%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU703^1 : 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 : n008.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 08:25:16 AM UTC 2026
% Result : Theorem 107.81s 14.03s
% Output : CNFRefutation 107.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU703^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n008.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 14:12:39 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.19/0.29 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.kCofj7HKpX/E---3.1_3219334.p
% 107.81/14.03 % Version: 3.5.1-ho
% 107.81/14.03 % Preprocessing class: HSLMSLSSLLLCHSA.
% 107.81/14.03 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 107.81/14.03 % Starting ho_unfolding_5 with 1200s (4) cores
% 107.81/14.03 % Starting pre_casc_3 with 300s (1) cores
% 107.81/14.03 % Starting new_ho_10_cnf2 with 300s (1) cores
% 107.81/14.03 % Starting full_lambda_10 with 300s (1) cores
% 107.81/14.03 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 107.81/14.03 % ho_unfolding_5 with pid 3219377 completed with status 0
% 107.81/14.03 % Result found by ho_unfolding_5
% 107.81/14.03 % Preprocessing class: HSLMSLSSLLLCHSA.
% 107.81/14.03 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 107.81/14.03 % Starting ho_unfolding_5 with 1200s (4) cores
% 107.81/14.03 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 107.81/14.03 % No SInE strategy applied
% 107.81/14.03 % Search class: HGHSM-FSLM32-MHSMMSBN
% 107.81/14.03 % Scheduled 12 strats onto 4 cores with 1200 seconds (1200 total)
% 107.81/14.03 % Starting SubtermCWHack with 109s (1) cores
% 107.81/14.03 % Starting ho_unfolding_5 with 121s (1) cores
% 107.81/14.03 % Starting new_ho_6 with 99s (1) cores
% 107.81/14.03 % Starting pre_casc_4 with 99s (1) cores
% 107.81/14.03 % pre_casc_4 with pid 3219407 completed with status 0
% 107.81/14.03 % Result found by pre_casc_4
% 107.81/14.03 % Preprocessing class: HSLMSLSSLLLCHSA.
% 107.81/14.03 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 107.81/14.03 % Starting ho_unfolding_5 with 1200s (4) cores
% 107.81/14.03 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 107.81/14.03 % No SInE strategy applied
% 107.81/14.03 % Search class: HGHSM-FSLM32-MHSMMSBN
% 107.81/14.03 % Scheduled 12 strats onto 4 cores with 1200 seconds (1200 total)
% 107.81/14.03 % Starting SubtermCWHack with 109s (1) cores
% 107.81/14.03 % Starting ho_unfolding_5 with 121s (1) cores
% 107.81/14.03 % Starting new_ho_6 with 99s (1) cores
% 107.81/14.03 % Starting pre_casc_4 with 99s (1) cores
% 107.81/14.03 % Preprocessing time : 0.009 s
% 107.81/14.03 % Presaturation interreduction done
% 107.81/14.03
% 107.81/14.03 % Proof found!
% 107.81/14.03 % SZS status Theorem
% 107.81/14.03 % SZS output start CNFRefutation
% 107.81/14.03 thf(decl_23, type, in: $i > $i > $o).
% 107.81/14.03 thf(decl_24, type, exu: ($i > $o) > $o).
% 107.81/14.03 thf(decl_25, type, setextAx: $o).
% 107.81/14.03 thf(decl_26, type, emptyset: $i).
% 107.81/14.03 thf(decl_27, type, emptysetAx: $o).
% 107.81/14.03 thf(decl_28, type, setadjoin: $i > $i > $i).
% 107.81/14.03 thf(decl_29, type, setadjoinAx: $o).
% 107.81/14.03 thf(decl_30, type, powerset: $i > $i).
% 107.81/14.03 thf(decl_31, type, powersetAx: $o).
% 107.81/14.03 thf(decl_32, type, setunion: $i > $i).
% 107.81/14.03 thf(decl_33, type, setunionAx: $o).
% 107.81/14.03 thf(decl_34, type, omega: $i).
% 107.81/14.03 thf(decl_35, type, omega0Ax: $o).
% 107.81/14.03 thf(decl_36, type, omegaSAx: $o).
% 107.81/14.03 thf(decl_37, type, omegaIndAx: $o).
% 107.81/14.03 thf(decl_38, type, replAx: $o).
% 107.81/14.03 thf(decl_39, type, foundationAx: $o).
% 107.81/14.03 thf(decl_40, type, wellorderingAx: $o).
% 107.81/14.03 thf(decl_41, type, descr: ($i > $o) > $i).
% 107.81/14.03 thf(decl_42, type, descrp: $o).
% 107.81/14.03 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 107.81/14.03 thf(decl_44, type, dsetconstrI: $o).
% 107.81/14.03 thf(decl_45, type, dsetconstrEL: $o).
% 107.81/14.03 thf(decl_46, type, dsetconstrER: $o).
% 107.81/14.03 thf(decl_47, type, exuE1: $o).
% 107.81/14.03 thf(decl_48, type, prop2set: $o > $i).
% 107.81/14.03 thf(decl_49, type, prop2setE: $o).
% 107.81/14.03 thf(decl_50, type, emptysetE: $o).
% 107.81/14.03 thf(decl_51, type, emptysetimpfalse: $o).
% 107.81/14.03 thf(decl_52, type, notinemptyset: $o).
% 107.81/14.03 thf(decl_53, type, exuE3e: $o).
% 107.81/14.03 thf(decl_54, type, setext: $o).
% 107.81/14.03 thf(decl_55, type, emptyI: $o).
% 107.81/14.03 thf(decl_56, type, noeltsimpempty: $o).
% 107.81/14.03 thf(decl_57, type, setbeta: $o).
% 107.81/14.03 thf(decl_58, type, nonempty: $i > $o).
% 107.81/14.03 thf(decl_59, type, nonemptyE1: $o).
% 107.81/14.03 thf(decl_60, type, nonemptyI: $o).
% 107.81/14.03 thf(decl_61, type, nonemptyI1: $o).
% 107.81/14.03 thf(decl_62, type, setadjoinIL: $o).
% 107.81/14.03 thf(decl_63, type, emptyinunitempty: $o).
% 107.81/14.03 thf(decl_64, type, setadjoinIR: $o).
% 107.81/14.03 thf(decl_65, type, setadjoinE: $o).
% 107.81/14.03 thf(decl_66, type, setadjoinOr: $o).
% 107.81/14.03 thf(decl_67, type, setoftrueEq: $o).
% 107.81/14.03 thf(decl_68, type, powersetI: $o).
% 107.81/14.03 thf(decl_69, type, emptyinPowerset: $o).
% 107.81/14.03 thf(decl_70, type, emptyInPowerset: $o).
% 107.81/14.03 thf(decl_71, type, powersetE: $o).
% 107.81/14.03 thf(decl_72, type, setunionI: $o).
% 107.81/14.03 thf(decl_73, type, setunionE: $o).
% 107.81/14.03 thf(decl_74, type, subPowSU: $o).
% 107.81/14.03 thf(decl_75, type, exuE2: $o).
% 107.81/14.03 thf(decl_76, type, nonemptyImpWitness: $o).
% 107.81/14.03 thf(decl_77, type, uniqinunit: $o).
% 107.81/14.03 thf(decl_78, type, notinsingleton: $o).
% 107.81/14.03 thf(decl_79, type, eqinunit: $o).
% 107.81/14.03 thf(decl_80, type, singletonsswitch: $o).
% 107.81/14.03 thf(decl_81, type, upairsetE: $o).
% 107.81/14.03 thf(decl_82, type, upairsetIL: $o).
% 107.81/14.03 thf(decl_83, type, upairsetIR: $o).
% 107.81/14.03 thf(decl_84, type, emptyE1: $o).
% 107.81/14.03 thf(decl_85, type, vacuousDall: $o).
% 107.81/14.03 thf(decl_86, type, quantDeMorgan1: $o).
% 107.81/14.03 thf(decl_87, type, quantDeMorgan2: $o).
% 107.81/14.03 thf(decl_88, type, quantDeMorgan3: $o).
% 107.81/14.03 thf(decl_89, type, quantDeMorgan4: $o).
% 107.81/14.03 thf(decl_90, type, prop2setI: $o).
% 107.81/14.03 thf(decl_91, type, set2prop: $i > $o).
% 107.81/14.03 thf(decl_92, type, prop2set2propI: $o).
% 107.81/14.03 thf(decl_93, type, notdexE: $o).
% 107.81/14.03 thf(decl_94, type, notdallE: $o).
% 107.81/14.03 thf(decl_95, type, exuI1: $o).
% 107.81/14.03 thf(decl_96, type, exuI3: $o).
% 107.81/14.03 thf(decl_97, type, exuI2: $o).
% 107.81/14.03 thf(decl_98, type, inCongP: $o).
% 107.81/14.03 thf(decl_99, type, in__Cong: $o).
% 107.81/14.03 thf(decl_100, type, exuE3u: $o).
% 107.81/14.03 thf(decl_101, type, exu__Cong: $o).
% 107.81/14.03 thf(decl_102, type, emptyset__Cong: $o).
% 107.81/14.03 thf(decl_103, type, setadjoin__Cong: $o).
% 107.81/14.03 thf(decl_104, type, powerset__Cong: $o).
% 107.81/14.03 thf(decl_105, type, setunion__Cong: $o).
% 107.81/14.03 thf(decl_106, type, omega__Cong: $o).
% 107.81/14.03 thf(decl_107, type, exuEu: $o).
% 107.81/14.03 thf(decl_108, type, descr__Cong: $o).
% 107.81/14.03 thf(decl_109, type, dsetconstr__Cong: $o).
% 107.81/14.03 thf(decl_110, type, subset: $i > $i > $o).
% 107.81/14.03 thf(decl_113, type, subsetI1: $o).
% 107.81/14.03 thf(decl_114, type, eqimpsubset2: $o).
% 107.81/14.03 thf(decl_115, type, eqimpsubset1: $o).
% 107.81/14.03 thf(decl_116, type, subsetI2: $o).
% 107.81/14.03 thf(decl_117, type, emptysetsubset: $o).
% 107.81/14.03 thf(decl_118, type, subsetE: $o).
% 107.81/14.03 thf(decl_119, type, subsetE2: $o).
% 107.81/14.03 thf(decl_120, type, notsubsetI: $o).
% 107.81/14.03 thf(decl_121, type, notequalI1: $o).
% 107.81/14.03 thf(decl_122, type, notequalI2: $o).
% 107.81/14.03 thf(decl_123, type, subsetRefl: $o).
% 107.81/14.03 thf(decl_124, type, subsetTrans: $o).
% 107.81/14.03 thf(decl_125, type, setadjoinSub: $o).
% 107.81/14.03 thf(decl_126, type, setadjoinSub2: $o).
% 107.81/14.03 thf(decl_127, type, subset2powerset: $o).
% 107.81/14.03 thf(decl_128, type, setextsub: $o).
% 107.81/14.03 thf(decl_129, type, subsetemptysetimpeq: $o).
% 107.81/14.03 thf(decl_130, type, powersetI1: $o).
% 107.81/14.03 thf(decl_131, type, powersetE1: $o).
% 107.81/14.03 thf(decl_132, type, inPowerset: $o).
% 107.81/14.03 thf(decl_133, type, powersetsubset: $o).
% 107.81/14.03 thf(decl_134, type, sepInPowerset: $o).
% 107.81/14.03 thf(decl_135, type, sepSubset: $o).
% 107.81/14.03 thf(decl_136, type, binunion: $i > $i > $i).
% 107.81/14.03 thf(decl_137, type, binunionIL: $o).
% 107.81/14.03 thf(decl_138, type, upairset2IR: $o).
% 107.81/14.03 thf(decl_139, type, binunionIR: $o).
% 107.81/14.03 thf(decl_140, type, binunionEcases: $o).
% 107.81/14.03 thf(decl_141, type, binunionE: $o).
% 107.81/14.03 thf(decl_142, type, binunionLsub: $o).
% 107.81/14.03 thf(decl_143, type, binunionRsub: $o).
% 107.81/14.03 thf(decl_144, type, binintersect: $i > $i > $i).
% 107.81/14.03 thf(decl_145, type, binintersectI: $o).
% 107.81/14.03 thf(decl_146, type, binintersectSubset5: $o).
% 107.81/14.03 thf(decl_147, type, binintersectEL: $o).
% 107.81/14.03 thf(decl_148, type, binintersectLsub: $o).
% 107.81/14.03 thf(decl_149, type, binintersectSubset2: $o).
% 107.81/14.03 thf(decl_150, type, binintersectSubset3: $o).
% 107.81/14.03 thf(decl_151, type, binintersectER: $o).
% 107.81/14.03 thf(decl_152, type, disjointsetsI1: $o).
% 107.81/14.03 thf(decl_153, type, binintersectRsub: $o).
% 107.81/14.03 thf(decl_154, type, binintersectSubset4: $o).
% 107.81/14.03 thf(decl_155, type, binintersectSubset1: $o).
% 107.81/14.03 thf(decl_156, type, bs114d: $o).
% 107.81/14.03 thf(decl_158, type, setminus: $i > $i > $i).
% 107.81/14.03 thf(decl_159, type, setminusI: $o).
% 107.81/14.03 thf(decl_160, type, setminusEL: $o).
% 107.81/14.03 thf(decl_161, type, setminusER: $o).
% 107.81/14.03 thf(decl_162, type, setminusSubset2: $o).
% 107.81/14.03 thf(decl_163, type, setminusERneg: $o).
% 107.81/14.03 thf(decl_164, type, setminusELneg: $o).
% 107.81/14.03 thf(decl_165, type, setminusILneg: $o).
% 107.81/14.03 thf(decl_166, type, setminusIRneg: $o).
% 107.81/14.03 thf(decl_167, type, setminusLsub: $o).
% 107.81/14.03 thf(decl_168, type, setminusSubset1: $o).
% 107.81/14.03 thf(decl_169, type, symdiff: $i > $i > $i).
% 107.81/14.03 thf(decl_170, type, symdiffE: $o).
% 107.81/14.03 thf(decl_171, type, symdiffI1: $o).
% 107.81/14.03 thf(decl_172, type, symdiffI2: $o).
% 107.81/14.03 thf(decl_173, type, symdiffIneg1: $o).
% 107.81/14.03 thf(decl_174, type, symdiffIneg2: $o).
% 107.81/14.03 thf(decl_175, type, iskpair: $i > $o).
% 107.81/14.03 thf(decl_176, type, secondinupair: $o).
% 107.81/14.03 thf(decl_177, type, setukpairIL: $o).
% 107.81/14.03 thf(decl_178, type, setukpairIR: $o).
% 107.81/14.03 thf(decl_179, type, kpairiskpair: $o).
% 107.81/14.03 thf(decl_180, type, kpair: $i > $i > $i).
% 107.81/14.03 thf(decl_181, type, kpairp: $o).
% 107.81/14.03 thf(decl_182, type, cartprod: $i > $i > $i).
% 107.81/14.03 thf(decl_183, type, singletonsubset: $o).
% 107.81/14.03 thf(decl_184, type, singletoninpowerset: $o).
% 107.81/14.03 thf(decl_185, type, singletoninpowunion: $o).
% 107.81/14.03 thf(decl_186, type, upairset2E: $o).
% 107.81/14.03 thf(decl_187, type, upairsubunion: $o).
% 107.81/14.03 thf(decl_188, type, upairinpowunion: $o).
% 107.81/14.03 thf(decl_189, type, ubforcartprodlem1: $o).
% 107.81/14.03 thf(decl_190, type, ubforcartprodlem2: $o).
% 107.81/14.03 thf(decl_191, type, ubforcartprodlem3: $o).
% 107.81/14.03 thf(decl_192, type, cartprodpairin: $o).
% 107.81/14.03 thf(decl_193, type, cartprodmempair1: $o).
% 107.81/14.03 thf(decl_194, type, cartprodmempair: $o).
% 107.81/14.03 thf(decl_195, type, setunionE2: $o).
% 107.81/14.03 thf(decl_196, type, setunionsingleton1: $o).
% 107.81/14.03 thf(decl_197, type, setunionsingleton2: $o).
% 107.81/14.03 thf(decl_198, type, setunionsingleton: $o).
% 107.81/14.03 thf(decl_199, type, singleton: $i > $o).
% 107.81/14.03 thf(decl_200, type, singletonprop: $o).
% 107.81/14.03 thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 107.81/14.03 thf(decl_202, type, ex1E1: $o).
% 107.81/14.03 thf(decl_203, type, ex1I: $o).
% 107.81/14.03 thf(decl_204, type, ex1I2: $o).
% 107.81/14.03 thf(decl_205, type, singletonsuniq: $o).
% 107.81/14.03 thf(decl_210, type, setukpairinjL1: $o).
% 107.81/14.03 thf(decl_211, type, kfstsingleton: $o).
% 107.81/14.03 thf(decl_212, type, theprop: $o).
% 107.81/14.03 thf(decl_213, type, kfst: $i > $i).
% 107.81/14.03 thf(decl_214, type, kfstpairEq: $o).
% 107.81/14.03 thf(decl_215, type, cartprodfstin: $o).
% 107.81/14.03 thf(decl_216, type, setukpairinjL2: $o).
% 107.81/14.03 thf(decl_217, type, setukpairinjL: $o).
% 107.81/14.03 thf(decl_218, type, setukpairinjR11: $o).
% 107.81/14.03 thf(decl_219, type, setukpairinjR12: $o).
% 107.81/14.03 thf(decl_220, type, setukpairinjR1: $o).
% 107.81/14.03 thf(decl_221, type, upairequniteq: $o).
% 107.81/14.03 thf(decl_222, type, setukpairinjR2: $o).
% 107.81/14.03 thf(decl_223, type, setukpairinjR: $o).
% 107.81/14.03 thf(decl_224, type, ksndsingleton: $o).
% 107.81/14.03 thf(decl_225, type, ksnd: $i > $i).
% 107.81/14.03 thf(decl_226, type, ksndpairEq: $o).
% 107.81/14.03 thf(decl_227, type, kpairsurjEq: $o).
% 107.81/14.03 thf(decl_228, type, cartprodsndin: $o).
% 107.81/14.03 thf(decl_229, type, cartprodpairmemEL: $o).
% 107.81/14.03 thf(decl_230, type, cartprodpairmemER: $o).
% 107.81/14.03 thf(decl_231, type, cartprodmempaircEq: $o).
% 107.81/14.03 thf(decl_232, type, cartprodfstpairEq: $o).
% 107.81/14.03 thf(decl_233, type, cartprodsndpairEq: $o).
% 107.81/14.03 thf(decl_234, type, cartprodpairsurjEq: $o).
% 107.81/14.03 thf(decl_235, type, breln: $i > $i > $i > $o).
% 107.81/14.03 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 107.81/14.03 thf(decl_237, type, dpsetconstrI: $o).
% 107.81/14.03 thf(decl_238, type, dpsetconstrSub: $o).
% 107.81/14.03 thf(decl_239, type, setOfPairsIsBReln: $o).
% 107.81/14.03 thf(decl_240, type, dpsetconstrERa: $o).
% 107.81/14.03 thf(decl_241, type, dpsetconstrEL1: $o).
% 107.81/14.03 thf(decl_242, type, dpsetconstrEL2: $o).
% 107.81/14.03 thf(decl_243, type, dpsetconstrER: $o).
% 107.81/14.03 thf(decl_244, type, func: $i > $i > $i > $o).
% 107.81/14.03 thf(decl_245, type, funcSet: $i > $i > $i).
% 107.81/14.03 thf(decl_246, type, funcImageSingleton: $o).
% 107.81/14.03 thf(decl_247, type, apProp: $o).
% 107.81/14.03 thf(decl_248, type, ap: $i > $i > $i > $i > $i).
% 107.81/14.03 thf(decl_249, type, app: $o).
% 107.81/14.03 thf(decl_250, type, infuncsetfunc: $o).
% 107.81/14.03 thf(decl_251, type, ap2p: $o).
% 107.81/14.03 thf(decl_252, type, funcinfuncset: $o).
% 107.81/14.03 thf(decl_253, type, lamProp: $o).
% 107.81/14.03 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
% 107.81/14.03 thf(decl_255, type, lamp: $o).
% 107.81/14.03 thf(decl_256, type, lam2p: $o).
% 107.81/14.03 thf(decl_257, type, brelnall1: $o).
% 107.81/14.03 thf(decl_258, type, brelnall2: $o).
% 107.81/14.03 thf(decl_259, type, ex1E2: $o).
% 107.81/14.03 thf(decl_260, type, funcGraphProp1: $o).
% 107.81/14.03 thf(decl_261, type, funcGraphProp3: $o).
% 107.81/14.03 thf(decl_262, type, funcGraphProp2: $o).
% 107.81/14.03 thf(decl_263, type, funcextLem: $o).
% 107.81/14.03 thf(decl_264, type, funcGraphProp4: $o).
% 107.81/14.03 thf(decl_265, type, subbreln: $o).
% 107.81/14.03 thf(decl_266, type, eqbreln: $o).
% 107.81/14.03 thf(decl_267, type, funcext: $o).
% 107.81/14.03 thf(decl_268, type, funcext2: $o).
% 107.81/14.03 thf(decl_269, type, ap2apEq1: $o).
% 107.81/14.03 thf(decl_270, type, ap2apEq2: $o).
% 107.81/14.03 thf(decl_271, type, beta1: $o).
% 107.81/14.03 thf(decl_272, type, eta1: $o).
% 107.81/14.03 thf(decl_273, type, lam2lamEq: $o).
% 107.81/14.03 thf(decl_274, type, beta2: $o).
% 107.81/14.03 thf(decl_275, type, eta2: $o).
% 107.81/14.03 thf(decl_276, type, iffalseProp1: $o).
% 107.81/14.03 thf(decl_277, type, iffalseProp2: $o).
% 107.81/14.03 thf(decl_278, type, iftrueProp1: $o).
% 107.81/14.03 thf(decl_279, type, epred1_0: $o).
% 107.81/14.03 thf(decl_280, type, esk1_2: $i > $i > $i).
% 107.81/14.03 thf(decl_281, type, esk2_2: $i > $i > $i).
% 107.81/14.03 thf(decl_282, type, esk3_2: $i > $i > $i).
% 107.81/14.03 thf(decl_283, type, esk4_1: $i > $i).
% 107.81/14.03 thf(decl_284, type, esk5_2: ($i > $i > $o) > $i > $i).
% 107.81/14.03 thf(decl_285, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 107.81/14.03 thf(decl_286, type, esk7_2: ($i > $i > $o) > $i > $i).
% 107.81/14.03 thf(decl_287, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 107.81/14.03 thf(decl_288, type, esk9_1: $i > $i).
% 107.81/14.03 thf(decl_289, type, esk10_2: ($i > $o) > $i > $i).
% 107.81/14.03 thf(decl_290, type, esk11_2: ($i > $o) > $i > $i).
% 107.81/14.03 thf(decl_291, type, esk12_1: ($i > $o) > $i).
% 107.81/14.03 thf(decl_292, type, esk13_2: ($i > $o) > $i > $i).
% 107.81/14.03 thf(decl_293, type, esk14_1: ($i > $o) > $i).
% 107.81/14.03 thf(decl_294, type, esk15_2: $i > $i > $i).
% 107.81/14.03 thf(decl_295, type, esk16_2: $i > $i > $i).
% 107.81/14.03 thf(decl_296, type, esk17_1: $i > $i).
% 107.81/14.03 thf(decl_297, type, esk18_1: $i > $i).
% 107.81/14.03 thf(decl_298, type, esk19_1: $i > $i).
% 107.81/14.03 thf(decl_299, type, esk20_2: $i > $i > $i).
% 107.81/14.03 thf(decl_300, type, esk21_3: $i > $i > $o > $i).
% 107.81/14.03 thf(decl_301, type, esk22_2: ($i > $o) > $i > $i).
% 107.81/14.03 thf(decl_302, type, esk23_1: ($i > $o) > $i).
% 107.81/14.03 thf(decl_303, type, esk24_1: $i > $i).
% 107.81/14.03 thf(decl_304, type, esk25_2: $i > ($i > $o) > $i).
% 107.81/14.03 thf(decl_305, type, esk26_2: $i > ($i > $o) > $i).
% 107.81/14.03 thf(decl_306, type, esk27_2: $i > ($i > $o) > $i).
% 107.81/14.03 thf(decl_307, type, esk28_2: $i > ($i > $o) > $i).
% 107.81/14.03 thf(decl_308, type, esk29_2: $i > ($i > $o) > $i).
% 107.81/14.03 thf(decl_309, type, esk30_2: $i > ($i > $o) > $i).
% 107.81/14.03 thf(decl_310, type, esk31_2: ($i > $o) > $i > $i).
% 107.81/14.03 thf(decl_311, type, esk32_1: ($i > $o) > $i).
% 107.81/14.03 thf(decl_312, type, esk33_1: ($i > $o) > $i).
% 107.81/14.03 thf(decl_313, type, esk34_1: ($i > $o) > $i).
% 107.81/14.03 thf(decl_314, type, esk35_1: ($i > $o) > $i).
% 107.81/14.03 thf(decl_315, type, esk36_2: ($i > $o) > $i > $i).
% 107.81/14.03 thf(decl_316, type, esk37_1: ($i > $o) > $i).
% 107.81/14.03 thf(decl_317, type, esk38_2: ($i > $o) > $i > $i).
% 107.81/14.03 thf(decl_318, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 107.81/14.03 thf(decl_319, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 107.81/14.03 thf(decl_320, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 107.81/14.03 thf(decl_321, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 107.81/14.03 thf(decl_322, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 107.81/14.03 thf(decl_323, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 107.81/14.03 thf(decl_324, type, esk45_2: ($i > $o) > $i > $i).
% 107.81/14.03 thf(decl_325, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 107.81/14.03 thf(decl_326, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 107.81/14.03 thf(decl_327, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 107.81/14.03 thf(decl_328, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 107.81/14.03 thf(decl_329, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 107.81/14.03 thf(decl_330, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 107.81/14.03 thf(decl_331, type, esk52_2: $i > $i > $i).
% 107.81/14.03 thf(decl_332, type, esk53_2: $i > $i > $i).
% 107.81/14.03 thf(decl_333, type, esk54_2: $i > $i > $i).
% 107.81/14.03 thf(decl_334, type, esk55_3: $i > $i > $i > $i).
% 107.81/14.03 thf(decl_335, type, esk56_3: $i > $i > $i > $i).
% 107.81/14.03 thf(decl_336, type, esk57_2: $i > $i > $i).
% 107.81/14.03 thf(decl_337, type, esk58_2: $i > ($i > $o) > $i).
% 107.81/14.03 thf(decl_338, type, esk59_2: $i > ($i > $o) > $i).
% 107.81/14.03 thf(decl_339, type, esk60_2: $i > ($i > $o) > $i).
% 107.81/14.03 thf(decl_340, type, esk61_2: $i > ($i > $o) > $i).
% 107.81/14.03 thf(decl_341, type, esk62_3: $i > ($i > $o) > $i > $i).
% 107.81/14.03 thf(decl_342, type, esk63_3: $i > ($i > $o) > $i > $i).
% 107.81/14.03 thf(decl_343, type, esk64_2: $i > ($i > $o) > $i).
% 107.81/14.03 thf(decl_344, type, esk65_2: $i > ($i > $o) > $i).
% 107.81/14.03 thf(decl_345, type, esk66_2: $i > ($i > $o) > $i).
% 107.81/14.03 thf(decl_346, type, esk67_1: $i > $i).
% 107.81/14.03 thf(decl_347, type, esk68_1: $i > $i).
% 107.81/14.03 thf(decl_348, type, esk69_4: $i > $i > $i > $i > $i).
% 107.81/14.03 thf(decl_349, type, esk70_3: $i > $i > ($i > $i) > $i).
% 107.81/14.03 thf(decl_350, type, esk71_3: $i > $i > ($i > $i) > $i).
% 107.81/14.03 thf(decl_351, type, esk72_3: $i > $i > ($i > $i) > $i).
% 107.81/14.03 thf(decl_352, type, esk73_4: $i > $i > $i > ($i > $o) > $i).
% 107.81/14.03 thf(decl_353, type, esk74_4: $i > $i > $i > ($i > $o) > $i).
% 107.81/14.03 thf(decl_354, type, esk75_4: $i > $i > $i > ($i > $o) > $i).
% 107.81/14.03 thf(decl_355, type, esk76_4: $i > $i > $i > ($i > $o) > $i).
% 107.81/14.03 thf(decl_356, type, esk77_4: $i > $i > $i > $i > $i).
% 107.81/14.03 thf(decl_357, type, esk78_4: $i > $i > $i > $i > $i).
% 107.81/14.03 thf(decl_358, type, esk79_4: $i > $i > $i > $i > $i).
% 107.81/14.03 thf(decl_359, type, esk80_4: $i > $i > $i > $i > $i).
% 107.81/14.03 thf(decl_360, type, esk81_4: $i > $i > $i > $i > $i).
% 107.81/14.03 thf(decl_361, type, esk82_4: $i > $i > $i > $i > $i).
% 107.81/14.03 thf(decl_362, type, esk83_4: $i > $i > $i > $i > $i).
% 107.81/14.03 thf(decl_363, type, esk84_4: $i > $i > $i > $i > $i).
% 107.81/14.03 thf(decl_364, type, esk85_4: $i > $i > $i > $i > $i).
% 107.81/14.03 thf(decl_365, type, esk86_3: $i > $i > ($i > $i) > $i).
% 107.81/14.03 thf(decl_366, type, esk87_3: $i > $i > ($i > $i) > $i).
% 107.81/14.03 thf(decl_367, type, esk88_3: $i > $i > ($i > $i) > $i).
% 107.81/14.03 thf(decl_368, type, esk89_0: $i).
% 107.81/14.03 thf(decl_369, type, epred2_0: $o).
% 107.81/14.03 thf(decl_370, type, esk90_0: $i).
% 107.81/14.03 thf(decl_371, type, esk91_0: $i).
% 107.81/14.03 thf(decl_377, type, epred3_0: $i > $o).
% 107.81/14.03 thf(decl_379, type, epred5_2: $i > $i > $i > $o).
% 107.81/14.03 thf(decl_444, type, esk82_0: $i).
% 107.81/14.03 thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', ex1)).
% 107.81/14.03 thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:((((in @ X2 @ X4))&(((X4)=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', singleton)).
% 107.81/14.03 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', replAx)).
% 107.81/14.03 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', exu)).
% 107.81/14.03 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', descrp)).
% 107.81/14.03 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', exuE1)).
% 107.81/14.03 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', exuE3e)).
% 107.81/14.03 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', nonempty)).
% 107.81/14.03 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', nonemptyI)).
% 107.81/14.03 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', exuE2)).
% 107.81/14.03 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.kCofj7HKpX/E---3.1_3219334.p', exuI1)).
% 107.81/14.03 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', exuI3)).
% 107.81/14.03 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', exuI2)).
% 107.81/14.03 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.kCofj7HKpX/E---3.1_3219334.p', exuE3u)).
% 107.81/14.03 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', exu__Cong)).
% 107.81/14.03 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', exuEu)).
% 107.81/14.03 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', descr__Cong)).
% 107.81/14.03 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', singletonprop)).
% 107.81/14.03 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', ex1E1)).
% 107.81/14.03 thf(ex1I, axiom, ((ex1I)<=>![X4:$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.kCofj7HKpX/E---3.1_3219334.p', ex1I)).
% 107.81/14.03 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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', ex1I2)).
% 107.81/14.03 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', kfstsingleton)).
% 107.81/14.03 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', ksndsingleton)).
% 107.81/14.03 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setOfPairsIsBReln)).
% 107.81/14.03 thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', breln)).
% 107.81/14.03 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', funcImageSingleton)).
% 107.81/14.03 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$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.kCofj7HKpX/E---3.1_3219334.p', ex1E2)).
% 107.81/14.03 thf(iftrueProp2, 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)=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X42))&(((X14)=(X2)))))|(((~((X42)))&(((X14)=(X3)))))))))=(setadjoin @ X2 @ emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', iftrueProp2)).
% 107.81/14.03 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', dsetconstrI)).
% 107.81/14.03 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', dsetconstrEL)).
% 107.81/14.03 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', dsetconstrER)).
% 107.81/14.03 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setbeta)).
% 107.81/14.03 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', nonemptyE1)).
% 107.81/14.03 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', nonemptyI1)).
% 107.81/14.03 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setoftrueEq)).
% 107.81/14.03 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', nonemptyImpWitness)).
% 107.81/14.03 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.kCofj7HKpX/E---3.1_3219334.p', emptyE1)).
% 107.81/14.03 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', dsetconstr__Cong)).
% 107.81/14.03 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', sepInPowerset)).
% 107.81/14.03 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', sepSubset)).
% 107.81/14.03 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', theprop)).
% 107.81/14.03 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', dpsetconstrI)).
% 107.81/14.03 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', dpsetconstrSub)).
% 107.81/14.03 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', dpsetconstrERa)).
% 107.81/14.03 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', dpsetconstrEL1)).
% 107.81/14.03 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', dpsetconstrEL2)).
% 107.81/14.03 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', dpsetconstrER)).
% 107.81/14.03 thf(apProp, axiom, ((apProp)<=>![X4:$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.kCofj7HKpX/E---3.1_3219334.p', apProp)).
% 107.81/14.03 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.kCofj7HKpX/E---3.1_3219334.p', lamProp)).
% 107.81/14.03 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:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', lamp)).
% 107.81/14.03 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', lam2p)).
% 107.81/14.03 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$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.kCofj7HKpX/E---3.1_3219334.p', brelnall1)).
% 107.81/14.03 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.kCofj7HKpX/E---3.1_3219334.p', brelnall2)).
% 107.81/14.03 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.kCofj7HKpX/E---3.1_3219334.p', subbreln)).
% 107.81/14.03 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.kCofj7HKpX/E---3.1_3219334.p', eqbreln)).
% 107.81/14.03 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.kCofj7HKpX/E---3.1_3219334.p', beta1)).
% 107.81/14.03 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.kCofj7HKpX/E---3.1_3219334.p', eta1)).
% 107.81/14.03 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.kCofj7HKpX/E---3.1_3219334.p', lam2lamEq)).
% 107.81/14.04 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.kCofj7HKpX/E---3.1_3219334.p', beta2)).
% 107.81/14.04 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.kCofj7HKpX/E---3.1_3219334.p', eta2)).
% 107.81/14.04 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X39))&(((X14)=(X2)))))|(((~((X39)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', iffalseProp1)).
% 107.81/14.04 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$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.kCofj7HKpX/E---3.1_3219334.p', iffalseProp2)).
% 107.81/14.04 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X41))&(((X14)=(X2)))))|(((~((X41)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', iftrueProp1)).
% 107.81/14.04 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setextAx)).
% 107.81/14.04 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', emptysetAx)).
% 107.81/14.04 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setadjoinAx)).
% 107.81/14.04 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', powersetAx)).
% 107.81/14.04 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setunionAx)).
% 107.81/14.04 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', omega0Ax)).
% 107.81/14.04 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', omegaSAx)).
% 107.81/14.04 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.kCofj7HKpX/E---3.1_3219334.p', omegaIndAx)).
% 107.81/14.04 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.kCofj7HKpX/E---3.1_3219334.p', foundationAx)).
% 107.81/14.04 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', wellorderingAx)).
% 107.81/14.04 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', prop2setE)).
% 107.81/14.04 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', emptysetE)).
% 107.81/14.04 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', emptysetimpfalse)).
% 107.81/14.04 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', notinemptyset)).
% 107.81/14.04 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.kCofj7HKpX/E---3.1_3219334.p', setext)).
% 107.81/14.04 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', emptyI)).
% 107.81/14.04 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', noeltsimpempty)).
% 107.81/14.04 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setadjoinIL)).
% 107.81/14.04 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', emptyinunitempty)).
% 107.81/14.04 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setadjoinIR)).
% 107.81/14.04 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setadjoinE)).
% 107.81/14.04 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setadjoinOr)).
% 107.81/14.04 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', powersetI)).
% 107.81/14.04 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', emptyinPowerset)).
% 107.81/14.04 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', emptyInPowerset)).
% 107.81/14.04 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', powersetE)).
% 107.81/14.04 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setunionI)).
% 107.81/14.04 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setunionE)).
% 107.81/14.04 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', subPowSU)).
% 107.81/14.04 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', uniqinunit)).
% 107.81/14.04 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', notinsingleton)).
% 107.81/14.04 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', eqinunit)).
% 107.81/14.04 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', singletonsswitch)).
% 107.81/14.04 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', upairsetE)).
% 107.81/14.04 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', upairsetIL)).
% 107.81/14.04 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', upairsetIR)).
% 107.81/14.04 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', vacuousDall)).
% 107.81/14.04 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', quantDeMorgan1)).
% 107.81/14.04 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', quantDeMorgan2)).
% 107.81/14.04 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', quantDeMorgan3)).
% 107.81/14.04 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', quantDeMorgan4)).
% 107.81/14.04 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', prop2setI)).
% 107.81/14.04 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', prop2set2propI)).
% 107.81/14.04 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', notdexE)).
% 107.81/14.04 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', notdallE)).
% 107.81/14.04 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', inCongP)).
% 107.81/14.04 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', in__Cong)).
% 107.81/14.04 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', emptyset__Cong)).
% 107.81/14.04 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setadjoin__Cong)).
% 107.81/14.04 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', powerset__Cong)).
% 107.81/14.04 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setunion__Cong)).
% 107.81/14.04 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', omega__Cong)).
% 107.81/14.04 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', subsetI1)).
% 107.81/14.04 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', eqimpsubset2)).
% 107.81/14.04 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', eqimpsubset1)).
% 107.81/14.04 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', subsetI2)).
% 107.81/14.04 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', emptysetsubset)).
% 107.81/14.04 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', subsetE)).
% 107.81/14.04 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', subsetE2)).
% 107.81/14.04 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', notsubsetI)).
% 107.81/14.04 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', notequalI1)).
% 107.81/14.04 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', notequalI2)).
% 107.81/14.04 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', subsetRefl)).
% 107.81/14.04 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', subsetTrans)).
% 107.81/14.04 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setadjoinSub)).
% 107.81/14.04 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setadjoinSub2)).
% 107.81/14.04 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', subset2powerset)).
% 107.81/14.04 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setextsub)).
% 107.81/14.04 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', subsetemptysetimpeq)).
% 107.81/14.04 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', powersetI1)).
% 107.81/14.04 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', powersetE1)).
% 107.81/14.04 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', inPowerset)).
% 107.81/14.04 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', powersetsubset)).
% 107.81/14.04 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', binunionIL)).
% 107.81/14.04 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', upairset2IR)).
% 107.81/14.04 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', binunionIR)).
% 107.81/14.04 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', binunionEcases)).
% 107.81/14.04 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', binunionE)).
% 107.81/14.04 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', binunionLsub)).
% 107.81/14.04 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', binunionRsub)).
% 107.81/14.04 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', binintersectI)).
% 107.81/14.04 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', binintersectSubset5)).
% 107.81/14.04 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', binintersectEL)).
% 107.81/14.04 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', binintersectLsub)).
% 107.81/14.04 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', binintersectSubset2)).
% 107.81/14.04 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', binintersectSubset3)).
% 107.81/14.04 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', binintersectER)).
% 107.81/14.04 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', disjointsetsI1)).
% 107.81/14.04 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', binintersectRsub)).
% 107.81/14.04 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', binintersectSubset4)).
% 107.81/14.04 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', binintersectSubset1)).
% 107.81/14.04 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', bs114d)).
% 107.81/14.04 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setminusI)).
% 107.81/14.04 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setminusEL)).
% 107.81/14.04 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setminusER)).
% 107.81/14.04 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setminusSubset2)).
% 107.81/14.04 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setminusERneg)).
% 107.81/14.04 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setminusELneg)).
% 107.81/14.04 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setminusILneg)).
% 107.81/14.04 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setminusIRneg)).
% 107.81/14.04 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setminusLsub)).
% 107.81/14.04 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setminusSubset1)).
% 107.81/14.04 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', symdiffE)).
% 107.81/14.04 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', symdiffI1)).
% 107.81/14.04 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', symdiffI2)).
% 107.81/14.04 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', symdiffIneg1)).
% 107.81/14.04 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', symdiffIneg2)).
% 107.81/14.04 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', secondinupair)).
% 107.81/14.04 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setukpairIL)).
% 107.81/14.04 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setukpairIR)).
% 107.81/14.04 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', kpairiskpair)).
% 107.81/14.04 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', kpairp)).
% 107.81/14.04 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', singletonsubset)).
% 107.81/14.04 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', singletoninpowerset)).
% 107.81/14.04 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', singletoninpowunion)).
% 107.81/14.04 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', upairset2E)).
% 107.81/14.04 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', upairsubunion)).
% 107.81/14.04 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', upairinpowunion)).
% 107.81/14.04 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', ubforcartprodlem1)).
% 107.81/14.04 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', ubforcartprodlem2)).
% 107.81/14.04 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', ubforcartprodlem3)).
% 107.81/14.04 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', cartprodpairin)).
% 107.81/14.04 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.kCofj7HKpX/E---3.1_3219334.p', cartprodmempair1)).
% 107.81/14.04 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', cartprodmempair)).
% 107.81/14.04 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setunionE2)).
% 107.81/14.04 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setunionsingleton1)).
% 107.81/14.04 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setunionsingleton2)).
% 107.81/14.04 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setunionsingleton)).
% 107.81/14.04 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', singletonsuniq)).
% 107.81/14.04 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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.kCofj7HKpX/E---3.1_3219334.p', setukpairinjL1)).
% 107.81/14.04 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', kfstpairEq)).
% 107.81/14.04 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', cartprodfstin)).
% 107.81/14.04 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setukpairinjL2)).
% 107.81/14.04 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setukpairinjL)).
% 107.81/14.04 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setukpairinjR11)).
% 107.81/14.04 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setukpairinjR12)).
% 107.81/14.04 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', setukpairinjR1)).
% 107.81/14.04 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', upairequniteq)).
% 107.81/14.04 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.kCofj7HKpX/E---3.1_3219334.p', setukpairinjR2)).
% 107.81/14.04 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.kCofj7HKpX/E---3.1_3219334.p', setukpairinjR)).
% 107.81/14.04 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', ksndpairEq)).
% 107.81/14.04 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', kpairsurjEq)).
% 107.81/14.04 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', cartprodsndin)).
% 107.81/14.04 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.kCofj7HKpX/E---3.1_3219334.p', cartprodpairmemEL)).
% 107.81/14.04 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.kCofj7HKpX/E---3.1_3219334.p', cartprodpairmemER)).
% 107.81/14.04 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.kCofj7HKpX/E---3.1_3219334.p', cartprodmempaircEq)).
% 107.81/14.04 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.kCofj7HKpX/E---3.1_3219334.p', cartprodfstpairEq)).
% 107.81/14.04 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.kCofj7HKpX/E---3.1_3219334.p', cartprodsndpairEq)).
% 107.81/14.04 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', cartprodpairsurjEq)).
% 107.81/14.04 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', app)).
% 107.81/14.04 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', infuncsetfunc)).
% 107.81/14.04 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.kCofj7HKpX/E---3.1_3219334.p', ap2p)).
% 107.81/14.04 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', funcinfuncset)).
% 107.81/14.04 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', funcGraphProp1)).
% 107.81/14.04 thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', funcGraphProp3)).
% 107.81/14.04 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$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.kCofj7HKpX/E---3.1_3219334.p', funcGraphProp2)).
% 107.81/14.04 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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', funcextLem)).
% 107.81/14.04 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$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.kCofj7HKpX/E---3.1_3219334.p', funcGraphProp4)).
% 107.81/14.04 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.kCofj7HKpX/E---3.1_3219334.p', funcext)).
% 107.81/14.04 thf(funcext2, axiom, ((funcext2)<=>![X4:$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.kCofj7HKpX/E---3.1_3219334.p', funcext2)).
% 107.81/14.04 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.kCofj7HKpX/E---3.1_3219334.p', ap2apEq1)).
% 107.81/14.04 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.kCofj7HKpX/E---3.1_3219334.p', ap2apEq2)).
% 107.81/14.04 thf(c_0_225, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((?[X746:$i]:((((in @ X746 @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))))&(((dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))=(setadjoin @ X746 @ emptyset))))))))), inference(fof_simplification,[status(thm)],[ex1])).
% 107.81/14.04 thf(c_0_226, plain, ((singleton)=(^[Z0:$i]:(?[X2:$i]:((((in @ X2 @ Z0))&(((Z0)=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[singleton])).
% 107.81/14.04 thf(c_0_227, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 107.81/14.04 thf(c_0_228, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 107.81/14.04 thf(c_0_229, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 107.81/14.04 thf(c_0_230, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 107.81/14.04 thf(c_0_231, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 107.81/14.04 thf(c_0_232, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 107.81/14.04 thf(c_0_233, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 107.81/14.04 thf(c_0_234, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 107.81/14.04 thf(c_0_235, 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])).
% 107.81/14.04 thf(c_0_236, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 107.81/14.04 thf(c_0_237, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 107.81/14.04 thf(c_0_238, 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])).
% 107.81/14.04 thf(c_0_239, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 107.81/14.04 thf(c_0_240, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 107.81/14.04 thf(c_0_241, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 107.81/14.04 thf(c_0_242, plain, ((singletonprop)<=>![X4:$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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 107.81/14.04 thf(c_0_243, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 107.81/14.04 thf(c_0_244, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((?[X746:$i]:((((in @ X746 @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))))&(((dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))=(setadjoin @ X746 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_225, c_0_226])).
% 107.81/14.04 thf(c_0_245, 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])).
% 107.81/14.04 thf(c_0_246, 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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 107.81/14.04 thf(c_0_247, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 107.81/14.04 thf(c_0_248, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 107.81/14.04 thf(c_0_249, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 107.81/14.04 thf(c_0_250, plain, ((breln)=(^[Z0:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
% 107.81/14.04 thf(c_0_251, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
% 107.81/14.04 thf(c_0_252, plain, ((ex1E2)<=>![X4:$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])).
% 107.81/14.04 thf(c_0_253, 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)=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X42))&(((X14)=(X2)))))|(((~((X42)))&(((X14)=(X3)))))))))=(setadjoin @ X2 @ emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[iftrueProp2])).
% 107.81/14.04 thf(c_0_254, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X717:$i]:(((((X6 @ X2 @ X717)))&(![X718:$i]:(((((X6 @ X2 @ X718)))=>(((X717)=(X718)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_227, c_0_228])).
% 107.81/14.04 thf(c_0_255, plain, ((descrp)=(![X1:$i > $o]:((((?[X719:$i]:(((((X1 @ X719)))&(![X720:$i]:(((((X1 @ X720)))=>(((X719)=(X720))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_229, c_0_228])).
% 107.81/14.04 thf(c_0_256, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 107.81/14.04 thf(c_0_257, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 107.81/14.04 thf(c_0_258, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 107.81/14.04 thf(c_0_259, plain, ((exuE1)=(![X1:$i > $o]:((((?[X721:$i]:(((((X1 @ X721)))&(![X722:$i]:(((((X1 @ X722)))=>(((X721)=(X722))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_230, c_0_228])).
% 107.81/14.04 thf(c_0_260, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X723:$i]:(((((X1 @ X723)))&(![X724:$i]:(((((X1 @ X724)))=>(((X723)=(X724))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_231, c_0_228])).
% 107.81/14.04 thf(c_0_261, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 107.81/14.04 thf(c_0_262, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_232])).
% 107.81/14.04 thf(c_0_263, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_233, c_0_232])).
% 107.81/14.04 thf(c_0_264, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_232])).
% 107.81/14.04 thf(c_0_265, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 107.81/14.04 thf(c_0_266, plain, ((exuE2)=(![X1:$i > $o]:((((?[X725:$i]:(((((X1 @ X725)))&(![X726:$i]:(((((X1 @ X726)))=>(((X725)=(X726))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_234, c_0_228])).
% 107.81/14.04 thf(c_0_267, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_232])).
% 107.81/14.04 thf(c_0_268, 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])).
% 107.81/14.04 thf(c_0_269, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X727:$i]:(((((X1 @ X727)))&(![X728:$i]:(((((X1 @ X728)))=>(((X727)=(X728)))))))))))))), inference(apply_def,[status(thm)],[c_0_235, c_0_228])).
% 107.81/14.04 thf(c_0_270, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X729:$i]:(((((X1 @ X729)))&(![X730:$i]:(((((X1 @ X730)))=>(((X729)=(X730)))))))))))))))), inference(apply_def,[status(thm)],[c_0_236, c_0_228])).
% 107.81/14.04 thf(c_0_271, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X731:$i]:(((((X1 @ X731)))&(![X732:$i]:(((((X1 @ X732)))=>(((X731)=(X732)))))))))))))), inference(apply_def,[status(thm)],[c_0_237, c_0_228])).
% 107.81/14.04 thf(c_0_272, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X733:$i]:(((((X1 @ X733)))&(![X734:$i]:(((((X1 @ X734)))=>(((X733)=(X734))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_238, c_0_228])).
% 107.81/14.04 thf(c_0_273, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X735:$i]:(((((X1 @ X735)))&(![X736:$i]:(((((X1 @ X736)))=>(((X735)=(X736))))))))))<=>((?[X737:$i]:(((((X17 @ X737)))&(![X738:$i]:(((((X17 @ X738)))=>(((X737)=(X738)))))))))))))))), inference(apply_def,[status(thm)],[c_0_239, c_0_228])).
% 107.81/14.04 thf(c_0_274, plain, ((exuEu)=(![X1:$i > $o]:((((?[X739:$i]:(((((X1 @ X739)))&(![X740:$i]:(((((X1 @ X740)))=>(((X739)=(X740))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_240, c_0_228])).
% 107.81/14.04 thf(c_0_275, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X741:$i]:(((((X1 @ X741)))&(![X742:$i]:(((((X1 @ X742)))=>(((X741)=(X742))))))))))=>((((?[X743:$i]:(((((X17 @ X743)))&(![X744:$i]:(((((X17 @ X744)))=>(((X743)=(X744))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_241, c_0_228])).
% 107.81/14.04 thf(c_0_276, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 107.81/14.04 thf(c_0_277, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 107.81/14.04 thf(c_0_278, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 107.81/14.04 thf(c_0_279, 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)))))=>((?[X745:$i]:((((in @ X745 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(setadjoin @ X745 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_242, c_0_226])).
% 107.81/14.04 thf(c_0_280, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:((((?[X747:$i]:((((in @ X747 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X747 @ emptyset)))))))=>(?[X2:$i]:((((in @ X2 @ X4))&((X1 @ X2))))))))), inference(apply_def,[status(thm)],[c_0_243, c_0_244])).
% 107.81/14.04 thf(c_0_281, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>(((![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X3))=>(((X3)=(X2))))))))=>((?[X748:$i]:((((in @ X748 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X748 @ emptyset))))))))))))))), inference(apply_def,[status(thm)],[c_0_245, c_0_244])).
% 107.81/14.04 thf(c_0_282, 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)))))=>((?[X749:$i]:((((in @ X749 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X749 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_246, c_0_244])).
% 107.81/14.04 thf(c_0_283, plain, ((kfstsingleton)=(![X18:$i]:((((iskpair @ X18))=>((?[X750:$i]:((((in @ X750 @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))))&(((dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))=(setadjoin @ X750 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_247, c_0_226])).
% 107.81/14.04 thf(c_0_284, axiom, ((theprop)=(![X21:$i]:((((?[X751:$i]:((((in @ X751 @ X21))&(((X21)=(setadjoin @ X751 @ emptyset)))))))=>((in @ (setunion @ X21) @ X21)))))), inference(apply_def,[status(thm)],[theprop, c_0_226])).
% 107.81/14.04 thf(c_0_285, plain, ((ksndsingleton)=(![X18:$i]:((((iskpair @ X18))=>((?[X752:$i]:((((in @ X752 @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))))&(((dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))=(setadjoin @ X752 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_248, c_0_226])).
% 107.81/14.04 thf(c_0_286, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 107.81/14.04 thf(c_0_287, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 107.81/14.04 thf(c_0_288, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_249, c_0_250])).
% 107.81/14.04 thf(c_0_289, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 107.81/14.04 thf(c_0_290, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 107.81/14.04 thf(c_0_291, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 107.81/14.04 thf(c_0_292, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 107.81/14.04 thf(c_0_293, plain, ((funcImageSingleton)=(![X4:$i, X5:$i, X29:$i]:((((func @ X4 @ X5 @ X29))=>(![X2:$i]:((((in @ X2 @ X4))=>((?[X753:$i]:((((in @ X753 @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))=(setadjoin @ X753 @ emptyset)))))))))))))), inference(apply_def,[status(thm)],[c_0_251, c_0_226])).
% 107.81/14.04 thf(c_0_294, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
% 107.81/14.04 thf(c_0_295, plain, ((lamProp)<=>![X4:$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])).
% 107.81/14.04 thf(c_0_296, 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:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
% 107.81/14.04 thf(c_0_297, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
% 107.81/14.04 thf(c_0_298, axiom, ((brelnall1)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((X1 @ (kpair @ X2 @ X3)))))))))))=>(![X2:$i]:((((in @ X2 @ X33))=>((X1 @ X2)))))))))))), inference(apply_def,[status(thm)],[brelnall1, c_0_250])).
% 107.81/14.04 thf(c_0_299, axiom, ((brelnall2)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((X1 @ (kpair @ X2 @ X3)))))))))))=>(![X2:$i]:((((in @ X2 @ X33))=>((X1 @ X2)))))))))))), inference(apply_def,[status(thm)],[brelnall2, c_0_250])).
% 107.81/14.04 thf(c_0_300, plain, ((ex1E2)=(![X4:$i, X1:$i > $o]:((((?[X754:$i]:((((in @ X754 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X754 @ emptyset)))))))=>(![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))))))))))), inference(apply_def,[status(thm)],[c_0_252, c_0_244])).
% 107.81/14.04 thf(c_0_301, axiom, ((subbreln)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X35:$i]:(((((subset @ X35 @ (cartprod @ X4 @ X5))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((in @ (kpair @ X2 @ X3) @ X35))))))))))=>((subset @ X33 @ X35))))))))))), inference(apply_def,[status(thm)],[subbreln, c_0_250])).
% 107.81/14.04 thf(c_0_302, axiom, ((eqbreln)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X35:$i]:(((((subset @ X35 @ (cartprod @ X4 @ X5))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((in @ (kpair @ X2 @ X3) @ X35))))))))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X35))=>((in @ (kpair @ X2 @ X3) @ X33))))))))))=>(((X33)=(X35)))))))))))))), inference(apply_def,[status(thm)],[eqbreln, c_0_250])).
% 107.81/14.04 thf(c_0_303, 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])).
% 107.81/14.04 thf(c_0_304, 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])).
% 107.81/14.04 thf(c_0_305, 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])).
% 107.81/14.04 thf(c_0_306, 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])).
% 107.81/14.04 thf(c_0_307, 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])).
% 107.81/14.04 thf(c_0_308, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X39))&(((Z0)=(X2)))))|(((~((X39)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
% 107.81/14.04 thf(c_0_309, plain, ((iffalseProp2)<=>![X4:$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])).
% 107.81/14.04 thf(c_0_310, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X41))&(((Z0)=(X2)))))|(((~((X41)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
% 107.81/14.04 thf(c_0_311, plain, ((epred1_0)<=>![X784:$i]:(?[X785:$i]:((((![X786:$i]:(((in @ X786 @ X785)=>![X787:$i]:(((in @ X787 @ X786)=>(in @ X787 @ X784)))))&![X788:$i, X789:$i]:((((in @ X788 @ X784)&(in @ X789 @ X784))=>(![X790:$i]:(((in @ X790 @ X785)=>((in @ X788 @ X790)<=>(in @ X789 @ X790))))=>((X788)=(X789))))))&![X791:$i, X792:$i]:((((in @ X791 @ X785)&(in @ X792 @ X785))=>(![X793:$i]:(((in @ X793 @ X791)=>(in @ X793 @ X792)))|![X794:$i]:(((in @ X794 @ X792)=>(in @ X794 @ X791)))))))&![X795:$i]:(((![X796:$i]:(((in @ X796 @ X795)=>(in @ X796 @ X784)))&?[X797:$i]:((in @ X797 @ X795)))=>?[X798:$i, X799:$i]:(((((in @ X798 @ X785)&(in @ X799 @ X795))&~(?[X800:$i]:(((in @ X800 @ X798)&(in @ X800 @ X795)))))&![X801:$i]:(((in @ X801 @ X785)=>(![X802:$i]:(((in @ X802 @ X801)=>(in @ X802 @ X798)))|(in @ X799 @ X801)))))))))))), introduced(definition)).
% 107.81/14.04 thf(c_0_312, negated_conjecture, ~((![X755:$i, X756:$i]:((![X757:$i]:(((in @ X757 @ X755)<=>(in @ X757 @ X756)))=>((X755)=(X756))))=>(![X758:$i]:(~(in @ X758 @ emptyset))=>(![X759:$i, X760:$i, X761:$i]:(((in @ X761 @ (setadjoin @ X759 @ X760))<=>(((X761)=(X759))|(in @ X761 @ X760))))=>(![X762:$i, X763:$i]:(((in @ X763 @ (powerset @ X762))<=>![X764:$i]:(((in @ X764 @ X763)=>(in @ X764 @ X762)))))=>(![X765:$i, X766:$i]:(((in @ X766 @ (setunion @ X765))<=>?[X767:$i]:(((in @ X766 @ X767)&(in @ X767 @ X765)))))=>((in @ emptyset @ omega)=>(![X768:$i]:(((in @ X768 @ omega)=>(in @ (setadjoin @ X768 @ X768) @ omega)))=>(![X769:$i]:((((in @ emptyset @ X769)&![X770:$i]:((((in @ X770 @ omega)&(in @ X770 @ X769))=>(in @ (setadjoin @ X770 @ X770) @ X769))))=>![X771:$i]:(((in @ X771 @ omega)=>(in @ X771 @ X769)))))=>(![X772:$i > $i > $o, X773:$i]:((![X774:$i]:(((in @ X774 @ X773)=>?[X775:$i]:(((X772 @ X774 @ X775)&![X776:$i]:(((X772 @ X774 @ X776)=>((X775)=(X776))))))))=>?[X777:$i]:(![X778:$i]:(((in @ X778 @ X777)<=>?[X779:$i]:(((in @ X779 @ X773)&(X772 @ X779 @ X778))))))))=>(![X780:$i]:((?[X781:$i]:((in @ X781 @ X780))=>?[X782:$i]:(((in @ X782 @ X780)&~(?[X783:$i]:(((in @ X783 @ X782)&(in @ X783 @ X780))))))))=>((epred1_0)=>(![X803:$i > $o]:((?[X804:$i]:(((X803 @ X804)&![X805:$i]:(((X803 @ X805)=>((X804)=(X805))))))=>(X803 @ (descr @ (^[Z0:$i]:(X803 @ Z0))))))=>(![X806:$i, X807:$i > $o, X808:$i]:(((in @ X808 @ X806)=>((X807 @ X808)=>(in @ X808 @ (dsetconstr @ X806 @ X807)))))=>(![X809:$i, X810:$i > $o, X811:$i]:(((in @ X811 @ (dsetconstr @ X809 @ X810))=>(in @ X811 @ X809)))=>(![X812:$i, X813:$i > $o, X814:$i]:(((in @ X814 @ (dsetconstr @ X812 @ X813))=>(X813 @ X814)))=>(![X815:$i > $o]:((?[X816:$i]:(((X815 @ X816)&![X817:$i]:(((X815 @ X817)=>((X816)=(X817))))))=>?[X818:$i]:(((X815 @ X818)&![X819:$i]:(((X815 @ X819)=>((X818)=(X819))))))))=>(![X820:$o, X821:$i]:(((in @ X821 @ (prop2set @ ((X820))))=>(X820)))=>(![X822:$i]:(((in @ X822 @ emptyset)=>![X823:$o]:((X823))))=>(![X824:$i]:(((in @ X824 @ emptyset)=>~($true)))=>(![X825:$i]:(~(in @ X825 @ emptyset))=>(![X826:$i > $o]:((?[X827:$i]:(((X826 @ X827)&![X828:$i]:(((X826 @ X828)=>((X827)=(X828))))))=>?[X829:$i]:((X826 @ X829))))=>(![X830:$i, X831:$i]:((![X832:$i]:(((in @ X832 @ X830)=>(in @ X832 @ X831)))=>(![X833:$i]:(((in @ X833 @ X831)=>(in @ X833 @ X830)))=>((X830)=(X831)))))=>(![X834:$i]:((![X835:$i]:(~(in @ X835 @ X834))=>((X834)=(emptyset))))=>(![X836:$i]:((![X837:$i]:(~(in @ X837 @ X836))=>((X836)=(emptyset))))=>(![X838:$i, X839:$i > $o, X840:$i]:(((in @ X840 @ X838)=>((in @ X840 @ (dsetconstr @ X838 @ X839))<=>(X839 @ X840))))=>(![X841:$i]:((((X841)!=(emptyset))=>?[X842:$i]:((in @ X842 @ X841))))=>(![X843:$i, X844:$i > $o, X845:$i]:(((in @ X845 @ X843)=>((X844 @ X845)=>((dsetconstr @ X843 @ X844)!=(emptyset)))))=>(![X846:$i]:((?[X847:$i]:((in @ X847 @ X846))=>((X846)!=(emptyset))))=>(![X848:$i, X849:$i]:((in @ X848 @ (setadjoin @ X848 @ X849)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X850:$i, X851:$i, X852:$i]:(((in @ X852 @ X851)=>(in @ X852 @ (setadjoin @ X850 @ X851))))=>(![X853:$i, X854:$i, X855:$i]:(((in @ X855 @ (setadjoin @ X853 @ X854))=>![X856:$o]:(((((X855)=(X853))=>(X856))=>(((in @ X855 @ X854)=>(X856))=>(X856))))))=>(![X857:$i, X858:$i, X859:$i]:(((in @ X859 @ (setadjoin @ X857 @ X858))=>(((X859)=(X857))|(in @ X859 @ X858))))=>(![X860:$i]:(((dsetconstr @ X860 @ (^[Z0:$i]:($true)))=(X860)))=>(![X861:$i, X862:$i]:((![X863:$i]:(((in @ X863 @ X862)=>(in @ X863 @ X861)))=>(in @ X862 @ (powerset @ X861))))=>(![X864:$i]:((in @ emptyset @ (powerset @ X864)))=>(![X865:$i]:((in @ emptyset @ (powerset @ X865)))=>(![X866:$i, X867:$i, X868:$i]:(((in @ X867 @ (powerset @ X866))=>((in @ X868 @ X867)=>(in @ X868 @ X866))))=>(![X869:$i, X870:$i, X871:$i]:(((in @ X870 @ X871)=>((in @ X871 @ X869)=>(in @ X870 @ (setunion @ X869)))))=>(![X872:$i, X873:$i]:(((in @ X873 @ (setunion @ X872))=>![X874:$o]:((![X875:$i]:(((in @ X873 @ X875)=>((in @ X875 @ X872)=>(X874))))=>(X874)))))=>(![X876:$i, X877:$i]:(((in @ X877 @ X876)=>(in @ X877 @ (powerset @ (setunion @ X876)))))=>(![X878:$i > $o]:((?[X879:$i]:(((X878 @ X879)&![X880:$i]:(((X878 @ X880)=>((X879)=(X880))))))=>?[X881:$i]:(![X882:$i]:(((X878 @ X882)<=>((X882)=(X881)))))))=>(![X883:$i]:((((X883)!=(emptyset))=>?[X884:$i]:(((in @ X884 @ X883)&$true))))=>(![X885:$i, X886:$i]:(((in @ X885 @ (setadjoin @ X886 @ emptyset))=>((X885)=(X886))))=>(![X887:$i, X888:$i]:((((X887)!=(X888))=>~(in @ X888 @ (setadjoin @ X887 @ emptyset))))=>(![X889:$i, X890:$i]:((((X889)=(X890))=>(in @ X889 @ (setadjoin @ X890 @ emptyset))))=>(![X891:$i, X892:$i]:(((in @ X891 @ (setadjoin @ X892 @ emptyset))=>(in @ X892 @ (setadjoin @ X891 @ emptyset))))=>(![X893:$i, X894:$i, X895:$i]:(((in @ X895 @ (setadjoin @ X893 @ (setadjoin @ X894 @ emptyset)))=>(((X895)=(X893))|((X895)=(X894)))))=>(![X896:$i, X897:$i]:((in @ X896 @ (setadjoin @ X896 @ (setadjoin @ X897 @ emptyset))))=>(![X898:$i, X899:$i]:((in @ X899 @ (setadjoin @ X898 @ (setadjoin @ X899 @ emptyset))))=>(![X900:$i, X901:$i > $o]:((?[X902:$i]:(((in @ X902 @ X900)&(X901 @ X902)))=>(((dsetconstr @ X900 @ X901)=(emptyset))=>~($true))))=>(![X903:$i > $o, X904:$i]:(((in @ X904 @ emptyset)=>(X903 @ X904)))=>(![X905:$i, X906:$i > $o]:((~(![X907:$i]:(((in @ X907 @ X905)=>(X906 @ X907))))=>?[X908:$i]:(((in @ X908 @ X905)&~((X906 @ X908))))))=>(![X909:$i, X910:$i > $o]:((![X911:$i]:(((in @ X911 @ X909)=>~((X910 @ X911))))=>~(?[X912:$i]:(((in @ X912 @ X909)&(X910 @ X912))))))=>(![X913:$i, X914:$i > $o]:((~(?[X915:$i]:(((in @ X915 @ X913)&(X914 @ X915))))=>![X916:$i]:(((in @ X916 @ X913)=>~((X914 @ X916))))))=>(![X917:$i, X918:$i > $o]:((?[X919:$i]:(((in @ X919 @ X917)&~((X918 @ X919))))=>~(![X920:$i]:(((in @ X920 @ X917)=>(X918 @ X920))))))=>(![X921:$o]:(((X921)=>(in @ emptyset @ (prop2set @ ((X921))))))=>(![X922:$o]:(((X922)=>(set2prop @ (prop2set @ ((X922))))))=>(![X923:$i, X924:$i > $o]:((~(?[X925:$i]:(((in @ X925 @ X923)&(X924 @ X925))))=>![X926:$i]:(((in @ X926 @ X923)=>~((X924 @ X926))))))=>(![X927:$i, X928:$i > $o]:((~(![X929:$i]:(((in @ X929 @ X927)=>(X928 @ X929))))=>?[X930:$i]:(((in @ X930 @ X927)&~((X928 @ X930))))))=>(![X931:$i > $o]:((?[X932:$i]:(((X931 @ X932)&![X933:$i]:(((X931 @ X933)=>((X932)=(X933))))))=>?[X934:$i]:(((X931 @ X934)&![X935:$i]:(((X931 @ X935)=>((X934)=(X935))))))))=>(![X936:$i > $o]:((?[X937:$i]:((X936 @ X937))=>(![X938:$i, X939:$i]:(((X936 @ X938)=>((X936 @ X939)=>((X938)=(X939)))))=>?[X940:$i]:(((X936 @ X940)&![X941:$i]:(((X936 @ X941)=>((X940)=(X941)))))))))=>(![X942:$i > $o]:((?[X943:$i]:(![X944:$i]:(((X942 @ X944)<=>((X944)=(X943)))))=>?[X945:$i]:(((X942 @ X945)&![X946:$i]:(((X942 @ X946)=>((X945)=(X946))))))))=>(![X947:$i, X948:$i]:((((X947)=(X948))=>![X949:$i, X950:$i]:((((X949)=(X950))=>((in @ X949 @ X947)=>(in @ X950 @ X948))))))=>(![X951:$i, X952:$i]:((((X951)=(X952))=>![X953:$i, X954:$i]:((((X953)=(X954))=>((in @ X953 @ X951)<=>(in @ X954 @ X952))))))=>(![X955:$i > $o]:((?[X956:$i]:(((X955 @ X956)&![X957:$i]:(((X955 @ X957)=>((X956)=(X957))))))=>![X958:$i, X959:$i]:(((X955 @ X958)=>((X955 @ X959)=>((X958)=(X959)))))))=>(![X960:$i > $o, X961:$i > $o]:((![X962:$i, X963:$i]:((((X962)=(X963))=>((X960 @ X962)<=>(X961 @ X963))))=>(?[X964:$i]:(((X960 @ X964)&![X965:$i]:(((X960 @ X965)=>((X964)=(X965))))))<=>?[X966:$i]:(((X961 @ X966)&![X967:$i]:(((X961 @ X967)=>((X966)=(X967)))))))))=>(((emptyset)=(emptyset))=>(![X968:$i, X969:$i]:((((X968)=(X969))=>![X970:$i, X971:$i]:((((X970)=(X971))=>((setadjoin @ X968 @ X970)=(setadjoin @ X969 @ X971))))))=>(![X972:$i, X973:$i]:((((X972)=(X973))=>((powerset @ X972)=(powerset @ X973))))=>(![X974:$i, X975:$i]:((((X974)=(X975))=>((setunion @ X974)=(setunion @ X975))))=>(((omega)=(omega))=>(![X976:$i > $o]:((?[X977:$i]:(((X976 @ X977)&![X978:$i]:(((X976 @ X978)=>((X977)=(X978))))))=>![X979:$i, X980:$i]:(((X976 @ X979)=>((X976 @ X980)=>((X979)=(X980)))))))=>(![X981:$i 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kpairiskpair]), kpairp]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1]), cartprodmempair]), setunionE2]), setunionsingleton1]), setunionsingleton2]), setunionsingleton]), c_0_279]), c_0_280]), c_0_281]), c_0_282]), singletonsuniq]), setukpairinjL1]), c_0_283]), c_0_284]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_285]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_286]), c_0_287]), c_0_288]), c_0_289]), c_0_290]), c_0_291]), c_0_292]), c_0_293]), c_0_294]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_295]), c_0_296]), c_0_297]), c_0_298]), c_0_299]), c_0_300]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), c_0_301]), c_0_302]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_303]), c_0_304]), c_0_305]), c_0_306]), c_0_307]), c_0_308]), c_0_309]), c_0_310])])]), c_0_311])).
% 107.81/14.04 thf(c_0_313, negated_conjecture, ![X1462:$i, X1463:$i, X1465:$i, X1466:$i, X1467:$i, X1468:$i, X1469:$i, X1470:$i, X1471:$i, X1472:$i, X1473:$i, X1475:$i, X1476:$i, X1478:$i, X1479:$i, X1480:$i, X1481:$i, X1482:$i, X1484:$i, X1485:$i > $i > $o, X1486:$i, X1488:$i, X1491:$i, X1493:$i, X1494:$i, X1495:$i, X1496:$i, X1498:$i, X1499:$i > $o, X1500:$i, X1502:$i, X1503:$i > $o, X1504:$i, X1505:$i, X1506:$i > $o, X1507:$i, X1508:$i, X1509:$i > $o, X1510:$i, X1511:$i > $o, X1512:$i, X1515:$i, X1516:$o, X1517:$i, X1518:$i, X1519:$o, X1520:$i, X1521:$i, X1522:$i > $o, X1523:$i, X1526:$i, X1527:$i, X1530:$i, X1532:$i, X1534:$i, X1535:$i > $o, X1536:$i, X1537:$i, X1539:$i, X1540:$i > $o, X1541:$i, X1542:$i, X1543:$i, X1544:$i, X1545:$i, X1546:$i, X1547:$i, X1548:$i, X1549:$i, X1550:$i, X1551:$i, X1552:$o, X1553:$i, X1554:$i, X1555:$i, X1556:$i, X1557:$i, X1558:$i, X1560:$i, X1561:$i, X1562:$i, X1563:$i, X1564:$i, X1565:$i, X1566:$i, X1567:$i, X1568:$i, X1569:$i, X1570:$o, X1572:$i, X1573:$i, X1574:$i > $o, X1575:$i, X1578:$i, X1579:$i, X1580:$i, X1582:$i, X1583:$i, X1584:$i, X1585:$i, X1586:$i, X1587:$i, X1588:$i, X1589:$i, X1590:$i, X1591:$i, X1592:$i, X1593:$i, X1594:$i, X1595:$i, X1596:$i, X1597:$i, X1598:$i > $o, X1599:$i, X1600:$i > $o, X1601:$i, X1602:$i, X1603:$i > $o, X1604:$i, X1606:$i, X1607:$i > $o, X1609:$i, X1610:$i, X1611:$i > $o, X1613:$i, X1614:$i, X1615:$i > $o, X1616:$i, X1618:$o, X1619:$o, X1620:$i, X1621:$i > $o, X1623:$i, X1624:$i, X1625:$i > $o, X1626:$i, X1628:$i > $o, X1629:$i, X1632:$i, X1633:$i > $o, X1634:$i, X1638:$i, X1639:$i > $o, X1640:$i, X1643:$i, X1644:$i, X1645:$i, X1646:$i, X1647:$i, X1648:$i, X1649:$i, X1650:$i, X1651:$i, X1652:$i > $o, X1653:$i, X1655:$i, X1656:$i, X1657:$i > $o, X1658:$i > $o, X1661:$i, X1664:$i, X1665:$i, X1668:$i, X1669:$i, X1670:$i, X1671:$i, X1672:$i, X1673:$i, X1674:$i, X1675:$i, X1676:$i, X1677:$i > $o, X1678:$i, X1680:$i, X1681:$i, X1682:$i > $o, X1683:$i > $o, X1686:$i, X1688:$i, X1690:$i, X1691:$i, X1692:$i > $o, X1693:$i > $o, X1696:$i, X1697:$i, X1699:$i, X1700:$i, X1701:$i, X1702:$i, X1703:$i, X1704:$i, X1706:$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:$i, X1724:$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 > $o, X1744:$i, X1745:$i > $o, X1746:$i, X1747:$i, X1748:$i, X1749:$i, X1750:$i, X1751:$i, X1752:$i, X1753:$i, X1754:$i, X1755:$i, X1756:$i, X1757:$o, X1758:$i, X1759:$i, X1760:$i, X1761:$i, X1762:$i, X1763:$i, X1764:$i, X1765:$i, X1766:$i, X1767:$i, X1768:$i, X1769:$i, X1770:$i, X1771:$i, X1772:$i, X1773:$i, X1774:$i, X1775:$i, X1776:$i, X1777:$i, X1778:$i, X1779:$i, X1780:$i, X1781:$i, X1782:$i, X1783:$i, X1784:$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, X1824:$i, X1825:$o, X1826:$i, X1827:$i, X1828:$i, X1829:$i, X1830:$i, X1831:$i, X1832:$i, X1833:$i, X1834:$i, X1835:$i, X1836:$i, X1837:$i, X1838:$i, X1839:$i, X1840:$i, X1841:$i, X1842:$i, X1843:$i, X1844:$i, X1845:$i, X1846:$i, X1847:$i, X1848:$i, X1849:$i, X1850:$i, X1851:$i, X1852:$i, X1853:$i, X1854:$i, X1855:$i, X1856:$i, X1857:$i, X1858:$i, X1859:$i, X1860:$i, X1861:$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:$i, X1887:$i, X1888:$i, X1889:$i, X1890:$i, X1891:$i, X1893:$i, X1894:$i, X1895:$i, X1896:$i, X1897:$i > $o, X1900:$i, X1902:$i, X1903:$i > $o, X1904:$i, X1906:$i, X1907:$i > $o, X1908:$i, X1911:$i, X1912:$i > $o, X1915:$i, X1917:$i, X1918:$i, X1919:$i, X1920:$i, X1921:$i, X1922:$i, X1924:$i, X1925:$i, X1926:$i, X1927:$i, X1928:$i, X1929:$i, X1930:$i, X1931:$i, X1932:$i, X1933:$i, X1934:$i, X1935:$i, X1936:$i, X1937:$i, X1938:$i, X1939:$i, X1940:$i, X1941:$i, X1942:$i, X1943:$i, X1944:$i, X1945:$i, X1946:$i, X1947:$i, X1948:$i, X1949:$i, X1950:$i, X1951:$i, X1952:$i, X1953:$i, X1954:$i, X1955:$i, X1956:$i, X1957:$i, X1958:$i, X1960:$i, X1961:$i, X1962:$i, X1963:$i, X1964:$i, X1965:$i, X1966:$i, X1967:$i, X1968:$i, X1969:$i, X1970:$i, X1971:$i, X1972:$i, X1973:$i, X1974:$i, X1975:$i, X1976:$i, X1977:$i, X1978:$i, X1979:$i, X1980:$i, X1981:$i, X1982:$i, X1983:$i, X1984:$i, X1985:$i, X1986:$i, X1987:$i, X1988:$i, X1989:$i, X1990:$i, X1991:$i > $i > $o, X1992:$i, X1993:$i, X1994:$i, X1995:$i, X1996:$i > $i > $o, X1997:$i, X1998:$i, X1999:$i > $i > $o, X2000:$i, X2001:$i, X2002:$i > $i > $o, X2003:$i, X2004:$i, X2005:$i, X2006:$i, X2007:$i > $i > $o, X2008:$i, X2009:$i, X2010:$i, X2011:$i, X2012:$i > $i > $o, X2013:$i, X2014:$i, X2015:$i, X2016:$i, X2017:$i > $i > $o, X2018:$i, X2019:$i, X2020:$i, X2021:$i, X2022:$i, X2023:$i, X2025:$i, X2026:$i, X2027:$i, X2028:$i, X2029:$i, X2030:$i, X2031:$i, X2032:$i, X2033:$i, X2034:$i, X2035:$i, X2036:$i, X2037:$i, X2038:$i, X2039:$i, X2040:$i, X2041:$i, X2042:$i, X2043:$i, X2044:$i, X2045:$i > $i, X2047:$i, X2048:$i, X2049:$i > $i, X2051:$i, X2052:$i, X2053:$i > $i, X2055:$i, X2056:$i, X2057:$i, X2058:$i > $o, X2061:$i, X2062:$i, X2063:$i, X2064:$i, X2065:$i > $o, X2068:$i, X2069:$i, X2070:$i > $o, X2071:$i, X2072:$i, X2073:$i, X2074:$i, X2075:$i, X2076:$i, X2077:$i, X2078:$i, X2079:$i, X2080:$i, X2081:$i, X2082:$i, X2083:$i, X2084:$i, X2085:$i, X2086:$i, X2087:$i, X2088:$i, X2089:$i, X2090:$i, X2092:$i, X2093:$i, X2094:$i, X2095:$i, X2096:$i, X2097:$i, X2098:$i, X2099:$i, X2100:$i, X2101:$i, X2102:$i, X2105:$i, X2106:$i, X2107:$i, X2108:$i, X2113:$i, X2114:$i, X2115:$i, X2116:$i, X2118:$i, X2119:$i, X2120:$i, X2121:$i, X2123:$i, X2124:$i, X2125:$i, X2126:$i, X2127:$i, X2128:$i, X2129:$i, X2130:$i, X2131:$i, X2132:$i, X2133:$i > $i, X2135:$i, X2136:$i, X2137:$i, X2138:$i, X2139:$i, X2140:$i, X2141:$i > $i, X2143:$i, X2144:$i, X2145:$i > $i, X2147:$i, X2148:$i, X2149:$i, X2150:$i, X2151:$i, X2152:$o, X2153:$i, X2154:$i, X2155:$i, X2156:$o, X2157:$i, X2158:$i, X2159:$i, X2160:$o, X2161:$i, X2162:$i]:((((~(in @ (esk1_2 @ X1462 @ X1463) @ X1462)|~(in @ (esk1_2 @ X1462 @ X1463) @ X1463)|((X1462)=(X1463)))&((in @ (esk1_2 @ X1462 @ X1463) @ X1462)|(in @ (esk1_2 @ X1462 @ X1463) @ X1463)|((X1462)=(X1463))))&(~(in @ X1465 @ emptyset)&(((~(in @ X1468 @ (setadjoin @ X1466 @ X1467))|(((X1468)=(X1466))|(in @ X1468 @ X1467)))&((((X1468)!=(X1466))|(in @ X1468 @ (setadjoin @ X1466 @ X1467)))&(~(in @ X1468 @ X1467)|(in @ X1468 @ (setadjoin @ X1466 @ X1467)))))&(((~(in @ X1470 @ (powerset @ X1469))|(~(in @ X1471 @ X1470)|(in @ X1471 @ X1469)))&(((in @ (esk2_2 @ X1472 @ X1473) @ X1473)|(in @ X1473 @ (powerset @ X1472)))&(~(in @ (esk2_2 @ X1472 @ X1473) @ X1472)|(in @ X1473 @ (powerset @ X1472)))))&(((((in @ X1476 @ (esk3_2 @ X1475 @ X1476))|~(in @ X1476 @ (setunion @ X1475)))&((in @ (esk3_2 @ X1475 @ X1476) @ X1475)|~(in @ X1476 @ (setunion @ X1475))))&(~(in @ X1479 @ X1480)|~(in @ X1480 @ X1478)|(in @ X1479 @ (setunion @ X1478))))&((in @ emptyset @ omega)&((~(in @ X1481 @ omega)|(in @ (setadjoin @ X1481 @ X1481) @ omega))&(((((in @ (esk4_1 @ X1482) @ omega)|~(in @ emptyset @ X1482)|(~(in @ X1484 @ omega)|(in @ X1484 @ X1482)))&((in @ (esk4_1 @ X1482) @ X1482)|~(in @ emptyset @ X1482)|(~(in @ X1484 @ omega)|(in @ X1484 @ X1482))))&(~(in @ (setadjoin @ (esk4_1 @ X1482) @ (esk4_1 @ X1482)) @ X1482)|~(in @ emptyset @ X1482)|(~(in @ X1484 @ omega)|(in @ X1484 @ X1482))))&((((((in @ (esk8_3 @ X1485 @ X1486 @ X1491) @ X1486)|~(in @ X1491 @ (esk7_2 @ X1485 @ X1486))|(in @ (esk5_2 @ X1485 @ X1486) @ X1486))&((X1485 @ (esk8_3 @ X1485 @ X1486 @ X1491) @ X1491)|~(in @ X1491 @ (esk7_2 @ X1485 @ X1486))|(in @ (esk5_2 @ X1485 @ X1486) @ X1486)))&(~(in @ X1494 @ X1486)|~(X1485 @ X1494 @ X1493)|(in @ X1493 @ (esk7_2 @ X1485 @ X1486))|(in @ (esk5_2 @ X1485 @ X1486) @ X1486)))&(((((in @ (esk8_3 @ X1485 @ X1486 @ X1491) @ X1486)|~(in @ X1491 @ (esk7_2 @ X1485 @ X1486))|((X1485 @ (esk5_2 @ X1485 @ X1486) @ (esk6_3 @ X1485 @ X1486 @ X1488))|~(X1485 @ (esk5_2 @ X1485 @ X1486) @ X1488)))&((X1485 @ (esk8_3 @ X1485 @ X1486 @ X1491) @ X1491)|~(in @ X1491 @ (esk7_2 @ X1485 @ X1486))|((X1485 @ (esk5_2 @ X1485 @ X1486) @ (esk6_3 @ X1485 @ X1486 @ X1488))|~(X1485 @ (esk5_2 @ X1485 @ X1486) @ X1488))))&(~(in @ X1494 @ X1486)|~(X1485 @ X1494 @ X1493)|(in @ X1493 @ (esk7_2 @ X1485 @ X1486))|((X1485 @ (esk5_2 @ X1485 @ X1486) @ (esk6_3 @ X1485 @ X1486 @ X1488))|~(X1485 @ (esk5_2 @ X1485 @ X1486) @ X1488))))&((((in @ (esk8_3 @ X1485 @ X1486 @ X1491) @ X1486)|~(in @ X1491 @ (esk7_2 @ X1485 @ X1486))|(((X1488)!=(esk6_3 @ X1485 @ X1486 @ X1488))|~(X1485 @ (esk5_2 @ X1485 @ X1486) @ X1488)))&((X1485 @ (esk8_3 @ X1485 @ X1486 @ X1491) @ X1491)|~(in @ X1491 @ (esk7_2 @ X1485 @ X1486))|(((X1488)!=(esk6_3 @ X1485 @ X1486 @ X1488))|~(X1485 @ (esk5_2 @ X1485 @ X1486) @ X1488))))&(~(in @ X1494 @ X1486)|~(X1485 @ X1494 @ X1493)|(in @ X1493 @ (esk7_2 @ X1485 @ X1486))|(((X1488)!=(esk6_3 @ X1485 @ X1486 @ X1488))|~(X1485 @ (esk5_2 @ X1485 @ X1486) @ X1488))))))&((((in @ (esk9_1 @ X1495) @ X1495)|~(in @ X1496 @ X1495))&(~(in @ X1498 @ (esk9_1 @ X1495))|~(in @ X1498 @ X1495)|~(in @ X1496 @ X1495)))&((epred1_0)&((((X1499 @ (esk10_2 @ X1499 @ X1500))|~(X1499 @ X1500)|(X1499 @ (descr @ X1499)))&(((X1500)!=(esk10_2 @ X1499 @ X1500))|~(X1499 @ X1500)|(X1499 @ (descr @ X1499))))&((~(in @ X1504 @ X1502)|(~(X1503 @ X1504)|(in @ X1504 @ (dsetconstr @ X1502 @ X1503))))&((~(in @ X1507 @ (dsetconstr @ X1505 @ X1506))|(in @ X1507 @ X1505))&((~(in @ X1510 @ (dsetconstr @ X1508 @ X1509))|(X1509 @ X1510))&(((((X1511 @ (esk12_1 @ X1511))|((X1511 @ (esk11_2 @ X1511 @ X1512))|~(X1511 @ X1512)))&(~(X1511 @ X1515)|((esk12_1 @ X1511)=(X1515))|((X1511 @ (esk11_2 @ X1511 @ X1512))|~(X1511 @ X1512))))&(((X1511 @ (esk12_1 @ X1511))|(((X1512)!=(esk11_2 @ X1511 @ X1512))|~(X1511 @ X1512)))&(~(X1511 @ X1515)|((esk12_1 @ X1511)=(X1515))|(((X1512)!=(esk11_2 @ X1511 @ X1512))|~(X1511 @ X1512)))))&((~(in @ X1517 @ (prop2set @ ((X1516))))|(X1516))&((~(in @ X1518 @ emptyset)|(X1519))&((~(in @ X1520 @ emptyset)|~($true))&(~(in @ X1521 @ emptyset)&((((X1522 @ (esk13_2 @ X1522 @ X1523))|~(X1522 @ X1523)|(X1522 @ (esk14_1 @ X1522)))&(((X1523)!=(esk13_2 @ X1522 @ X1523))|~(X1522 @ X1523)|(X1522 @ (esk14_1 @ X1522))))&(((((in @ (esk16_2 @ X1526 @ X1527) @ X1527)|((X1526)=(X1527))|(in @ (esk15_2 @ X1526 @ X1527) @ X1526))&(~(in @ (esk16_2 @ X1526 @ X1527) @ X1526)|((X1526)=(X1527))|(in @ (esk15_2 @ X1526 @ X1527) @ X1526)))&(((in @ (esk16_2 @ X1526 @ X1527) @ X1527)|((X1526)=(X1527))|~(in @ (esk15_2 @ X1526 @ X1527) @ X1527))&(~(in @ (esk16_2 @ X1526 @ X1527) @ X1526)|((X1526)=(X1527))|~(in @ (esk15_2 @ X1526 @ X1527) @ X1527))))&(((in @ (esk17_1 @ X1530) @ X1530)|((X1530)=(emptyset)))&(((in @ (esk18_1 @ X1532) @ X1532)|((X1532)=(emptyset)))&(((~(in @ X1536 @ (dsetconstr @ X1534 @ X1535))|(X1535 @ X1536)|~(in @ X1536 @ X1534))&(~(X1535 @ X1536)|(in @ X1536 @ (dsetconstr @ X1534 @ X1535))|~(in @ X1536 @ X1534)))&((((X1537)=(emptyset))|(in @ (esk19_1 @ X1537) @ X1537))&((~(in @ X1541 @ X1539)|(~(X1540 @ X1541)|((dsetconstr @ X1539 @ X1540)!=(emptyset))))&((~(in @ X1543 @ X1542)|((X1542)!=(emptyset)))&((in @ X1544 @ (setadjoin @ X1544 @ X1545))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X1548 @ X1547)|(in @ X1548 @ (setadjoin @ X1546 @ X1547)))&(((((in @ X1551 @ X1550)|(X1552)|((X1551)=(X1549))|~(in @ X1551 @ (setadjoin @ X1549 @ X1550)))&(~(X1552)|(X1552)|((X1551)=(X1549))|~(in @ X1551 @ (setadjoin @ X1549 @ X1550))))&(((in @ X1551 @ X1550)|(X1552)|~(X1552)|~(in @ X1551 @ (setadjoin @ X1549 @ 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(kpair @ X1980 @ X1981))=(X1980))))&((~(in @ X1984 @ X1982)|(~(in @ X1985 @ X1983)|((ksnd @ (kpair @ X1984 @ X1985))=(X1985))))&((~(in @ X1988 @ (cartprod @ X1986 @ X1987))|((kpair @ (kfst @ X1988) @ (ksnd @ X1988))=(X1988)))&((~(in @ X1992 @ X1989)|(~(in @ X1993 @ X1990)|(~(X1991 @ X1992 @ X1993)|(in @ (kpair @ X1992 @ X1993) @ (dpsetconstr @ X1989 @ X1990 @ X1991)))))&((subset @ (dpsetconstr @ X1994 @ X1995 @ X1996) @ (cartprod @ X1994 @ X1995))&((subset @ (dpsetconstr @ X1997 @ X1998 @ X1999) @ (cartprod @ X1997 @ X1998))&((~(in @ X2003 @ X2000)|(~(in @ X2004 @ X2001)|(~(in @ (kpair @ X2003 @ X2004) @ (dpsetconstr @ X2000 @ X2001 @ X2002))|(X2002 @ X2003 @ X2004))))&((~(in @ (kpair @ X2008 @ X2009) @ (dpsetconstr @ X2005 @ X2006 @ X2007))|(in @ X2008 @ X2005))&((~(in @ (kpair @ X2013 @ X2014) @ (dpsetconstr @ X2010 @ X2011 @ X2012))|(in @ X2014 @ X2011))&((~(in @ (kpair @ X2018 @ X2019) @ (dpsetconstr @ X2015 @ X2016 @ X2017))|(X2017 @ X2018 @ X2019))&((((in @ (esk69_4 @ X2020 @ X2021 @ X2022 @ X2023) @ (dsetconstr @ X2021 @ (^[Z0:$i]:((in @ (kpair @ X2023 @ Z0) @ X2022)))))|~(in @ X2023 @ X2020)|~(func @ X2020 @ X2021 @ X2022))&(((dsetconstr @ X2021 @ (^[Z0:$i]:((in @ (kpair @ X2023 @ Z0) @ X2022))))=(setadjoin @ (esk69_4 @ X2020 @ X2021 @ X2022 @ X2023) @ emptyset))|~(in @ X2023 @ X2020)|~(func @ X2020 @ X2021 @ X2022)))&((~(func @ X2025 @ X2026 @ X2027)|(~(in @ X2028 @ X2025)|(in @ (setunion @ (dsetconstr @ X2026 @ (^[Z0:$i]:((in @ (kpair @ X2028 @ Z0) @ X2027))))) @ X2026)))&((~(func @ X2029 @ X2030 @ X2031)|(~(in @ X2032 @ X2029)|(in @ (ap @ X2029 @ X2030 @ X2031 @ X2032) @ X2030)))&((~(in @ X2035 @ (funcSet @ X2033 @ X2034))|(func @ X2033 @ X2034 @ X2035))&((~(in @ X2038 @ (funcSet @ X2036 @ X2037))|(~(in @ X2039 @ X2036)|(in @ (ap @ X2036 @ X2037 @ X2038 @ X2039) @ X2037)))&((~(func @ X2040 @ X2041 @ X2042)|(in @ X2042 @ (funcSet @ X2040 @ X2041)))&((((in @ (esk70_3 @ X2043 @ X2044 @ X2045) @ X2043)|(func @ X2043 @ X2044 @ (dpsetconstr @ X2043 @ X2044 @ (^[Z0:$i]:($eq @ (X2045 @ Z0))))))&(~(in @ (X2045 @ (esk70_3 @ X2043 @ X2044 @ X2045)) @ X2044)|(func @ X2043 @ X2044 @ (dpsetconstr @ X2043 @ X2044 @ (^[Z0:$i]:($eq @ (X2045 @ Z0)))))))&((((in @ (esk71_3 @ X2047 @ X2048 @ X2049) @ X2047)|(func @ X2047 @ X2048 @ (lam @ X2047 @ X2048 @ X2049)))&(~(in @ (X2049 @ (esk71_3 @ X2047 @ X2048 @ X2049)) @ X2048)|(func @ X2047 @ X2048 @ (lam @ X2047 @ X2048 @ X2049))))&((((in @ (esk72_3 @ X2051 @ X2052 @ X2053) @ X2051)|(in @ (lam @ X2051 @ X2052 @ X2053) @ (funcSet @ X2051 @ X2052)))&(~(in @ (X2053 @ (esk72_3 @ X2051 @ X2052 @ X2053)) @ X2052)|(in @ (lam @ X2051 @ X2052 @ X2053) @ (funcSet @ X2051 @ X2052))))&((((in @ (esk73_4 @ X2055 @ X2056 @ X2057 @ X2058) @ X2055)|(~(in @ X2061 @ X2057)|(X2058 @ X2061))|~(subset @ X2057 @ (cartprod @ X2055 @ X2056)))&(((in @ (esk74_4 @ X2055 @ X2056 @ X2057 @ X2058) @ X2056)|(~(in @ X2061 @ X2057)|(X2058 @ X2061))|~(subset @ X2057 @ (cartprod @ X2055 @ X2056)))&(((in @ (kpair @ (esk73_4 @ X2055 @ X2056 @ X2057 @ X2058) @ (esk74_4 @ X2055 @ X2056 @ X2057 @ X2058)) @ X2057)|(~(in @ X2061 @ X2057)|(X2058 @ X2061))|~(subset @ X2057 @ (cartprod @ X2055 @ X2056)))&(~(X2058 @ (kpair @ (esk73_4 @ X2055 @ X2056 @ X2057 @ X2058) @ (esk74_4 @ X2055 @ X2056 @ X2057 @ X2058)))|(~(in @ X2061 @ X2057)|(X2058 @ X2061))|~(subset @ X2057 @ (cartprod @ X2055 @ X2056))))))&((((in @ (esk75_4 @ X2062 @ X2063 @ X2064 @ X2065) @ X2062)|(~(in @ X2068 @ X2064)|(X2065 @ X2068))|~(subset @ X2064 @ (cartprod @ X2062 @ X2063)))&(((in @ (esk76_4 @ X2062 @ X2063 @ X2064 @ X2065) @ X2063)|(~(in @ X2068 @ X2064)|(X2065 @ X2068))|~(subset @ X2064 @ (cartprod @ X2062 @ X2063)))&(((in @ (kpair @ (esk75_4 @ X2062 @ X2063 @ X2064 @ X2065) @ (esk76_4 @ X2062 @ X2063 @ X2064 @ X2065)) @ X2064)|(~(in @ X2068 @ X2064)|(X2065 @ X2068))|~(subset @ X2064 @ (cartprod @ X2062 @ X2063)))&(~(X2065 @ (kpair @ (esk75_4 @ X2062 @ X2063 @ X2064 @ X2065) @ (esk76_4 @ X2062 @ X2063 @ X2064 @ X2065)))|(~(in @ X2068 @ X2064)|(X2065 @ X2068))|~(subset @ X2064 @ (cartprod @ X2062 @ X2063))))))&((~(in @ X2071 @ (dsetconstr @ X2069 @ X2070))|((dsetconstr @ X2069 @ X2070)!=(setadjoin @ X2071 @ emptyset))|(~(in @ X2072 @ X2069)|(~(in @ X2073 @ X2069)|(~(X2070 @ X2072)|(~(X2070 @ X2073)|((X2072)=(X2073)))))))&((~(func @ X2074 @ X2075 @ X2076)|(~(in @ X2077 @ X2074)|(in @ (kpair @ X2077 @ (ap @ X2074 @ X2075 @ X2076 @ X2077)) @ X2076)))&((~(in @ X2080 @ (funcSet @ X2078 @ X2079))|(~(in @ X2081 @ X2078)|(in @ (kpair @ X2081 @ (ap @ X2078 @ X2079 @ X2080 @ X2081)) @ X2080)))&((~(func @ X2082 @ X2083 @ X2084)|(~(in @ X2085 @ X2082)|(~(in @ X2086 @ X2083)|(~(in @ (kpair @ X2085 @ X2086) @ X2084)|((ap @ X2082 @ X2083 @ X2084 @ X2085)=(X2086))))))&((((in @ (esk77_4 @ X2087 @ X2088 @ X2089 @ X2090) @ X2087)|(~(in @ X2092 @ X2087)|(~(in @ X2093 @ X2088)|(~(in @ (kpair @ X2092 @ X2093) @ X2090)|(in @ (kpair @ X2092 @ X2093) @ X2089))))|~(func @ X2087 @ X2088 @ X2090)|~(func @ X2087 @ X2088 @ X2089))&(((ap @ X2087 @ X2088 @ X2089 @ (esk77_4 @ X2087 @ X2088 @ X2089 @ X2090))!=(ap @ X2087 @ X2088 @ X2090 @ (esk77_4 @ X2087 @ X2088 @ X2089 @ X2090)))|(~(in @ X2092 @ X2087)|(~(in @ X2093 @ X2088)|(~(in @ (kpair @ X2092 @ X2093) @ X2090)|(in @ (kpair @ X2092 @ X2093) @ X2089))))|~(func @ X2087 @ X2088 @ X2090)|~(func @ X2087 @ X2088 @ X2089)))&((~(in @ X2096 @ (funcSet @ X2094 @ X2095))|(~(in @ X2097 @ X2094)|(~(in @ X2098 @ X2095)|(~(in @ (kpair @ X2097 @ X2098) @ X2096)|((ap @ X2094 @ X2095 @ X2096 @ X2097)=(X2098))))))&((((in @ (esk78_4 @ X2099 @ X2100 @ X2101 @ X2102) @ X2099)|(subset @ X2101 @ X2102)|~(subset @ X2102 @ (cartprod @ X2099 @ X2100))|~(subset @ X2101 @ (cartprod @ X2099 @ X2100)))&(((in @ (esk79_4 @ X2099 @ X2100 @ X2101 @ X2102) @ X2100)|(subset @ X2101 @ X2102)|~(subset @ X2102 @ (cartprod @ X2099 @ X2100))|~(subset @ X2101 @ (cartprod @ X2099 @ X2100)))&(((in @ (kpair @ (esk78_4 @ X2099 @ X2100 @ X2101 @ X2102) @ (esk79_4 @ X2099 @ X2100 @ X2101 @ X2102)) @ X2101)|(subset @ X2101 @ X2102)|~(subset @ X2102 @ (cartprod @ X2099 @ X2100))|~(subset @ X2101 @ (cartprod @ X2099 @ X2100)))&(~(in @ (kpair @ (esk78_4 @ X2099 @ X2100 @ X2101 @ X2102) @ (esk79_4 @ X2099 @ X2100 @ X2101 @ X2102)) @ X2102)|(subset @ X2101 @ X2102)|~(subset @ X2102 @ (cartprod @ X2099 @ X2100))|~(subset @ X2101 @ (cartprod @ X2099 @ X2100))))))&(((((in @ (esk82_4 @ X2105 @ X2106 @ X2107 @ X2108) @ X2105)|((X2107)=(X2108))|(in @ (esk80_4 @ X2105 @ X2106 @ X2107 @ X2108) @ X2105)|~(subset @ X2108 @ (cartprod @ X2105 @ X2106))|~(subset @ X2107 @ (cartprod @ X2105 @ X2106)))&(((in @ (esk83_4 @ X2105 @ X2106 @ X2107 @ X2108) @ X2106)|((X2107)=(X2108))|(in @ (esk80_4 @ X2105 @ X2106 @ X2107 @ X2108) @ X2105)|~(subset @ X2108 @ (cartprod @ X2105 @ X2106))|~(subset @ X2107 @ (cartprod @ X2105 @ X2106)))&(((in @ (kpair @ (esk82_4 @ X2105 @ X2106 @ X2107 @ X2108) @ (esk83_4 @ X2105 @ X2106 @ X2107 @ X2108)) @ X2108)|((X2107)=(X2108))|(in @ (esk80_4 @ X2105 @ X2106 @ X2107 @ X2108) @ X2105)|~(subset @ X2108 @ (cartprod @ X2105 @ X2106))|~(subset @ X2107 @ (cartprod @ X2105 @ X2106)))&(~(in @ (kpair @ (esk82_4 @ X2105 @ X2106 @ X2107 @ X2108) @ (esk83_4 @ X2105 @ X2106 @ X2107 @ X2108)) @ X2107)|((X2107)=(X2108))|(in @ (esk80_4 @ X2105 @ X2106 @ X2107 @ X2108) @ X2105)|~(subset @ X2108 @ (cartprod @ X2105 @ X2106))|~(subset @ X2107 @ (cartprod @ X2105 @ X2106))))))&((((in @ (esk82_4 @ X2105 @ X2106 @ X2107 @ X2108) @ X2105)|((X2107)=(X2108))|(in @ (esk81_4 @ X2105 @ X2106 @ X2107 @ X2108) @ X2106)|~(subset @ X2108 @ (cartprod @ X2105 @ X2106))|~(subset @ X2107 @ (cartprod @ X2105 @ X2106)))&(((in @ (esk83_4 @ X2105 @ X2106 @ X2107 @ X2108) @ X2106)|((X2107)=(X2108))|(in @ (esk81_4 @ X2105 @ X2106 @ X2107 @ X2108) @ X2106)|~(subset @ X2108 @ (cartprod @ X2105 @ X2106))|~(subset @ X2107 @ (cartprod @ X2105 @ X2106)))&(((in @ (kpair @ (esk82_4 @ X2105 @ X2106 @ X2107 @ X2108) @ (esk83_4 @ X2105 @ X2106 @ X2107 @ X2108)) @ X2108)|((X2107)=(X2108))|(in @ (esk81_4 @ X2105 @ X2106 @ X2107 @ X2108) @ X2106)|~(subset @ X2108 @ (cartprod @ X2105 @ X2106))|~(subset @ X2107 @ (cartprod @ X2105 @ X2106)))&(~(in @ (kpair @ (esk82_4 @ X2105 @ X2106 @ X2107 @ X2108) @ (esk83_4 @ X2105 @ X2106 @ X2107 @ X2108)) @ X2107)|((X2107)=(X2108))|(in @ (esk81_4 @ X2105 @ X2106 @ X2107 @ X2108) @ X2106)|~(subset @ X2108 @ (cartprod @ X2105 @ X2106))|~(subset @ X2107 @ (cartprod @ X2105 @ X2106))))))&((((in @ (esk82_4 @ X2105 @ X2106 @ X2107 @ X2108) @ X2105)|((X2107)=(X2108))|(in @ (kpair @ (esk80_4 @ X2105 @ X2106 @ X2107 @ X2108) @ (esk81_4 @ X2105 @ X2106 @ X2107 @ X2108)) @ X2107)|~(subset @ X2108 @ (cartprod @ X2105 @ X2106))|~(subset @ X2107 @ (cartprod @ X2105 @ X2106)))&(((in @ (esk83_4 @ X2105 @ X2106 @ X2107 @ X2108) @ X2106)|((X2107)=(X2108))|(in @ (kpair @ (esk80_4 @ X2105 @ X2106 @ X2107 @ X2108) @ (esk81_4 @ X2105 @ X2106 @ X2107 @ X2108)) @ X2107)|~(subset @ X2108 @ (cartprod @ X2105 @ X2106))|~(subset @ X2107 @ (cartprod @ X2105 @ X2106)))&(((in @ (kpair @ (esk82_4 @ X2105 @ X2106 @ X2107 @ X2108) @ (esk83_4 @ X2105 @ X2106 @ X2107 @ X2108)) @ X2108)|((X2107)=(X2108))|(in @ (kpair @ (esk80_4 @ X2105 @ X2106 @ X2107 @ X2108) @ (esk81_4 @ X2105 @ X2106 @ X2107 @ X2108)) @ X2107)|~(subset @ X2108 @ (cartprod @ X2105 @ X2106))|~(subset @ X2107 @ (cartprod @ X2105 @ X2106)))&(~(in @ (kpair @ (esk82_4 @ X2105 @ X2106 @ X2107 @ X2108) @ (esk83_4 @ X2105 @ X2106 @ X2107 @ X2108)) @ X2107)|((X2107)=(X2108))|(in @ (kpair @ (esk80_4 @ X2105 @ X2106 @ X2107 @ X2108) @ (esk81_4 @ X2105 @ X2106 @ X2107 @ X2108)) @ X2107)|~(subset @ X2108 @ (cartprod @ X2105 @ X2106))|~(subset @ X2107 @ (cartprod @ X2105 @ X2106))))))&(((in @ (esk82_4 @ X2105 @ X2106 @ X2107 @ X2108) @ X2105)|((X2107)=(X2108))|~(in @ (kpair @ (esk80_4 @ X2105 @ X2106 @ X2107 @ X2108) @ (esk81_4 @ X2105 @ X2106 @ X2107 @ X2108)) @ X2108)|~(subset @ X2108 @ (cartprod @ X2105 @ X2106))|~(subset @ X2107 @ (cartprod @ X2105 @ X2106)))&(((in @ (esk83_4 @ X2105 @ X2106 @ X2107 @ X2108) @ X2106)|((X2107)=(X2108))|~(in @ (kpair @ (esk80_4 @ X2105 @ X2106 @ X2107 @ X2108) @ (esk81_4 @ X2105 @ X2106 @ X2107 @ X2108)) @ X2108)|~(subset @ X2108 @ (cartprod @ X2105 @ X2106))|~(subset @ X2107 @ (cartprod @ X2105 @ X2106)))&(((in @ (kpair @ (esk82_4 @ X2105 @ X2106 @ X2107 @ X2108) @ (esk83_4 @ X2105 @ X2106 @ X2107 @ X2108)) @ X2108)|((X2107)=(X2108))|~(in @ (kpair @ (esk80_4 @ X2105 @ X2106 @ X2107 @ X2108) @ (esk81_4 @ X2105 @ X2106 @ X2107 @ X2108)) @ X2108)|~(subset @ X2108 @ (cartprod @ X2105 @ X2106))|~(subset @ X2107 @ (cartprod @ X2105 @ X2106)))&(~(in @ (kpair @ (esk82_4 @ X2105 @ X2106 @ X2107 @ X2108) @ (esk83_4 @ X2105 @ X2106 @ X2107 @ X2108)) @ X2107)|((X2107)=(X2108))|~(in @ (kpair @ (esk80_4 @ X2105 @ X2106 @ X2107 @ X2108) @ (esk81_4 @ X2105 @ X2106 @ X2107 @ X2108)) @ X2108)|~(subset @ X2108 @ (cartprod @ X2105 @ X2106))|~(subset @ X2107 @ (cartprod @ X2105 @ X2106)))))))))&((((in @ (esk84_4 @ X2113 @ X2114 @ X2115 @ X2116) @ X2113)|((X2115)=(X2116))|~(func @ X2113 @ X2114 @ X2116)|~(func @ X2113 @ X2114 @ X2115))&(((ap @ X2113 @ X2114 @ X2115 @ (esk84_4 @ X2113 @ X2114 @ X2115 @ X2116))!=(ap @ X2113 @ X2114 @ X2116 @ (esk84_4 @ X2113 @ X2114 @ X2115 @ X2116)))|((X2115)=(X2116))|~(func @ X2113 @ X2114 @ X2116)|~(func @ X2113 @ X2114 @ X2115)))&((((in @ (esk85_4 @ X2118 @ X2119 @ X2120 @ X2121) @ X2118)|((X2120)=(X2121))|~(in @ X2121 @ (funcSet @ X2118 @ X2119))|~(in @ X2120 @ (funcSet @ X2118 @ X2119)))&(((ap @ X2118 @ X2119 @ X2120 @ (esk85_4 @ X2118 @ X2119 @ X2120 @ X2121))!=(ap @ X2118 @ X2119 @ X2121 @ (esk85_4 @ X2118 @ X2119 @ X2120 @ X2121)))|((X2120)=(X2121))|~(in @ X2121 @ (funcSet @ X2118 @ X2119))|~(in @ X2120 @ (funcSet @ X2118 @ X2119))))&((~(in @ X2125 @ (funcSet @ X2123 @ X2124))|(~(in @ X2126 @ X2123)|((ap @ X2123 @ X2124 @ X2125 @ X2126)=(ap @ X2123 @ X2124 @ X2125 @ X2126))))&((~(func @ X2127 @ X2128 @ X2129)|(~(in @ X2130 @ X2127)|((ap @ X2127 @ X2128 @ X2129 @ X2130)=(ap @ X2127 @ X2128 @ X2129 @ X2130))))&((((in @ (esk86_3 @ X2131 @ X2132 @ X2133) @ X2131)|(~(in @ X2135 @ X2131)|((ap @ X2131 @ X2132 @ (lam @ X2131 @ X2132 @ X2133) @ X2135)=(X2133 @ X2135))))&(~(in @ (X2133 @ (esk86_3 @ X2131 @ X2132 @ X2133)) @ X2132)|(~(in @ X2135 @ X2131)|((ap @ X2131 @ X2132 @ (lam @ X2131 @ X2132 @ X2133) @ X2135)=(X2133 @ X2135)))))&((~(func @ X2136 @ X2137 @ X2138)|((lam @ X2136 @ X2137 @ (ap @ X2136 @ X2137 @ X2138))=(X2138)))&((((in @ (esk87_3 @ X2139 @ X2140 @ X2141) @ X2139)|((lam @ X2139 @ X2140 @ X2141)=(lam @ X2139 @ X2140 @ X2141)))&(~(in @ (X2141 @ (esk87_3 @ X2139 @ X2140 @ X2141)) @ X2140)|((lam @ X2139 @ X2140 @ X2141)=(lam @ X2139 @ X2140 @ X2141))))&((((in @ (esk88_3 @ X2143 @ X2144 @ X2145) @ X2143)|(~(in @ X2147 @ X2143)|((ap @ X2143 @ X2144 @ (lam @ X2143 @ X2144 @ X2145) @ X2147)=(X2145 @ X2147))))&(~(in @ (X2145 @ (esk88_3 @ X2143 @ X2144 @ X2145)) @ X2144)|(~(in @ X2147 @ X2143)|((ap @ X2143 @ X2144 @ (lam @ X2143 @ X2144 @ X2145) @ X2147)=(X2145 @ X2147)))))&((~(in @ X2150 @ (funcSet @ X2148 @ X2149))|((lam @ X2148 @ X2149 @ (ap @ X2148 @ X2149 @ X2150))=(X2150)))&((~(in @ X2153 @ X2151)|(~(in @ X2154 @ X2151)|((X2152)|(in @ X2154 @ (dsetconstr @ X2151 @ (^[Z0:$i]:((((((X2152))&(((Z0)=(X2153)))))|(((~((X2152)))&(((Z0)=(X2154)))))))))))))&((~(in @ X2157 @ X2155)|(~(in @ X2158 @ X2155)|((X2156)|((dsetconstr @ X2155 @ (^[Z0:$i]:((((((X2156))&(((Z0)=(X2157)))))|(((~((X2156)))&(((Z0)=(X2158)))))))))=(setadjoin @ X2158 @ emptyset)))))&((~(in @ X2161 @ X2159)|(~(in @ X2162 @ X2159)|(~(X2160)|(in @ X2161 @ (dsetconstr @ X2159 @ (^[Z0:$i]:((((((X2160))&(((Z0)=(X2161)))))|(((~((X2160)))&(((Z0)=(X2162)))))))))))))&((in @ esk90_0 @ esk89_0)&((in @ esk91_0 @ esk89_0)&((epred2_0)&((dsetconstr @ esk89_0 @ (^[Z0:$i]:((((((epred2_0))&(((Z0)=(esk90_0)))))|(((~((epred2_0)))&(((Z0)=(esk91_0)))))))))!=(setadjoin @ esk90_0 @ emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_312])])])])])])])).
% 107.81/14.04 thf(c_0_314, plain, ![X2186:$i]:(((epred3_0 @ X2186)<=>(((epred2_0)&((X2186)=(esk90_0)))|(~((epred2_0))&((X2186)=(esk91_0)))))), introduced(definition)).
% 107.81/14.04 thf(c_0_315, plain, ![X2188:$i, X2:$i, X4:$i]:(((epred5_2 @ X4 @ X2 @ X2188)<=>((~($true)&((X2188)=(X2)))|(~(~($true))&((X2188)=(X4)))))), introduced(definition)).
% 107.81/14.04 thf(c_0_316, negated_conjecture, ((dsetconstr @ esk89_0 @ epred3_0)!=(setadjoin @ esk90_0 @ emptyset)), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_313]), c_0_314])).
% 107.81/14.04 thf(c_0_317, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:((((dsetconstr @ X3 @ (epred5_2 @ X4 @ X2))=(setadjoin @ X4 @ emptyset))|~((in @ X2 @ X3))|~((in @ X4 @ X3)))), inference(lift_lambdas,[status(thm)],[inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_313])])]), c_0_315])).
% 107.81/14.04 thf(c_0_318, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (setminus @ X3 @ X4))|(in @ X2 @ X4)|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_313])).
% 107.81/14.04 thf(c_0_319, negated_conjecture, (in @ esk91_0 @ esk89_0), inference(split_conjunct,[status(thm)],[c_0_313])).
% 107.81/14.04 thf(c_0_320, negated_conjecture, ![X2:$i, X3:$i]:((((setminus @ X2 @ X3)=(emptyset))|~((subset @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_313])).
% 107.81/14.04 thf(c_0_321, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X3 @ X2)|((binintersect @ X2 @ X3)!=(X3)))), inference(split_conjunct,[status(thm)],[c_0_313])).
% 107.81/14.04 thf(c_0_322, plain, ![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)!=(setadjoin @ esk90_0 @ emptyset))|((epred5_2 @ X2 @ X3)!=(epred3_0))|~((in @ X2 @ esk89_0))|~((in @ X3 @ esk89_0)))), inference(er,[status(thm)],[inference(ext_sup,[status(thm)],[c_0_316, c_0_317])])).
% 107.81/14.04 thf(c_0_323, negated_conjecture, (in @ esk90_0 @ esk89_0), inference(split_conjunct,[status(thm)],[c_0_313])).
% 107.81/14.04 thf(c_0_324, negated_conjecture, ![X2:$i]:(((in @ esk91_0 @ (setminus @ esk89_0 @ X2))|(in @ esk91_0 @ X2))), inference(spm,[status(thm)],[c_0_318, c_0_319])).
% 107.81/14.04 thf(c_0_325, negated_conjecture, ![X3:$i, X2:$i]:((((setminus @ X2 @ X3)=(emptyset))|((binintersect @ X3 @ X2)!=(X2)))), inference(spm,[status(thm)],[c_0_320, c_0_321])).
% 107.81/14.04 thf(c_0_326, negated_conjecture, ![X2:$i]:(~((in @ X2 @ emptyset))), inference(split_conjunct,[status(thm)],[c_0_313])).
% 107.81/14.04 thf(c_0_327, negated_conjecture, ![X2:$i, X3:$i]:((((binintersect @ X3 @ X2)=(X2))|~((subset @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_313])).
% 107.81/14.04 thf(c_0_328, negated_conjecture, ![X2:$i]:((subset @ X2 @ X2)), inference(split_conjunct,[status(thm)],[c_0_313])).
% 107.81/14.04 thf(c_0_329, negated_conjecture, ![X2:$i]:((((epred5_2 @ esk90_0 @ X2)!=(epred3_0))|~((in @ X2 @ esk89_0)))), inference(spm,[status(thm)],[c_0_322, c_0_323])).
% 107.81/14.04 thf(c_0_330, negated_conjecture, ![X2:$i]:(((in @ esk91_0 @ X2)|((binintersect @ X2 @ esk89_0)!=(esk89_0)))), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_324, c_0_325]), c_0_326])).
% 107.81/14.04 thf(c_0_331, negated_conjecture, ![X2:$i]:(((binintersect @ X2 @ X2)=(X2))), inference(spm,[status(thm)],[c_0_327, c_0_328])).
% 107.81/14.04 thf(c_0_332, plain, ![X2204:$i, X2205:$i, X2206:$i]:(((((($true)|~($true)|~(epred5_2 @ X2206 @ X2205 @ X2204))&(((X2204)=(X2206))|~($true)|~(epred5_2 @ X2206 @ X2205 @ X2204)))&((($true)|((X2204)=(X2205))|~(epred5_2 @ X2206 @ X2205 @ X2204))&(((X2204)=(X2206))|((X2204)=(X2205))|~(epred5_2 @ X2206 @ X2205 @ X2204))))&((($true)|((X2204)!=(X2205))|(epred5_2 @ X2206 @ X2205 @ X2204))&(~($true)|((X2204)!=(X2206))|(epred5_2 @ X2206 @ X2205 @ X2204))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])])])).
% 107.81/14.04 thf(c_0_333, negated_conjecture, ((epred5_2 @ esk90_0 @ esk91_0)!=(epred3_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_329, c_0_330]), c_0_331])])).
% 107.81/14.04 thf(c_0_334, plain, ![X2200:$i]:(((((~(epred2_0)|(epred2_0)|~(epred3_0 @ X2200))&(((X2200)=(esk91_0))|(epred2_0)|~(epred3_0 @ X2200)))&((~(epred2_0)|((X2200)=(esk90_0))|~(epred3_0 @ X2200))&(((X2200)=(esk91_0))|((X2200)=(esk90_0))|~(epred3_0 @ X2200))))&((~(epred2_0)|((X2200)!=(esk90_0))|(epred3_0 @ X2200))&((epred2_0)|((X2200)!=(esk91_0))|(epred3_0 @ X2200))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[])])])])])).
% 107.81/14.04 thf(c_0_335, plain, ![X4:$i, X3:$i, X2:$i]:((((X2)=(X3))|~(($true))|~((epred5_2 @ X3 @ X4 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_332])).
% 107.81/14.04 thf(c_0_336, negated_conjecture, ((epred5_2 @ esk90_0 @ esk91_0 @ esk82_0)<~>(epred3_0 @ esk82_0)), inference(neg_ext,[status(thm)],[c_0_333])).
% 107.81/14.04 thf(c_0_337, plain, ![X2:$i]:((((X2)=(esk90_0))|~((epred2_0))|~((epred3_0 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_334])).
% 107.81/14.04 thf(c_0_338, negated_conjecture, (epred2_0), inference(split_conjunct,[status(thm)],[c_0_313])).
% 107.81/14.04 thf(c_0_339, plain, ![X2:$i, X4:$i, X3:$i]:(((epred5_2 @ X3 @ X4 @ X2)|~(($true))|((X2)!=(X3)))), inference(split_conjunct,[status(thm)],[c_0_332])).
% 107.81/14.04 thf(c_0_340, plain, ![X4:$i, X3:$i, X2:$i]:((((X2)=(X3))|~((epred5_2 @ X3 @ X4 @ X2)))), inference(cn,[status(thm)],[c_0_335])).
% 107.81/14.04 thf(c_0_341, negated_conjecture, ((epred5_2 @ esk90_0 @ esk91_0 @ esk82_0)|(epred3_0 @ esk82_0)), inference(dynamic_cnf,[status(thm)],[c_0_336])).
% 107.81/14.04 thf(c_0_342, plain, ![X2:$i]:((((X2)=(esk90_0))|~((epred3_0 @ X2)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_337, c_0_338])])).
% 107.81/14.04 thf(c_0_343, plain, ![X2:$i, X4:$i, X3:$i]:(((epred5_2 @ X3 @ X4 @ X2)|((X2)!=(X3)))), inference(cn,[status(thm)],[c_0_339])).
% 107.81/14.04 thf(c_0_344, plain, ![X2:$i]:(((epred3_0 @ X2)|~((epred2_0))|((X2)!=(esk90_0)))), inference(split_conjunct,[status(thm)],[c_0_334])).
% 107.81/14.04 thf(c_0_345, negated_conjecture, (~((epred5_2 @ esk90_0 @ esk91_0 @ esk82_0))|~((epred3_0 @ esk82_0))), inference(dynamic_cnf,[status(thm)],[c_0_336])).
% 107.81/14.04 thf(c_0_346, plain, ((esk90_0)=(esk82_0)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_340, c_0_341]), c_0_342])).
% 107.81/14.04 thf(c_0_347, plain, ![X3:$i, X2:$i]:((epred5_2 @ X2 @ X3 @ X2)), inference(er,[status(thm)],[c_0_343])).
% 107.81/14.04 thf(c_0_348, plain, (epred3_0 @ esk90_0), inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_344, c_0_338])])])).
% 107.81/14.04 thf(c_0_349, negated_conjecture, ~((epred3_0 @ esk82_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_345, c_0_346]), c_0_347])])).
% 107.81/14.04 thf(c_0_350, plain, ($false), inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_348, c_0_346]), c_0_349]), ['proof']).
% 107.81/14.04 % SZS output end CNFRefutation
% 107.81/14.04 % Parsed axioms : 481
% 107.81/14.04 % Removed by relevancy pruning/SinE : 0
% 107.81/14.04 % Initial clauses : 691
% 107.81/14.04 % Removed in clause preprocessing : 295
% 107.81/14.04 % Initial clauses in saturation : 396
% 107.81/14.04 % Processed clauses : 21602
% 107.81/14.04 % ...of these trivial : 440
% 107.81/14.04 % ...subsumed : 15677
% 107.81/14.04 % ...remaining for further processing : 5484
% 107.81/14.04 % Other redundant clauses eliminated : 616
% 107.81/14.04 % Clauses deleted for lack of memory : 0
% 107.81/14.04 % Backward-subsumed : 872
% 107.81/14.04 % Backward-rewritten : 707
% 107.81/14.04 % Generated clauses : 487966
% 107.81/14.04 % ...of the previous two non-redundant : 472325
% 107.81/14.04 % ...aggressively subsumed : 0
% 107.81/14.04 % Contextual simplify-reflections : 15
% 107.81/14.04 % Paramodulations : 487032
% 107.81/14.04 % Factorizations : 46
% 107.81/14.04 % NegExts : 175
% 107.81/14.04 % Equation resolutions : 621
% 107.81/14.04 % Disequality decompositions : 0
% 107.81/14.04 % Total rewrite steps : 32757
% 107.81/14.04 % ...of those cached : 30603
% 107.81/14.04 % Propositional unsat checks : 1
% 107.81/14.04 % Propositional check models : 0
% 107.81/14.04 % Propositional check unsatisfiable : 0
% 107.81/14.04 % Propositional clauses : 0
% 107.81/14.04 % Propositional clauses after purity: 0
% 107.81/14.04 % Propositional unsat core size : 0
% 107.81/14.04 % Propositional preprocessing time : 0.000
% 107.81/14.04 % Propositional encoding time : 1.591
% 107.81/14.04 % Propositional solver time : 0.919
% 107.81/14.04 % Success case prop preproc time : 0.000
% 107.81/14.04 % Success case prop encoding time : 0.000
% 107.81/14.04 % Success case prop solver time : 0.000
% 107.81/14.04 % Current number of processed clauses : 3507
% 107.81/14.04 % Positive orientable unit clauses : 404
% 107.81/14.04 % Positive unorientable unit clauses: 0
% 107.81/14.04 % Negative unit clauses : 355
% 107.81/14.04 % Non-unit-clauses : 2748
% 107.81/14.04 % Current number of unprocessed clauses: 449709
% 107.81/14.04 % ...number of literals in the above : 1442048
% 107.81/14.04 % Current number of archived formulas : 0
% 107.81/14.04 % Current number of archived clauses : 1960
% 107.81/14.04 % Clause-clause subsumption calls (NU) : 983323
% 107.81/14.04 % Rec. Clause-clause subsumption calls : 632005
% 107.81/14.04 % Non-unit clause-clause subsumptions : 6697
% 107.81/14.04 % Unit Clause-clause subsumption calls : 153755
% 107.81/14.04 % Rewrite failures with RHS unbound : 0
% 107.81/14.04 % BW rewrite match attempts : 172
% 107.81/14.04 % BW rewrite match successes : 34
% 107.81/14.04 % Condensation attempts : 0
% 107.81/14.04 % Condensation successes : 0
% 107.81/14.04 % Termbank termtop insertions : 16287132
% 107.81/14.04 % Search garbage collected termcells : 23368
% 107.81/14.04
% 107.81/14.04 % -------------------------------------------------
% 107.81/14.04 % User time : 12.873 s
% 107.81/14.04 % System time : 0.552 s
% 107.81/14.04 % Total time : 13.425 s
% 107.81/14.04 % Maximum resident set size: 9268 pages
% 107.81/14.04
% 107.81/14.04 % -------------------------------------------------
% 107.81/14.04 % User time : 51.737 s
% 107.81/14.04 % System time : 1.936 s
% 107.81/14.04 % Total time : 53.673 s
% 107.81/14.04 % Maximum resident set size: 5632 pages
% 107.81/14.04 % E exiting
%------------------------------------------------------------------------------