decl_98, type, inCongP: $o).
% 4.65/0.99 thf(decl_99, type, in__Cong: $o).
% 4.65/0.99 thf(decl_100, type, exuE3u: $o).
% 4.65/0.99 thf(decl_101, type, exu__Cong: $o).
% 4.65/0.99 thf(decl_102, type, emptyset__Cong: $o).
% 4.65/0.99 thf(decl_103, type, setadjoin__Cong: $o).
% 4.65/0.99 thf(decl_104, type, powerset__Cong: $o).
% 4.65/0.99 thf(decl_105, type, setunion__Cong: $o).
% 4.65/0.99 thf(decl_106, type, omega__Cong: $o).
% 4.65/0.99 thf(decl_107, type, exuEu: $o).
% 4.65/0.99 thf(decl_108, type, descr__Cong: $o).
% 4.65/0.99 thf(decl_109, type, dsetconstr__Cong: $o).
% 4.65/0.99 thf(decl_110, type, subset: $i > $i > $o).
% 4.65/0.99 thf(decl_113, type, subsetI1: $o).
% 4.65/0.99 thf(decl_114, type, eqimpsubset2: $o).
% 4.65/0.99 thf(decl_115, type, eqimpsubset1: $o).
% 4.65/0.99 thf(decl_116, type, subsetI2: $o).
% 4.65/0.99 thf(decl_117, type, emptysetsubset: $o).
% 4.65/0.99 thf(decl_118, type, subsetE: $o).
% 4.65/0.99 thf(decl_119, type, subsetE2: $o).
% 4.65/0.99 thf(decl_120, type, notsubsetI: $o).
% 4.65/0.99 thf(decl_121, type, notequalI1: $o).
% 4.65/0.99 thf(decl_122, type, notequalI2: $o).
% 4.65/0.99 thf(decl_123, type, subsetRefl: $o).
% 4.65/0.99 thf(decl_124, type, subsetTrans: $o).
% 4.65/0.99 thf(decl_125, type, setadjoinSub: $o).
% 4.65/0.99 thf(decl_126, type, setadjoinSub2: $o).
% 4.65/0.99 thf(decl_127, type, subset2powerset: $o).
% 4.65/0.99 thf(decl_128, type, setextsub: $o).
% 4.65/0.99 thf(decl_129, type, subsetemptysetimpeq: $o).
% 4.65/0.99 thf(decl_130, type, powersetI1: $o).
% 4.65/0.99 thf(decl_131, type, powersetE1: $o).
% 4.65/0.99 thf(decl_132, type, inPowerset: $o).
% 4.65/0.99 thf(decl_133, type, powersetsubset: $o).
% 4.65/0.99 thf(decl_134, type, sepInPowerset: $o).
% 4.65/0.99 thf(decl_135, type, sepSubset: $o).
% 4.65/0.99 thf(decl_136, type, binunion: $i > $i > $i).
% 4.65/0.99 thf(decl_137, type, binunionIL: $o).
% 4.65/0.99 thf(decl_138, type, upairset2IR: $o).
% 4.65/0.99 thf(decl_139, type, binunionIR: $o).
% 4.65/0.99 thf(decl_140, type, binunionEcases: $o).
% 4.65/0.99 thf(decl_141, type, binunionE: $o).
% 4.65/0.99 thf(decl_142, type, binunionLsub: $o).
% 4.65/0.99 thf(decl_143, type, binunionRsub: $o).
% 4.65/0.99 thf(decl_144, type, binintersect: $i > $i > $i).
% 4.65/0.99 thf(decl_145, type, binintersectI: $o).
% 4.65/0.99 thf(decl_146, type, binintersectSubset5: $o).
% 4.65/0.99 thf(decl_147, type, binintersectEL: $o).
% 4.65/0.99 thf(decl_148, type, binintersectLsub: $o).
% 4.65/0.99 thf(decl_149, type, binintersectSubset2: $o).
% 4.65/0.99 thf(decl_150, type, binintersectSubset3: $o).
% 4.65/0.99 thf(decl_151, type, binintersectER: $o).
% 4.65/0.99 thf(decl_152, type, disjointsetsI1: $o).
% 4.65/0.99 thf(decl_153, type, binintersectRsub: $o).
% 4.65/0.99 thf(decl_154, type, binintersectSubset4: $o).
% 4.65/0.99 thf(decl_155, type, binintersectSubset1: $o).
% 4.65/0.99 thf(decl_156, type, bs114d: $o).
% 4.65/0.99 thf(decl_158, type, setminus: $i > $i > $i).
% 4.65/0.99 thf(decl_159, type, setminusI: $o).
% 4.65/0.99 thf(decl_160, type, setminusEL: $o).
% 4.65/0.99 thf(decl_161, type, setminusER: $o).
% 4.65/0.99 thf(decl_162, type, setminusSubset2: $o).
% 4.65/0.99 thf(decl_163, type, setminusERneg: $o).
% 4.65/0.99 thf(decl_164, type, setminusELneg: $o).
% 4.65/0.99 thf(decl_165, type, setminusILneg: $o).
% 4.65/0.99 thf(decl_166, type, setminusIRneg: $o).
% 4.65/0.99 thf(decl_167, type, setminusLsub: $o).
% 4.65/0.99 thf(decl_168, type, setminusSubset1: $o).
% 4.65/0.99 thf(decl_169, type, symdiff: $i > $i > $i).
% 4.65/0.99 thf(decl_170, type, symdiffE: $o).
% 4.65/0.99 thf(decl_171, type, symdiffI1: $o).
% 4.65/0.99 thf(decl_172, type, symdiffI2: $o).
% 4.65/0.99 thf(decl_173, type, symdiffIneg1: $o).
% 4.65/0.99 thf(decl_174, type, symdiffIneg2: $o).
% 4.65/0.99 thf(decl_175, type, iskpair: $i > $o).
% 4.65/0.99 thf(decl_176, type, secondinupair: $o).
% 4.65/0.99 thf(decl_177, type, setukpairIL: $o).
% 4.65/0.99 thf(decl_178, type, setukpairIR: $o).
% 4.65/0.99 thf(decl_179, type, kpairiskpair: $o).
% 4.65/0.99 thf(decl_180, type, kpair: $i > $i > $i).
% 4.65/0.99 thf(decl_181, type, kpairp: $o).
% 4.65/0.99 thf(decl_182, type, cartprod: $i > $i > $i).
% 4.65/0.99 thf(decl_183, type, singletonsubset: $o).
% 4.65/0.99 thf(decl_184, type, singletoninpowerset: $o).
% 4.65/0.99 thf(decl_185, type, singletoninpowunion: $o).
% 4.65/0.99 thf(decl_186, type, upairset2E: $o).
% 4.65/0.99 thf(decl_187, type, upairsubunion: $o).
% 4.65/0.99 thf(decl_188, type, upairinpowunion: $o).
% 4.65/0.99 thf(decl_189, type, ubforcartprodlem1: $o).
% 4.65/0.99 thf(decl_190, type, ubforcartprodlem2: $o).
% 4.65/0.99 thf(decl_191, type, ubforcartprodlem3: $o).
% 4.65/0.99 thf(decl_192, type, cartprodpairin: $o).
% 4.65/0.99 thf(decl_193, type, cartprodmempair1: $o).
% 4.65/0.99 thf(decl_194, type, cartprodmempair: $o).
% 4.65/0.99 thf(decl_195, type, setunionE2: $o).
% 4.65/0.99 thf(decl_196, type, setunionsingleton1: $o).
% 4.65/0.99 thf(decl_197, type, setunionsingleton2: $o).
% 4.65/0.99 thf(decl_198, type, setunionsingleton: $o).
% 4.65/0.99 thf(decl_199, type, singleton: $i > $o).
% 4.65/0.99 thf(decl_200, type, singletonprop: $o).
% 4.65/0.99 thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 4.65/0.99 thf(decl_202, type, ex1E1: $o).
% 4.65/0.99 thf(decl_203, type, ex1I: $o).
% 4.65/0.99 thf(decl_204, type, ex1I2: $o).
% 4.65/0.99 thf(decl_205, type, singletonsuniq: $o).
% 4.65/0.99 thf(decl_210, type, setukpairinjL1: $o).
% 4.65/0.99 thf(decl_211, type, kfstsingleton: $o).
% 4.65/0.99 thf(decl_212, type, theprop: $o).
% 4.65/0.99 thf(decl_213, type, kfst: $i > $i).
% 4.65/0.99 thf(decl_214, type, kfstpairEq: $o).
% 4.65/0.99 thf(decl_215, type, cartprodfstin: $o).
% 4.65/0.99 thf(decl_216, type, setukpairinjL2: $o).
% 4.65/0.99 thf(decl_217, type, setukpairinjL: $o).
% 4.65/0.99 thf(decl_218, type, setukpairinjR11: $o).
% 4.65/0.99 thf(decl_219, type, setukpairinjR12: $o).
% 4.65/0.99 thf(decl_220, type, setukpairinjR1: $o).
% 4.65/0.99 thf(decl_221, type, upairequniteq: $o).
% 4.65/0.99 thf(decl_222, type, setukpairinjR2: $o).
% 4.65/0.99 thf(decl_223, type, setukpairinjR: $o).
% 4.65/0.99 thf(decl_224, type, ksndsingleton: $o).
% 4.65/0.99 thf(decl_225, type, ksnd: $i > $i).
% 4.65/0.99 thf(decl_226, type, ksndpairEq: $o).
% 4.65/0.99 thf(decl_227, type, kpairsurjEq: $o).
% 4.65/0.99 thf(decl_228, type, cartprodsndin: $o).
% 4.65/0.99 thf(decl_229, type, cartprodpairmemEL: $o).
% 4.65/0.99 thf(decl_230, type, cartprodpairmemER: $o).
% 4.65/0.99 thf(decl_231, type, cartprodmempaircEq: $o).
% 4.65/0.99 thf(decl_232, type, cartprodfstpairEq: $o).
% 4.65/0.99 thf(decl_233, type, cartprodsndpairEq: $o).
% 4.65/0.99 thf(decl_234, type, cartprodpairsurjEq: $o).
% 4.65/0.99 thf(decl_235, type, breln: $i > $i > $i > $o).
% 4.65/0.99 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 4.65/0.99 thf(decl_237, type, dpsetconstrI: $o).
% 4.65/0.99 thf(decl_238, type, dpsetconstrSub: $o).
% 4.65/0.99 thf(decl_239, type, setOfPairsIsBReln: $o).
% 4.65/0.99 thf(decl_240, type, dpsetconstrERa: $o).
% 4.65/0.99 thf(decl_241, type, dpsetconstrEL1: $o).
% 4.65/0.99 thf(decl_242, type, dpsetconstrEL2: $o).
% 4.65/0.99 thf(decl_243, type, dpsetconstrER: $o).
% 4.65/0.99 thf(decl_244, type, func: $i > $i > $i > $o).
% 4.65/0.99 thf(decl_245, type, funcSet: $i > $i > $i).
% 4.65/0.99 thf(decl_246, type, funcImageSingleton: $o).
% 4.65/0.99 thf(decl_247, type, apProp: $o).
% 4.65/0.99 thf(decl_248, type, ap: $i > $i > $i > $i > $i).
% 4.65/0.99 thf(decl_249, type, app: $o).
% 4.65/0.99 thf(decl_250, type, infuncsetfunc: $o).
% 4.65/0.99 thf(decl_251, type, ap2p: $o).
% 4.65/0.99 thf(decl_252, type, funcinfuncset: $o).
% 4.65/0.99 thf(decl_253, type, lamProp: $o).
% 4.65/0.99 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
% 4.65/0.99 thf(decl_255, type, lamp: $o).
% 4.65/0.99 thf(decl_256, type, lam2p: $o).
% 4.65/0.99 thf(decl_257, type, brelnall1: $o).
% 4.65/0.99 thf(decl_258, type, brelnall2: $o).
% 4.65/0.99 thf(decl_259, type, ex1E2: $o).
% 4.65/0.99 thf(decl_260, type, funcGraphProp1: $o).
% 4.65/0.99 thf(decl_261, type, funcGraphProp3: $o).
% 4.65/0.99 thf(decl_262, type, funcGraphProp2: $o).
% 4.65/0.99 thf(decl_263, type, funcextLem: $o).
% 4.65/0.99 thf(decl_264, type, funcGraphProp4: $o).
% 4.65/0.99 thf(decl_265, type, subbreln: $o).
% 4.65/0.99 thf(decl_266, type, eqbreln: $o).
% 4.65/0.99 thf(decl_267, type, funcext: $o).
% 4.65/0.99 thf(decl_268, type, funcext2: $o).
% 4.65/0.99 thf(decl_269, type, ap2apEq1: $o).
% 4.65/0.99 thf(decl_270, type, ap2apEq2: $o).
% 4.65/0.99 thf(decl_271, type, beta1: $o).
% 4.65/0.99 thf(decl_272, type, eta1: $o).
% 4.65/0.99 thf(decl_273, type, lam2lamEq: $o).
% 4.65/0.99 thf(decl_274, type, beta2: $o).
% 4.65/0.99 thf(decl_275, type, eta2: $o).
% 4.65/0.99 thf(decl_276, type, iffalseProp1: $o).
% 4.65/0.99 thf(decl_277, type, iffalseProp2: $o).
% 4.65/0.99 thf(decl_278, type, iftrueProp1: $o).
% 4.65/0.99 thf(decl_279, type, iftrueProp2: $o).
% 4.65/0.99 thf(decl_280, type, ifSingleton: $o).
% 4.65/0.99 thf(decl_281, type, if: $i > $o > $i > $i > $i).
% 4.65/0.99 thf(decl_282, type, ifp: $o).
% 4.65/0.99 thf(decl_283, type, theeq: $o).
% 4.65/0.99 thf(decl_284, type, iftrue: $o).
% 4.65/0.99 thf(decl_285, type, iffalse: $o).
% 4.65/0.99 thf(decl_286, type, epred1_0: $o).
% 4.65/0.99 thf(decl_287, type, esk1_2: $i > $i > $i).
% 4.65/0.99 thf(decl_288, type, esk2_2: $i > $i > $i).
% 4.65/0.99 thf(decl_289, type, esk3_2: $i > $i > $i).
% 4.65/0.99 thf(decl_290, type, esk4_1: $i > $i).
% 4.65/0.99 thf(decl_291, type, esk5_2: ($i > $i > $o) > $i > $i).
% 4.65/0.99 thf(decl_292, type, esk6_2: ($i > $i > $o) > $i > $i).
% 4.65/0.99 thf(decl_293, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
% 4.65/0.99 thf(decl_294, type, esk8_1: $i > $i).
% 4.65/0.99 thf(decl_295, type, esk9_1: ($i > $o) > $i).
% 4.65/0.99 thf(decl_296, type, esk10_1: ($i > $o) > $i).
% 4.65/0.99 thf(decl_297, type, esk11_2: $i > $i > $i).
% 4.65/0.99 thf(decl_298, type, esk12_2: $i > $i > $i).
% 4.65/0.99 thf(decl_299, type, esk13_1: $i > $i).
% 4.65/0.99 thf(decl_300, type, esk14_1: $i > $i).
% 4.65/0.99 thf(decl_301, type, esk15_1: $i > $i).
% 4.65/0.99 thf(decl_302, type, esk16_2: $i > $i > $i).
% 4.65/0.99 thf(decl_303, type, esk17_3: $i > $i > $o > $i).
% 4.65/0.99 thf(decl_304, type, esk18_1: ($i > $o) > $i).
% 4.65/0.99 thf(decl_305, type, esk19_1: $i > $i).
% 4.65/0.99 thf(decl_306, type, esk20_2: $i > ($i > $o) > $i).
% 4.65/0.99 thf(decl_307, type, esk21_2: $i > ($i > $o) > $i).
% 4.65/0.99 thf(decl_308, type, esk22_2: $i > ($i > $o) > $i).
% 4.65/0.99 thf(decl_309, type, esk23_2: $i > ($i > $o) > $i).
% 4.65/0.99 thf(decl_310, type, esk24_2: $i > ($i > $o) > $i).
% 4.65/0.99 thf(decl_311, type, esk25_2: $i > ($i > $o) > $i).
% 4.65/0.99 thf(decl_312, type, esk26_2: ($i > $o) > $i > $i).
% 4.65/0.99 thf(decl_313, type, esk27_1: ($i > $o) > $i).
% 4.65/0.99 thf(decl_314, type, esk28_1: ($i > $o) > $i).
% 4.65/0.99 thf(decl_315, type, esk29_2: ($i > $o) > $i > $i).
% 4.65/0.99 thf(decl_316, type, esk30_2: ($i > $o) > ($i > $o) > $i).
% 4.65/0.99 thf(decl_317, type, esk31_2: ($i > $o) > ($i > $o) > $i).
% 4.65/0.99 thf(decl_318, type, esk32_2: ($i > $o) > ($i > $o) > $i).
% 4.65/0.99 thf(decl_319, type, esk33_2: ($i > $o) > ($i > $o) > $i).
% 4.65/0.99 thf(decl_320, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 4.65/0.99 thf(decl_321, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 4.65/0.99 thf(decl_322, type, esk36_2: $i > $i > $i).
% 4.65/0.99 thf(decl_323, type, esk37_2: $i > $i > $i).
% 4.65/0.99 thf(decl_324, type, esk38_2: $i > $i > $i).
% 4.65/0.99 thf(decl_325, type, esk39_3: $i > $i > $i > $i).
% 4.65/0.99 thf(decl_326, type, esk40_3: $i > $i > $i > $i).
% 4.65/0.99 thf(decl_327, type, esk41_2: $i > $i > $i).
% 4.65/0.99 thf(decl_328, type, esk42_2: $i > ($i > $o) > $i).
% 4.65/0.99 thf(decl_329, type, esk43_2: $i > ($i > $o) > $i).
% 4.65/0.99 thf(decl_330, type, esk44_2: $i > ($i > $o) > $i).
% 4.65/0.99 thf(decl_331, type, esk45_3: $i > ($i > $o) > $i > $i).
% 4.65/0.99 thf(decl_332, type, esk46_2: $i > ($i > $o) > $i).
% 4.65/0.99 thf(decl_333, type, esk47_2: $i > ($i > $o) > $i).
% 4.65/0.99 thf(decl_334, type, esk48_3: $i > $i > ($i > $i) > $i).
% 4.65/0.99 thf(decl_335, type, esk49_3: $i > $i > ($i > $i) > $i).
% 4.65/0.99 thf(decl_336, type, esk50_3: $i > $i > ($i > $i) > $i).
% 4.65/0.99 thf(decl_337, type, esk51_4: $i > $i > $i > ($i > $o) > $i).
% 4.65/0.99 thf(decl_338, type, esk52_4: $i > $i > $i > ($i > $o) > $i).
% 4.65/0.99 thf(decl_339, type, esk53_4: $i > $i > $i > ($i > $o) > $i).
% 4.65/0.99 thf(decl_340, type, esk54_4: $i > $i > $i > ($i > $o) > $i).
% 4.65/0.99 thf(decl_341, type, esk55_4: $i > $i > $i > $i > $i).
% 4.65/0.99 thf(decl_342, type, esk56_4: $i > $i > $i > $i > $i).
% 4.65/0.99 thf(decl_343, type, esk57_4: $i > $i > $i > $i > $i).
% 4.65/0.99 thf(decl_344, type, esk58_4: $i > $i > $i > $i > $i).
% 4.65/0.99 thf(decl_345, type, esk59_4: $i > $i > $i > $i > $i).
% 4.65/0.99 thf(decl_346, type, esk60_4: $i > $i > $i > $i > $i).
% 4.65/0.99 thf(decl_347, type, esk61_4: $i > $i > $i > $i > $i).
% 4.65/0.99 thf(decl_348, type, esk62_4: $i > $i > $i > $i > $i).
% 4.65/0.99 thf(decl_349, type, esk63_4: $i > $i > $i > $i > $i).
% 4.65/0.99 thf(decl_350, type, esk64_3: $i > $i > ($i > $i) > $i).
% 4.65/0.99 thf(decl_351, type, esk65_3: $i > $i > ($i > $i) > $i).
% 4.65/0.99 thf(decl_352, type, esk66_3: $i > $i > ($i > $i) > $i).
% 4.65/0.99 thf(decl_353, type, esk67_0: $i).
% 4.65/0.99 thf(decl_354, type, epred2_0: $o).
% 4.65/0.99 thf(decl_355, type, esk68_0: $i).
% 4.65/0.99 thf(decl_356, type, esk69_0: $i).
% 4.65/0.99 thf(iftrueorfalse, 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)=>((theeq)=>((iftrue)=>((iffalse)=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', iftrueorfalse)).
% 4.65/0.99 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', dpsetconstrI)).
% 4.65/0.99 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', dpsetconstrSub)).
% 4.65/0.99 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', setOfPairsIsBReln)).
% 4.65/0.99 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', dpsetconstrERa)).
% 4.65/0.99 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', dpsetconstrEL1)).
% 4.65/0.99 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', dpsetconstrEL2)).
% 4.65/0.99 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', dpsetconstrER)).
% 4.65/0.99 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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.ulj0i2I61i/E---3.1_2918013.p', funcImageSingleton)).
% 4.65/0.99 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', apProp)).
% 4.65/0.99 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', exuE2)).
% 4.65/0.99 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.ulj0i2I61i/E---3.1_2918013.p', lamProp)).
% 4.65/0.99 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:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', lamp)).
% 4.65/0.99 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', lam2p)).
% 4.65/0.99 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$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.ulj0i2I61i/E---3.1_2918013.p', ex1E2)).
% 4.65/0.99 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.ulj0i2I61i/E---3.1_2918013.p', emptyE1)).
% 4.65/0.99 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.ulj0i2I61i/E---3.1_2918013.p', beta1)).
% 4.65/0.99 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.ulj0i2I61i/E---3.1_2918013.p', eta1)).
% 4.65/0.99 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.ulj0i2I61i/E---3.1_2918013.p', lam2lamEq)).
% 4.65/0.99 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.ulj0i2I61i/E---3.1_2918013.p', beta2)).
% 4.65/0.99 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.ulj0i2I61i/E---3.1_2918013.p', eta2)).
% 4.65/0.99 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X39))&(((X14)=(X2)))))|(((~((X39)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', iffalseProp1)).
% 4.65/0.99 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$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.ulj0i2I61i/E---3.1_2918013.p', iffalseProp2)).
% 4.65/0.99 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X41))&(((X14)=(X2)))))|(((~((X41)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', iftrueProp1)).
% 4.65/0.99 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$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.ulj0i2I61i/E---3.1_2918013.p', iftrueProp2)).
% 4.65/0.99 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X43))&(((X14)=(X2)))))|(((~((X43)))&(((X14)=(X3))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', ifSingleton)).
% 4.65/0.99 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', exuI2)).
% 4.65/0.99 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', exuI3)).
% 4.65/0.99 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', exuI1)).
% 4.65/0.99 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', exu__Cong)).
% 4.65/0.99 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', exuE3u)).
% 4.65/0.99 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', dsetconstr__Cong)).
% 4.65/0.99 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', descr__Cong)).
% 4.65/0.99 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', exuEu)).
% 4.65/0.99 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', sepSubset)).
% 4.65/0.99 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', sepInPowerset)).
% 4.65/0.99 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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', ex1I2)).
% 4.65/0.99 thf(ex1I, axiom, ((ex1I)<=>![X4:$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.ulj0i2I61i/E---3.1_2918013.p', ex1I)).
% 4.65/0.99 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', ex1E1)).
% 4.65/0.99 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', singletonprop)).
% 4.65/0.99 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', kfstsingleton)).
% 4.65/0.99 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', ksndsingleton)).
% 4.65/0.99 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', setoftrueEq)).
% 4.65/0.99 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', nonemptyI)).
% 4.65/0.99 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', setbeta)).
% 4.65/0.99 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', exuE3e)).
% 4.65/0.99 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', exuE1)).
% 4.65/0.99 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', dsetconstrER)).
% 4.65/0.99 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', dsetconstrEL)).
% 4.65/0.99 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', dsetconstrI)).
% 4.65/0.99 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', descrp)).
% 4.65/0.99 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', replAx)).
% 4.65/0.99 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', cartprodpairsurjEq)).
% 4.65/0.99 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', eqinunit)).
% 4.65/0.99 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', notinsingleton)).
% 4.65/0.99 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', uniqinunit)).
% 4.65/0.99 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', nonemptyImpWitness)).
% 4.65/0.99 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', app)).
% 4.65/0.99 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', infuncsetfunc)).
% 4.65/0.99 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', subPowSU)).
% 4.65/0.99 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.ulj0i2I61i/E---3.1_2918013.p', ap2p)).
% 4.65/0.99 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.ulj0i2I61i/E---3.1_2918013.p', setunionE)).
% 4.65/0.99 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', funcinfuncset)).
% 4.65/0.99 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', singletonsswitch)).
% 4.65/0.99 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$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.ulj0i2I61i/E---3.1_2918013.p', brelnall1)).
% 4.65/0.99 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.ulj0i2I61i/E---3.1_2918013.p', brelnall2)).
% 4.65/0.99 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.ulj0i2I61i/E---3.1_2918013.p', funcGraphProp1)).
% 4.65/0.99 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.ulj0i2I61i/E---3.1_2918013.p', funcGraphProp3)).
% 4.65/0.99 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', funcGraphProp2)).
% 4.65/0.99 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$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.ulj0i2I61i/E---3.1_2918013.p', funcextLem)).
% 4.65/0.99 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', funcGraphProp4)).
% 4.65/0.99 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', subbreln)).
% 4.65/0.99 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', eqbreln)).
% 4.65/0.99 thf(funcext, axiom, ((funcext)<=>![X4:$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.ulj0i2I61i/E---3.1_2918013.p', funcext)).
% 4.65/0.99 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', quantDeMorgan2)).
% 4.65/0.99 thf(funcext2, axiom, ((funcext2)<=>![X4:$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.ulj0i2I61i/E---3.1_2918013.p', funcext2)).
% 4.65/0.99 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', quantDeMorgan1)).
% 4.65/0.99 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', ap2apEq1)).
% 4.65/0.99 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', vacuousDall)).
% 4.65/0.99 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.ulj0i2I61i/E---3.1_2918013.p', ap2apEq2)).
% 4.65/0.99 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', upairsetIR)).
% 4.65/0.99 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', upairsetIL)).
% 4.65/0.99 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', upairsetE)).
% 4.65/0.99 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', quantDeMorgan3)).
% 4.65/0.99 thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', ifp)).
% 4.65/0.99 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', theeq)).
% 4.65/0.99 thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', iftrue)).
% 4.65/0.99 thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', iffalse)).
% 4.65/0.99 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', notdallE)).
% 4.65/0.99 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', notdexE)).
% 4.65/0.99 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', prop2setI)).
% 4.65/0.99 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', quantDeMorgan4)).
% 4.65/0.99 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', inCongP)).
% 4.65/0.99 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', setunion__Cong)).
% 4.65/0.99 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', powerset__Cong)).
% 4.65/0.99 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', setadjoin__Cong)).
% 4.65/0.99 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', emptyset__Cong)).
% 4.65/0.99 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', in__Cong)).
% 4.65/0.99 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', omega__Cong)).
% 4.65/0.99 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', subsetI2)).
% 4.65/0.99 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', eqimpsubset1)).
% 4.65/0.99 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', eqimpsubset2)).
% 4.65/0.99 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', subsetI1)).
% 4.65/0.99 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', emptysetsubset)).
% 4.65/0.99 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', subsetTrans)).
% 4.65/0.99 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', subsetRefl)).
% 4.65/0.99 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', notequalI2)).
% 4.65/0.99 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', notequalI1)).
% 4.65/0.99 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', notsubsetI)).
% 4.65/0.99 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', subsetE2)).
% 4.65/0.99 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', subsetE)).
% 4.65/0.99 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', setadjoinSub)).
% 4.65/0.99 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', inPowerset)).
% 4.65/0.99 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', powersetE1)).
% 4.65/0.99 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', powersetI1)).
% 4.65/0.99 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', subsetemptysetimpeq)).
% 4.65/0.99 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', setextsub)).
% 4.65/0.99 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', subset2powerset)).
% 4.65/0.99 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', setadjoinSub2)).
% 4.65/0.99 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', powersetsubset)).
% 4.65/0.99 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', binunionE)).
% 4.65/0.99 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.ulj0i2I61i/E---3.1_2918013.p', binunionEcases)).
% 4.65/0.99 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', binunionIR)).
% 4.65/0.99 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', upairset2IR)).
% 4.65/0.99 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', binunionIL)).
% 4.65/0.99 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', binunionLsub)).
% 4.65/0.99 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', binintersectSubset3)).
% 4.65/0.99 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', binintersectSubset2)).
% 4.65/0.99 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', binintersectLsub)).
% 4.65/0.99 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', binintersectEL)).
% 4.65/0.99 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', binintersectSubset5)).
% 4.65/0.99 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', binintersectI)).
% 4.65/0.99 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', binunionRsub)).
% 4.65/0.99 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', binintersectER)).
% 4.65/0.99 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', setminusEL)).
% 4.65/0.99 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', setminusI)).
% 4.65/0.99 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', bs114d)).
% 4.65/0.99 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', binintersectSubset1)).
% 4.65/0.99 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', binintersectSubset4)).
% 4.65/0.99 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', binintersectRsub)).
% 4.65/0.99 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', disjointsetsI1)).
% 4.65/0.99 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', setminusER)).
% 4.65/0.99 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', setminusSubset1)).
% 4.65/0.99 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', setminusLsub)).
% 4.65/0.99 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', setminusIRneg)).
% 4.65/0.99 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', setminusILneg)).
% 4.65/0.99 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', setminusELneg)).
% 4.65/0.99 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', setminusERneg)).
% 4.65/0.99 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', setminusSubset2)).
% 4.65/0.99 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', symdiffE)).
% 4.65/0.99 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', setukpairIR)).
% 4.65/0.99 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', setukpairIL)).
% 4.65/0.99 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', secondinupair)).
% 4.65/0.99 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', symdiffIneg2)).
% 4.65/0.99 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', symdiffIneg1)).
% 4.65/0.99 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', symdiffI2)).
% 4.65/0.99 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', symdiffI1)).
% 4.65/0.99 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', kpairiskpair)).
% 4.65/0.99 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', upairinpowunion)).
% 4.65/0.99 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', upairsubunion)).
% 4.65/0.99 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', upairset2E)).
% 4.65/0.99 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', singletoninpowunion)).
% 4.65/0.99 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', singletoninpowerset)).
% 4.65/0.99 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', singletonsubset)).
% 4.65/0.99 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', kpairp)).
% 4.65/0.99 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', ubforcartprodlem1)).
% 4.65/0.99 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', setunionsingleton1)).
% 4.65/0.99 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', setunionE2)).
% 4.65/0.99 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', cartprodmempair)).
% 4.65/0.99 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', cartprodmempair1)).
% 4.65/0.99 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', cartprodpairin)).
% 4.65/0.99 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', ubforcartprodlem3)).
% 4.65/0.99 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', ubforcartprodlem2)).
% 4.65/0.99 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', setunionsingleton2)).
% 4.65/0.99 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', setukpairinjL1)).
% 4.65/0.99 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', singletonsuniq)).
% 4.65/0.99 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', setunionsingleton)).
% 4.65/0.99 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.ulj0i2I61i/E---3.1_2918013.p', setukpairinjR12)).
% 4.65/0.99 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', setukpairinjR11)).
% 4.65/0.99 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.ulj0i2I61i/E---3.1_2918013.p', setukpairinjL)).
% 4.65/0.99 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.ulj0i2I61i/E---3.1_2918013.p', setukpairinjL2)).
% 4.65/0.99 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', cartprodfstin)).
% 4.65/0.99 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', kfstpairEq)).
% 4.65/0.99 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', theprop)).
% 4.65/0.99 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.ulj0i2I61i/E---3.1_2918013.p', setukpairinjR1)).
% 4.65/0.99 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', cartprodsndin)).
% 4.65/0.99 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', kpairsurjEq)).
% 4.65/0.99 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', ksndpairEq)).
% 4.65/0.99 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.ulj0i2I61i/E---3.1_2918013.p', setukpairinjR)).
% 4.65/0.99 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.ulj0i2I61i/E---3.1_2918013.p', setukpairinjR2)).
% 4.65/0.99 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', upairequniteq)).
% 4.65/0.99 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', cartprodpairmemER)).
% 4.65/0.99 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', cartprodmempaircEq)).
% 4.65/0.99 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', cartprodfstpairEq)).
% 4.65/0.99 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', cartprodsndpairEq)).
% 4.65/0.99 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', cartprodpairmemEL)).
% 4.65/0.99 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', setunionI)).
% 4.65/0.99 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', powersetE)).
% 4.65/0.99 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', emptyInPowerset)).
% 4.65/0.99 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', emptyinPowerset)).
% 4.65/0.99 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', powersetI)).
% 4.65/0.99 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', setadjoinOr)).
% 4.65/0.99 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', setadjoinE)).
% 4.65/0.99 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', setadjoinIR)).
% 4.65/0.99 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', emptyinunitempty)).
% 4.65/0.99 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', setadjoinIL)).
% 4.65/0.99 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', nonemptyI1)).
% 4.65/0.99 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', nonemptyE1)).
% 4.65/0.99 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', noeltsimpempty)).
% 4.65/0.99 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', emptyI)).
% 4.65/0.99 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.ulj0i2I61i/E---3.1_2918013.p', setext)).
% 4.65/0.99 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', notinemptyset)).
% 4.65/0.99 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', emptysetimpfalse)).
% 4.65/0.99 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', emptysetE)).
% 4.65/0.99 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', prop2setE)).
% 4.65/0.99 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.ulj0i2I61i/E---3.1_2918013.p', wellorderingAx)).
% 4.65/0.99 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.ulj0i2I61i/E---3.1_2918013.p', foundationAx)).
% 4.65/0.99 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', omegaIndAx)).
% 4.65/0.99 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', omegaSAx)).
% 4.65/0.99 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', omega0Ax)).
% 4.65/0.99 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', setunionAx)).
% 4.65/0.99 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', powersetAx)).
% 4.65/0.99 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', setadjoinAx)).
% 4.65/0.99 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', emptysetAx)).
% 4.65/0.99 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.ulj0i2I61i/E---3.1_2918013.p', setextAx)).
% 4.65/0.99 thf(c_0_225, 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)=>((theeq)=>((iftrue)=>((iffalse)=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[iftrueorfalse])).
% 4.65/0.99 thf(c_0_226, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 4.65/0.99 thf(c_0_227, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 4.65/0.99 thf(c_0_228, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 4.65/0.99 thf(c_0_229, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 4.65/0.99 thf(c_0_230, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 4.65/0.99 thf(c_0_231, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 4.65/0.99 thf(c_0_232, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 4.65/0.99 thf(c_0_233, plain, ((funcImageSingleton)<=>![X4:$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])).
% 4.65/0.99 thf(c_0_234, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
% 4.65/0.99 thf(c_0_235, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 4.65/0.99 thf(c_0_236, 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])).
% 4.65/0.99 thf(c_0_237, 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:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
% 4.65/0.99 thf(c_0_238, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
% 4.65/0.99 thf(c_0_239, plain, ((ex1E2)<=>![X4:$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])).
% 4.65/0.99 thf(c_0_240, 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])).
% 4.65/0.99 thf(c_0_241, 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])).
% 4.65/0.99 thf(c_0_242, 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])).
% 4.65/0.99 thf(c_0_243, 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])).
% 4.65/0.99 thf(c_0_244, 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])).
% 4.65/0.99 thf(c_0_245, 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])).
% 4.65/0.99 thf(c_0_246, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X39))&(((Z0)=(X2)))))|(((~((X39)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
% 4.65/0.99 thf(c_0_247, plain, ((iffalseProp2)<=>![X4:$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])).
% 4.65/0.99 thf(c_0_248, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X41))&(((Z0)=(X2)))))|(((~((X41)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
% 4.65/0.99 thf(c_0_249, plain, ((iftrueProp2)<=>![X4:$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])).
% 4.65/0.99 thf(c_0_250, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X43))&(((Z0)=(X2)))))|(((~((X43)))&(((Z0)=(X3))))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
% 4.65/0.99 thf(c_0_251, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 4.65/0.99 thf(c_0_252, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 4.65/0.99 thf(c_0_253, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 4.65/0.99 thf(c_0_254, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 4.65/0.99 thf(c_0_255, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 4.65/0.99 thf(c_0_256, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 4.65/0.99 thf(c_0_257, plain, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 4.65/0.99 thf(c_0_258, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 4.65/0.99 thf(c_0_259, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 4.65/0.99 thf(c_0_260, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 4.65/0.99 thf(c_0_261, 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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 4.65/0.99 thf(c_0_262, plain, ((ex1I)<=>![X4:$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])).
% 4.65/0.99 thf(c_0_263, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 4.65/0.99 thf(c_0_264, plain, ((singletonprop)<=>![X4:$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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 4.65/0.99 thf(c_0_265, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 4.65/0.99 thf(c_0_266, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 4.65/0.99 thf(c_0_267, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 4.65/0.99 thf(c_0_268, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 4.65/0.99 thf(c_0_269, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 4.65/0.99 thf(c_0_270, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 4.65/0.99 thf(c_0_271, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 4.65/0.99 thf(c_0_272, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 4.65/0.99 thf(c_0_273, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 4.65/0.99 thf(c_0_274, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 4.65/0.99 thf(c_0_275, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 4.65/0.99 thf(c_0_276, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 4.65/0.99 thf(c_0_277, plain, ((epred1_0)<=>![X770:$i]:(?[X771:$i]:((((![X772:$i]:(((in @ X772 @ X771)=>![X773:$i]:(((in @ X773 @ X772)=>(in @ X773 @ X770)))))&![X774:$i, X775:$i]:((((in @ X774 @ X770)&(in @ X775 @ X770))=>(![X776:$i]:(((in @ X776 @ X771)=>((in @ X774 @ X776)<=>(in @ X775 @ X776))))=>((X774)=(X775))))))&![X777:$i, X778:$i]:((((in @ X777 @ X771)&(in @ X778 @ X771))=>(![X779:$i]:(((in @ X779 @ X777)=>(in @ X779 @ X778)))|![X780:$i]:(((in @ X780 @ X778)=>(in @ X780 @ X777)))))))&![X781:$i]:(((![X782:$i]:(((in @ X782 @ X781)=>(in @ X782 @ X770)))&?[X783:$i]:((in @ X783 @ X781)))=>?[X784:$i, X785:$i]:(((((in @ X784 @ X771)&(in @ X785 @ X781))&~(?[X786:$i]:(((in @ X786 @ X784)&(in @ X786 @ X781)))))&![X787:$i]:(((in @ X787 @ X771)=>(![X788:$i]:(((in @ X788 @ X787)=>(in @ X788 @ X784)))|(in @ X785 @ X787)))))))))))), introduced(definition)).
% 4.65/0.99 thf(c_0_278, negated_conjecture, ~((![X743:$i, X744:$i]:((![X745:$i]:(((in @ X745 @ X743)<=>(in @ X745 @ X744)))=>((X743)=(X744))))=>(![X746:$i]:(~(in @ X746 @ emptyset))=>(![X747:$i, X748:$i, X749:$i]:(((in @ X749 @ (setadjoin @ X747 @ X748))<=>(((X749)=(X747))|(in @ X749 @ X748))))=>(![X750:$i, X751:$i]:(((in @ X751 @ (powerset @ X750))<=>![X752:$i]:(((in @ X752 @ X751)=>(in @ X752 @ X750)))))=>(![X753:$i, X754:$i]:(((in @ X754 @ (setunion @ X753))<=>?[X755:$i]:(((in @ X754 @ X755)&(in @ X755 @ X753)))))=>((in @ emptyset @ omega)=>(![X756:$i]:(((in @ X756 @ omega)=>(in @ (setadjoin @ X756 @ X756) @ omega)))=>(![X757:$i]:((((in @ emptyset @ X757)&![X758:$i]:((((in @ X758 @ omega)&(in @ X758 @ X757))=>(in @ (setadjoin @ X758 @ X758) @ X757))))=>![X759:$i]:(((in @ X759 @ omega)=>(in @ X759 @ X757)))))=>(![X760:$i > $i > $o, X761:$i]:((![X762:$i]:(((in @ X762 @ X761)=>(exu @ (X760 @ X762))))=>?[X763:$i]:(![X764:$i]:(((in @ X764 @ X763)<=>?[X765:$i]:(((in @ X765 @ X761)&(X760 @ X765 @ X764))))))))=>(![X766:$i]:((?[X767:$i]:((in @ X767 @ X766))=>?[X768:$i]:(((in @ X768 @ X766)&~(?[X769:$i]:(((in @ X769 @ X768)&(in @ X769 @ X766))))))))=>((epred1_0)=>(![X789:$i > $o]:(((exu @ X789)=>(X789 @ (descr @ (^[Z0:$i]:(X789 @ Z0))))))=>(![X790:$i, X791:$i > $o, X792:$i]:(((in @ X792 @ X790)=>((X791 @ X792)=>(in @ X792 @ (dsetconstr @ X790 @ X791)))))=>(![X793:$i, X794:$i > $o, X795:$i]:(((in @ X795 @ (dsetconstr @ X793 @ X794))=>(in @ X795 @ X793)))=>(![X796:$i, X797:$i > $o, X798:$i]:(((in @ X798 @ (dsetconstr @ X796 @ X797))=>(X797 @ X798)))=>(![X799:$i > $o]:(((exu @ X799)=>?[X800:$i]:(((X799 @ X800)&![X801:$i]:(((X799 @ X801)=>((X800)=(X801))))))))=>(![X802:$o, X803:$i]:(((in @ X803 @ (prop2set @ ((X802))))=>(X802)))=>(![X804:$i]:(((in @ X804 @ emptyset)=>![X805:$o]:((X805))))=>(![X806:$i]:(((in @ X806 @ emptyset)=>~($true)))=>(![X807:$i]:(~(in @ X807 @ emptyset))=>(![X808:$i > $o]:(((exu @ X808)=>?[X809:$i]:((X808 @ X809))))=>(![X810:$i, X811:$i]:((![X812:$i]:(((in @ X812 @ X810)=>(in @ X812 @ X811)))=>(![X813:$i]:(((in @ X813 @ X811)=>(in @ X813 @ X810)))=>((X810)=(X811)))))=>(![X814:$i]:((![X815:$i]:(~(in @ X815 @ X814))=>((X814)=(emptyset))))=>(![X816:$i]:((![X817:$i]:(~(in @ X817 @ X816))=>((X816)=(emptyset))))=>(![X818:$i, X819:$i > $o, X820:$i]:(((in @ X820 @ X818)=>((in @ X820 @ (dsetconstr @ X818 @ X819))<=>(X819 @ X820))))=>(![X821:$i]:(((nonempty @ X821)=>?[X822:$i]:((in @ X822 @ X821))))=>(![X823:$i, X824:$i > $o, X825:$i]:(((in @ X825 @ X823)=>((X824 @ X825)=>(nonempty @ (dsetconstr @ X823 @ X824)))))=>(![X826:$i]:((?[X827:$i]:((in @ X827 @ X826))=>(nonempty @ X826)))=>(![X828:$i, X829:$i]:((in @ X828 @ (setadjoin @ X828 @ X829)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X830:$i, X831:$i, X832:$i]:(((in @ X832 @ X831)=>(in @ X832 @ (setadjoin @ X830 @ X831))))=>(![X833:$i, X834:$i, X835:$i]:(((in @ X835 @ (setadjoin @ X833 @ X834))=>![X836:$o]:(((((X835)=(X833))=>(X836))=>(((in @ X835 @ X834)=>(X836))=>(X836))))))=>(![X837:$i, X838:$i, X839:$i]:(((in @ X839 @ (setadjoin @ X837 @ X838))=>(((X839)=(X837))|(in @ X839 @ X838))))=>(![X840:$i]:(((dsetconstr @ X840 @ (^[Z0:$i]:($true)))=(X840)))=>(![X841:$i, X842:$i]:((![X843:$i]:(((in @ X843 @ X842)=>(in @ X843 @ X841)))=>(in @ X842 @ (powerset @ X841))))=>(![X844:$i]:((in @ emptyset @ (powerset @ X844)))=>(![X845:$i]:((in @ emptyset @ (powerset @ X845)))=>(![X846:$i, X847:$i, X848:$i]:(((in @ X847 @ (powerset @ X846))=>((in @ X848 @ X847)=>(in @ X848 @ X846))))=>(![X849:$i, X850:$i, X851:$i]:(((in @ X850 @ X851)=>((in @ X851 @ X849)=>(in @ X850 @ (setunion @ X849)))))=>(![X852:$i, X853:$i]:(((in @ X853 @ (setunion @ X852))=>![X854:$o]:((![X855:$i]:(((in @ X853 @ X855)=>((in @ X855 @ X852)=>(X854))))=>(X854)))))=>(![X856:$i, X857:$i]:(((in @ X857 @ X856)=>(in @ X857 @ (powerset @ (setunion @ X856)))))=>(![X858:$i > $o]:(((exu @ X858)=>?[X859:$i]:(![X860:$i]:(((X858 @ X860)<=>((X860)=(X859)))))))=>(![X861:$i]:(((nonempty @ X861)=>?[X862:$i]:(((in @ X862 @ X861)&$true))))=>(![X863:$i, X864:$i]:(((in @ X863 @ (setadjoin @ X864 @ emptyset))=>((X863)=(X864))))=>(![X865:$i, X866:$i]:((((X865)!=(X866))=>~(in @ X866 @ (setadjoin @ X865 @ emptyset))))=>(![X867:$i, X868:$i]:((((X867)=(X868))=>(in @ X867 @ (setadjoin @ X868 @ emptyset))))=>(![X869:$i, X870:$i]:(((in @ X869 @ (setadjoin @ X870 @ emptyset))=>(in @ X870 @ (setadjoin @ X869 @ emptyset))))=>(![X871:$i, X872:$i, X873:$i]:(((in @ X873 @ (setadjoin @ X871 @ (setadjoin @ X872 @ emptyset)))=>(((X873)=(X871))|((X873)=(X872)))))=>(![X874:$i, X875:$i]:((in @ X874 @ (setadjoin @ X874 @ (setadjoin @ X875 @ emptyset))))=>(![X876:$i, X877:$i]:((in @ X877 @ (setadjoin @ X876 @ (setadjoin @ X877 @ emptyset))))=>(![X878:$i, X879:$i > $o]:((?[X880:$i]:(((in @ X880 @ X878)&(X879 @ X880)))=>(((dsetconstr @ X878 @ X879)=(emptyset))=>~($true))))=>(![X881:$i > $o, X882:$i]:(((in @ X882 @ emptyset)=>(X881 @ X882)))=>(![X883:$i, X884:$i > $o]:((~(![X885:$i]:(((in @ X885 @ 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X912))=>(![X913:$i, X914:$i]:(((X911 @ X913)=>((X911 @ X914)=>((X913)=(X914)))))=>(exu @ X911))))=>(![X915:$i > $o]:((?[X916:$i]:(![X917:$i]:(((X915 @ X917)<=>((X917)=(X916)))))=>(exu @ X915)))=>(![X918:$i, X919:$i]:((((X918)=(X919))=>![X920:$i, X921:$i]:((((X920)=(X921))=>((in @ X920 @ X918)=>(in @ X921 @ X919))))))=>(![X922:$i, X923:$i]:((((X922)=(X923))=>![X924:$i, X925:$i]:((((X924)=(X925))=>((in @ X924 @ X922)<=>(in @ X925 @ X923))))))=>(![X926:$i > $o]:(((exu @ X926)=>![X927:$i, X928:$i]:(((X926 @ X927)=>((X926 @ X928)=>((X927)=(X928)))))))=>(![X929:$i > $o, X930:$i > $o]:((![X931:$i, X932:$i]:((((X931)=(X932))=>((X929 @ X931)<=>(X930 @ X932))))=>((exu @ X929)<=>(exu @ X930))))=>(((emptyset)=(emptyset))=>(![X933:$i, X934:$i]:((((X933)=(X934))=>![X935:$i, X936:$i]:((((X935)=(X936))=>((setadjoin @ X933 @ X935)=(setadjoin @ X934 @ X936))))))=>(![X937:$i, X938:$i]:((((X937)=(X938))=>((powerset @ X937)=(powerset @ X938))))=>(![X939:$i, X940:$i]:((((X939)=(X940))=>((setunion @ 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c_0_226]), cartprodpairsurjEq]), c_0_227]), c_0_228]), c_0_229]), c_0_230]), c_0_231]), eqinunit]), c_0_232]), notinsingleton]), c_0_233]), uniqinunit]), c_0_234]), nonemptyImpWitness]), app]), c_0_235]), infuncsetfunc]), subPowSU]), ap2p]), setunionE]), funcinfuncset]), singletonsswitch]), c_0_236]), c_0_237]), c_0_238]), brelnall1]), brelnall2]), c_0_239]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), subbreln]), eqbreln]), funcext]), quantDeMorgan2]), funcext2]), quantDeMorgan1]), ap2apEq1]), vacuousDall]), ap2apEq2]), c_0_240]), c_0_241]), upairsetIR]), c_0_242]), upairsetIL]), c_0_243]), upairsetE]), c_0_244]), quantDeMorgan3]), c_0_245]), c_0_246]), c_0_247]), c_0_248]), c_0_249]), c_0_250]), ifp]), theeq]), iftrue]), iffalse]), c_0_251]), c_0_252]), c_0_253]), notdallE]), notdexE]), prop2setI]), quantDeMorgan4]), inCongP]), setunion__Cong]), powerset__Cong]), setadjoin__Cong]), emptyset__Cong]), c_0_254]), c_0_255]), in__Cong]), omega__Cong]), subsetI2]), eqimpsubset1]), eqimpsubset2]), subsetI1]), c_0_256]), c_0_257]), c_0_258]), emptysetsubset]), subsetTrans]), subsetRefl]), notequalI2]), notequalI1]), notsubsetI]), subsetE2]), subsetE]), setadjoinSub]), inPowerset]), powersetE1]), powersetI1]), subsetemptysetimpeq]), setextsub]), subset2powerset]), setadjoinSub2]), powersetsubset]), binunionE]), binunionEcases]), binunionIR]), upairset2IR]), binunionIL]), c_0_259]), c_0_260]), binunionLsub]), binintersectSubset3]), binintersectSubset2]), binintersectLsub]), binintersectEL]), binintersectSubset5]), binintersectI]), binunionRsub]), binintersectER]), setminusEL]), setminusI]), bs114d]), binintersectSubset1]), binintersectSubset4]), binintersectRsub]), disjointsetsI1]), setminusER]), setminusSubset1]), setminusLsub]), setminusIRneg]), setminusILneg]), setminusELneg]), setminusERneg]), setminusSubset2]), symdiffE]), setukpairIR]), setukpairIL]), secondinupair]), symdiffIneg2]), symdiffIneg1]), symdiffI2]), symdiffI1]), kpairiskpair]), upairinpowunion]), upairsubunion]), upairset2E]), singletoninpowunion]), singletoninpowerset]), singletonsubset]), kpairp]), ubforcartprodlem1]), setunionsingleton1]), setunionE2]), cartprodmempair]), cartprodmempair1]), cartprodpairin]), ubforcartprodlem3]), ubforcartprodlem2]), setunionsingleton2]), setukpairinjL1]), singletonsuniq]), c_0_261]), c_0_262]), c_0_263]), c_0_264]), setunionsingleton]), c_0_265]), setukpairinjR12]), setukpairinjR11]), setukpairinjL]), setukpairinjL2]), cartprodfstin]), kfstpairEq]), theprop]), setukpairinjR1]), cartprodsndin]), kpairsurjEq]), ksndpairEq]), c_0_266]), setukpairinjR]), setukpairinjR2]), upairequniteq]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairmemEL]), setunionI]), powersetE]), emptyInPowerset]), emptyinPowerset]), powersetI]), c_0_267]), setadjoinOr]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), nonemptyI1]), c_0_268]), nonemptyE1]), c_0_269]), noeltsimpempty]), emptyI]), setext]), c_0_270]), notinemptyset]), emptysetimpfalse]), emptysetE]), prop2setE]), c_0_271]), c_0_272]), c_0_273]), c_0_274]), c_0_275]), wellorderingAx]), foundationAx]), c_0_276]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_277])).
% 4.65/0.99 thf(c_0_279, negated_conjecture, ![X1434:$i, X1435:$i, X1437:$i, X1438:$i, X1439:$i, X1440:$i, X1441:$i, X1442:$i, X1443:$i, X1444:$i, X1445:$i, X1447:$i, X1448:$i, X1450:$i, X1451:$i, X1452:$i, X1453:$i, X1454:$i, X1456:$i, X1457:$i > $i > $o, X1458:$i, X1461:$i, X1463:$i, X1464:$i, X1465:$i, X1466:$i, X1468:$i, X1469:$i > $o, X1470:$i, X1471:$i > $o, X1472:$i, X1473:$i, X1474:$i > $o, X1475:$i, X1476:$i, X1477:$i > $o, X1478:$i, X1479:$i > $o, X1481:$i, X1482:$o, X1483:$i, X1484:$i, X1485:$o, X1486:$i, X1487:$i, X1488:$i > $o, X1490:$i, X1491:$i, X1494:$i, X1496:$i, X1498:$i, X1499:$i > $o, X1500:$i, X1501:$i, X1503:$i, X1504:$i > $o, X1505:$i, X1506:$i, X1507:$i, X1508:$i, X1509:$i, X1510:$i, X1511:$i, X1512:$i, X1513:$i, X1514:$i, X1515:$i, X1516:$o, X1517:$i, X1518:$i, X1519:$i, X1520:$i, X1521:$i, X1522:$i, X1524:$i, X1525:$i, X1526:$i, X1527:$i, X1528:$i, X1529:$i, X1530:$i, X1531:$i, X1532:$i, X1533:$i, X1534:$o, X1536:$i, X1537:$i, X1538:$i > $o, X1540:$i, X1541:$i, X1542:$i, X1544:$i, X1545:$i, X1546:$i, X1547:$i, X1548:$i, X1549:$i, X1550:$i, X1551:$i, X1552:$i, X1553:$i, X1554:$i, X1555:$i, X1556:$i, X1557:$i, X1558:$i, X1559:$i, X1560:$i > $o, X1561:$i, X1562:$i > $o, X1563:$i, X1564:$i, X1565:$i > $o, X1566:$i, X1568:$i, X1569:$i > $o, X1571:$i, X1572:$i, X1573:$i > $o, X1575:$i, X1576:$i, X1577:$i > $o, X1578:$i, X1580:$o, X1581:$i, X1582:$i > $o, X1584:$i, X1585:$i, X1586:$i > $o, X1587:$i, X1589:$i > $o, X1590:$i, X1592:$i > $o, X1593:$i, X1596:$i > $o, X1597:$i, X1599:$i, X1600:$i, X1601:$i, X1602:$i, X1603:$i, X1604:$i, X1605:$i, X1606:$i, X1607:$i > $o, X1608:$i, X1609:$i, X1610:$i > $o, X1611:$i > $o, X1614:$i, X1615:$i, X1616:$i, X1617:$i, X1618:$i, X1619:$i, X1620:$i, X1621:$i, X1622:$i > $o, X1623:$i, X1624:$i, X1625:$i > $o, X1626:$i > $o, X1629:$i, X1630:$i, X1631:$i > $o, X1632:$i > $o, X1635:$i, X1636:$i, X1638:$i, X1639:$i, X1640:$i, X1641:$i, X1642:$i, X1643:$i, X1645:$i, X1646:$i, X1647:$i, X1648:$i, X1649:$i, X1650:$i, X1651:$i, X1652:$i, X1653:$i, X1654:$i, X1655:$i, X1656:$i, X1657:$i, X1658:$i, X1659:$i, X1660:$i, X1661:$i, X1662:$i, X1663:$i, X1664:$i, X1665:$i, X1666:$i, X1667:$i, X1668:$i, X1669:$i, X1670:$i, X1671:$i, X1672:$i, X1673:$i, X1674:$i, X1675:$i, X1676:$i, X1677:$i, X1678:$i, X1679:$i, X1680:$i, X1681:$i, X1682:$i > $o, X1683:$i, X1684:$i > $o, X1685:$i, X1686:$i, X1687:$i, X1688:$i, X1689:$i, X1690:$i, X1691:$i, X1692:$i, X1693:$i, X1694:$i, X1695:$i, X1696:$o, X1697:$i, X1698:$i, X1699:$i, X1700:$i, X1701:$i, X1702:$i, X1703:$i, X1704:$i, X1705:$i, X1706:$i, X1707:$i, X1708:$i, X1709:$i, X1710:$i, X1711:$i, X1712:$i, X1713:$i, X1714:$i, X1715:$i, X1716:$i, X1717:$i, X1718:$i, X1719:$i, X1720:$i, X1721:$i, X1722:$i, X1723:$i, X1725:$i, X1726:$i, X1727:$i, X1728:$i, X1729:$i, X1730:$i, X1731:$i, X1732:$i, X1733:$i, X1734:$i, X1735:$i, X1736:$i, X1737:$i, X1738:$i, X1739:$i, X1740:$i, X1741:$i, X1742:$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:$i, X1764:$o, 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:$i, X1780:$i, X1781:$i, X1782:$i, X1783:$i, X1784:$i, X1785:$i, X1786:$i, X1787:$i, X1788:$i, X1789:$i, X1790:$i, X1791:$i, X1792:$i, X1793:$i, X1794:$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, X1821:$i, X1822:$i, X1823:$i, X1826:$i, X1827:$i, X1828:$i, X1829:$i, X1830:$i, X1832:$i, X1833:$i, X1834:$i, X1835:$i, X1836:$i > $o, X1839:$i, X1840:$i, X1841:$i > $o, X1843:$i, X1844:$i > $o, X1845:$i, X1847:$i, X1848:$i > $o, X1851:$i, X1852:$i, X1853:$i, X1854:$i, X1855:$i, X1856:$i, X1857:$i, X1858:$i, X1859:$i, X1860:$i, X1861:$i, 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:$i, X1921:$i, X1922:$i, X1923:$i > $i > $o, X1924:$i, X1925:$i, X1926:$i, X1927:$i, X1928:$i > $i > $o, X1929:$i, X1930:$i, X1931:$i > $i > $o, X1932:$i, X1933:$i, X1934:$i > $i > $o, X1935:$i, X1936:$i, X1937:$i, X1938:$i, X1939:$i > $i > $o, X1940:$i, X1941:$i, X1942:$i, X1943:$i, X1944:$i > $i > $o, X1945:$i, X1946:$i, X1947:$i, X1948:$i, X1949:$i > $i > $o, X1950:$i, X1951:$i, X1952:$i, X1953:$i, X1954:$i, X1955:$i, X1956:$i, X1957:$i, X1958:$i, X1959:$i, X1960:$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 > $i, X1978:$i, X1979:$i, X1980:$i > $i, X1982:$i, X1983:$i, X1984:$i > $i, X1986:$i, X1987:$i, X1988:$i, X1989:$i > $o, X1992:$i, X1993:$i, X1994:$i, X1995:$i, X1996:$i > $o, X1999:$i, X2000:$i, X2001:$i > $o, X2002:$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, X2022:$i, X2023:$i, X2024:$i, X2025:$i, X2026:$i, X2027:$i, X2028:$i, X2029:$i, X2030:$i, X2031:$i, X2032:$i, X2035:$i, X2036:$i, X2037:$i, X2038:$i, X2043:$i, X2044:$i, X2045:$i, X2046:$i, X2048:$i, X2049:$i, X2050:$i, X2051:$i, X2053:$i, X2054:$i, X2055:$i, X2056:$i, X2057:$i, X2058:$i, X2059:$i, X2060:$i, X2061:$i, X2062:$i, X2063:$i > $i, X2065:$i, X2066:$i, X2067:$i, X2068:$i, X2069:$i, X2070:$i, X2071:$i > $i, X2073:$i, X2074:$i, X2075:$i > $i, X2077:$i, X2078:$i, X2079:$i, X2080:$i, X2081:$i, X2082:$o, X2083:$i, X2084:$i, X2085:$i, X2086:$o, X2087:$i, X2088:$i, X2089:$i, X2090:$o, X2091:$i, X2092:$i, X2093:$i, X2094:$o, X2095:$i, X2096:$i, X2097:$i, X2098:$o, X2099:$i, X2100:$i, X2101:$i, X2102:$o, X2103:$i, X2104:$i, X2105:$i, X2106:$i, X2107:$i, X2108:$o, X2109:$i, X2110:$i, X2111:$i, X2112:$o, X2113:$i, X2114:$i]:((((~(in @ (esk1_2 @ X1434 @ X1435) @ X1434)|~(in @ (esk1_2 @ X1434 @ X1435) @ X1435)|((X1434)=(X1435)))&((in @ (esk1_2 @ X1434 @ X1435) @ X1434)|(in @ (esk1_2 @ X1434 @ X1435) @ X1435)|((X1434)=(X1435))))&(~(in @ X1437 @ emptyset)&(((~(in @ X1440 @ (setadjoin @ X1438 @ X1439))|(((X1440)=(X1438))|(in @ X1440 @ X1439)))&((((X1440)!=(X1438))|(in @ X1440 @ (setadjoin @ X1438 @ X1439)))&(~(in @ X1440 @ X1439)|(in @ X1440 @ (setadjoin @ X1438 @ X1439)))))&(((~(in @ X1442 @ (powerset @ 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X2029 @ X2030 @ X2032)|~(breln @ X2029 @ X2030 @ X2031))&(((in @ (esk57_4 @ X2029 @ X2030 @ X2031 @ X2032) @ X2030)|(subset @ X2031 @ X2032)|~(breln @ X2029 @ X2030 @ X2032)|~(breln @ X2029 @ X2030 @ X2031))&(((in @ (kpair @ (esk56_4 @ X2029 @ X2030 @ X2031 @ X2032) @ (esk57_4 @ X2029 @ X2030 @ X2031 @ X2032)) @ X2031)|(subset @ X2031 @ X2032)|~(breln @ X2029 @ X2030 @ X2032)|~(breln @ X2029 @ X2030 @ X2031))&(~(in @ (kpair @ (esk56_4 @ X2029 @ X2030 @ X2031 @ X2032) @ (esk57_4 @ X2029 @ X2030 @ X2031 @ X2032)) @ X2032)|(subset @ X2031 @ X2032)|~(breln @ X2029 @ X2030 @ X2032)|~(breln @ X2029 @ X2030 @ X2031)))))&(((((in @ (esk60_4 @ X2035 @ X2036 @ X2037 @ X2038) @ X2035)|((X2037)=(X2038))|(in @ (esk58_4 @ X2035 @ X2036 @ X2037 @ X2038) @ X2035)|~(breln @ X2035 @ X2036 @ X2038)|~(breln @ X2035 @ X2036 @ X2037))&(((in @ (esk61_4 @ X2035 @ X2036 @ X2037 @ X2038) @ X2036)|((X2037)=(X2038))|(in @ (esk58_4 @ X2035 @ X2036 @ X2037 @ X2038) @ X2035)|~(breln @ X2035 @ X2036 @ X2038)|~(breln @ X2035 @ X2036 @ X2037))&(((in @ (kpair @ (esk60_4 @ X2035 @ X2036 @ X2037 @ X2038) @ (esk61_4 @ X2035 @ X2036 @ X2037 @ X2038)) @ X2038)|((X2037)=(X2038))|(in @ (esk58_4 @ X2035 @ X2036 @ X2037 @ X2038) @ X2035)|~(breln @ X2035 @ X2036 @ X2038)|~(breln @ X2035 @ X2036 @ X2037))&(~(in @ (kpair @ (esk60_4 @ X2035 @ X2036 @ X2037 @ X2038) @ (esk61_4 @ X2035 @ X2036 @ X2037 @ X2038)) @ X2037)|((X2037)=(X2038))|(in @ (esk58_4 @ X2035 @ X2036 @ X2037 @ X2038) @ X2035)|~(breln @ X2035 @ X2036 @ X2038)|~(breln @ X2035 @ X2036 @ X2037)))))&((((in @ (esk60_4 @ X2035 @ X2036 @ X2037 @ X2038) @ X2035)|((X2037)=(X2038))|(in @ (esk59_4 @ X2035 @ X2036 @ X2037 @ X2038) @ X2036)|~(breln @ X2035 @ X2036 @ X2038)|~(breln @ X2035 @ X2036 @ X2037))&(((in @ (esk61_4 @ X2035 @ X2036 @ X2037 @ X2038) @ X2036)|((X2037)=(X2038))|(in @ (esk59_4 @ X2035 @ X2036 @ X2037 @ X2038) @ X2036)|~(breln @ X2035 @ X2036 @ X2038)|~(breln @ X2035 @ X2036 @ X2037))&(((in @ (kpair @ (esk60_4 @ X2035 @ X2036 @ X2037 @ X2038) @ (esk61_4 @ X2035 @ X2036 @ X2037 @ X2038)) @ X2038)|((X2037)=(X2038))|(in @ (esk59_4 @ X2035 @ X2036 @ X2037 @ X2038) @ X2036)|~(breln @ X2035 @ X2036 @ X2038)|~(breln @ X2035 @ X2036 @ X2037))&(~(in @ (kpair @ (esk60_4 @ X2035 @ X2036 @ X2037 @ X2038) @ (esk61_4 @ X2035 @ X2036 @ X2037 @ X2038)) @ X2037)|((X2037)=(X2038))|(in @ (esk59_4 @ X2035 @ X2036 @ X2037 @ X2038) @ X2036)|~(breln @ X2035 @ X2036 @ X2038)|~(breln @ X2035 @ X2036 @ X2037)))))&((((in @ (esk60_4 @ X2035 @ X2036 @ X2037 @ X2038) @ X2035)|((X2037)=(X2038))|(in @ (kpair @ (esk58_4 @ X2035 @ X2036 @ X2037 @ X2038) @ (esk59_4 @ X2035 @ X2036 @ X2037 @ X2038)) @ X2037)|~(breln @ X2035 @ X2036 @ X2038)|~(breln @ X2035 @ X2036 @ X2037))&(((in @ (esk61_4 @ X2035 @ X2036 @ X2037 @ X2038) @ X2036)|((X2037)=(X2038))|(in @ (kpair @ (esk58_4 @ X2035 @ X2036 @ X2037 @ X2038) @ (esk59_4 @ X2035 @ X2036 @ X2037 @ X2038)) @ X2037)|~(breln @ X2035 @ X2036 @ X2038)|~(breln @ X2035 @ X2036 @ X2037))&(((in @ (kpair @ (esk60_4 @ X2035 @ X2036 @ X2037 @ X2038) @ (esk61_4 @ X2035 @ X2036 @ X2037 @ X2038)) @ X2038)|((X2037)=(X2038))|(in @ (kpair @ (esk58_4 @ X2035 @ X2036 @ X2037 @ X2038) @ (esk59_4 @ X2035 @ X2036 @ X2037 @ X2038)) @ X2037)|~(breln @ X2035 @ X2036 @ X2038)|~(breln @ X2035 @ X2036 @ X2037))&(~(in @ (kpair @ (esk60_4 @ X2035 @ X2036 @ X2037 @ X2038) @ (esk61_4 @ X2035 @ X2036 @ X2037 @ X2038)) @ X2037)|((X2037)=(X2038))|(in @ (kpair @ (esk58_4 @ X2035 @ X2036 @ X2037 @ X2038) @ (esk59_4 @ X2035 @ X2036 @ X2037 @ X2038)) @ X2037)|~(breln @ X2035 @ X2036 @ X2038)|~(breln @ X2035 @ X2036 @ X2037)))))&(((in @ (esk60_4 @ X2035 @ X2036 @ X2037 @ X2038) @ X2035)|((X2037)=(X2038))|~(in @ (kpair @ (esk58_4 @ X2035 @ X2036 @ X2037 @ X2038) @ (esk59_4 @ X2035 @ X2036 @ X2037 @ X2038)) @ X2038)|~(breln @ X2035 @ X2036 @ X2038)|~(breln @ X2035 @ X2036 @ X2037))&(((in @ (esk61_4 @ X2035 @ X2036 @ X2037 @ X2038) @ X2036)|((X2037)=(X2038))|~(in @ (kpair @ (esk58_4 @ X2035 @ X2036 @ X2037 @ X2038) @ (esk59_4 @ X2035 @ X2036 @ X2037 @ X2038)) @ X2038)|~(breln @ X2035 @ X2036 @ X2038)|~(breln @ X2035 @ X2036 @ X2037))&(((in @ (kpair @ (esk60_4 @ X2035 @ X2036 @ X2037 @ X2038) @ (esk61_4 @ X2035 @ X2036 @ X2037 @ X2038)) @ X2038)|((X2037)=(X2038))|~(in @ (kpair @ (esk58_4 @ X2035 @ X2036 @ X2037 @ X2038) @ (esk59_4 @ X2035 @ X2036 @ X2037 @ X2038)) @ X2038)|~(breln @ X2035 @ X2036 @ X2038)|~(breln @ X2035 @ X2036 @ X2037))&(~(in @ (kpair @ (esk60_4 @ X2035 @ X2036 @ X2037 @ X2038) @ (esk61_4 @ X2035 @ X2036 @ X2037 @ X2038)) @ X2037)|((X2037)=(X2038))|~(in @ (kpair @ (esk58_4 @ X2035 @ X2036 @ X2037 @ X2038) @ (esk59_4 @ X2035 @ X2036 @ X2037 @ X2038)) @ X2038)|~(breln @ X2035 @ X2036 @ X2038)|~(breln @ X2035 @ X2036 @ X2037))))))))&((((in @ (esk62_4 @ X2043 @ X2044 @ X2045 @ X2046) @ X2043)|((X2045)=(X2046))|~(func @ X2043 @ X2044 @ X2046)|~(func @ X2043 @ X2044 @ X2045))&(((ap @ X2043 @ X2044 @ X2045 @ (esk62_4 @ X2043 @ X2044 @ X2045 @ X2046))!=(ap @ X2043 @ X2044 @ X2046 @ (esk62_4 @ X2043 @ X2044 @ X2045 @ X2046)))|((X2045)=(X2046))|~(func @ X2043 @ X2044 @ X2046)|~(func @ X2043 @ X2044 @ X2045)))&((((in @ (esk63_4 @ X2048 @ X2049 @ X2050 @ X2051) @ X2048)|((X2050)=(X2051))|~(in @ X2051 @ (funcSet @ X2048 @ X2049))|~(in @ X2050 @ (funcSet @ X2048 @ X2049)))&(((ap @ X2048 @ X2049 @ X2050 @ (esk63_4 @ X2048 @ X2049 @ X2050 @ X2051))!=(ap @ X2048 @ X2049 @ X2051 @ (esk63_4 @ X2048 @ X2049 @ X2050 @ X2051)))|((X2050)=(X2051))|~(in @ X2051 @ (funcSet @ X2048 @ X2049))|~(in @ X2050 @ (funcSet @ X2048 @ X2049))))&((~(in @ X2055 @ (funcSet @ X2053 @ X2054))|(~(in @ X2056 @ X2053)|((ap @ X2053 @ X2054 @ X2055 @ X2056)=(ap @ X2053 @ X2054 @ X2055 @ X2056))))&((~(func @ X2057 @ X2058 @ X2059)|(~(in @ X2060 @ X2057)|((ap @ X2057 @ X2058 @ X2059 @ X2060)=(ap @ X2057 @ X2058 @ X2059 @ X2060))))&((((in @ (esk64_3 @ X2061 @ X2062 @ X2063) @ X2061)|(~(in @ X2065 @ X2061)|((ap @ X2061 @ X2062 @ (lam @ X2061 @ X2062 @ X2063) @ X2065)=(X2063 @ X2065))))&(~(in @ (X2063 @ (esk64_3 @ X2061 @ X2062 @ X2063)) @ X2062)|(~(in @ X2065 @ X2061)|((ap @ X2061 @ X2062 @ (lam @ X2061 @ X2062 @ X2063) @ X2065)=(X2063 @ X2065)))))&((~(func @ X2066 @ X2067 @ X2068)|((lam @ X2066 @ X2067 @ (ap @ X2066 @ X2067 @ X2068))=(X2068)))&((((in @ (esk65_3 @ X2069 @ X2070 @ X2071) @ X2069)|((lam @ X2069 @ X2070 @ X2071)=(lam @ X2069 @ X2070 @ X2071)))&(~(in @ (X2071 @ (esk65_3 @ X2069 @ X2070 @ X2071)) @ X2070)|((lam @ X2069 @ X2070 @ X2071)=(lam @ X2069 @ X2070 @ X2071))))&((((in @ (esk66_3 @ X2073 @ X2074 @ X2075) @ X2073)|(~(in @ X2077 @ X2073)|((ap @ X2073 @ X2074 @ (lam @ X2073 @ X2074 @ X2075) @ X2077)=(X2075 @ X2077))))&(~(in @ (X2075 @ (esk66_3 @ X2073 @ X2074 @ X2075)) @ X2074)|(~(in @ X2077 @ X2073)|((ap @ X2073 @ X2074 @ (lam @ X2073 @ X2074 @ X2075) @ X2077)=(X2075 @ X2077)))))&((~(in @ X2080 @ (funcSet @ X2078 @ X2079))|((lam @ X2078 @ X2079 @ (ap @ X2078 @ X2079 @ X2080))=(X2080)))&((~(in @ X2083 @ X2081)|(~(in @ X2084 @ X2081)|((X2082)|(in @ X2084 @ (dsetconstr @ X2081 @ (^[Z0:$i]:((((((X2082))&(((Z0)=(X2083)))))|(((~((X2082)))&(((Z0)=(X2084)))))))))))))&((~(in @ X2087 @ X2085)|(~(in @ X2088 @ X2085)|((X2086)|((dsetconstr @ X2085 @ (^[Z0:$i]:((((((X2086))&(((Z0)=(X2087)))))|(((~((X2086)))&(((Z0)=(X2088)))))))))=(setadjoin @ X2088 @ emptyset)))))&((~(in @ X2091 @ X2089)|(~(in @ X2092 @ X2089)|(~(X2090)|(in @ X2091 @ (dsetconstr @ X2089 @ (^[Z0:$i]:((((((X2090))&(((Z0)=(X2091)))))|(((~((X2090)))&(((Z0)=(X2092)))))))))))))&((~(in @ X2095 @ X2093)|(~(in @ X2096 @ X2093)|(~(X2094)|((dsetconstr @ X2093 @ (^[Z0:$i]:((((((X2094))&(((Z0)=(X2095)))))|(((~((X2094)))&(((Z0)=(X2096)))))))))=(setadjoin @ X2095 @ emptyset)))))&((~(in @ X2099 @ X2097)|(~(in @ X2100 @ X2097)|(singleton @ (dsetconstr @ X2097 @ (^[Z0:$i]:((((((X2098))&(((Z0)=(X2099)))))|(((~((X2098)))&(((Z0)=(X2100))))))))))))&((~(in @ X2103 @ X2101)|(~(in @ X2104 @ X2101)|(in @ (if @ X2101 @ ((X2102)) @ X2103 @ X2104) @ X2101)))&((~(singleton @ X2105)|(~(in @ X2106 @ X2105)|((setunion @ X2105)=(X2106))))&((~(in @ X2109 @ X2107)|(~(in @ X2110 @ X2107)|(~(X2108)|((if @ X2107 @ ((X2108)) @ X2109 @ X2110)=(X2109)))))&((~(in @ X2113 @ X2111)|(~(in @ X2114 @ X2111)|((X2112)|((if @ X2111 @ ((X2112)) @ X2113 @ X2114)=(X2114)))))&((in @ esk68_0 @ esk67_0)&((in @ esk69_0 @ esk67_0)&(((~(epred2_0)|(epred2_0))&(~(in @ (if @ esk67_0 @ $false @ esk68_0 @ esk69_0) @ (setadjoin @ esk68_0 @ (setadjoin @ esk69_0 @ emptyset)))|(epred2_0)))&((~(epred2_0)|~(in @ (if @ esk67_0 @ $true @ esk68_0 @ esk69_0) @ (setadjoin @ esk68_0 @ (setadjoin @ esk69_0 @ emptyset))))&(~(in @ (if @ esk67_0 @ $false @ esk68_0 @ esk69_0) @ (setadjoin @ esk68_0 @ (setadjoin @ esk69_0 @ emptyset)))|~(in @ (if @ esk67_0 @ $true @ esk68_0 @ esk69_0) @ (setadjoin @ esk68_0 @ (setadjoin @ esk69_0 @ emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_278])])])])])])])])).
% 4.65/0.99 thf(c_0_280, negated_conjecture, ((epred2_0)|~((in @ (if @ esk67_0 @ (~($true)) @ esk68_0 @ esk69_0) @ (setadjoin @ esk68_0 @ (setadjoin @ esk69_0 @ emptyset))))), inference(split_conjunct,[status(thm)],[c_0_279])).
% 4.65/0.99 thf(c_0_281, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:((((if @ X3 @ (~($true)) @ X2 @ X4)=(X4))|~((in @ X2 @ X3))|~((in @ X4 @ X3)))), inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_279])])])).
% 4.65/0.99 thf(c_0_282, negated_conjecture, ![X3:$i, X2:$i]:((in @ X2 @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset)))), inference(split_conjunct,[status(thm)],[c_0_279])).
% 4.65/0.99 thf(c_0_283, negated_conjecture, (in @ esk69_0 @ esk67_0), inference(split_conjunct,[status(thm)],[c_0_279])).
% 4.65/0.99 thf(c_0_284, negated_conjecture, (in @ esk68_0 @ esk67_0), inference(split_conjunct,[status(thm)],[c_0_279])).
% 4.65/0.99 thf(c_0_285, negated_conjecture, (~((epred2_0))|~((in @ (if @ esk67_0 @ (($true)) @ esk68_0 @ esk69_0) @ (setadjoin @ esk68_0 @ (setadjoin @ esk69_0 @ emptyset))))), inference(split_conjunct,[status(thm)],[c_0_279])).
% 4.65/0.99 thf(c_0_286, negated_conjecture, (epred2_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_280, c_0_281]), c_0_282]), c_0_283]), c_0_284])])).
% 4.65/0.99 thf(c_0_287, negated_conjecture, ~((in @ (if @ esk67_0 @ (($true)) @ esk68_0 @ esk69_0) @ (setadjoin @ esk68_0 @ (setadjoin @ esk69_0 @ emptyset)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_285, c_0_286])])).
% 4.65/0.99 thf(c_0_288, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:((((if @ X3 @ (($true)) @ X2 @ X4)=(X2))|~((in @ X2 @ X3))|~((in @ X4 @ X3)))), inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_279])])])).
% 4.65/0.99 thf(c_0_289, negated_conjecture, ![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_279])).
% 4.65/0.99 thf(c_0_290, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_287, c_0_288]), c_0_289]), c_0_283]), c_0_284])]), ['proof']).
% 4.65/0.99 % SZS output end CNFRefutation
% 4.65/0.99 % Parsed axioms : 493
% 4.65/0.99 % Removed by relevancy pruning/SinE : 268
% 4.65/0.99 % Initial clauses : 376
% 4.65/0.99 % Removed in clause preprocessing : 35
% 4.65/0.99 % Initial clauses in saturation : 341
% 4.65/0.99 % Processed clauses : 2519
% 4.65/0.99 % ...of these trivial : 74
% 4.65/0.99 % ...subsumed : 1530
% 4.65/0.99 % ...remaining for further processing : 915
% 4.65/0.99 % Other redundant clauses eliminated : 99
% 4.65/0.99 % Clauses deleted for lack of memory : 0
% 4.65/0.99 % Backward-subsumed : 92
% 4.65/0.99 % Backward-rewritten : 27
% 4.65/0.99 % Generated clauses : 21841
% 4.65/0.99 % ...of the previous two non-redundant : 19213
% 4.65/0.99 % ...aggressively subsumed : 0
% 4.65/0.99 % Contextual simplify-reflections : 0
% 4.65/0.99 % Paramodulations : 21720
% 4.65/0.99 % Factorizations : 16
% 4.65/0.99 % NegExts : 0
% 4.65/0.99 % Equation resolutions : 104
% 4.65/0.99 % Disequality decompositions : 0
% 4.65/0.99 % Total rewrite steps : 3065
% 4.65/0.99 % ...of those cached : 2805
% 4.65/0.99 % Propositional unsat checks : 0
% 4.65/0.99 % Propositional check models : 0
% 4.65/0.99 % Propositional check unsatisfiable : 0
% 4.65/0.99 % Propositional clauses : 0
% 4.65/0.99 % Propositional clauses after purity: 0
% 4.65/0.99 % Propositional unsat core size : 0
% 4.65/0.99 % Propositional preprocessing time : 0.000
% 4.65/0.99 % Propositional encoding time : 0.000
% 4.65/0.99 % Propositional solver time : 0.000
% 4.65/0.99 % Success case prop preproc time : 0.000
% 4.65/0.99 % Success case prop encoding time : 0.000
% 4.65/0.99 % Success case prop solver time : 0.000
% 4.65/0.99 % Current number of processed clauses : 782
% 4.65/0.99 % Positive orientable unit clauses : 137
% 4.65/0.99 % Positive unorientable unit clauses: 0
% 4.65/0.99 % Negative unit clauses : 4
% 4.65/0.99 % Non-unit-clauses : 641
% 4.65/0.99 % Current number of unprocessed clauses: 16459
% 4.65/0.99 % ...number of literals in the above : 54507
% 4.65/0.99 % Current number of archived formulas : 0
% 4.65/0.99 % Current number of archived clauses : 119
% 4.65/0.99 % Clause-clause subsumption calls (NU) : 99313
% 4.65/0.99 % Rec. Clause-clause subsumption calls : 76126
% 4.65/0.99 % Non-unit clause-clause subsumptions : 1467
% 4.65/0.99 % Unit Clause-clause subsumption calls : 2842
% 4.65/0.99 % Rewrite failures with RHS unbound : 0
% 4.65/0.99 % BW rewrite match attempts : 128
% 4.65/0.99 % BW rewrite match successes : 14
% 4.65/0.99 % Condensation attempts : 0
% 4.65/0.99 % Condensation successes : 0
% 4.65/0.99 % Termbank termtop insertions : 309761
% 4.65/0.99 % Search garbage collected termcells : 23529
% 4.65/0.99
% 4.65/0.99 % -------------------------------------------------
% 4.65/0.99 % User time : 0.616 s
% 4.65/0.99 % System time : 0.042 s
% 4.65/0.99 % Total time : 0.658 s
% 4.65/0.99 % Maximum resident set size: 9028 pages
% 4.65/0.99
% 4.65/0.99 % -------------------------------------------------
% 4.65/0.99 % User time : 0.628 s
% 4.65/0.99 % System time : 0.052 s
% 4.65/0.99 % Total time : 0.680 s
% 4.65/0.99 % Maximum resident set size: 5632 pages
% 4.65/0.99 % E exiting
%------------------------------------------------------------------------------