%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU684^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 08:25:01 AM UTC 2026
% Result : Theorem 209.27s 30.44s
% Output : CNFRefutation 209.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU684^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 14:08:18 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running higher-order theorem proving
% 0.08/0.14 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p
% 209.27/30.44 % Version: 3.5.1-ho
% 209.27/30.44 % Preprocessing class: HSLMSLSSLLLCHFA.
% 209.27/30.44 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 209.27/30.44 % Starting ehoh_best5 with 300s (1) cores
% 209.27/30.44 % Starting almost_fo_3_lam with 300s (1) cores
% 209.27/30.44 % Starting new_bool_5 with 300s (1) cores
% 209.27/30.44 % Starting pre_casc_3 with 300s (1) cores
% 209.27/30.44 % Starting ho_unfolding_8 with 300s (1) cores
% 209.27/30.44 % Starting new_ho_10_cnf2 with 300s (1) cores
% 209.27/30.44 % Starting new_bool_3 with 300s (1) cores
% 209.27/30.44 % Starting new_ho_5 with 300s (1) cores
% 209.27/30.44 % ehoh_best5 with pid 159965 completed with status 0
% 209.27/30.44 % Result found by ehoh_best5
% 209.27/30.44 % Preprocessing class: HSLMSLSSLLLCHFA.
% 209.27/30.44 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 209.27/30.44 % Starting ehoh_best5 with 300s (1) cores
% 209.27/30.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 209.27/30.44 % No SInE strategy applied
% 209.27/30.44 % Search class: HGHSM-FSLM32-MHFMMSBN
% 209.27/30.44 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 209.27/30.44 % Starting SubtermCWHack with 28s (1) cores
% 209.27/30.44 % SubtermCWHack with pid 159978 completed with status 8
% 209.27/30.44 % Starting ehoh_best5 with 31s (1) cores
% 209.27/30.44 % ehoh_best5 with pid 160139 completed with status 0
% 209.27/30.44 % Result found by ehoh_best5
% 209.27/30.44 % Preprocessing class: HSLMSLSSLLLCHFA.
% 209.27/30.44 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 209.27/30.44 % Starting ehoh_best5 with 300s (1) cores
% 209.27/30.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 209.27/30.44 % No SInE strategy applied
% 209.27/30.44 % Search class: HGHSM-FSLM32-MHFMMSBN
% 209.27/30.44 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 209.27/30.44 % Starting SubtermCWHack with 28s (1) cores
% 209.27/30.44 % SubtermCWHack with pid 159978 completed with status 8
% 209.27/30.44 % Starting ehoh_best5 with 31s (1) cores
% 209.27/30.44 % Preprocessing time : 0.005 s
% 209.27/30.44 % Presaturation interreduction done
% 209.27/30.44
% 209.27/30.44 % Proof found!
% 209.27/30.44 % SZS status Theorem
% 209.27/30.44 % SZS output start CNFRefutation
% 209.27/30.44 thf(decl_23, type, in: $i > $i > $o).
% 209.27/30.44 thf(decl_24, type, exu: ($i > $o) > $o).
% 209.27/30.44 thf(decl_25, type, setextAx: $o).
% 209.27/30.44 thf(decl_26, type, emptyset: $i).
% 209.27/30.44 thf(decl_27, type, emptysetAx: $o).
% 209.27/30.44 thf(decl_28, type, setadjoin: $i > $i > $i).
% 209.27/30.44 thf(decl_29, type, setadjoinAx: $o).
% 209.27/30.44 thf(decl_30, type, powerset: $i > $i).
% 209.27/30.44 thf(decl_31, type, powersetAx: $o).
% 209.27/30.44 thf(decl_32, type, setunion: $i > $i).
% 209.27/30.44 thf(decl_33, type, setunionAx: $o).
% 209.27/30.44 thf(decl_34, type, omega: $i).
% 209.27/30.44 thf(decl_35, type, omega0Ax: $o).
% 209.27/30.44 thf(decl_36, type, omegaSAx: $o).
% 209.27/30.44 thf(decl_37, type, omegaIndAx: $o).
% 209.27/30.44 thf(decl_38, type, replAx: $o).
% 209.27/30.44 thf(decl_39, type, foundationAx: $o).
% 209.27/30.44 thf(decl_40, type, wellorderingAx: $o).
% 209.27/30.44 thf(decl_41, type, descr: ($i > $o) > $i).
% 209.27/30.44 thf(decl_42, type, descrp: $o).
% 209.27/30.44 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 209.27/30.44 thf(decl_44, type, dsetconstrI: $o).
% 209.27/30.44 thf(decl_45, type, dsetconstrEL: $o).
% 209.27/30.44 thf(decl_46, type, dsetconstrER: $o).
% 209.27/30.44 thf(decl_47, type, exuE1: $o).
% 209.27/30.44 thf(decl_48, type, prop2set: $o > $i).
% 209.27/30.44 thf(decl_49, type, prop2setE: $o).
% 209.27/30.44 thf(decl_50, type, emptysetE: $o).
% 209.27/30.44 thf(decl_51, type, emptysetimpfalse: $o).
% 209.27/30.44 thf(decl_52, type, notinemptyset: $o).
% 209.27/30.44 thf(decl_53, type, exuE3e: $o).
% 209.27/30.44 thf(decl_54, type, setext: $o).
% 209.27/30.44 thf(decl_55, type, emptyI: $o).
% 209.27/30.44 thf(decl_56, type, noeltsimpempty: $o).
% 209.27/30.44 thf(decl_57, type, setbeta: $o).
% 209.27/30.44 thf(decl_58, type, nonempty: $i > $o).
% 209.27/30.44 thf(decl_59, type, nonemptyE1: $o).
% 209.27/30.44 thf(decl_60, type, nonemptyI: $o).
% 209.27/30.44 thf(decl_61, type, nonemptyI1: $o).
% 209.27/30.44 thf(decl_62, type, setadjoinIL: $o).
% 209.27/30.44 thf(decl_63, type, emptyinunitempty: $o).
% 209.27/30.44 thf(decl_64, type, setadjoinIR: $o).
% 209.27/30.44 thf(decl_65, type, setadjoinE: $o).
% 209.27/30.44 thf(decl_66, type, setadjoinOr: $o).
% 209.27/30.44 thf(decl_67, type, setoftrueEq: $o).
% 209.27/30.44 thf(decl_68, type, powersetI: $o).
% 209.27/30.44 thf(decl_69, type, emptyinPowerset: $o).
% 209.27/30.44 thf(decl_70, type, emptyInPowerset: $o).
% 209.27/30.44 thf(decl_71, type, powersetE: $o).
% 209.27/30.44 thf(decl_72, type, setunionI: $o).
% 209.27/30.44 thf(decl_73, type, setunionE: $o).
% 209.27/30.44 thf(decl_74, type, subPowSU: $o).
% 209.27/30.44 thf(decl_75, type, exuE2: $o).
% 209.27/30.44 thf(decl_76, type, nonemptyImpWitness: $o).
% 209.27/30.44 thf(decl_77, type, uniqinunit: $o).
% 209.27/30.44 thf(decl_78, type, notinsingleton: $o).
% 209.27/30.44 thf(decl_79, type, eqinunit: $o).
% 209.27/30.44 thf(decl_80, type, singletonsswitch: $o).
% 209.27/30.44 thf(decl_81, type, upairsetE: $o).
% 209.27/30.44 thf(decl_82, type, upairsetIL: $o).
% 209.27/30.44 thf(decl_83, type, upairsetIR: $o).
% 209.27/30.44 thf(decl_84, type, emptyE1: $o).
% 209.27/30.44 thf(decl_85, type, vacuousDall: $o).
% 209.27/30.44 thf(decl_86, type, quantDeMorgan1: $o).
% 209.27/30.44 thf(decl_87, type, quantDeMorgan2: $o).
% 209.27/30.44 thf(decl_88, type, quantDeMorgan3: $o).
% 209.27/30.44 thf(decl_89, type, quantDeMorgan4: $o).
% 209.27/30.44 thf(decl_90, type, prop2setI: $o).
% 209.27/30.44 thf(decl_91, type, set2prop: $i > $o).
% 209.27/30.44 thf(decl_92, type, prop2set2propI: $o).
% 209.27/30.44 thf(decl_93, type, notdexE: $o).
% 209.27/30.44 thf(decl_94, type, notdallE: $o).
% 209.27/30.44 thf(decl_95, type, exuI1: $o).
% 209.27/30.44 thf(decl_96, type, exuI3: $o).
% 209.27/30.44 thf(decl_97, type, exuI2: $o).
% 209.27/30.44 thf(decl_98, type, inCongP: $o).
% 209.27/30.44 thf(decl_99, type, in__Cong: $o).
% 209.27/30.44 thf(decl_100, type, exuE3u: $o).
% 209.27/30.44 thf(decl_101, type, exu__Cong: $o).
% 209.27/30.44 thf(decl_102, type, emptyset__Cong: $o).
% 209.27/30.44 thf(decl_103, type, setadjoin__Cong: $o).
% 209.27/30.44 thf(decl_104, type, powerset__Cong: $o).
% 209.27/30.44 thf(decl_105, type, setunion__Cong: $o).
% 209.27/30.44 thf(decl_106, type, omega__Cong: $o).
% 209.27/30.44 thf(decl_107, type, exuEu: $o).
% 209.27/30.44 thf(decl_108, type, descr__Cong: $o).
% 209.27/30.44 thf(decl_109, type, dsetconstr__Cong: $o).
% 209.27/30.44 thf(decl_110, type, subset: $i > $i > $o).
% 209.27/30.44 thf(decl_113, type, subsetI1: $o).
% 209.27/30.44 thf(decl_114, type, eqimpsubset2: $o).
% 209.27/30.44 thf(decl_115, type, eqimpsubset1: $o).
% 209.27/30.44 thf(decl_116, type, subsetI2: $o).
% 209.27/30.44 thf(decl_117, type, emptysetsubset: $o).
% 209.27/30.44 thf(decl_118, type, subsetE: $o).
% 209.27/30.44 thf(decl_119, type, subsetE2: $o).
% 209.27/30.44 thf(decl_120, type, notsubsetI: $o).
% 209.27/30.44 thf(decl_121, type, notequalI1: $o).
% 209.27/30.44 thf(decl_122, type, notequalI2: $o).
% 209.27/30.44 thf(decl_123, type, subsetRefl: $o).
% 209.27/30.44 thf(decl_124, type, subsetTrans: $o).
% 209.27/30.44 thf(decl_125, type, setadjoinSub: $o).
% 209.27/30.44 thf(decl_126, type, setadjoinSub2: $o).
% 209.27/30.44 thf(decl_127, type, subset2powerset: $o).
% 209.27/30.44 thf(decl_128, type, setextsub: $o).
% 209.27/30.44 thf(decl_129, type, subsetemptysetimpeq: $o).
% 209.27/30.44 thf(decl_130, type, powersetI1: $o).
% 209.27/30.44 thf(decl_131, type, powersetE1: $o).
% 209.27/30.44 thf(decl_132, type, inPowerset: $o).
% 209.27/30.44 thf(decl_133, type, powersetsubset: $o).
% 209.27/30.44 thf(decl_134, type, sepInPowerset: $o).
% 209.27/30.44 thf(decl_135, type, sepSubset: $o).
% 209.27/30.44 thf(decl_136, type, binunion: $i > $i > $i).
% 209.27/30.44 thf(decl_137, type, binunionIL: $o).
% 209.27/30.44 thf(decl_138, type, upairset2IR: $o).
% 209.27/30.44 thf(decl_139, type, binunionIR: $o).
% 209.27/30.44 thf(decl_140, type, binunionEcases: $o).
% 209.27/30.44 thf(decl_141, type, binunionE: $o).
% 209.27/30.44 thf(decl_142, type, binunionLsub: $o).
% 209.27/30.44 thf(decl_143, type, binunionRsub: $o).
% 209.27/30.44 thf(decl_144, type, binintersect: $i > $i > $i).
% 209.27/30.44 thf(decl_145, type, binintersectI: $o).
% 209.27/30.44 thf(decl_146, type, binintersectSubset5: $o).
% 209.27/30.44 thf(decl_147, type, binintersectEL: $o).
% 209.27/30.44 thf(decl_148, type, binintersectLsub: $o).
% 209.27/30.44 thf(decl_149, type, binintersectSubset2: $o).
% 209.27/30.44 thf(decl_150, type, binintersectSubset3: $o).
% 209.27/30.44 thf(decl_151, type, binintersectER: $o).
% 209.27/30.44 thf(decl_152, type, disjointsetsI1: $o).
% 209.27/30.44 thf(decl_153, type, binintersectRsub: $o).
% 209.27/30.44 thf(decl_154, type, binintersectSubset4: $o).
% 209.27/30.44 thf(decl_155, type, binintersectSubset1: $o).
% 209.27/30.44 thf(decl_156, type, bs114d: $o).
% 209.27/30.44 thf(decl_158, type, setminus: $i > $i > $i).
% 209.27/30.44 thf(decl_159, type, setminusI: $o).
% 209.27/30.44 thf(decl_160, type, setminusEL: $o).
% 209.27/30.44 thf(decl_161, type, setminusER: $o).
% 209.27/30.44 thf(decl_162, type, setminusSubset2: $o).
% 209.27/30.44 thf(decl_163, type, setminusERneg: $o).
% 209.27/30.44 thf(decl_164, type, setminusELneg: $o).
% 209.27/30.44 thf(decl_165, type, setminusILneg: $o).
% 209.27/30.44 thf(decl_166, type, setminusIRneg: $o).
% 209.27/30.44 thf(decl_167, type, setminusLsub: $o).
% 209.27/30.44 thf(decl_168, type, setminusSubset1: $o).
% 209.27/30.44 thf(decl_169, type, symdiff: $i > $i > $i).
% 209.27/30.44 thf(decl_170, type, symdiffE: $o).
% 209.27/30.44 thf(decl_171, type, symdiffI1: $o).
% 209.27/30.44 thf(decl_172, type, symdiffI2: $o).
% 209.27/30.44 thf(decl_173, type, symdiffIneg1: $o).
% 209.27/30.44 thf(decl_174, type, symdiffIneg2: $o).
% 209.27/30.44 thf(decl_175, type, iskpair: $i > $o).
% 209.27/30.44 thf(decl_176, type, secondinupair: $o).
% 209.27/30.44 thf(decl_177, type, setukpairIL: $o).
% 209.27/30.44 thf(decl_178, type, setukpairIR: $o).
% 209.27/30.44 thf(decl_179, type, kpairiskpair: $o).
% 209.27/30.44 thf(decl_180, type, kpair: $i > $i > $i).
% 209.27/30.44 thf(decl_181, type, kpairp: $o).
% 209.27/30.44 thf(decl_182, type, cartprod: $i > $i > $i).
% 209.27/30.44 thf(decl_183, type, singletonsubset: $o).
% 209.27/30.44 thf(decl_184, type, singletoninpowerset: $o).
% 209.27/30.44 thf(decl_185, type, singletoninpowunion: $o).
% 209.27/30.44 thf(decl_186, type, upairset2E: $o).
% 209.27/30.44 thf(decl_187, type, upairsubunion: $o).
% 209.27/30.44 thf(decl_188, type, upairinpowunion: $o).
% 209.27/30.44 thf(decl_189, type, ubforcartprodlem1: $o).
% 209.27/30.44 thf(decl_190, type, ubforcartprodlem2: $o).
% 209.27/30.44 thf(decl_191, type, ubforcartprodlem3: $o).
% 209.27/30.44 thf(decl_192, type, cartprodpairin: $o).
% 209.27/30.44 thf(decl_193, type, cartprodmempair1: $o).
% 209.27/30.44 thf(decl_194, type, cartprodmempair: $o).
% 209.27/30.44 thf(decl_195, type, setunionE2: $o).
% 209.27/30.44 thf(decl_196, type, setunionsingleton1: $o).
% 209.27/30.44 thf(decl_197, type, setunionsingleton2: $o).
% 209.27/30.44 thf(decl_198, type, setunionsingleton: $o).
% 209.27/30.44 thf(decl_199, type, singleton: $i > $o).
% 209.27/30.44 thf(decl_200, type, singletonprop: $o).
% 209.27/30.44 thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 209.27/30.44 thf(decl_202, type, ex1E1: $o).
% 209.27/30.44 thf(decl_203, type, ex1I: $o).
% 209.27/30.44 thf(decl_204, type, ex1I2: $o).
% 209.27/30.44 thf(decl_205, type, singletonsuniq: $o).
% 209.27/30.44 thf(decl_210, type, setukpairinjL1: $o).
% 209.27/30.44 thf(decl_211, type, kfstsingleton: $o).
% 209.27/30.44 thf(decl_212, type, theprop: $o).
% 209.27/30.44 thf(decl_213, type, kfst: $i > $i).
% 209.27/30.44 thf(decl_214, type, kfstpairEq: $o).
% 209.27/30.44 thf(decl_215, type, cartprodfstin: $o).
% 209.27/30.44 thf(decl_216, type, setukpairinjL2: $o).
% 209.27/30.44 thf(decl_217, type, setukpairinjL: $o).
% 209.27/30.44 thf(decl_218, type, setukpairinjR11: $o).
% 209.27/30.44 thf(decl_219, type, setukpairinjR12: $o).
% 209.27/30.44 thf(decl_220, type, setukpairinjR1: $o).
% 209.27/30.44 thf(decl_221, type, upairequniteq: $o).
% 209.27/30.44 thf(decl_222, type, setukpairinjR2: $o).
% 209.27/30.44 thf(decl_223, type, setukpairinjR: $o).
% 209.27/30.44 thf(decl_224, type, ksndsingleton: $o).
% 209.27/30.44 thf(decl_225, type, ksnd: $i > $i).
% 209.27/30.44 thf(decl_226, type, ksndpairEq: $o).
% 209.27/30.44 thf(decl_227, type, kpairsurjEq: $o).
% 209.27/30.44 thf(decl_228, type, cartprodsndin: $o).
% 209.27/30.44 thf(decl_229, type, cartprodpairmemEL: $o).
% 209.27/30.44 thf(decl_230, type, cartprodpairmemER: $o).
% 209.27/30.44 thf(decl_231, type, cartprodmempaircEq: $o).
% 209.27/30.44 thf(decl_232, type, cartprodfstpairEq: $o).
% 209.27/30.44 thf(decl_233, type, cartprodsndpairEq: $o).
% 209.27/30.44 thf(decl_234, type, cartprodpairsurjEq: $o).
% 209.27/30.44 thf(decl_235, type, breln: $i > $i > $i > $o).
% 209.27/30.44 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 209.27/30.44 thf(decl_237, type, dpsetconstrI: $o).
% 209.27/30.44 thf(decl_238, type, dpsetconstrSub: $o).
% 209.27/30.44 thf(decl_239, type, setOfPairsIsBReln: $o).
% 209.27/30.44 thf(decl_240, type, dpsetconstrERa: $o).
% 209.27/30.44 thf(decl_241, type, dpsetconstrEL1: $o).
% 209.27/30.44 thf(decl_242, type, dpsetconstrEL2: $o).
% 209.27/30.44 thf(decl_243, type, dpsetconstrER: $o).
% 209.27/30.44 thf(decl_244, type, func: $i > $i > $i > $o).
% 209.27/30.44 thf(decl_245, type, funcSet: $i > $i > $i).
% 209.27/30.44 thf(decl_246, type, funcImageSingleton: $o).
% 209.27/30.44 thf(decl_247, type, apProp: $o).
% 209.27/30.44 thf(decl_248, type, ap: $i > $i > $i > $i > $i).
% 209.27/30.44 thf(decl_249, type, app: $o).
% 209.27/30.44 thf(decl_250, type, infuncsetfunc: $o).
% 209.27/30.44 thf(decl_251, type, ap2p: $o).
% 209.27/30.44 thf(decl_252, type, funcinfuncset: $o).
% 209.27/30.44 thf(decl_253, type, lamProp: $o).
% 209.27/30.44 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
% 209.27/30.44 thf(decl_255, type, lamp: $o).
% 209.27/30.44 thf(decl_256, type, lam2p: $o).
% 209.27/30.44 thf(decl_257, type, brelnall1: $o).
% 209.27/30.44 thf(decl_258, type, brelnall2: $o).
% 209.27/30.44 thf(decl_259, type, ex1E2: $o).
% 209.27/30.44 thf(decl_260, type, epred1_0: $o).
% 209.27/30.44 thf(decl_261, type, esk1_2: $i > $i > $i).
% 209.27/30.44 thf(decl_262, type, esk2_2: $i > $i > $i).
% 209.27/30.44 thf(decl_263, type, esk3_2: $i > $i > $i).
% 209.27/30.44 thf(decl_264, type, esk4_1: $i > $i).
% 209.27/30.44 thf(decl_265, type, esk5_2: ($i > $i > $o) > $i > $i).
% 209.27/30.44 thf(decl_266, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 209.27/30.44 thf(decl_267, type, esk7_2: ($i > $i > $o) > $i > $i).
% 209.27/30.44 thf(decl_268, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 209.27/30.44 thf(decl_269, type, esk9_1: $i > $i).
% 209.27/30.44 thf(decl_270, type, esk10_2: ($i > $o) > $i > $i).
% 209.27/30.44 thf(decl_271, type, esk11_2: ($i > $o) > $i > $i).
% 209.27/30.44 thf(decl_272, type, esk12_1: ($i > $o) > $i).
% 209.27/30.44 thf(decl_273, type, esk13_2: ($i > $o) > $i > $i).
% 209.27/30.44 thf(decl_274, type, esk14_1: ($i > $o) > $i).
% 209.27/30.44 thf(decl_275, type, esk15_2: $i > $i > $i).
% 209.27/30.44 thf(decl_276, type, esk16_2: $i > $i > $i).
% 209.27/30.44 thf(decl_277, type, esk17_1: $i > $i).
% 209.27/30.44 thf(decl_278, type, esk18_1: $i > $i).
% 209.27/30.44 thf(decl_279, type, esk19_1: $i > $i).
% 209.27/30.44 thf(decl_280, type, esk20_2: $i > $i > $i).
% 209.27/30.44 thf(decl_281, type, esk21_3: $i > $i > $o > $i).
% 209.27/30.44 thf(decl_282, type, esk22_2: ($i > $o) > $i > $i).
% 209.27/30.44 thf(decl_283, type, esk23_1: ($i > $o) > $i).
% 209.27/30.44 thf(decl_284, type, esk24_1: $i > $i).
% 209.27/30.44 thf(decl_285, type, esk25_2: $i > ($i > $o) > $i).
% 209.27/30.44 thf(decl_286, type, esk26_2: $i > ($i > $o) > $i).
% 209.27/30.44 thf(decl_287, type, esk27_2: $i > ($i > $o) > $i).
% 209.27/30.44 thf(decl_288, type, esk28_2: $i > ($i > $o) > $i).
% 209.27/30.44 thf(decl_289, type, esk29_2: $i > ($i > $o) > $i).
% 209.27/30.44 thf(decl_290, type, esk30_2: $i > ($i > $o) > $i).
% 209.27/30.44 thf(decl_291, type, esk31_2: ($i > $o) > $i > $i).
% 209.27/30.44 thf(decl_292, type, esk32_1: ($i > $o) > $i).
% 209.27/30.44 thf(decl_293, type, esk33_1: ($i > $o) > $i).
% 209.27/30.44 thf(decl_294, type, esk34_1: ($i > $o) > $i).
% 209.27/30.44 thf(decl_295, type, esk35_1: ($i > $o) > $i).
% 209.27/30.44 thf(decl_296, type, esk36_2: ($i > $o) > $i > $i).
% 209.27/30.44 thf(decl_297, type, esk37_1: ($i > $o) > $i).
% 209.27/30.44 thf(decl_298, type, esk38_2: ($i > $o) > $i > $i).
% 209.27/30.44 thf(decl_299, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 209.27/30.44 thf(decl_300, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 209.27/30.44 thf(decl_301, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 209.27/30.44 thf(decl_302, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 209.27/30.44 thf(decl_303, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 209.27/30.44 thf(decl_304, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 209.27/30.44 thf(decl_305, type, esk45_2: ($i > $o) > $i > $i).
% 209.27/30.44 thf(decl_306, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 209.27/30.44 thf(decl_307, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 209.27/30.44 thf(decl_308, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 209.27/30.44 thf(decl_309, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 209.27/30.44 thf(decl_310, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 209.27/30.44 thf(decl_311, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 209.27/30.44 thf(decl_312, type, esk52_2: $i > $i > $i).
% 209.27/30.44 thf(decl_313, type, esk53_2: $i > $i > $i).
% 209.27/30.44 thf(decl_314, type, esk54_2: $i > $i > $i).
% 209.27/30.44 thf(decl_315, type, esk55_3: $i > $i > $i > $i).
% 209.27/30.44 thf(decl_316, type, esk56_3: $i > $i > $i > $i).
% 209.27/30.44 thf(decl_317, type, esk57_2: $i > $i > $i).
% 209.27/30.44 thf(decl_318, type, esk58_2: $i > ($i > $o) > $i).
% 209.27/30.44 thf(decl_319, type, esk59_2: $i > ($i > $o) > $i).
% 209.27/30.44 thf(decl_320, type, esk60_2: $i > ($i > $o) > $i).
% 209.27/30.44 thf(decl_321, type, esk61_2: $i > ($i > $o) > $i).
% 209.27/30.44 thf(decl_322, type, esk62_3: $i > ($i > $o) > $i > $i).
% 209.27/30.44 thf(decl_323, type, esk63_3: $i > ($i > $o) > $i > $i).
% 209.27/30.44 thf(decl_324, type, esk64_2: $i > ($i > $o) > $i).
% 209.27/30.44 thf(decl_325, type, esk65_2: $i > ($i > $o) > $i).
% 209.27/30.44 thf(decl_326, type, esk66_2: $i > ($i > $o) > $i).
% 209.27/30.44 thf(decl_327, type, esk67_1: $i > $i).
% 209.27/30.44 thf(decl_328, type, esk68_1: $i > $i).
% 209.27/30.44 thf(decl_329, type, esk69_3: $i > $i > $i > $i).
% 209.27/30.44 thf(decl_330, type, esk70_4: $i > $i > $i > $i > $i).
% 209.27/30.44 thf(decl_331, type, esk71_3: $i > $i > $i > $i).
% 209.27/30.44 thf(decl_332, type, esk72_3: $i > $i > $i > $i).
% 209.27/30.44 thf(decl_333, type, esk73_4: $i > $i > $i > $i > $i).
% 209.27/30.44 thf(decl_334, type, esk74_3: $i > $i > $i > $i).
% 209.27/30.44 thf(decl_335, type, esk75_3: $i > $i > ($i > $i) > $i).
% 209.27/30.44 thf(decl_336, type, esk76_4: $i > $i > ($i > $i) > $i > $i).
% 209.27/30.44 thf(decl_337, type, esk77_3: $i > $i > ($i > $i) > $i).
% 209.27/30.44 thf(decl_338, type, esk78_4: $i > $i > ($i > $i) > $i > $i).
% 209.27/30.44 thf(decl_339, type, esk79_3: $i > $i > ($i > $i) > $i).
% 209.27/30.44 thf(decl_340, type, esk80_4: $i > $i > $i > ($i > $o) > $i).
% 209.27/30.44 thf(decl_341, type, esk81_4: $i > $i > $i > ($i > $o) > $i).
% 209.27/30.44 thf(decl_342, type, esk82_4: $i > $i > $i > ($i > $o) > $i).
% 209.27/30.44 thf(decl_343, type, esk83_4: $i > $i > $i > ($i > $o) > $i).
% 209.27/30.44 thf(decl_344, type, esk84_0: $i).
% 209.27/30.44 thf(decl_345, type, esk85_0: $i).
% 209.27/30.44 thf(decl_346, type, esk86_0: $i).
% 209.27/30.44 thf(decl_347, type, esk87_1: $i > $i).
% 209.27/30.44 thf(decl_348, type, esk88_0: $i).
% 209.27/30.44 thf(decl_354, type, epred2_2: $i > $i > $i > $o).
% 209.27/30.44 thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', ex1)).
% 209.27/30.44 thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:((((in @ X2 @ X4))&(((X4)=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', singleton)).
% 209.27/30.44 thf(func, axiom, ((func)=(^[X4:$i, X5:$i, X29:$i]:((((breln @ X4 @ X5 @ X29))&(![X2:$i]:((((in @ X2 @ X4))=>((ex1 @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', func)).
% 209.27/30.44 thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', breln)).
% 209.27/30.44 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', replAx)).
% 209.27/30.44 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', exu)).
% 209.27/30.44 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', descrp)).
% 209.27/30.44 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', exuE1)).
% 209.27/30.44 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', exuE3e)).
% 209.27/30.44 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', nonempty)).
% 209.27/30.44 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', nonemptyI)).
% 209.27/30.44 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', exuE2)).
% 209.27/30.44 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', exuI1)).
% 209.27/30.44 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', exuI3)).
% 209.27/30.44 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', exuI2)).
% 209.27/30.44 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', exuE3u)).
% 209.27/30.44 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', exu__Cong)).
% 209.27/30.44 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', exuEu)).
% 209.27/30.44 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', descr__Cong)).
% 209.27/30.44 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', singletonprop)).
% 209.27/30.44 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', ex1E1)).
% 209.27/30.44 thf(ex1I, axiom, ((ex1I)<=>![X4:$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/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', ex1I)).
% 209.27/30.44 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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', ex1I2)).
% 209.27/30.44 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', kfstsingleton)).
% 209.27/30.44 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', ksndsingleton)).
% 209.27/30.44 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setOfPairsIsBReln)).
% 209.27/30.44 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X30)))))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', funcImageSingleton)).
% 209.27/30.44 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X30))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', apProp)).
% 209.27/30.44 thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X31 @ X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', lamProp)).
% 209.27/30.44 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X33:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X33 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X33 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', lamp)).
% 209.27/30.44 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$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/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', ex1E2)).
% 209.27/30.44 thf(funcGraphProp1, 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)=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X30 @ X2)) @ X30))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', funcGraphProp1)).
% 209.27/30.44 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', dsetconstrI)).
% 209.27/30.44 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', dsetconstrEL)).
% 209.27/30.44 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', dsetconstrER)).
% 209.27/30.44 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setbeta)).
% 209.27/30.44 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', nonemptyE1)).
% 209.27/30.44 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', nonemptyI1)).
% 209.27/30.44 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setoftrueEq)).
% 209.27/30.44 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', nonemptyImpWitness)).
% 209.27/30.44 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', emptyE1)).
% 209.27/30.44 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', dsetconstr__Cong)).
% 209.27/30.44 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', sepInPowerset)).
% 209.27/30.44 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', sepSubset)).
% 209.27/30.44 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', theprop)).
% 209.27/30.44 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', dpsetconstrI)).
% 209.27/30.44 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', dpsetconstrSub)).
% 209.27/30.44 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', dpsetconstrERa)).
% 209.27/30.44 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', dpsetconstrEL1)).
% 209.27/30.44 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', dpsetconstrEL2)).
% 209.27/30.44 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', dpsetconstrER)).
% 209.27/30.44 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X30 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', app)).
% 209.27/30.44 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X30)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', infuncsetfunc)).
% 209.27/30.44 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>(in @ X30 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', funcinfuncset)).
% 209.27/30.44 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X34:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X34 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X34 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', lam2p)).
% 209.27/30.44 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X29:$i]:(((breln @ X4 @ X5 @ X29)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X29)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', brelnall1)).
% 209.27/30.44 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X29:$i]:(((breln @ X4 @ X5 @ X29)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X29)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', brelnall2)).
% 209.27/30.44 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setextAx)).
% 209.27/30.44 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', emptysetAx)).
% 209.27/30.44 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setadjoinAx)).
% 209.27/30.44 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', powersetAx)).
% 209.27/30.44 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setunionAx)).
% 209.27/30.44 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', omega0Ax)).
% 209.27/30.44 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', omegaSAx)).
% 209.27/30.44 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', omegaIndAx)).
% 209.27/30.44 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', foundationAx)).
% 209.27/30.44 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', wellorderingAx)).
% 209.27/30.44 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', prop2setE)).
% 209.27/30.44 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', emptysetE)).
% 209.27/30.44 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', emptysetimpfalse)).
% 209.27/30.44 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', notinemptyset)).
% 209.27/30.44 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setext)).
% 209.27/30.44 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', emptyI)).
% 209.27/30.44 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', noeltsimpempty)).
% 209.27/30.44 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setadjoinIL)).
% 209.27/30.44 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', emptyinunitempty)).
% 209.27/30.44 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setadjoinIR)).
% 209.27/30.44 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setadjoinE)).
% 209.27/30.44 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setadjoinOr)).
% 209.27/30.44 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', powersetI)).
% 209.27/30.44 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', emptyinPowerset)).
% 209.27/30.44 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', emptyInPowerset)).
% 209.27/30.44 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', powersetE)).
% 209.27/30.44 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setunionI)).
% 209.27/30.44 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setunionE)).
% 209.27/30.44 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', subPowSU)).
% 209.27/30.44 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', uniqinunit)).
% 209.27/30.44 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', notinsingleton)).
% 209.27/30.44 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', eqinunit)).
% 209.27/30.44 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', singletonsswitch)).
% 209.27/30.44 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', upairsetE)).
% 209.27/30.44 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', upairsetIL)).
% 209.27/30.44 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', upairsetIR)).
% 209.27/30.44 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', vacuousDall)).
% 209.27/30.44 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', quantDeMorgan1)).
% 209.27/30.44 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', quantDeMorgan2)).
% 209.27/30.44 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', quantDeMorgan3)).
% 209.27/30.44 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', quantDeMorgan4)).
% 209.27/30.44 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', prop2setI)).
% 209.27/30.44 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', prop2set2propI)).
% 209.27/30.44 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', notdexE)).
% 209.27/30.44 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', notdallE)).
% 209.27/30.44 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', inCongP)).
% 209.27/30.44 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', in__Cong)).
% 209.27/30.44 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', emptyset__Cong)).
% 209.27/30.44 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setadjoin__Cong)).
% 209.27/30.44 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', powerset__Cong)).
% 209.27/30.44 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setunion__Cong)).
% 209.27/30.44 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', omega__Cong)).
% 209.27/30.44 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', subsetI1)).
% 209.27/30.44 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', eqimpsubset2)).
% 209.27/30.44 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', eqimpsubset1)).
% 209.27/30.44 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', subsetI2)).
% 209.27/30.44 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', emptysetsubset)).
% 209.27/30.44 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', subsetE)).
% 209.27/30.44 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', subsetE2)).
% 209.27/30.44 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', notsubsetI)).
% 209.27/30.44 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', notequalI1)).
% 209.27/30.44 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', notequalI2)).
% 209.27/30.44 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', subsetRefl)).
% 209.27/30.44 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', subsetTrans)).
% 209.27/30.44 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setadjoinSub)).
% 209.27/30.44 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setadjoinSub2)).
% 209.27/30.44 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', subset2powerset)).
% 209.27/30.44 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setextsub)).
% 209.27/30.44 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', subsetemptysetimpeq)).
% 209.27/30.44 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', powersetI1)).
% 209.27/30.44 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', powersetE1)).
% 209.27/30.44 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', inPowerset)).
% 209.27/30.44 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', powersetsubset)).
% 209.27/30.44 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', binunionIL)).
% 209.27/30.44 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', upairset2IR)).
% 209.27/30.44 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', binunionIR)).
% 209.27/30.44 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', binunionEcases)).
% 209.27/30.44 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', binunionE)).
% 209.27/30.44 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', binunionLsub)).
% 209.27/30.44 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', binunionRsub)).
% 209.27/30.44 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', binintersectI)).
% 209.27/30.44 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', binintersectSubset5)).
% 209.27/30.44 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', binintersectEL)).
% 209.27/30.44 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', binintersectLsub)).
% 209.27/30.44 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', binintersectSubset2)).
% 209.27/30.44 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', binintersectSubset3)).
% 209.27/30.44 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', binintersectER)).
% 209.27/30.44 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', disjointsetsI1)).
% 209.27/30.44 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', binintersectRsub)).
% 209.27/30.44 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', binintersectSubset4)).
% 209.27/30.44 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', binintersectSubset1)).
% 209.27/30.44 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', bs114d)).
% 209.27/30.44 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setminusI)).
% 209.27/30.44 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setminusEL)).
% 209.27/30.44 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setminusER)).
% 209.27/30.44 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setminusSubset2)).
% 209.27/30.44 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setminusERneg)).
% 209.27/30.44 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setminusELneg)).
% 209.27/30.44 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setminusILneg)).
% 209.27/30.44 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setminusIRneg)).
% 209.27/30.44 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setminusLsub)).
% 209.27/30.44 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setminusSubset1)).
% 209.27/30.44 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', symdiffE)).
% 209.27/30.44 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', symdiffI1)).
% 209.27/30.44 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', symdiffI2)).
% 209.27/30.44 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', symdiffIneg1)).
% 209.27/30.44 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', symdiffIneg2)).
% 209.27/30.44 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', secondinupair)).
% 209.27/30.44 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setukpairIL)).
% 209.27/30.44 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setukpairIR)).
% 209.27/30.44 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', kpairiskpair)).
% 209.27/30.44 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', kpairp)).
% 209.27/30.44 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', singletonsubset)).
% 209.27/30.44 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', singletoninpowerset)).
% 209.27/30.44 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', singletoninpowunion)).
% 209.27/30.44 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', upairset2E)).
% 209.27/30.44 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', upairsubunion)).
% 209.27/30.44 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', upairinpowunion)).
% 209.27/30.44 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', ubforcartprodlem1)).
% 209.27/30.44 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', ubforcartprodlem2)).
% 209.27/30.44 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', ubforcartprodlem3)).
% 209.27/30.44 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', cartprodpairin)).
% 209.27/30.44 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', cartprodmempair1)).
% 209.27/30.44 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', cartprodmempair)).
% 209.27/30.44 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setunionE2)).
% 209.27/30.44 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setunionsingleton1)).
% 209.27/30.44 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setunionsingleton2)).
% 209.27/30.44 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setunionsingleton)).
% 209.27/30.44 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', singletonsuniq)).
% 209.27/30.44 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setukpairinjL1)).
% 209.27/30.44 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', kfstpairEq)).
% 209.27/30.44 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', cartprodfstin)).
% 209.27/30.44 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setukpairinjL2)).
% 209.27/30.44 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setukpairinjL)).
% 209.27/30.44 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setukpairinjR11)).
% 209.27/30.44 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setukpairinjR12)).
% 209.27/30.44 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setukpairinjR1)).
% 209.27/30.44 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', upairequniteq)).
% 209.27/30.44 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/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setukpairinjR2)).
% 209.27/30.44 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', setukpairinjR)).
% 209.27/30.44 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', ksndpairEq)).
% 209.27/30.44 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', kpairsurjEq)).
% 209.27/30.44 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', cartprodsndin)).
% 209.27/30.44 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/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', cartprodpairmemEL)).
% 209.27/30.44 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/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', cartprodpairmemER)).
% 209.27/30.44 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/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', cartprodmempaircEq)).
% 209.27/30.44 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/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', cartprodfstpairEq)).
% 209.27/30.44 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/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', cartprodsndpairEq)).
% 209.27/30.44 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', cartprodpairsurjEq)).
% 209.27/30.44 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X30 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', ap2p)).
% 209.27/30.44 thf(ap, axiom, ((ap)=(^[X4:$i, X5:$i, X30:$i, X2:$i]:(setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X30))))))), file('/export/starexec/sandbox/tmp/tmp.0ZW5DV2ZUh/E---3.1_159952.p', ap)).
% 209.27/30.44 thf(c_0_208, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((?[X649:$i]:((((in @ X649 @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))))&(((dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))=(setadjoin @ X649 @ emptyset))))))))), inference(fof_simplification,[status(thm)],[ex1])).
% 209.27/30.44 thf(c_0_209, plain, ((singleton)=(^[Z0:$i]:(?[X2:$i]:((((in @ X2 @ Z0))&(((Z0)=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[singleton])).
% 209.27/30.44 thf(c_0_210, plain, ((func)=(^[Z0:$i, Z1:$i, Z2:$i]:(((((subset @ Z2 @ (cartprod @ Z0 @ Z1))))&(![X2:$i]:((((in @ X2 @ Z0))=>((?[X656:$i]:((((in @ X656 @ (dsetconstr @ Z1 @ (^[Z3:$i]:(((in @ (kpair @ X2 @ Z3) @ Z2)))))))&(((dsetconstr @ Z1 @ (^[Z3:$i]:(((in @ (kpair @ X2 @ Z3) @ Z2)))))=(setadjoin @ X656 @ emptyset)))))))))))))), inference(fof_simplification,[status(thm)],[func])).
% 209.27/30.44 thf(c_0_211, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((?[X649:$i]:((((in @ X649 @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))))&(((dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))=(setadjoin @ X649 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_208, c_0_209])).
% 209.27/30.44 thf(c_0_212, plain, ((breln)=(^[Z0:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
% 209.27/30.44 thf(c_0_213, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 209.27/30.44 thf(c_0_214, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 209.27/30.44 thf(c_0_215, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 209.27/30.44 thf(c_0_216, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 209.27/30.44 thf(c_0_217, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 209.27/30.44 thf(c_0_218, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 209.27/30.44 thf(c_0_219, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 209.27/30.44 thf(c_0_220, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 209.27/30.44 thf(c_0_221, 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])).
% 209.27/30.44 thf(c_0_222, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 209.27/30.44 thf(c_0_223, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 209.27/30.44 thf(c_0_224, 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])).
% 209.27/30.44 thf(c_0_225, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 209.27/30.44 thf(c_0_226, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 209.27/30.44 thf(c_0_227, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 209.27/30.44 thf(c_0_228, plain, ((singletonprop)<=>![X4:$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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 209.27/30.44 thf(c_0_229, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 209.27/30.44 thf(c_0_230, plain, ((ex1I)<=>![X4:$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])).
% 209.27/30.44 thf(c_0_231, 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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 209.27/30.44 thf(c_0_232, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 209.27/30.44 thf(c_0_233, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 209.27/30.44 thf(c_0_234, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 209.27/30.44 thf(c_0_235, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X30)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
% 209.27/30.44 thf(c_0_236, plain, ((func)=(^[Z0:$i, Z1:$i, Z2:$i]:(((((subset @ Z2 @ (cartprod @ Z0 @ Z1))))&(![X2:$i]:((((in @ X2 @ Z0))=>((?[X656:$i]:((((in @ X656 @ (dsetconstr @ Z1 @ (^[Z3:$i]:(((in @ (kpair @ X2 @ Z3) @ Z2)))))))&(((dsetconstr @ Z1 @ (^[Z3:$i]:(((in @ (kpair @ X2 @ Z3) @ Z2)))))=(setadjoin @ X656 @ emptyset)))))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_210, c_0_211]), c_0_212])).
% 209.27/30.44 thf(c_0_237, plain, ((apProp)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X30))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
% 209.27/30.44 thf(c_0_238, plain, ((lamProp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:(((X31 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])).
% 209.27/30.44 thf(c_0_239, plain, ((lamp)<=>![X4:$i, X5:$i, X33:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X33 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X33 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
% 209.27/30.44 thf(c_0_240, plain, ((ex1E2)<=>![X4:$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])).
% 209.27/30.44 thf(c_0_241, 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)=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X30 @ X2)) @ X30)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[funcGraphProp1])).
% 209.27/30.44 thf(c_0_242, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X620:$i]:(((((X6 @ X2 @ X620)))&(![X621:$i]:(((((X6 @ X2 @ X621)))=>(((X620)=(X621)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_213, c_0_214])).
% 209.27/30.44 thf(c_0_243, plain, ((descrp)=(![X1:$i > $o]:((((?[X622:$i]:(((((X1 @ X622)))&(![X623:$i]:(((((X1 @ X623)))=>(((X622)=(X623))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_215, c_0_214])).
% 209.27/30.44 thf(c_0_244, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 209.27/30.44 thf(c_0_245, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 209.27/30.44 thf(c_0_246, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 209.27/30.44 thf(c_0_247, plain, ((exuE1)=(![X1:$i > $o]:((((?[X624:$i]:(((((X1 @ X624)))&(![X625:$i]:(((((X1 @ X625)))=>(((X624)=(X625))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_216, c_0_214])).
% 209.27/30.44 thf(c_0_248, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X626:$i]:(((((X1 @ X626)))&(![X627:$i]:(((((X1 @ X627)))=>(((X626)=(X627))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_217, c_0_214])).
% 209.27/30.44 thf(c_0_249, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 209.27/30.44 thf(c_0_250, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_218])).
% 209.27/30.44 thf(c_0_251, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_219, c_0_218])).
% 209.27/30.44 thf(c_0_252, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_218])).
% 209.27/30.44 thf(c_0_253, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 209.27/30.44 thf(c_0_254, plain, ((exuE2)=(![X1:$i > $o]:((((?[X628:$i]:(((((X1 @ X628)))&(![X629:$i]:(((((X1 @ X629)))=>(((X628)=(X629))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_220, c_0_214])).
% 209.27/30.44 thf(c_0_255, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_218])).
% 209.27/30.44 thf(c_0_256, 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])).
% 209.27/30.44 thf(c_0_257, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X630:$i]:(((((X1 @ X630)))&(![X631:$i]:(((((X1 @ X631)))=>(((X630)=(X631)))))))))))))), inference(apply_def,[status(thm)],[c_0_221, c_0_214])).
% 209.27/30.44 thf(c_0_258, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X632:$i]:(((((X1 @ X632)))&(![X633:$i]:(((((X1 @ X633)))=>(((X632)=(X633)))))))))))))))), inference(apply_def,[status(thm)],[c_0_222, c_0_214])).
% 209.27/30.44 thf(c_0_259, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X634:$i]:(((((X1 @ X634)))&(![X635:$i]:(((((X1 @ X635)))=>(((X634)=(X635)))))))))))))), inference(apply_def,[status(thm)],[c_0_223, c_0_214])).
% 209.27/30.44 thf(c_0_260, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X636:$i]:(((((X1 @ X636)))&(![X637:$i]:(((((X1 @ X637)))=>(((X636)=(X637))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_224, c_0_214])).
% 209.27/30.44 thf(c_0_261, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X638:$i]:(((((X1 @ X638)))&(![X639:$i]:(((((X1 @ X639)))=>(((X638)=(X639))))))))))<=>((?[X640:$i]:(((((X17 @ X640)))&(![X641:$i]:(((((X17 @ X641)))=>(((X640)=(X641)))))))))))))))), inference(apply_def,[status(thm)],[c_0_225, c_0_214])).
% 209.27/30.44 thf(c_0_262, plain, ((exuEu)=(![X1:$i > $o]:((((?[X642:$i]:(((((X1 @ X642)))&(![X643:$i]:(((((X1 @ X643)))=>(((X642)=(X643))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_226, c_0_214])).
% 209.27/30.44 thf(c_0_263, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X644:$i]:(((((X1 @ X644)))&(![X645:$i]:(((((X1 @ X645)))=>(((X644)=(X645))))))))))=>((((?[X646:$i]:(((((X17 @ X646)))&(![X647:$i]:(((((X17 @ X647)))=>(((X646)=(X647))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_227, c_0_214])).
% 209.27/30.44 thf(c_0_264, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 209.27/30.44 thf(c_0_265, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 209.27/30.44 thf(c_0_266, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 209.27/30.44 thf(c_0_267, 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)))))=>((?[X648:$i]:((((in @ X648 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(setadjoin @ X648 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_228, c_0_209])).
% 209.27/30.44 thf(c_0_268, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:((((?[X650:$i]:((((in @ X650 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X650 @ emptyset)))))))=>(?[X2:$i]:((((in @ X2 @ X4))&((X1 @ X2))))))))), inference(apply_def,[status(thm)],[c_0_229, c_0_211])).
% 209.27/30.44 thf(c_0_269, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>(((![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X3))=>(((X3)=(X2))))))))=>((?[X651:$i]:((((in @ X651 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X651 @ emptyset))))))))))))))), inference(apply_def,[status(thm)],[c_0_230, c_0_211])).
% 209.27/30.44 thf(c_0_270, 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)))))=>((?[X652:$i]:((((in @ X652 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X652 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_231, c_0_211])).
% 209.27/30.44 thf(c_0_271, plain, ((kfstsingleton)=(![X18:$i]:((((iskpair @ X18))=>((?[X653:$i]:((((in @ X653 @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))))&(((dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))=(setadjoin @ X653 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_232, c_0_209])).
% 209.27/30.44 thf(c_0_272, axiom, ((theprop)=(![X21:$i]:((((?[X654:$i]:((((in @ X654 @ X21))&(((X21)=(setadjoin @ X654 @ emptyset)))))))=>((in @ (setunion @ X21) @ X21)))))), inference(apply_def,[status(thm)],[theprop, c_0_209])).
% 209.27/30.44 thf(c_0_273, plain, ((ksndsingleton)=(![X18:$i]:((((iskpair @ X18))=>((?[X655:$i]:((((in @ X655 @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))))&(((dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))=(setadjoin @ X655 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_233, c_0_209])).
% 209.27/30.44 thf(c_0_274, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 209.27/30.44 thf(c_0_275, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 209.27/30.44 thf(c_0_276, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_234, c_0_212])).
% 209.27/30.44 thf(c_0_277, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 209.27/30.44 thf(c_0_278, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 209.27/30.44 thf(c_0_279, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 209.27/30.44 thf(c_0_280, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 209.27/30.44 thf(c_0_281, plain, ((funcImageSingleton)=(![X4:$i, X5:$i, X30:$i]:((((((((subset @ X30 @ (cartprod @ X4 @ X5))))&(![X657:$i]:((((in @ X657 @ X4))=>((?[X658:$i]:((((in @ X658 @ (dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X657 @ Z0) @ X30)))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X657 @ Z0) @ X30)))))=(setadjoin @ X658 @ emptyset)))))))))))))=>(![X2:$i]:((((in @ X2 @ X4))=>((?[X659:$i]:((((in @ X659 @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X30))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X30))))=(setadjoin @ X659 @ emptyset)))))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_235, c_0_209]), c_0_236])).
% 209.27/30.44 thf(c_0_282, plain, ((apProp)=(![X4:$i, X5:$i, X30:$i]:((((((((subset @ X30 @ (cartprod @ X4 @ X5))))&(![X660:$i]:((((in @ X660 @ X4))=>((?[X661:$i]:((((in @ X661 @ (dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X660 @ Z0) @ X30)))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X660 @ Z0) @ X30)))))=(setadjoin @ X661 @ emptyset)))))))))))))=>(![X2:$i]:((((in @ X2 @ X4))=>((in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X30))))) @ X5))))))))), inference(apply_def,[status(thm)],[c_0_237, c_0_236])).
% 209.27/30.44 thf(c_0_283, axiom, ((app)=(![X4:$i, X5:$i, X30:$i]:((((((((subset @ X30 @ (cartprod @ X4 @ X5))))&(![X662:$i]:((((in @ X662 @ X4))=>((?[X663:$i]:((((in @ X663 @ (dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X662 @ Z0) @ X30)))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X662 @ Z0) @ X30)))))=(setadjoin @ X663 @ emptyset)))))))))))))=>(![X2:$i]:((((in @ X2 @ X4))=>((in @ (ap @ X4 @ X5 @ X30 @ X2) @ X5))))))))), inference(apply_def,[status(thm)],[app, c_0_236])).
% 209.27/30.44 thf(c_0_284, axiom, ((infuncsetfunc)=(![X4:$i, X5:$i, X30:$i]:((((in @ X30 @ (funcSet @ X4 @ X5)))=>((((((subset @ X30 @ (cartprod @ X4 @ X5))))&(![X664:$i]:((((in @ X664 @ X4))=>((?[X665:$i]:((((in @ X665 @ (dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X664 @ Z0) @ X30)))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X664 @ Z0) @ X30)))))=(setadjoin @ X665 @ emptyset))))))))))))))))), inference(apply_def,[status(thm)],[infuncsetfunc, c_0_236])).
% 209.27/30.44 thf(c_0_285, axiom, ((funcinfuncset)=(![X4:$i, X5:$i, X30:$i]:((((((((subset @ X30 @ (cartprod @ X4 @ X5))))&(![X666:$i]:((((in @ X666 @ X4))=>((?[X667:$i]:((((in @ X667 @ (dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X666 @ Z0) @ X30)))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X666 @ Z0) @ X30)))))=(setadjoin @ X667 @ emptyset)))))))))))))=>((in @ X30 @ (funcSet @ X4 @ X5))))))), inference(apply_def,[status(thm)],[funcinfuncset, c_0_236])).
% 209.27/30.44 thf(c_0_286, plain, ((lamProp)=(![X4:$i, X5:$i, X31:$i > $i]:(((![X2:$i]:((((in @ X2 @ X4))=>((in @ (X31 @ X2) @ X5)))))=>((((((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:(((X31 @ Z0)=(Z1))))) @ (cartprod @ X4 @ X5))))&(![X668:$i]:((((in @ X668 @ X4))=>((?[X669:$i]:((((in @ X669 @ (dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X668 @ Z0) @ (dpsetconstr @ X4 @ X5 @ (^[Z1:$i, Z2:$i]:(((X31 @ Z1)=(Z2))))))))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X668 @ Z0) @ (dpsetconstr @ X4 @ X5 @ (^[Z1:$i, Z2:$i]:(((X31 @ Z1)=(Z2))))))))))=(setadjoin @ X669 @ emptyset))))))))))))))))), inference(apply_def,[status(thm)],[c_0_238, c_0_236])).
% 209.27/30.44 thf(c_0_287, plain, ((lamp)=(![X4:$i, X5:$i, X33:$i > $i]:(((![X2:$i]:((((in @ X2 @ X4))=>((in @ (X33 @ X2) @ X5)))))=>((((((subset @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X33 @ Z0))) @ (cartprod @ X4 @ X5))))&(![X670:$i]:((((in @ X670 @ X4))=>((?[X671:$i]:((((in @ X671 @ (dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X670 @ Z0) @ (lam @ X4 @ X5 @ (^[Z1:$i]:(X33 @ Z1))))))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X670 @ Z0) @ (lam @ X4 @ X5 @ (^[Z1:$i]:(X33 @ Z1))))))))=(setadjoin @ X671 @ emptyset))))))))))))))))), inference(apply_def,[status(thm)],[c_0_239, c_0_236])).
% 209.27/30.44 thf(c_0_288, plain, ((lam2p)<=>![X4:$i, X5:$i, X34:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X34 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X34 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
% 209.27/30.44 thf(c_0_289, axiom, ((brelnall1)=(![X4:$i, X5:$i, X29:$i]:(((((subset @ X29 @ (cartprod @ X4 @ X5))))=>(![X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X29))=>((X1 @ (kpair @ X2 @ X3)))))))))))=>(![X2:$i]:((((in @ X2 @ X29))=>((X1 @ X2)))))))))))), inference(apply_def,[status(thm)],[brelnall1, c_0_212])).
% 209.27/30.44 thf(c_0_290, axiom, ((brelnall2)=(![X4:$i, X5:$i, X29:$i]:(((((subset @ X29 @ (cartprod @ X4 @ X5))))=>(![X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X29))=>((X1 @ (kpair @ X2 @ X3)))))))))))=>(![X2:$i]:((((in @ X2 @ X29))=>((X1 @ X2)))))))))))), inference(apply_def,[status(thm)],[brelnall2, c_0_212])).
% 209.27/30.44 thf(c_0_291, plain, ((ex1E2)=(![X4:$i, X1:$i > $o]:((((?[X672:$i]:((((in @ X672 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X672 @ emptyset)))))))=>(![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))))))))))), inference(apply_def,[status(thm)],[c_0_240, c_0_211])).
% 209.27/30.44 thf(c_0_292, plain, ((epred1_0)<=>![X702:$i]:(?[X703:$i]:((((![X704:$i]:(((in @ X704 @ X703)=>![X705:$i]:(((in @ X705 @ X704)=>(in @ X705 @ X702)))))&![X706:$i, X707:$i]:((((in @ X706 @ X702)&(in @ X707 @ X702))=>(![X708:$i]:(((in @ X708 @ X703)=>((in @ X706 @ X708)<=>(in @ X707 @ X708))))=>((X706)=(X707))))))&![X709:$i, X710:$i]:((((in @ X709 @ X703)&(in @ X710 @ X703))=>(![X711:$i]:(((in @ X711 @ X709)=>(in @ X711 @ X710)))|![X712:$i]:(((in @ X712 @ X710)=>(in @ X712 @ X709)))))))&![X713:$i]:(((![X714:$i]:(((in @ X714 @ X713)=>(in @ X714 @ X702)))&?[X715:$i]:((in @ X715 @ X713)))=>?[X716:$i, X717:$i]:(((((in @ X716 @ X703)&(in @ X717 @ X713))&~(?[X718:$i]:(((in @ X718 @ X716)&(in @ X718 @ X713)))))&![X719:$i]:(((in @ X719 @ X703)=>(![X720:$i]:(((in @ X720 @ X719)=>(in @ X720 @ X716)))|(in @ X717 @ X719)))))))))))), introduced(definition)).
% 209.27/30.44 thf(c_0_293, negated_conjecture, ~((![X673:$i, X674:$i]:((![X675:$i]:(((in @ X675 @ X673)<=>(in @ X675 @ X674)))=>((X673)=(X674))))=>(![X676:$i]:(~(in @ X676 @ emptyset))=>(![X677:$i, X678:$i, X679:$i]:(((in @ X679 @ (setadjoin @ X677 @ X678))<=>(((X679)=(X677))|(in @ X679 @ X678))))=>(![X680:$i, X681:$i]:(((in @ X681 @ (powerset @ X680))<=>![X682:$i]:(((in @ X682 @ X681)=>(in @ X682 @ X680)))))=>(![X683:$i, X684:$i]:(((in @ X684 @ (setunion @ X683))<=>?[X685:$i]:(((in @ X684 @ X685)&(in @ X685 @ X683)))))=>((in @ emptyset @ omega)=>(![X686:$i]:(((in @ X686 @ omega)=>(in @ (setadjoin @ X686 @ X686) @ omega)))=>(![X687:$i]:((((in @ emptyset @ X687)&![X688:$i]:((((in @ X688 @ omega)&(in @ X688 @ X687))=>(in @ (setadjoin @ X688 @ X688) @ X687))))=>![X689:$i]:(((in @ X689 @ omega)=>(in @ X689 @ X687)))))=>(![X690:$i > $i > $o, X691:$i]:((![X692:$i]:(((in @ X692 @ X691)=>?[X693:$i]:(((X690 @ X692 @ X693)&![X694:$i]:(((X690 @ X692 @ X694)=>((X693)=(X694))))))))=>?[X695:$i]:(![X696:$i]:(((in @ X696 @ X695)<=>?[X697:$i]:(((in @ X697 @ X691)&(X690 @ X697 @ X696))))))))=>(![X698:$i]:((?[X699:$i]:((in @ X699 @ X698))=>?[X700:$i]:(((in @ X700 @ X698)&~(?[X701:$i]:(((in @ X701 @ X700)&(in @ X701 @ X698))))))))=>((epred1_0)=>(![X721:$i > $o]:((?[X722:$i]:(((X721 @ X722)&![X723:$i]:(((X721 @ X723)=>((X722)=(X723))))))=>(X721 @ (descr @ (^[Z0:$i]:(X721 @ Z0))))))=>(![X724:$i, X725:$i > $o, X726:$i]:(((in @ X726 @ X724)=>((X725 @ X726)=>(in @ X726 @ (dsetconstr @ X724 @ X725)))))=>(![X727:$i, X728:$i > $o, X729:$i]:(((in @ X729 @ (dsetconstr @ X727 @ X728))=>(in @ X729 @ X727)))=>(![X730:$i, X731:$i > $o, X732:$i]:(((in @ X732 @ (dsetconstr @ X730 @ X731))=>(X731 @ X732)))=>(![X733:$i > $o]:((?[X734:$i]:(((X733 @ X734)&![X735:$i]:(((X733 @ X735)=>((X734)=(X735))))))=>?[X736:$i]:(((X733 @ X736)&![X737:$i]:(((X733 @ X737)=>((X736)=(X737))))))))=>(![X738:$o, X739:$i]:(((in @ X739 @ (prop2set @ ((X738))))=>(X738)))=>(![X740:$i]:(((in @ X740 @ emptyset)=>![X741:$o]:((X741))))=>(![X742:$i]:(((in @ X742 @ emptyset)=>~($true)))=>(![X743:$i]:(~(in @ X743 @ emptyset))=>(![X744:$i > $o]:((?[X745:$i]:(((X744 @ X745)&![X746:$i]:(((X744 @ X746)=>((X745)=(X746))))))=>?[X747:$i]:((X744 @ X747))))=>(![X748:$i, X749:$i]:((![X750:$i]:(((in @ X750 @ X748)=>(in @ X750 @ X749)))=>(![X751:$i]:(((in @ X751 @ X749)=>(in @ X751 @ X748)))=>((X748)=(X749)))))=>(![X752:$i]:((![X753:$i]:(~(in @ X753 @ X752))=>((X752)=(emptyset))))=>(![X754:$i]:((![X755:$i]:(~(in @ X755 @ X754))=>((X754)=(emptyset))))=>(![X756:$i, X757:$i > $o, X758:$i]:(((in @ X758 @ X756)=>((in @ X758 @ (dsetconstr @ X756 @ X757))<=>(X757 @ X758))))=>(![X759:$i]:((((X759)!=(emptyset))=>?[X760:$i]:((in @ X760 @ X759))))=>(![X761:$i, X762:$i > $o, X763:$i]:(((in @ X763 @ X761)=>((X762 @ X763)=>((dsetconstr @ X761 @ X762)!=(emptyset)))))=>(![X764:$i]:((?[X765:$i]:((in @ X765 @ X764))=>((X764)!=(emptyset))))=>(![X766:$i, X767:$i]:((in @ 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X1299)))))))=>(![X1300:$i, X1301:$i > $o]:((?[X1302:$i]:(((in @ X1302 @ (dsetconstr @ X1300 @ X1301))&((dsetconstr @ X1300 @ X1301)=(setadjoin @ X1302 @ emptyset))))=>![X1303:$i]:(((in @ X1303 @ X1300)=>![X1304:$i]:(((in @ X1304 @ X1300)=>((X1301 @ X1303)=>((X1301 @ X1304)=>((X1303)=(X1304))))))))))=>![X4:$i, X5:$i, X30:$i]:((((subset @ X30 @ (cartprod @ X4 @ X5))&![X1305:$i]:(((in @ X1305 @ X4)=>?[X1306:$i]:(((in @ X1306 @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X1305 @ Z0) @ X30)))))&((dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X1305 @ Z0) @ X30))))=(setadjoin @ X1306 @ emptyset)))))))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X30 @ X2)) @ X30)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_241, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_242]), foundationAx]), wellorderingAx]), c_0_243]), c_0_244]), c_0_245]), c_0_246]), c_0_247]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_248]), setext]), emptyI]), noeltsimpempty]), c_0_249]), c_0_250]), c_0_251]), c_0_252]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_253]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_254]), c_0_255]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_256]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_257]), c_0_258]), c_0_259]), inCongP]), in__Cong]), c_0_260]), c_0_261]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_262]), c_0_263]), c_0_264]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_265]), c_0_266]), binunionIL]), upairset2IR]), binunionIR]), binunionEcases]), binunionE]), binunionLsub]), binunionRsub]), binintersectI]), binintersectSubset5]), binintersectEL]), binintersectLsub]), binintersectSubset2]), binintersectSubset3]), binintersectER]), disjointsetsI1]), binintersectRsub]), binintersectSubset4]), binintersectSubset1]), bs114d]), setminusI]), setminusEL]), setminusER]), setminusSubset2]), setminusERneg]), setminusELneg]), setminusILneg]), setminusIRneg]), setminusLsub]), setminusSubset1]), symdiffE]), symdiffI1]), symdiffI2]), symdiffIneg1]), symdiffIneg2]), secondinupair]), setukpairIL]), setukpairIR]), kpairiskpair]), kpairp]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1]), cartprodmempair]), setunionE2]), setunionsingleton1]), setunionsingleton2]), setunionsingleton]), c_0_267]), c_0_268]), c_0_269]), c_0_270]), singletonsuniq]), setukpairinjL1]), c_0_271]), c_0_272]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_273]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_274]), c_0_275]), c_0_276]), c_0_277]), c_0_278]), c_0_279]), c_0_280]), c_0_236]), c_0_281]), c_0_282]), c_0_283]), c_0_284]), ap2p]), c_0_285]), c_0_286]), c_0_287]), c_0_288]), c_0_289]), c_0_290]), c_0_291])])]), c_0_292])).
% 209.27/30.44 thf(c_0_294, negated_conjecture, ![X1321:$i, X1322:$i, X1324:$i, X1325:$i, X1326:$i, X1327:$i, X1328:$i, X1329:$i, X1330:$i, X1331:$i, X1332:$i, X1334:$i, X1335:$i, X1337:$i, X1338:$i, X1339:$i, X1340:$i, X1341:$i, X1343:$i, X1344:$i > $i > $o, X1345:$i, X1347:$i, X1350:$i, X1352:$i, X1353:$i, X1354:$i, X1355:$i, X1357:$i, X1358:$i > $o, X1359:$i, X1361:$i, X1362:$i > $o, X1363:$i, X1364:$i, X1365:$i > $o, X1366:$i, X1367:$i, X1368:$i > $o, X1369:$i, X1370:$i > $o, X1371:$i, X1374:$i, X1375:$o, X1376:$i, X1377:$i, X1378:$o, X1379:$i, X1380:$i, X1381:$i > $o, X1382:$i, X1385:$i, X1386:$i, X1389:$i, X1391:$i, X1393:$i, X1394:$i > $o, X1395:$i, X1396:$i, X1398:$i, X1399:$i > $o, X1400:$i, X1401:$i, X1402:$i, X1403:$i, X1404:$i, X1405:$i, X1406:$i, X1407:$i, X1408:$i, X1409:$i, X1410:$i, X1411:$o, X1412:$i, X1413:$i, X1414:$i, X1415:$i, X1416:$i, X1417:$i, X1419:$i, X1420:$i, X1421:$i, X1422:$i, X1423:$i, X1424:$i, X1425:$i, X1426:$i, X1427:$i, X1428:$i, X1429:$o, X1431:$i, X1432:$i, X1433:$i > $o, X1434:$i, X1437:$i, X1438:$i, X1439:$i, X1441:$i, X1442:$i, X1443:$i, X1444:$i, X1445:$i, X1446:$i, X1447:$i, X1448:$i, X1449:$i, X1450:$i, X1451:$i, X1452:$i, X1453:$i, X1454:$i, X1455:$i, X1456:$i, X1457:$i > $o, X1458:$i, X1459:$i > $o, X1460:$i, X1461:$i, X1462:$i > $o, X1463:$i, X1465:$i, X1466:$i > $o, X1468:$i, X1469:$i, X1470:$i > $o, X1472:$i, X1473:$i, X1474:$i > $o, X1475:$i, X1477:$o, X1478:$o, X1479:$i, X1480:$i > $o, X1482:$i, X1483:$i, X1484:$i > $o, X1485:$i, X1487:$i > $o, X1488:$i, X1491:$i, X1492:$i > $o, X1493:$i, X1497:$i, X1498:$i > $o, X1499:$i, X1502:$i, X1503:$i, X1504:$i, X1505:$i, X1506:$i, X1507:$i, X1508:$i, X1509:$i, X1510:$i, X1511:$i > $o, X1512:$i, X1514:$i, X1515:$i, X1516:$i > $o, X1517:$i > $o, X1520:$i, X1523:$i, X1524:$i, X1527:$i, X1528:$i, X1529:$i, X1530:$i, X1531:$i, X1532:$i, X1533:$i, X1534:$i, X1535:$i, X1536:$i > $o, X1537:$i, X1539:$i, X1540:$i, X1541:$i > $o, X1542:$i > $o, X1545:$i, X1547:$i, X1549:$i, X1550:$i, X1551:$i > $o, X1552:$i > $o, X1555:$i, X1556:$i, X1558:$i, X1559:$i, X1560:$i, X1561:$i, X1562:$i, X1563:$i, X1565:$i, X1566:$i, X1567:$i, X1568:$i, X1569:$i, X1570:$i, X1571:$i, X1572:$i, X1573:$i, X1574:$i, X1575:$i, X1576:$i, X1577:$i, X1578:$i, X1579:$i, X1580:$i, X1581:$i, X1582:$i, X1583:$i, X1584:$i, X1585:$i, X1586:$i, X1587:$i, X1588:$i, X1589:$i, X1590:$i, X1591:$i, X1592:$i, X1593:$i, X1594:$i, X1595:$i, X1596:$i, X1597:$i, X1598:$i, X1599:$i, X1600:$i, X1601:$i, X1602:$i > $o, X1603:$i, X1604:$i > $o, X1605:$i, X1606:$i, X1607:$i, X1608:$i, X1609:$i, X1610:$i, X1611:$i, X1612:$i, X1613:$i, X1614:$i, X1615:$i, X1616:$o, X1617:$i, X1618:$i, X1619:$i, X1620:$i, X1621:$i, X1622:$i, X1623:$i, X1624:$i, X1625:$i, X1626:$i, X1627:$i, X1628:$i, X1629:$i, X1630:$i, X1631:$i, X1632:$i, X1633:$i, X1634:$i, X1635:$i, X1636:$i, X1637:$i, X1638:$i, X1639:$i, X1640:$i, X1641:$i, X1642:$i, X1643:$i, X1645:$i, X1646:$i, X1647:$i, X1648:$i, X1649:$i, X1650:$i, X1651:$i, X1652:$i, X1653:$i, X1654:$i, X1655:$i, X1656:$i, X1657:$i, X1658:$i, X1659:$i, X1660:$i, X1661:$i, X1662:$i, X1663:$i, X1664:$i, X1665:$i, X1666:$i, X1667:$i, X1668:$i, X1669:$i, X1670:$i, X1671:$i, X1672:$i, X1673:$i, X1674:$i, X1675:$i, X1676:$i, X1677:$i, X1678:$i, X1679:$i, X1680:$i, X1681:$i, X1682:$i, X1683:$i, X1684:$o, X1685:$i, X1686:$i, X1687:$i, X1688:$i, X1689:$i, X1690:$i, X1691:$i, X1692:$i, X1693:$i, X1694:$i, X1695:$i, X1696:$i, X1697:$i, X1698:$i, X1699:$i, X1700:$i, X1701:$i, X1702:$i, X1703:$i, X1704:$i, X1705:$i, X1706:$i, X1707:$i, X1708:$i, X1709:$i, X1710:$i, X1711:$i, X1712:$i, X1713:$i, X1714:$i, X1715:$i, X1716:$i, X1717:$i, X1718:$i, X1719:$i, X1720:$i, X1721:$i, X1722:$i, X1723:$i, X1724:$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:$i, X1746:$i, X1747:$i, X1748:$i, X1749:$i, X1750:$i, X1752:$i, X1753:$i, X1754:$i, X1755:$i, X1756:$i > $o, X1759:$i, X1761:$i, X1762:$i > $o, X1763:$i, X1765:$i, X1766:$i > $o, X1767:$i, X1770:$i, X1771:$i > $o, X1774:$i, X1776:$i, X1777:$i, X1778:$i, X1779:$i, X1780:$i, X1781:$i, X1783:$i, X1784:$i, X1785:$i, X1786:$i, X1787:$i, X1788:$i, X1789:$i, X1790:$i, X1791:$i, X1792:$i, X1793:$i, X1794:$i, X1795:$i, X1796:$i, X1797:$i, X1798:$i, X1799:$i, X1800:$i, X1801:$i, X1802:$i, X1803:$i, X1804:$i, X1805:$i, X1806:$i, X1807:$i, X1808:$i, X1809:$i, X1810:$i, X1811:$i, X1812:$i, X1813:$i, X1814:$i, X1815:$i, X1816:$i, X1817:$i, X1819:$i, X1820:$i, X1821:$i, X1822:$i, X1823:$i, X1824:$i, X1825:$i, X1826:$i, X1827:$i, X1828:$i, X1829:$i, X1830:$i, X1831:$i, X1832:$i, X1833:$i, X1834:$i, X1835:$i, X1836:$i, X1837:$i, X1838:$i, X1839:$i, X1840:$i, X1841:$i, X1842:$i, X1843:$i, X1844:$i, X1845:$i, X1846:$i, X1847:$i, X1848:$i, X1849:$i, X1850:$i > $i > $o, X1851:$i, X1852:$i, X1853:$i, X1854:$i, X1855:$i > $i > $o, X1856:$i, X1857:$i, X1858:$i > $i > $o, X1859:$i, X1860:$i, X1861:$i > $i > $o, X1862:$i, X1863:$i, X1864:$i, X1865:$i, X1866:$i > $i > $o, X1867:$i, X1868:$i, X1869:$i, X1870:$i, X1871:$i > $i > $o, X1872:$i, X1873:$i, X1874:$i, X1875:$i, X1876:$i > $i > $o, X1877:$i, X1878:$i, X1879:$i, X1880:$i, X1881:$i, X1883:$i, X1884:$i, X1886:$i, X1887:$i, X1888:$i, X1890:$i, X1891:$i, X1892:$i, X1893:$i, X1894:$i, X1896:$i, X1897:$i, X1898:$i, X1899:$i, X1900:$i, X1901:$i, X1903:$i, X1904:$i, X1905:$i, X1906:$i, X1907:$i, X1908:$i, X1909:$i, X1911:$i, X1912:$i, X1913:$i, X1914:$i > $i, X1916:$i, X1918:$i, X1919:$i, X1920:$i > $i, X1922:$i, X1924:$i, X1925:$i, X1926:$i > $i, X1928:$i, X1929:$i, X1930:$i, X1931:$i > $o, X1934:$i, X1935:$i, X1936:$i, X1937:$i, X1938:$i > $o, X1941:$i, X1942:$i, X1943:$i > $o, X1944:$i, X1945:$i, X1946:$i, X1950:$i]:((((~(in @ (esk1_2 @ X1321 @ X1322) @ X1321)|~(in @ (esk1_2 @ X1321 @ X1322) @ X1322)|((X1321)=(X1322)))&((in @ (esk1_2 @ X1321 @ X1322) @ X1321)|(in @ (esk1_2 @ X1321 @ X1322) @ X1322)|((X1321)=(X1322))))&(~(in @ X1324 @ emptyset)&(((~(in @ X1327 @ (setadjoin @ X1325 @ X1326))|(((X1327)=(X1325))|(in @ X1327 @ X1326)))&((((X1327)!=(X1325))|(in @ X1327 @ (setadjoin @ X1325 @ X1326)))&(~(in @ X1327 @ X1326)|(in @ X1327 @ (setadjoin @ X1325 @ X1326)))))&(((~(in @ X1329 @ (powerset @ X1328))|(~(in @ X1330 @ X1329)|(in @ X1330 @ X1328)))&(((in @ (esk2_2 @ X1331 @ X1332) @ X1332)|(in @ X1332 @ (powerset @ X1331)))&(~(in @ (esk2_2 @ X1331 @ X1332) @ X1331)|(in @ X1332 @ (powerset @ X1331)))))&(((((in @ X1335 @ (esk3_2 @ X1334 @ X1335))|~(in @ X1335 @ (setunion @ X1334)))&((in @ (esk3_2 @ X1334 @ X1335) @ X1334)|~(in @ X1335 @ (setunion @ X1334))))&(~(in @ X1338 @ X1339)|~(in @ X1339 @ X1337)|(in @ X1338 @ (setunion @ X1337))))&((in @ emptyset @ omega)&((~(in @ X1340 @ omega)|(in @ (setadjoin @ X1340 @ X1340) @ omega))&(((((in @ (esk4_1 @ X1341) @ omega)|~(in @ emptyset @ X1341)|(~(in @ X1343 @ omega)|(in @ X1343 @ X1341)))&((in @ (esk4_1 @ X1341) @ X1341)|~(in @ emptyset @ X1341)|(~(in @ X1343 @ omega)|(in @ 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X1920) @ (cartprod @ X1918 @ X1919))|~(in @ (X1920 @ (esk77_3 @ X1918 @ X1919 @ X1920)) @ X1919))&(((in @ (esk78_4 @ X1918 @ X1919 @ X1920 @ X1922) @ (dsetconstr @ X1919 @ (^[Z0:$i]:((in @ (kpair @ X1922 @ Z0) @ (lam @ X1918 @ X1919 @ X1920))))))|~(in @ X1922 @ X1918)|~(in @ (X1920 @ (esk77_3 @ X1918 @ X1919 @ X1920)) @ X1919))&(((dsetconstr @ X1919 @ (^[Z0:$i]:((in @ (kpair @ X1922 @ Z0) @ (lam @ X1918 @ X1919 @ X1920)))))=(setadjoin @ (esk78_4 @ X1918 @ X1919 @ X1920 @ X1922) @ emptyset))|~(in @ X1922 @ X1918)|~(in @ (X1920 @ (esk77_3 @ X1918 @ X1919 @ X1920)) @ X1919)))))&((((in @ (esk79_3 @ X1924 @ X1925 @ X1926) @ X1924)|(in @ (lam @ X1924 @ X1925 @ X1926) @ (funcSet @ X1924 @ X1925)))&(~(in @ (X1926 @ (esk79_3 @ X1924 @ X1925 @ X1926)) @ X1925)|(in @ (lam @ X1924 @ X1925 @ X1926) @ (funcSet @ X1924 @ X1925))))&((((in @ (esk80_4 @ X1928 @ X1929 @ X1930 @ X1931) @ X1928)|(~(in @ X1934 @ X1930)|(X1931 @ X1934))|~(subset @ X1930 @ (cartprod @ X1928 @ X1929)))&(((in @ (esk81_4 @ X1928 @ X1929 @ X1930 @ X1931) @ X1929)|(~(in @ X1934 @ X1930)|(X1931 @ X1934))|~(subset @ X1930 @ (cartprod @ X1928 @ X1929)))&(((in @ (kpair @ (esk80_4 @ X1928 @ X1929 @ X1930 @ X1931) @ (esk81_4 @ X1928 @ X1929 @ X1930 @ X1931)) @ X1930)|(~(in @ X1934 @ X1930)|(X1931 @ X1934))|~(subset @ X1930 @ (cartprod @ X1928 @ X1929)))&(~(X1931 @ (kpair @ (esk80_4 @ X1928 @ X1929 @ X1930 @ X1931) @ (esk81_4 @ X1928 @ X1929 @ X1930 @ X1931)))|(~(in @ X1934 @ X1930)|(X1931 @ X1934))|~(subset @ X1930 @ (cartprod @ X1928 @ X1929))))))&((((in @ (esk82_4 @ X1935 @ X1936 @ X1937 @ X1938) @ X1935)|(~(in @ X1941 @ X1937)|(X1938 @ X1941))|~(subset @ X1937 @ (cartprod @ X1935 @ X1936)))&(((in @ (esk83_4 @ X1935 @ X1936 @ X1937 @ X1938) @ X1936)|(~(in @ X1941 @ X1937)|(X1938 @ X1941))|~(subset @ X1937 @ (cartprod @ X1935 @ X1936)))&(((in @ (kpair @ (esk82_4 @ X1935 @ X1936 @ X1937 @ X1938) @ (esk83_4 @ X1935 @ X1936 @ X1937 @ X1938)) @ X1937)|(~(in @ X1941 @ X1937)|(X1938 @ X1941))|~(subset @ X1937 @ (cartprod @ X1935 @ X1936)))&(~(X1938 @ (kpair @ (esk82_4 @ X1935 @ X1936 @ X1937 @ X1938) @ (esk83_4 @ X1935 @ X1936 @ X1937 @ X1938)))|(~(in @ X1941 @ X1937)|(X1938 @ X1941))|~(subset @ X1937 @ (cartprod @ X1935 @ X1936))))))&((~(in @ X1944 @ (dsetconstr @ X1942 @ X1943))|((dsetconstr @ X1942 @ X1943)!=(setadjoin @ X1944 @ emptyset))|(~(in @ X1945 @ X1942)|(~(in @ X1946 @ X1942)|(~(X1943 @ X1945)|(~(X1943 @ X1946)|((X1945)=(X1946)))))))&(((subset @ esk86_0 @ (cartprod @ esk84_0 @ esk85_0))&(((in @ (esk87_1 @ X1950) @ (dsetconstr @ esk85_0 @ (^[Z0:$i]:((in @ (kpair @ X1950 @ Z0) @ esk86_0)))))|~(in @ X1950 @ esk84_0))&(((dsetconstr @ esk85_0 @ (^[Z0:$i]:((in @ (kpair @ X1950 @ Z0) @ esk86_0))))=(setadjoin @ (esk87_1 @ X1950) @ emptyset))|~(in @ X1950 @ esk84_0))))&((in @ esk88_0 @ esk84_0)&~(in @ (kpair @ esk88_0 @ (ap @ esk84_0 @ esk85_0 @ esk86_0 @ esk88_0)) @ esk86_0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_293])])])])])])])).
% 209.27/30.44 thf(c_0_295, plain, ![X1307:$i, X1308:$i, X1309:$i, X1310:$i]:(((ap @ X1307 @ X1308 @ X1309 @ X1310)=(setunion @ (dsetconstr @ X1308 @ (^[Z0:$i]:((in @ (kpair @ X1310 @ Z0) @ X1309))))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[ap])])).
% 209.27/30.44 thf(c_0_296, negated_conjecture, ![X3:$i, X2:$i]:((((X2)=(X3))|~((in @ X3 @ (setadjoin @ X2 @ emptyset))))), inference(split_conjunct,[status(thm)],[c_0_294])).
% 209.27/30.44 thf(c_0_297, negated_conjecture, ![X2:$i]:(((in @ (esk17_1 @ X2) @ X2)|((X2)=(emptyset)))), inference(split_conjunct,[status(thm)],[c_0_294])).
% 209.27/30.44 thf(c_0_298, plain, ![X1972:$i, X5:$i, X4:$i]:(((epred2_2 @ X4 @ X5 @ X1972)<=>(in @ (kpair @ X5 @ X1972) @ X4))), introduced(definition)).
% 209.27/30.44 thf(c_0_299, plain, ![X2013:$i, X2014:$i, X2015:$i]:(((~(epred2_2 @ X2015 @ X2014 @ X2013)|(in @ (kpair @ X2014 @ X2013) @ X2015))&(~(in @ (kpair @ X2014 @ X2013) @ X2015)|(epred2_2 @ X2015 @ X2014 @ X2013)))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])])).
% 209.27/30.44 thf(c_0_300, plain, ![X1314:$i, X1315:$i, X1316:$i, X1317:$i]:(((ap @ X1314 @ X1315 @ X1316 @ X1317)=(setunion @ (dsetconstr @ X1315 @ (^[Z0:$i]:((in @ (kpair @ X1317 @ Z0) @ X1316))))))), inference(variable_rename,[status(thm)],[c_0_295])).
% 209.27/30.44 thf(c_0_301, negated_conjecture, ![X2:$i]:((((esk17_1 @ (setadjoin @ X2 @ emptyset))=(X2))|((setadjoin @ X2 @ emptyset)=(emptyset)))), inference(spm,[status(thm)],[c_0_296, c_0_297])).
% 209.27/30.44 thf(c_0_302, negated_conjecture, ![X2:$i]:((((dsetconstr @ esk85_0 @ (epred2_2 @ esk86_0 @ X2))=(setadjoin @ (esk87_1 @ X2) @ emptyset))|~((in @ X2 @ esk84_0)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_294]), c_0_298])).
% 209.27/30.44 thf(c_0_303, negated_conjecture, ~((in @ (kpair @ esk88_0 @ (ap @ esk84_0 @ esk85_0 @ esk86_0 @ esk88_0)) @ esk86_0)), inference(split_conjunct,[status(thm)],[c_0_294])).
% 209.27/30.44 thf(c_0_304, plain, ![X2:$i, X3:$i, X4:$i]:(((in @ (kpair @ X3 @ X4) @ X2)|~((epred2_2 @ X2 @ X3 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_299])).
% 209.27/30.44 thf(c_0_305, plain, ![X2:$i, X3:$i, X4:$i, X5:$i]:(((ap @ X2 @ X3 @ X4 @ X5)=(setunion @ (dsetconstr @ X3 @ (epred2_2 @ X4 @ X5))))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_300]), c_0_298])).
% 209.27/30.44 thf(c_0_306, negated_conjecture, ![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2))), inference(split_conjunct,[status(thm)],[c_0_294])).
% 209.27/30.44 thf(c_0_307, negated_conjecture, ![X3:$i, X2:$i, X1:$i > $o]:(((X1 @ X2)|~((in @ X2 @ (dsetconstr @ X3 @ X1))))), inference(split_conjunct,[status(thm)],[c_0_294])).
% 209.27/30.44 thf(c_0_308, negated_conjecture, ![X2:$i]:((((esk17_1 @ (dsetconstr @ esk85_0 @ (epred2_2 @ esk86_0 @ X2)))=(esk87_1 @ X2))|((dsetconstr @ esk85_0 @ (epred2_2 @ esk86_0 @ X2))=(emptyset))|~((in @ X2 @ esk84_0)))), inference(spm,[status(thm)],[c_0_301, c_0_302])).
% 209.27/30.44 thf(c_0_309, negated_conjecture, (in @ esk88_0 @ esk84_0), inference(split_conjunct,[status(thm)],[c_0_294])).
% 209.27/30.44 thf(c_0_310, negated_conjecture, ~((epred2_2 @ esk86_0 @ esk88_0 @ (ap @ esk84_0 @ esk85_0 @ esk86_0 @ esk88_0))), inference(spm,[status(thm)],[c_0_303, c_0_304])).
% 209.27/30.44 thf(c_0_311, plain, ![X7:$i, X2:$i, X3:$i, X4:$i, X5:$i]:(((ap @ X2 @ X3 @ X4 @ X5)=(ap @ X7 @ X3 @ X4 @ X5))), inference(spm,[status(thm)],[c_0_305, c_0_305])).
% 209.27/30.44 thf(c_0_312, negated_conjecture, ![X2:$i]:((((setunion @ (dsetconstr @ esk85_0 @ (epred2_2 @ esk86_0 @ X2)))=(esk87_1 @ X2))|~((in @ X2 @ esk84_0)))), inference(spm,[status(thm)],[c_0_306, c_0_302])).
% 209.27/30.44 thf(c_0_313, negated_conjecture, ![X2:$i, X1:$i > $o]:((((dsetconstr @ X2 @ X1)=(emptyset))|(X1 @ (esk17_1 @ (dsetconstr @ X2 @ X1))))), inference(spm,[status(thm)],[c_0_307, c_0_297])).
% 209.27/30.44 thf(c_0_314, negated_conjecture, (((esk17_1 @ (dsetconstr @ esk85_0 @ (epred2_2 @ esk86_0 @ esk88_0)))=(esk87_1 @ esk88_0))|((dsetconstr @ esk85_0 @ (epred2_2 @ esk86_0 @ esk88_0))=(emptyset))), inference(spm,[status(thm)],[c_0_308, c_0_309])).
% 209.27/30.44 thf(c_0_315, negated_conjecture, ![X2:$i]:(~((epred2_2 @ esk86_0 @ esk88_0 @ (ap @ X2 @ esk85_0 @ esk86_0 @ esk88_0)))), inference(spm,[status(thm)],[c_0_310, c_0_311])).
% 209.27/30.44 thf(c_0_316, negated_conjecture, ![X2:$i, X3:$i]:((((ap @ X2 @ esk85_0 @ esk86_0 @ X3)=(esk87_1 @ X3))|~((in @ X3 @ esk84_0)))), inference(spm,[status(thm)],[c_0_312, c_0_305])).
% 209.27/30.44 thf(c_0_317, negated_conjecture, ![X2:$i]:(((((in @ (esk87_1 @ X2) @ (dsetconstr @ esk85_0 @ (epred2_2 @ esk86_0 @ X2))))=(($true)))|~((in @ X2 @ esk84_0)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_294]), c_0_298])).
% 209.27/30.44 thf(c_0_318, negated_conjecture, (((dsetconstr @ esk85_0 @ (epred2_2 @ esk86_0 @ esk88_0))=(emptyset))|(epred2_2 @ esk86_0 @ esk88_0 @ (esk87_1 @ esk88_0))), inference(spm,[status(thm)],[c_0_313, c_0_314])).
% 209.27/30.44 thf(c_0_319, negated_conjecture, ~((epred2_2 @ esk86_0 @ esk88_0 @ (esk87_1 @ esk88_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_315, c_0_316]), c_0_309])])).
% 209.27/30.44 thf(c_0_320, negated_conjecture, ![X2:$i]:(((in @ (esk87_1 @ X2) @ (dsetconstr @ esk85_0 @ (epred2_2 @ esk86_0 @ X2)))|~((in @ X2 @ esk84_0)))), inference(cn,[status(thm)],[c_0_317])).
% 209.27/30.44 thf(c_0_321, negated_conjecture, ((dsetconstr @ esk85_0 @ (epred2_2 @ esk86_0 @ esk88_0))=(emptyset)), inference(sr,[status(thm)],[c_0_318, c_0_319])).
% 209.27/30.44 thf(c_0_322, negated_conjecture, ![X2:$i]:(~((in @ X2 @ emptyset))), inference(split_conjunct,[status(thm)],[c_0_294])).
% 209.27/30.44 thf(c_0_323, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_320, c_0_321]), c_0_309])]), c_0_322]), ['proof']).
% 209.27/30.44 % SZS output end CNFRefutation
% 209.27/30.44 % Parsed axioms : 446
% 209.27/30.44 % Removed by relevancy pruning/SinE : 0
% 209.27/30.44 % Initial clauses : 629
% 209.27/30.44 % Removed in clause preprocessing : 263
% 209.27/30.44 % Initial clauses in saturation : 366
% 209.27/30.44 % Processed clauses : 5912
% 209.27/30.44 % ...of these trivial : 32
% 209.27/30.44 % ...subsumed : 3609
% 209.27/30.44 % ...remaining for further processing : 2271
% 209.27/30.44 % Other redundant clauses eliminated : 178
% 209.27/30.44 % Clauses deleted for lack of memory : 0
% 209.27/30.44 % Backward-subsumed : 144
% 209.27/30.44 % Backward-rewritten : 23
% 209.27/30.44 % Generated clauses : 64800
% 209.27/30.44 % ...of the previous two non-redundant : 63464
% 209.27/30.44 % ...aggressively subsumed : 0
% 209.27/30.44 % Contextual simplify-reflections : 11
% 209.27/30.44 % Paramodulations : 64379
% 209.27/30.44 % Factorizations : 29
% 209.27/30.44 % NegExts : 78
% 209.27/30.44 % Equation resolutions : 183
% 209.27/30.44 % Disequality decompositions : 0
% 209.27/30.44 % Total rewrite steps : 22516
% 209.27/30.44 % ...of those cached : 21697
% 209.27/30.44 % Propositional unsat checks : 0
% 209.27/30.44 % Propositional check models : 0
% 209.27/30.44 % Propositional check unsatisfiable : 0
% 209.27/30.44 % Propositional clauses : 0
% 209.27/30.44 % Propositional clauses after purity: 0
% 209.27/30.44 % Propositional unsat core size : 0
% 209.27/30.44 % Propositional preprocessing time : 0.000
% 209.27/30.44 % Propositional encoding time : 0.000
% 209.27/30.44 % Propositional solver time : 0.000
% 209.27/30.44 % Success case prop preproc time : 0.000
% 209.27/30.44 % Success case prop encoding time : 0.000
% 209.27/30.44 % Success case prop solver time : 0.000
% 209.27/30.44 % Current number of processed clauses : 1764
% 209.27/30.44 % Positive orientable unit clauses : 179
% 209.27/30.44 % Positive unorientable unit clauses: 3
% 209.27/30.44 % Negative unit clauses : 18
% 209.27/30.44 % Non-unit-clauses : 1564
% 209.27/30.44 % Current number of unprocessed clauses: 58005
% 209.27/30.44 % ...number of literals in the above : 216045
% 209.27/30.44 % Current number of archived formulas : 0
% 209.27/30.44 % Current number of archived clauses : 491
% 209.27/30.44 % Clause-clause subsumption calls (NU) : 223467
% 209.27/30.44 % Rec. Clause-clause subsumption calls : 158266
% 209.27/30.44 % Non-unit clause-clause subsumptions : 1566
% 209.27/30.44 % Unit Clause-clause subsumption calls : 4868
% 209.27/30.44 % Rewrite failures with RHS unbound : 207
% 209.27/30.44 % BW rewrite match attempts : 130
% 209.27/30.44 % BW rewrite match successes : 28
% 209.27/30.44 % Condensation attempts : 0
% 209.27/30.44 % Condensation successes : 0
% 209.27/30.44 % Termbank termtop insertions : 1427541
% 209.27/30.44 % Search garbage collected termcells : 21207
% 209.27/30.44
% 209.27/30.44 % -------------------------------------------------
% 209.27/30.44 % User time : 28.153 s
% 209.27/30.44 % System time : 0.993 s
% 209.27/30.44 % Total time : 29.146 s
% 209.27/30.44 % Maximum resident set size: 8452 pages
% 209.27/30.44
% 209.27/30.44 % -------------------------------------------------
% 209.27/30.44 % User time : 28.160 s
% 209.27/30.44 % System time : 0.997 s
% 209.27/30.44 % Total time : 29.158 s
% 209.27/30.44 % Maximum resident set size: 5376 pages
% 209.27/30.44 % E exiting
%------------------------------------------------------------------------------