%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU688^1 : 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 : n020.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 08:27:14 AM UTC 2026
% Result : Theorem 205.15s 30.12s
% Output : CNFRefutation 205.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU688^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 % Computer : n020.cluster.edu
% 0.07/0.23 % Model : x86_64 x86_64
% 0.07/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.23 % Memory : 8046.5625MB
% 0.07/0.23 % OS : Linux 6.8.0-71-generic
% 0.07/0.23 % CPULimit : 300
% 0.07/0.23 % WCLimit : 300
% 0.07/0.23 % DateTime : Tue Sep 29 14:10:04 UTC 2026
% 0.07/0.23 % CPUTime :
% 0.07/0.23 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.29 Running higher-order theorem proving
% 0.25/0.36 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.1WL119PuhP/E---3.1_1110736.p
% 205.15/30.11 % Version: 3.5.1-ho
% 205.15/30.11 % Preprocessing class: HSLMSLSSLLLCHFA.
% 205.15/30.11 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 205.15/30.11 % Starting ehoh_best5 with 300s (1) cores
% 205.15/30.11 % Starting almost_fo_3_lam with 300s (1) cores
% 205.15/30.11 % Starting new_bool_5 with 300s (1) cores
% 205.15/30.11 % Starting pre_casc_3 with 300s (1) cores
% 205.15/30.11 % Starting ho_unfolding_8 with 300s (1) cores
% 205.15/30.11 % Starting new_ho_10_cnf2 with 300s (1) cores
% 205.15/30.11 % Starting new_bool_3 with 300s (1) cores
% 205.15/30.11 % Starting new_ho_5 with 300s (1) cores
% 205.15/30.11 % new_bool_5 with pid 1110758 completed with status 0
% 205.15/30.11 % Result found by new_bool_5
% 205.15/30.11 % Preprocessing class: HSLMSLSSLLLCHFA.
% 205.15/30.11 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 205.15/30.11 % Starting ehoh_best5 with 300s (1) cores
% 205.15/30.11 % Starting almost_fo_3_lam with 300s (1) cores
% 205.15/30.11 % Starting new_bool_5 with 300s (1) cores
% 205.15/30.11 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 205.15/30.11 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 205.15/30.11 % Search class: HGHSM-FSLM32-MHFMMSBN
% 205.15/30.11 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 205.15/30.12 % Starting SubtermCWHack with 28s (1) cores
% 205.15/30.12 % SubtermCWHack with pid 1110767 completed with status 8
% 205.15/30.12 % Starting new_bool_5 with 31s (1) cores
% 205.15/30.12 % new_bool_5 with pid 1110947 completed with status 0
% 205.15/30.12 % Result found by new_bool_5
% 205.15/30.12 % Preprocessing class: HSLMSLSSLLLCHFA.
% 205.15/30.12 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 205.15/30.12 % Starting ehoh_best5 with 300s (1) cores
% 205.15/30.12 % Starting almost_fo_3_lam with 300s (1) cores
% 205.15/30.12 % Starting new_bool_5 with 300s (1) cores
% 205.15/30.12 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 205.15/30.12 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 205.15/30.12 % Search class: HGHSM-FSLM32-MHFMMSBN
% 205.15/30.12 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 205.15/30.12 % Starting SubtermCWHack with 28s (1) cores
% 205.15/30.12 % SubtermCWHack with pid 1110767 completed with status 8
% 205.15/30.12 % Starting new_bool_5 with 31s (1) cores
% 205.15/30.12 % Preprocessing time : 0.007 s
% 205.15/30.12 % Presaturation interreduction done
% 205.15/30.12
% 205.15/30.12 % Proof found!
% 205.15/30.12 % SZS status Theorem
% 205.15/30.12 % SZS output start CNFRefutation
% 205.15/30.12 thf(decl_23, type, in: $i > $i > $o).
% 205.15/30.12 thf(decl_24, type, exu: ($i > $o) > $o).
% 205.15/30.12 thf(decl_25, type, setextAx: $o).
% 205.15/30.12 thf(decl_26, type, emptyset: $i).
% 205.15/30.12 thf(decl_27, type, emptysetAx: $o).
% 205.15/30.12 thf(decl_28, type, setadjoin: $i > $i > $i).
% 205.15/30.12 thf(decl_29, type, setadjoinAx: $o).
% 205.15/30.12 thf(decl_30, type, powerset: $i > $i).
% 205.15/30.12 thf(decl_31, type, powersetAx: $o).
% 205.15/30.12 thf(decl_32, type, setunion: $i > $i).
% 205.15/30.12 thf(decl_33, type, setunionAx: $o).
% 205.15/30.12 thf(decl_34, type, omega: $i).
% 205.15/30.12 thf(decl_35, type, omega0Ax: $o).
% 205.15/30.12 thf(decl_36, type, omegaSAx: $o).
% 205.15/30.12 thf(decl_37, type, omegaIndAx: $o).
% 205.15/30.12 thf(decl_38, type, replAx: $o).
% 205.15/30.12 thf(decl_39, type, foundationAx: $o).
% 205.15/30.12 thf(decl_40, type, wellorderingAx: $o).
% 205.15/30.12 thf(decl_41, type, descr: ($i > $o) > $i).
% 205.15/30.12 thf(decl_42, type, descrp: $o).
% 205.15/30.12 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 205.15/30.12 thf(decl_44, type, dsetconstrI: $o).
% 205.15/30.12 thf(decl_45, type, dsetconstrEL: $o).
% 205.15/30.12 thf(decl_46, type, dsetconstrER: $o).
% 205.15/30.12 thf(decl_47, type, exuE1: $o).
% 205.15/30.12 thf(decl_48, type, prop2set: $o > $i).
% 205.15/30.12 thf(decl_49, type, prop2setE: $o).
% 205.15/30.12 thf(decl_50, type, emptysetE: $o).
% 205.15/30.12 thf(decl_51, type, emptysetimpfalse: $o).
% 205.15/30.12 thf(decl_52, type, notinemptyset: $o).
% 205.15/30.12 thf(decl_53, type, exuE3e: $o).
% 205.15/30.12 thf(decl_54, type, setext: $o).
% 205.15/30.12 thf(decl_55, type, emptyI: $o).
% 205.15/30.12 thf(decl_56, type, noeltsimpempty: $o).
% 205.15/30.12 thf(decl_57, type, setbeta: $o).
% 205.15/30.12 thf(decl_58, type, nonempty: $i > $o).
% 205.15/30.12 thf(decl_59, type, nonemptyE1: $o).
% 205.15/30.12 thf(decl_60, type, nonemptyI: $o).
% 205.15/30.12 thf(decl_61, type, nonemptyI1: $o).
% 205.15/30.12 thf(decl_62, type, setadjoinIL: $o).
% 205.15/30.12 thf(decl_63, type, emptyinunitempty: $o).
% 205.15/30.12 thf(decl_64, type, setadjoinIR: $o).
% 205.15/30.12 thf(decl_65, type, setadjoinE: $o).
% 205.15/30.12 thf(decl_66, type, setadjoinOr: $o).
% 205.15/30.12 thf(decl_67, type, setoftrueEq: $o).
% 205.15/30.12 thf(decl_68, type, powersetI: $o).
% 205.15/30.12 thf(decl_69, type, emptyinPowerset: $o).
% 205.15/30.12 thf(decl_70, type, emptyInPowerset: $o).
% 205.15/30.12 thf(decl_71, type, powersetE: $o).
% 205.15/30.12 thf(decl_72, type, setunionI: $o).
% 205.15/30.12 thf(decl_73, type, setunionE: $o).
% 205.15/30.12 thf(decl_74, type, subPowSU: $o).
% 205.15/30.12 thf(decl_75, type, exuE2: $o).
% 205.15/30.12 thf(decl_76, type, nonemptyImpWitness: $o).
% 205.15/30.12 thf(decl_77, type, uniqinunit: $o).
% 205.15/30.12 thf(decl_78, type, notinsingleton: $o).
% 205.15/30.12 thf(decl_79, type, eqinunit: $o).
% 205.15/30.12 thf(decl_80, type, singletonsswitch: $o).
% 205.15/30.12 thf(decl_81, type, upairsetE: $o).
% 205.15/30.12 thf(decl_82, type, upairsetIL: $o).
% 205.15/30.12 thf(decl_83, type, upairsetIR: $o).
% 205.15/30.12 thf(decl_84, type, emptyE1: $o).
% 205.15/30.12 thf(decl_85, type, vacuousDall: $o).
% 205.15/30.12 thf(decl_86, type, quantDeMorgan1: $o).
% 205.15/30.12 thf(decl_87, type, quantDeMorgan2: $o).
% 205.15/30.12 thf(decl_88, type, quantDeMorgan3: $o).
% 205.15/30.12 thf(decl_89, type, quantDeMorgan4: $o).
% 205.15/30.12 thf(decl_90, type, prop2setI: $o).
% 205.15/30.12 thf(decl_92, type, prop2set2propI: $o).
% 205.15/30.12 thf(decl_93, type, notdexE: $o).
% 205.15/30.12 thf(decl_94, type, notdallE: $o).
% 205.15/30.12 thf(decl_95, type, exuI1: $o).
% 205.15/30.12 thf(decl_96, type, exuI3: $o).
% 205.15/30.12 thf(decl_97, type, exuI2: $o).
% 205.15/30.12 thf(decl_98, type, inCongP: $o).
% 205.15/30.12 thf(decl_99, type, in__Cong: $o).
% 205.15/30.12 thf(decl_100, type, exuE3u: $o).
% 205.15/30.12 thf(decl_101, type, exu__Cong: $o).
% 205.15/30.12 thf(decl_102, type, emptyset__Cong: $o).
% 205.15/30.12 thf(decl_103, type, setadjoin__Cong: $o).
% 205.15/30.12 thf(decl_104, type, powerset__Cong: $o).
% 205.15/30.12 thf(decl_105, type, setunion__Cong: $o).
% 205.15/30.12 thf(decl_106, type, omega__Cong: $o).
% 205.15/30.12 thf(decl_107, type, exuEu: $o).
% 205.15/30.12 thf(decl_108, type, descr__Cong: $o).
% 205.15/30.12 thf(decl_109, type, dsetconstr__Cong: $o).
% 205.15/30.12 thf(decl_110, type, subset: $i > $i > $o).
% 205.15/30.12 thf(decl_113, type, subsetI1: $o).
% 205.15/30.12 thf(decl_114, type, eqimpsubset2: $o).
% 205.15/30.12 thf(decl_115, type, eqimpsubset1: $o).
% 205.15/30.12 thf(decl_116, type, subsetI2: $o).
% 205.15/30.12 thf(decl_117, type, emptysetsubset: $o).
% 205.15/30.12 thf(decl_118, type, subsetE: $o).
% 205.15/30.12 thf(decl_119, type, subsetE2: $o).
% 205.15/30.12 thf(decl_120, type, notsubsetI: $o).
% 205.15/30.12 thf(decl_121, type, notequalI1: $o).
% 205.15/30.12 thf(decl_122, type, notequalI2: $o).
% 205.15/30.12 thf(decl_123, type, subsetRefl: $o).
% 205.15/30.12 thf(decl_124, type, subsetTrans: $o).
% 205.15/30.12 thf(decl_125, type, setadjoinSub: $o).
% 205.15/30.12 thf(decl_126, type, setadjoinSub2: $o).
% 205.15/30.12 thf(decl_127, type, subset2powerset: $o).
% 205.15/30.12 thf(decl_128, type, setextsub: $o).
% 205.15/30.12 thf(decl_129, type, subsetemptysetimpeq: $o).
% 205.15/30.12 thf(decl_130, type, powersetI1: $o).
% 205.15/30.12 thf(decl_131, type, powersetE1: $o).
% 205.15/30.12 thf(decl_132, type, inPowerset: $o).
% 205.15/30.12 thf(decl_133, type, powersetsubset: $o).
% 205.15/30.12 thf(decl_134, type, sepInPowerset: $o).
% 205.15/30.12 thf(decl_135, type, sepSubset: $o).
% 205.15/30.12 thf(decl_136, type, binunion: $i > $i > $i).
% 205.15/30.12 thf(decl_137, type, binunionIL: $o).
% 205.15/30.12 thf(decl_138, type, upairset2IR: $o).
% 205.15/30.12 thf(decl_139, type, binunionIR: $o).
% 205.15/30.12 thf(decl_140, type, binunionEcases: $o).
% 205.15/30.12 thf(decl_141, type, binunionE: $o).
% 205.15/30.12 thf(decl_142, type, binunionLsub: $o).
% 205.15/30.12 thf(decl_143, type, binunionRsub: $o).
% 205.15/30.12 thf(decl_144, type, binintersect: $i > $i > $i).
% 205.15/30.12 thf(decl_145, type, binintersectI: $o).
% 205.15/30.12 thf(decl_146, type, binintersectSubset5: $o).
% 205.15/30.12 thf(decl_147, type, binintersectEL: $o).
% 205.15/30.12 thf(decl_148, type, binintersectLsub: $o).
% 205.15/30.12 thf(decl_149, type, binintersectSubset2: $o).
% 205.15/30.12 thf(decl_150, type, binintersectSubset3: $o).
% 205.15/30.12 thf(decl_151, type, binintersectER: $o).
% 205.15/30.12 thf(decl_152, type, disjointsetsI1: $o).
% 205.15/30.12 thf(decl_153, type, binintersectRsub: $o).
% 205.15/30.12 thf(decl_154, type, binintersectSubset4: $o).
% 205.15/30.12 thf(decl_155, type, binintersectSubset1: $o).
% 205.15/30.12 thf(decl_156, type, bs114d: $o).
% 205.15/30.12 thf(decl_158, type, setminus: $i > $i > $i).
% 205.15/30.12 thf(decl_159, type, setminusI: $o).
% 205.15/30.12 thf(decl_160, type, setminusEL: $o).
% 205.15/30.12 thf(decl_161, type, setminusER: $o).
% 205.15/30.12 thf(decl_162, type, setminusSubset2: $o).
% 205.15/30.12 thf(decl_163, type, setminusERneg: $o).
% 205.15/30.12 thf(decl_164, type, setminusELneg: $o).
% 205.15/30.12 thf(decl_165, type, setminusILneg: $o).
% 205.15/30.12 thf(decl_166, type, setminusIRneg: $o).
% 205.15/30.12 thf(decl_167, type, setminusLsub: $o).
% 205.15/30.12 thf(decl_168, type, setminusSubset1: $o).
% 205.15/30.12 thf(decl_169, type, symdiff: $i > $i > $i).
% 205.15/30.12 thf(decl_170, type, symdiffE: $o).
% 205.15/30.12 thf(decl_171, type, symdiffI1: $o).
% 205.15/30.12 thf(decl_172, type, symdiffI2: $o).
% 205.15/30.12 thf(decl_173, type, symdiffIneg1: $o).
% 205.15/30.12 thf(decl_174, type, symdiffIneg2: $o).
% 205.15/30.12 thf(decl_175, type, iskpair: $i > $o).
% 205.15/30.12 thf(decl_176, type, secondinupair: $o).
% 205.15/30.12 thf(decl_177, type, setukpairIL: $o).
% 205.15/30.12 thf(decl_178, type, setukpairIR: $o).
% 205.15/30.12 thf(decl_179, type, kpairiskpair: $o).
% 205.15/30.12 thf(decl_180, type, kpair: $i > $i > $i).
% 205.15/30.12 thf(decl_181, type, kpairp: $o).
% 205.15/30.12 thf(decl_182, type, cartprod: $i > $i > $i).
% 205.15/30.12 thf(decl_183, type, singletonsubset: $o).
% 205.15/30.12 thf(decl_184, type, singletoninpowerset: $o).
% 205.15/30.12 thf(decl_185, type, singletoninpowunion: $o).
% 205.15/30.12 thf(decl_186, type, upairset2E: $o).
% 205.15/30.12 thf(decl_187, type, upairsubunion: $o).
% 205.15/30.12 thf(decl_188, type, upairinpowunion: $o).
% 205.15/30.12 thf(decl_189, type, ubforcartprodlem1: $o).
% 205.15/30.12 thf(decl_190, type, ubforcartprodlem2: $o).
% 205.15/30.12 thf(decl_191, type, ubforcartprodlem3: $o).
% 205.15/30.12 thf(decl_192, type, cartprodpairin: $o).
% 205.15/30.12 thf(decl_193, type, cartprodmempair1: $o).
% 205.15/30.12 thf(decl_194, type, cartprodmempair: $o).
% 205.15/30.12 thf(decl_195, type, setunionE2: $o).
% 205.15/30.12 thf(decl_196, type, setunionsingleton1: $o).
% 205.15/30.12 thf(decl_197, type, setunionsingleton2: $o).
% 205.15/30.12 thf(decl_198, type, setunionsingleton: $o).
% 205.15/30.12 thf(decl_199, type, singleton: $i > $o).
% 205.15/30.12 thf(decl_200, type, singletonprop: $o).
% 205.15/30.12 thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 205.15/30.12 thf(decl_202, type, ex1E1: $o).
% 205.15/30.12 thf(decl_203, type, ex1I: $o).
% 205.15/30.12 thf(decl_204, type, ex1I2: $o).
% 205.15/30.12 thf(decl_205, type, singletonsuniq: $o).
% 205.15/30.12 thf(decl_210, type, setukpairinjL1: $o).
% 205.15/30.12 thf(decl_211, type, kfstsingleton: $o).
% 205.15/30.12 thf(decl_212, type, theprop: $o).
% 205.15/30.12 thf(decl_213, type, kfst: $i > $i).
% 205.15/30.12 thf(decl_214, type, kfstpairEq: $o).
% 205.15/30.12 thf(decl_215, type, cartprodfstin: $o).
% 205.15/30.12 thf(decl_216, type, setukpairinjL2: $o).
% 205.15/30.12 thf(decl_217, type, setukpairinjL: $o).
% 205.15/30.12 thf(decl_218, type, setukpairinjR11: $o).
% 205.15/30.12 thf(decl_219, type, setukpairinjR12: $o).
% 205.15/30.12 thf(decl_220, type, setukpairinjR1: $o).
% 205.15/30.12 thf(decl_221, type, upairequniteq: $o).
% 205.15/30.12 thf(decl_222, type, setukpairinjR2: $o).
% 205.15/30.12 thf(decl_223, type, setukpairinjR: $o).
% 205.15/30.12 thf(decl_224, type, ksndsingleton: $o).
% 205.15/30.12 thf(decl_225, type, ksnd: $i > $i).
% 205.15/30.12 thf(decl_226, type, ksndpairEq: $o).
% 205.15/30.12 thf(decl_227, type, kpairsurjEq: $o).
% 205.15/30.12 thf(decl_228, type, cartprodsndin: $o).
% 205.15/30.12 thf(decl_229, type, cartprodpairmemEL: $o).
% 205.15/30.12 thf(decl_230, type, cartprodpairmemER: $o).
% 205.15/30.12 thf(decl_231, type, cartprodmempaircEq: $o).
% 205.15/30.12 thf(decl_232, type, cartprodfstpairEq: $o).
% 205.15/30.12 thf(decl_233, type, cartprodsndpairEq: $o).
% 205.15/30.12 thf(decl_234, type, cartprodpairsurjEq: $o).
% 205.15/30.12 thf(decl_235, type, breln: $i > $i > $i > $o).
% 205.15/30.12 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 205.15/30.12 thf(decl_237, type, dpsetconstrI: $o).
% 205.15/30.12 thf(decl_238, type, dpsetconstrSub: $o).
% 205.15/30.12 thf(decl_239, type, setOfPairsIsBReln: $o).
% 205.15/30.12 thf(decl_240, type, dpsetconstrERa: $o).
% 205.15/30.12 thf(decl_241, type, dpsetconstrEL1: $o).
% 205.15/30.12 thf(decl_242, type, dpsetconstrEL2: $o).
% 205.15/30.12 thf(decl_243, type, dpsetconstrER: $o).
% 205.15/30.12 thf(decl_244, type, func: $i > $i > $i > $o).
% 205.15/30.12 thf(decl_245, type, funcSet: $i > $i > $i).
% 205.15/30.12 thf(decl_246, type, funcImageSingleton: $o).
% 205.15/30.12 thf(decl_247, type, apProp: $o).
% 205.15/30.12 thf(decl_248, type, ap: $i > $i > $i > $i > $i).
% 205.15/30.12 thf(decl_249, type, app: $o).
% 205.15/30.12 thf(decl_250, type, infuncsetfunc: $o).
% 205.15/30.12 thf(decl_251, type, ap2p: $o).
% 205.15/30.12 thf(decl_252, type, funcinfuncset: $o).
% 205.15/30.12 thf(decl_253, type, lamProp: $o).
% 205.15/30.12 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
% 205.15/30.12 thf(decl_255, type, lamp: $o).
% 205.15/30.12 thf(decl_256, type, lam2p: $o).
% 205.15/30.12 thf(decl_257, type, brelnall1: $o).
% 205.15/30.12 thf(decl_258, type, brelnall2: $o).
% 205.15/30.12 thf(decl_259, type, ex1E2: $o).
% 205.15/30.12 thf(decl_260, type, funcGraphProp1: $o).
% 205.15/30.12 thf(decl_261, type, funcGraphProp3: $o).
% 205.15/30.12 thf(decl_262, type, funcGraphProp2: $o).
% 205.15/30.12 thf(decl_263, type, funcextLem: $o).
% 205.15/30.12 thf(decl_264, type, epred1_0: $o).
% 205.15/30.12 thf(decl_265, type, esk1_2: $i > $i > $i).
% 205.15/30.12 thf(decl_266, type, esk2_2: $i > $i > $i).
% 205.15/30.12 thf(decl_267, type, esk3_2: $i > $i > $i).
% 205.15/30.12 thf(decl_268, type, esk4_1: $i > $i).
% 205.15/30.12 thf(decl_269, type, esk5_2: ($i > $i > $o) > $i > $i).
% 205.15/30.12 thf(decl_270, type, esk6_2: ($i > $i > $o) > $i > $i).
% 205.15/30.12 thf(decl_271, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
% 205.15/30.12 thf(decl_272, type, esk8_1: $i > $i).
% 205.15/30.12 thf(decl_273, type, esk9_1: ($i > $o) > $i).
% 205.15/30.12 thf(decl_274, type, esk10_1: ($i > $o) > $i).
% 205.15/30.12 thf(decl_275, type, esk11_2: $i > $i > $i).
% 205.15/30.12 thf(decl_276, type, esk12_2: $i > $i > $i).
% 205.15/30.12 thf(decl_277, type, esk13_1: $i > $i).
% 205.15/30.12 thf(decl_278, type, esk14_1: $i > $i).
% 205.15/30.12 thf(decl_279, type, esk15_1: $i > $i).
% 205.15/30.12 thf(decl_280, type, esk16_2: $i > $i > $i).
% 205.15/30.12 thf(decl_281, type, esk17_3: $i > $i > $o > $i).
% 205.15/30.12 thf(decl_282, type, esk18_1: ($i > $o) > $i).
% 205.15/30.12 thf(decl_283, type, esk19_1: $i > $i).
% 205.15/30.12 thf(decl_284, type, esk20_2: $i > ($i > $o) > $i).
% 205.15/30.12 thf(decl_285, type, esk21_2: $i > ($i > $o) > $i).
% 205.15/30.12 thf(decl_286, type, esk22_2: $i > ($i > $o) > $i).
% 205.15/30.12 thf(decl_287, type, esk23_2: $i > ($i > $o) > $i).
% 205.15/30.12 thf(decl_288, type, esk24_2: $i > ($i > $o) > $i).
% 205.15/30.12 thf(decl_289, type, esk25_2: $i > ($i > $o) > $i).
% 205.15/30.12 thf(decl_290, type, esk26_2: ($i > $o) > $i > $i).
% 205.15/30.12 thf(decl_291, type, esk27_1: ($i > $o) > $i).
% 205.15/30.12 thf(decl_292, type, esk28_1: ($i > $o) > $i).
% 205.15/30.12 thf(decl_293, type, esk29_2: ($i > $o) > $i > $i).
% 205.15/30.12 thf(decl_294, type, esk30_2: ($i > $o) > ($i > $o) > $i).
% 205.15/30.12 thf(decl_295, type, esk31_2: ($i > $o) > ($i > $o) > $i).
% 205.15/30.12 thf(decl_296, type, esk32_2: ($i > $o) > ($i > $o) > $i).
% 205.15/30.12 thf(decl_297, type, esk33_2: ($i > $o) > ($i > $o) > $i).
% 205.15/30.12 thf(decl_298, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 205.15/30.12 thf(decl_299, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 205.15/30.12 thf(decl_300, type, esk36_2: $i > $i > $i).
% 205.15/30.12 thf(decl_301, type, esk37_2: $i > $i > $i).
% 205.15/30.12 thf(decl_302, type, esk38_2: $i > $i > $i).
% 205.15/30.12 thf(decl_303, type, esk39_3: $i > $i > $i > $i).
% 205.15/30.12 thf(decl_304, type, esk40_3: $i > $i > $i > $i).
% 205.15/30.12 thf(decl_305, type, esk41_2: $i > $i > $i).
% 205.15/30.12 thf(decl_306, type, esk42_2: $i > ($i > $o) > $i).
% 205.15/30.12 thf(decl_307, type, esk43_2: $i > ($i > $o) > $i).
% 205.15/30.12 thf(decl_308, type, esk44_2: $i > ($i > $o) > $i).
% 205.15/30.12 thf(decl_309, type, esk45_3: $i > ($i > $o) > $i > $i).
% 205.15/30.12 thf(decl_310, type, esk46_2: $i > ($i > $o) > $i).
% 205.15/30.12 thf(decl_311, type, esk47_2: $i > ($i > $o) > $i).
% 205.15/30.12 thf(decl_312, type, esk48_3: $i > $i > ($i > $i) > $i).
% 205.15/30.12 thf(decl_313, type, esk49_3: $i > $i > ($i > $i) > $i).
% 205.15/30.12 thf(decl_314, type, esk50_3: $i > $i > ($i > $i) > $i).
% 205.15/30.12 thf(decl_315, type, esk51_4: $i > $i > $i > ($i > $o) > $i).
% 205.15/30.12 thf(decl_316, type, esk52_4: $i > $i > $i > ($i > $o) > $i).
% 205.15/30.12 thf(decl_317, type, esk53_4: $i > $i > $i > ($i > $o) > $i).
% 205.15/30.12 thf(decl_318, type, esk54_4: $i > $i > $i > ($i > $o) > $i).
% 205.15/30.12 thf(decl_319, type, esk55_4: $i > $i > $i > $i > $i).
% 205.15/30.12 thf(decl_320, type, esk56_0: $i).
% 205.15/30.12 thf(decl_321, type, esk57_0: $i).
% 205.15/30.12 thf(decl_322, type, esk58_0: $i).
% 205.15/30.12 thf(decl_323, type, esk59_0: $i).
% 205.15/30.12 thf(decl_324, type, esk60_0: $i).
% 205.15/30.12 thf(funcGraphProp4, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X30)=>((ap @ X4 @ X5 @ X30 @ X2)=(X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', funcGraphProp4)).
% 205.15/30.12 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.1WL119PuhP/E---3.1_1110736.p', kfstsingleton)).
% 205.15/30.12 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.1WL119PuhP/E---3.1_1110736.p', ksndsingleton)).
% 205.15/30.12 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', setoftrueEq)).
% 205.15/30.12 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', dpsetconstrI)).
% 205.15/30.12 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', dpsetconstrSub)).
% 205.15/30.12 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', setOfPairsIsBReln)).
% 205.15/30.12 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', dpsetconstrERa)).
% 205.15/30.12 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', dpsetconstrEL1)).
% 205.15/30.12 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', dpsetconstrEL2)).
% 205.15/30.12 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', dpsetconstrER)).
% 205.15/30.12 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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.1WL119PuhP/E---3.1_1110736.p', funcImageSingleton)).
% 205.15/30.12 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X30))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', apProp)).
% 205.15/30.12 thf(lamProp, axiom, ((lamProp)<=>![X4:$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.1WL119PuhP/E---3.1_1110736.p', lamProp)).
% 205.15/30.12 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:$i]:(X33 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', lamp)).
% 205.15/30.12 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X34:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X34 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X34 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', lam2p)).
% 205.15/30.12 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$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.1WL119PuhP/E---3.1_1110736.p', ex1E2)).
% 205.15/30.12 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.1WL119PuhP/E---3.1_1110736.p', exuE2)).
% 205.15/30.12 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.1WL119PuhP/E---3.1_1110736.p', emptyE1)).
% 205.15/30.12 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.1WL119PuhP/E---3.1_1110736.p', exuI2)).
% 205.15/30.12 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', exuI3)).
% 205.15/30.12 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', exuI1)).
% 205.15/30.12 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', exu__Cong)).
% 205.15/30.12 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', exuE3u)).
% 205.15/30.12 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.1WL119PuhP/E---3.1_1110736.p', exuEu)).
% 205.15/30.12 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', dsetconstr__Cong)).
% 205.15/30.12 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', descr__Cong)).
% 205.15/30.12 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', sepInPowerset)).
% 205.15/30.12 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', sepSubset)).
% 205.15/30.12 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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', singletonprop)).
% 205.15/30.12 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', ex1E1)).
% 205.15/30.12 thf(ex1I, axiom, ((ex1I)<=>![X4:$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.1WL119PuhP/E---3.1_1110736.p', ex1I)).
% 205.15/30.12 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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', ex1I2)).
% 205.15/30.12 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', nonemptyI)).
% 205.15/30.12 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', setbeta)).
% 205.15/30.12 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', exuE3e)).
% 205.15/30.12 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', exuE1)).
% 205.15/30.12 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', dsetconstrER)).
% 205.15/30.12 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', dsetconstrEL)).
% 205.15/30.12 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', dsetconstrI)).
% 205.15/30.12 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', descrp)).
% 205.15/30.12 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', replAx)).
% 205.15/30.12 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', emptyInPowerset)).
% 205.15/30.12 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', setukpairinjL1)).
% 205.15/30.12 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', singletonsuniq)).
% 205.15/30.12 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', theprop)).
% 205.15/30.12 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', setadjoinIR)).
% 205.15/30.12 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', kfstpairEq)).
% 205.15/30.12 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', setadjoinE)).
% 205.15/30.12 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', cartprodfstin)).
% 205.15/30.12 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.1WL119PuhP/E---3.1_1110736.p', setukpairinjL2)).
% 205.15/30.12 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.1WL119PuhP/E---3.1_1110736.p', setukpairinjL)).
% 205.15/30.12 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', setukpairinjR11)).
% 205.15/30.12 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.1WL119PuhP/E---3.1_1110736.p', setukpairinjR12)).
% 205.15/30.12 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.1WL119PuhP/E---3.1_1110736.p', setukpairinjR1)).
% 205.15/30.12 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', upairequniteq)).
% 205.15/30.12 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', setukpairinjR2)).
% 205.15/30.12 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', setukpairinjR)).
% 205.15/30.12 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', ksndpairEq)).
% 205.15/30.12 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', setadjoinIL)).
% 205.15/30.12 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', kpairsurjEq)).
% 205.15/30.12 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', cartprodsndin)).
% 205.15/30.12 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', cartprodpairmemEL)).
% 205.15/30.12 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', setunionI)).
% 205.15/30.12 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.1WL119PuhP/E---3.1_1110736.p', cartprodpairmemER)).
% 205.15/30.12 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', powersetE)).
% 205.15/30.12 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', cartprodmempaircEq)).
% 205.15/30.12 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', quantDeMorgan1)).
% 205.15/30.12 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', vacuousDall)).
% 205.15/30.12 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.1WL119PuhP/E---3.1_1110736.p', cartprodfstpairEq)).
% 205.15/30.12 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', emptyinPowerset)).
% 205.15/30.12 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', cartprodsndpairEq)).
% 205.15/30.12 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', powersetI)).
% 205.15/30.12 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', cartprodpairsurjEq)).
% 205.15/30.12 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', setadjoinOr)).
% 205.15/30.12 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.1WL119PuhP/E---3.1_1110736.p', setunionE)).
% 205.15/30.12 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.1WL119PuhP/E---3.1_1110736.p', app)).
% 205.15/30.12 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X30)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', infuncsetfunc)).
% 205.15/30.12 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X30 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', ap2p)).
% 205.15/30.12 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>(in @ X30 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', funcinfuncset)).
% 205.15/30.12 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', singletonsswitch)).
% 205.15/30.12 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', eqinunit)).
% 205.15/30.12 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.1WL119PuhP/E---3.1_1110736.p', brelnall1)).
% 205.15/30.12 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', notinsingleton)).
% 205.15/30.12 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.1WL119PuhP/E---3.1_1110736.p', brelnall2)).
% 205.15/30.12 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', uniqinunit)).
% 205.15/30.12 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', nonemptyImpWitness)).
% 205.15/30.12 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X30 @ X2)) @ X30)))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', funcGraphProp1)).
% 205.15/30.12 thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X30 @ X2)) @ X30)))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', funcGraphProp3)).
% 205.15/30.12 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X30)=>((ap @ X4 @ X5 @ X30 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', funcGraphProp2)).
% 205.15/30.12 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', subPowSU)).
% 205.15/30.12 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X35:$i]:(((func @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X30 @ X2)=(ap @ X4 @ X5 @ X35 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X30)))))))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', funcextLem)).
% 205.15/30.12 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', upairsetE)).
% 205.15/30.12 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', quantDeMorgan3)).
% 205.15/30.12 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', quantDeMorgan2)).
% 205.15/30.12 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', subsetTrans)).
% 205.15/30.12 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', subsetRefl)).
% 205.15/30.12 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', notequalI2)).
% 205.15/30.12 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', notequalI1)).
% 205.15/30.12 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', notsubsetI)).
% 205.15/30.12 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', subsetE2)).
% 205.15/30.12 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', upairsetIR)).
% 205.15/30.12 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', upairsetIL)).
% 205.15/30.12 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', quantDeMorgan4)).
% 205.15/30.12 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', inCongP)).
% 205.15/30.12 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', notdallE)).
% 205.15/30.12 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', emptyinunitempty)).
% 205.15/30.12 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', notdexE)).
% 205.15/30.12 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', prop2setI)).
% 205.15/30.12 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.1WL119PuhP/E---3.1_1110736.p', in__Cong)).
% 205.15/30.12 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', omega__Cong)).
% 205.15/30.12 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', setunion__Cong)).
% 205.15/30.12 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', powerset__Cong)).
% 205.15/30.12 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.1WL119PuhP/E---3.1_1110736.p', setadjoin__Cong)).
% 205.15/30.12 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', emptyset__Cong)).
% 205.15/30.12 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', emptysetsubset)).
% 205.15/30.12 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', subsetI2)).
% 205.15/30.12 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', eqimpsubset1)).
% 205.15/30.12 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', eqimpsubset2)).
% 205.15/30.12 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', subsetI1)).
% 205.15/30.12 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', subsetE)).
% 205.15/30.12 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', setadjoinSub)).
% 205.15/30.12 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', setadjoinSub2)).
% 205.15/30.12 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', powersetsubset)).
% 205.15/30.12 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', inPowerset)).
% 205.15/30.12 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', powersetE1)).
% 205.15/30.12 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', powersetI1)).
% 205.15/30.12 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', subsetemptysetimpeq)).
% 205.15/30.12 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', setextsub)).
% 205.15/30.12 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', subset2powerset)).
% 205.15/30.12 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', binunionLsub)).
% 205.15/30.12 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', binunionE)).
% 205.15/30.12 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.1WL119PuhP/E---3.1_1110736.p', binunionEcases)).
% 205.15/30.12 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', binunionIR)).
% 205.15/30.12 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', upairset2IR)).
% 205.15/30.12 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', binunionIL)).
% 205.15/30.12 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', binunionRsub)).
% 205.15/30.12 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', binintersectER)).
% 205.15/30.12 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', binintersectSubset3)).
% 205.15/30.12 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', binintersectSubset2)).
% 205.15/30.12 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', binintersectLsub)).
% 205.15/30.12 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', binintersectEL)).
% 205.15/30.12 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', binintersectSubset5)).
% 205.15/30.12 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', binintersectI)).
% 205.15/30.12 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', disjointsetsI1)).
% 205.15/30.12 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', setminusER)).
% 205.15/30.12 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', setminusEL)).
% 205.15/30.12 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', setminusI)).
% 205.15/30.12 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', bs114d)).
% 205.15/30.12 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', binintersectSubset1)).
% 205.15/30.12 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', binintersectSubset4)).
% 205.15/30.12 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', binintersectRsub)).
% 205.15/30.12 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', setminusSubset2)).
% 205.15/30.12 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', symdiffE)).
% 205.15/30.12 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', setminusSubset1)).
% 205.15/30.12 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', setminusLsub)).
% 205.15/30.12 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', setminusIRneg)).
% 205.15/30.12 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', setminusILneg)).
% 205.15/30.12 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', setminusELneg)).
% 205.15/30.12 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', setminusERneg)).
% 205.15/30.12 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', symdiffI1)).
% 205.15/30.12 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.1WL119PuhP/E---3.1_1110736.p', kpairiskpair)).
% 205.15/30.12 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.1WL119PuhP/E---3.1_1110736.p', setukpairIR)).
% 205.15/30.12 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.1WL119PuhP/E---3.1_1110736.p', setukpairIL)).
% 205.15/30.12 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', secondinupair)).
% 205.15/30.12 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', symdiffIneg2)).
% 205.15/30.12 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', symdiffIneg1)).
% 205.15/30.12 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', symdiffI2)).
% 205.15/30.12 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', kpairp)).
% 205.15/30.12 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', ubforcartprodlem1)).
% 205.15/30.12 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', upairinpowunion)).
% 205.15/30.12 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', upairsubunion)).
% 205.15/30.12 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', upairset2E)).
% 205.15/30.12 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', singletoninpowunion)).
% 205.15/30.12 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', singletoninpowerset)).
% 205.15/30.12 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', singletonsubset)).
% 205.15/30.12 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', ubforcartprodlem2)).
% 205.15/30.12 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', setunionsingleton2)).
% 205.15/30.12 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', setunionsingleton1)).
% 205.15/30.12 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', setunionE2)).
% 205.15/30.12 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', cartprodmempair)).
% 205.15/30.12 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.1WL119PuhP/E---3.1_1110736.p', cartprodmempair1)).
% 205.15/30.12 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.1WL119PuhP/E---3.1_1110736.p', cartprodpairin)).
% 205.15/30.12 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.1WL119PuhP/E---3.1_1110736.p', ubforcartprodlem3)).
% 205.15/30.12 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', setunionsingleton)).
% 205.15/30.12 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', nonemptyI1)).
% 205.15/30.12 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', nonemptyE1)).
% 205.15/30.12 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', noeltsimpempty)).
% 205.15/30.12 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', emptyI)).
% 205.15/30.12 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', setext)).
% 205.15/30.12 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', notinemptyset)).
% 205.15/30.12 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', emptysetimpfalse)).
% 205.15/30.12 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', emptysetE)).
% 205.15/30.12 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', prop2setE)).
% 205.15/30.12 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', wellorderingAx)).
% 205.15/30.12 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', foundationAx)).
% 205.15/30.12 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.1WL119PuhP/E---3.1_1110736.p', omegaIndAx)).
% 205.15/30.12 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', omegaSAx)).
% 205.15/30.12 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', omega0Ax)).
% 205.15/30.12 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', setunionAx)).
% 205.15/30.12 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', powersetAx)).
% 205.15/30.12 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', setadjoinAx)).
% 205.15/30.12 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', emptysetAx)).
% 205.15/30.12 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.1WL119PuhP/E---3.1_1110736.p', setextAx)).
% 205.15/30.12 thf(c_0_204, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X30)=>((ap @ X4 @ X5 @ X30 @ X2)=(X3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[funcGraphProp4])).
% 205.15/30.12 thf(c_0_205, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 205.15/30.12 thf(c_0_206, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 205.15/30.12 thf(c_0_207, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 205.15/30.12 thf(c_0_208, 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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 205.15/30.12 thf(c_0_209, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 205.15/30.12 thf(c_0_210, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 205.15/30.12 thf(c_0_211, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 205.15/30.12 thf(c_0_212, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 205.15/30.12 thf(c_0_213, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 205.15/30.12 thf(c_0_214, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 205.15/30.12 thf(c_0_215, plain, ((funcImageSingleton)<=>![X4:$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])).
% 205.15/30.12 thf(c_0_216, plain, ((apProp)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X30))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
% 205.15/30.12 thf(c_0_217, plain, ((lamProp)<=>![X4:$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])).
% 205.15/30.12 thf(c_0_218, 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:$i]:(X33 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
% 205.15/30.12 thf(c_0_219, plain, ((lam2p)<=>![X4:$i, X5:$i, X34:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X34 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X34 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
% 205.15/30.12 thf(c_0_220, plain, ((ex1E2)<=>![X4:$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])).
% 205.15/30.12 thf(c_0_221, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 205.15/30.12 thf(c_0_222, 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])).
% 205.15/30.12 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])).
% 205.15/30.12 thf(c_0_224, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 205.15/30.12 thf(c_0_225, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 205.15/30.12 thf(c_0_226, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 205.15/30.12 thf(c_0_227, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 205.15/30.12 thf(c_0_228, 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])).
% 205.15/30.12 thf(c_0_229, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 205.15/30.12 thf(c_0_230, plain, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 205.15/30.12 thf(c_0_231, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 205.15/30.12 thf(c_0_232, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 205.15/30.12 thf(c_0_233, 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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 205.15/30.12 thf(c_0_234, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 205.15/30.12 thf(c_0_235, plain, ((ex1I)<=>![X4:$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])).
% 205.15/30.12 thf(c_0_236, 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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 205.15/30.12 thf(c_0_237, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 205.15/30.12 thf(c_0_238, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 205.15/30.12 thf(c_0_239, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 205.15/30.12 thf(c_0_240, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 205.15/30.12 thf(c_0_241, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 205.15/30.12 thf(c_0_242, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 205.15/30.12 thf(c_0_243, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 205.15/30.12 thf(c_0_244, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 205.15/30.12 thf(c_0_245, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 205.15/30.12 thf(c_0_246, plain, ((epred1_0)<=>![X668:$i]:(?[X669:$i]:((((![X670:$i]:(((in @ X670 @ X669)=>![X671:$i]:(((in @ X671 @ X670)=>(in @ X671 @ X668)))))&![X672:$i, X673:$i]:((((in @ X672 @ X668)&(in @ X673 @ X668))=>(![X674:$i]:(((in @ X674 @ X669)=>((in @ X672 @ X674)<=>(in @ X673 @ X674))))=>((X672)=(X673))))))&![X675:$i, X676:$i]:((((in @ X675 @ X669)&(in @ X676 @ X669))=>(![X677:$i]:(((in @ X677 @ X675)=>(in @ X677 @ X676)))|![X678:$i]:(((in @ X678 @ X676)=>(in @ X678 @ X675)))))))&![X679:$i]:(((![X680:$i]:(((in @ X680 @ X679)=>(in @ X680 @ X668)))&?[X681:$i]:((in @ X681 @ X679)))=>?[X682:$i, X683:$i]:(((((in @ X682 @ X669)&(in @ X683 @ X679))&~(?[X684:$i]:(((in @ X684 @ X682)&(in @ X684 @ X679)))))&![X685:$i]:(((in @ X685 @ X669)=>(![X686:$i]:(((in @ X686 @ X685)=>(in @ X686 @ X682)))|(in @ X683 @ X685)))))))))))), introduced(definition)).
% 205.15/30.12 thf(c_0_247, negated_conjecture, ~((![X641:$i, X642:$i]:((![X643:$i]:(((in @ X643 @ X641)<=>(in @ X643 @ X642)))=>((X641)=(X642))))=>(![X644:$i]:(~(in @ X644 @ emptyset))=>(![X645:$i, X646:$i, X647:$i]:(((in @ X647 @ (setadjoin @ X645 @ X646))<=>(((X647)=(X645))|(in @ X647 @ X646))))=>(![X648:$i, X649:$i]:(((in @ X649 @ (powerset @ X648))<=>![X650:$i]:(((in @ X650 @ X649)=>(in @ X650 @ X648)))))=>(![X651:$i, X652:$i]:(((in @ X652 @ (setunion @ X651))<=>?[X653:$i]:(((in @ X652 @ X653)&(in @ X653 @ X651)))))=>((in @ emptyset @ omega)=>(![X654:$i]:(((in @ X654 @ omega)=>(in @ (setadjoin @ X654 @ X654) @ omega)))=>(![X655:$i]:((((in @ emptyset @ X655)&![X656:$i]:((((in @ X656 @ omega)&(in @ X656 @ X655))=>(in @ (setadjoin @ X656 @ X656) @ X655))))=>![X657:$i]:(((in @ X657 @ omega)=>(in @ X657 @ X655)))))=>(![X658:$i > $i > $o, X659:$i]:((![X660:$i]:(((in @ X660 @ X659)=>(exu @ (X658 @ X660))))=>?[X661:$i]:(![X662:$i]:(((in @ X662 @ X661)<=>?[X663:$i]:(((in @ X663 @ X659)&(X658 @ X663 @ X662))))))))=>(![X664:$i]:((?[X665:$i]:((in @ X665 @ X664))=>?[X666:$i]:(((in @ X666 @ X664)&~(?[X667:$i]:(((in @ X667 @ X666)&(in @ X667 @ X664))))))))=>((epred1_0)=>(![X687:$i > $o]:(((exu @ X687)=>(X687 @ (descr @ (^[Z0:$i]:(X687 @ Z0))))))=>(![X688:$i, X689:$i > $o, X690:$i]:(((in @ X690 @ X688)=>((X689 @ X690)=>(in @ X690 @ (dsetconstr @ X688 @ X689)))))=>(![X691:$i, X692:$i > $o, X693:$i]:(((in @ X693 @ (dsetconstr @ X691 @ X692))=>(in @ X693 @ X691)))=>(![X694:$i, X695:$i > $o, X696:$i]:(((in @ X696 @ (dsetconstr @ X694 @ X695))=>(X695 @ X696)))=>(![X697:$i > $o]:(((exu @ X697)=>?[X698:$i]:(((X697 @ X698)&![X699:$i]:(((X697 @ X699)=>((X698)=(X699))))))))=>(![X700:$o, X701:$i]:(((in @ X701 @ (prop2set @ ((X700))))=>(X700)))=>(![X702:$i]:(((in @ X702 @ emptyset)=>![X703:$o]:((X703))))=>(![X704:$i]:(((in @ X704 @ emptyset)=>~($true)))=>(![X705:$i]:(~(in @ X705 @ emptyset))=>(![X706:$i > $o]:(((exu @ X706)=>?[X707:$i]:((X706 @ X707))))=>(![X708:$i, X709:$i]:((![X710:$i]:(((in @ X710 @ X708)=>(in @ X710 @ X709)))=>(![X711:$i]:(((in @ X711 @ X709)=>(in @ X711 @ X708)))=>((X708)=(X709)))))=>(![X712:$i]:((![X713:$i]:(~(in @ X713 @ X712))=>((X712)=(emptyset))))=>(![X714:$i]:((![X715:$i]:(~(in @ X715 @ X714))=>((X714)=(emptyset))))=>(![X716:$i, X717:$i > $o, X718:$i]:(((in @ X718 @ X716)=>((in @ X718 @ (dsetconstr @ X716 @ X717))<=>(X717 @ X718))))=>(![X719:$i]:(((nonempty @ X719)=>?[X720:$i]:((in @ X720 @ X719))))=>(![X721:$i, X722:$i > $o, X723:$i]:(((in @ X723 @ X721)=>((X722 @ X723)=>(nonempty @ (dsetconstr @ X721 @ X722)))))=>(![X724:$i]:((?[X725:$i]:((in @ X725 @ X724))=>(nonempty @ X724)))=>(![X726:$i, X727:$i]:((in @ X726 @ (setadjoin @ X726 @ X727)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X728:$i, X729:$i, X730:$i]:(((in @ X730 @ X729)=>(in @ X730 @ (setadjoin @ X728 @ X729))))=>(![X731:$i, X732:$i, X733:$i]:(((in @ X733 @ (setadjoin @ X731 @ X732))=>![X734:$o]:(((((X733)=(X731))=>(X734))=>(((in @ X733 @ X732)=>(X734))=>(X734))))))=>(![X735:$i, X736:$i, X737:$i]:(((in @ X737 @ (setadjoin @ X735 @ X736))=>(((X737)=(X735))|(in @ X737 @ X736))))=>(![X738:$i]:(((dsetconstr @ X738 @ (^[Z0:$i]:($true)))=(X738)))=>(![X739:$i, X740:$i]:((![X741:$i]:(((in @ X741 @ X740)=>(in @ X741 @ X739)))=>(in @ X740 @ (powerset @ X739))))=>(![X742:$i]:((in @ emptyset @ (powerset @ X742)))=>(![X743:$i]:((in @ emptyset @ (powerset @ X743)))=>(![X744:$i, X745:$i, X746:$i]:(((in @ X745 @ (powerset @ X744))=>((in @ X746 @ X745)=>(in @ X746 @ X744))))=>(![X747:$i, X748:$i, X749:$i]:(((in @ X748 @ X749)=>((in @ X749 @ X747)=>(in @ X748 @ (setunion @ X747)))))=>(![X750:$i, X751:$i]:(((in @ X751 @ (setunion @ X750))=>![X752:$o]:((![X753:$i]:(((in @ X751 @ X753)=>((in @ X753 @ X750)=>(X752))))=>(X752)))))=>(![X754:$i, X755:$i]:(((in @ X755 @ X754)=>(in @ X755 @ (powerset @ (setunion @ X754)))))=>(![X756:$i > $o]:(((exu @ X756)=>?[X757:$i]:(![X758:$i]:(((X756 @ X758)<=>((X758)=(X757)))))))=>(![X759:$i]:(((nonempty @ X759)=>?[X760:$i]:(((in @ X760 @ X759)&$true))))=>(![X761:$i, X762:$i]:(((in @ X761 @ (setadjoin @ X762 @ emptyset))=>((X761)=(X762))))=>(![X763:$i, X764:$i]:((((X763)!=(X764))=>~(in @ X764 @ (setadjoin @ X763 @ emptyset))))=>(![X765:$i, X766:$i]:((((X765)=(X766))=>(in @ X765 @ (setadjoin @ X766 @ emptyset))))=>(![X767:$i, X768:$i]:(((in @ X767 @ (setadjoin @ X768 @ emptyset))=>(in @ X768 @ (setadjoin @ X767 @ emptyset))))=>(![X769:$i, X770:$i, X771:$i]:(((in @ X771 @ (setadjoin @ X769 @ (setadjoin @ X770 @ emptyset)))=>(((X771)=(X769))|((X771)=(X770)))))=>(![X772:$i, X773:$i]:((in @ X772 @ (setadjoin @ X772 @ (setadjoin @ X773 @ emptyset))))=>(![X774:$i, X775:$i]:((in @ X775 @ (setadjoin @ X774 @ (setadjoin @ X775 @ emptyset))))=>(![X776:$i, X777:$i > $o]:((?[X778:$i]:(((in @ X778 @ X776)&(X777 @ X778)))=>(((dsetconstr @ X776 @ X777)=(emptyset))=>~($true))))=>(![X779:$i > $o, X780:$i]:(((in @ X780 @ emptyset)=>(X779 @ X780)))=>(![X781:$i, X782:$i > $o]:((~(![X783:$i]:(((in @ X783 @ X781)=>(X782 @ X783))))=>?[X784:$i]:(((in @ X784 @ X781)&~((X782 @ X784))))))=>(![X785:$i, X786:$i > $o]:((![X787:$i]:(((in @ X787 @ X785)=>~((X786 @ X787))))=>~(?[X788:$i]:(((in @ X788 @ X785)&(X786 @ X788))))))=>(![X789:$i, X790:$i > $o]:((~(?[X791:$i]:(((in @ X791 @ X789)&(X790 @ X791))))=>![X792:$i]:(((in @ X792 @ X789)=>~((X790 @ X792))))))=>(![X793:$i, X794:$i > $o]:((?[X795:$i]:(((in @ X795 @ X793)&~((X794 @ X795))))=>~(![X796:$i]:(((in @ X796 @ X793)=>(X794 @ X796))))))=>(![X797:$o]:(((X797)=>(in @ emptyset @ (prop2set @ ((X797))))))=>((prop2set2propI)=>(![X798:$i, X799:$i > $o]:((~(?[X800:$i]:(((in @ X800 @ X798)&(X799 @ X800))))=>![X801:$i]:(((in @ X801 @ X798)=>~((X799 @ X801))))))=>(![X802:$i, X803:$i > $o]:((~(![X804:$i]:(((in @ X804 @ X802)=>(X803 @ X804))))=>?[X805:$i]:(((in @ X805 @ X802)&~((X803 @ X805))))))=>(![X806:$i > $o]:((?[X807:$i]:(((X806 @ X807)&![X808:$i]:(((X806 @ X808)=>((X807)=(X808))))))=>(exu @ X806)))=>(![X809:$i > $o]:((?[X810:$i]:((X809 @ X810))=>(![X811:$i, X812:$i]:(((X809 @ X811)=>((X809 @ X812)=>((X811)=(X812)))))=>(exu @ X809))))=>(![X813:$i > $o]:((?[X814:$i]:(![X815:$i]:(((X813 @ X815)<=>((X815)=(X814)))))=>(exu @ X813)))=>(![X816:$i, X817:$i]:((((X816)=(X817))=>![X818:$i, X819:$i]:((((X818)=(X819))=>((in @ X818 @ X816)=>(in @ X819 @ X817))))))=>(![X820:$i, X821:$i]:((((X820)=(X821))=>![X822:$i, X823:$i]:((((X822)=(X823))=>((in @ X822 @ X820)<=>(in @ X823 @ X821))))))=>(![X824:$i > $o]:(((exu @ X824)=>![X825:$i, X826:$i]:(((X824 @ X825)=>((X824 @ X826)=>((X825)=(X826)))))))=>(![X827:$i > $o, X828:$i > $o]:((![X829:$i, X830:$i]:((((X829)=(X830))=>((X827 @ X829)<=>(X828 @ X830))))=>((exu @ X827)<=>(exu @ X828))))=>(((emptyset)=(emptyset))=>(![X831:$i, X832:$i]:((((X831)=(X832))=>![X833:$i, X834:$i]:((((X833)=(X834))=>((setadjoin @ X831 @ X833)=(setadjoin @ X832 @ X834))))))=>(![X835:$i, X836:$i]:((((X835)=(X836))=>((powerset @ X835)=(powerset @ X836))))=>(![X837:$i, X838:$i]:((((X837)=(X838))=>((setunion @ X837)=(setunion @ X838))))=>(((omega)=(omega))=>(![X839:$i > $o]:(((exu @ X839)=>![X840:$i, X841:$i]:(((X839 @ X840)=>((X839 @ X841)=>((X840)=(X841)))))))=>(![X842:$i > $o, X843:$i > $o]:((![X844:$i, X845:$i]:((((X844)=(X845))=>((X842 @ X844)<=>(X843 @ X845))))=>((exu @ X842)=>((exu @ X843)=>((descr @ X842)=(descr @ X843))))))=>(![X846:$i, X847:$i]:((((X846)=(X847))=>![X848:$i > $o, X849:$i > $o]:((![X850:$i]:(((in @ X850 @ X846)=>![X851:$i]:(((in @ X851 @ X847)=>(((X850)=(X851))=>((X848 @ X850)<=>(X849 @ X851)))))))=>((dsetconstr @ X846 @ X848)=(dsetconstr @ X847 @ X849))))))=>(![X852:$i, X853:$i]:((![X854:$i]:(((in @ X854 @ X852)=>(in @ X854 @ X853)))=>(subset @ X852 @ X853)))=>(![X855:$i, X856:$i]:((((X855)=(X856))=>(subset @ X856 @ X855)))=>(![X857:$i, X858:$i]:((((X857)=(X858))=>(subset @ X857 @ X858)))=>(![X859:$i, X860:$i]:((![X861:$i]:(((in @ X861 @ X859)=>(in @ X861 @ X860)))=>(subset @ X859 @ X860)))=>(![X862:$i]:((subset @ emptyset @ X862))=>(![X863:$i, X864:$i, X865:$i]:(((subset @ X863 @ X864)=>((in @ X865 @ X863)=>(in @ X865 @ X864))))=>(![X866:$i, X867:$i, X868:$i]:(((subset @ X866 @ X867)=>(~(in @ X868 @ X867)=>~(in @ X868 @ X866))))=>(![X869:$i, X870:$i, X871:$i]:(((in @ X871 @ X869)=>(~(in @ X871 @ X870)=>~(subset @ X869 @ X870))))=>(![X872:$i, X873:$i]:((~(subset @ X872 @ X873)=>((X872)!=(X873))))=>(![X874:$i, X875:$i, X876:$i]:(((in @ X876 @ X874)=>(~(in @ X876 @ X875)=>((X874)!=(X875)))))=>(![X877:$i]:((subset @ X877 @ X877))=>(![X878:$i, X879:$i, X880:$i]:(((subset @ X878 @ X879)=>((subset @ X879 @ X880)=>(subset @ X878 @ X880))))=>(![X881:$i, X882:$i]:((subset @ X882 @ (setadjoin @ X881 @ X882)))=>(![X883:$i, X884:$i, X885:$i]:(((subset @ X883 @ X885)=>(subset @ X883 @ (setadjoin @ X884 @ X885))))=>(![X886:$i, X887:$i]:(((subset @ X886 @ X887)=>(in @ X886 @ (powerset @ X887))))=>(![X888:$i, X889:$i]:(((subset @ X888 @ X889)=>((subset @ X889 @ X888)=>((X888)=(X889)))))=>(![X890:$i]:(((subset @ X890 @ emptyset)=>((X890)=(emptyset))))=>(![X891:$i, X892:$i]:(((subset @ X892 @ X891)=>(in @ X892 @ (powerset @ X891))))=>(![X893:$i, X894:$i]:(((in @ X894 @ (powerset @ X893))=>(subset @ X894 @ X893)))=>(![X895:$i]:((in @ X895 @ (powerset @ X895)))=>(![X896:$i, X897:$i]:(((subset @ X896 @ X897)=>(subset @ (powerset @ X896) @ (powerset @ X897))))=>(![X898:$i, X899:$i > $o]:((in @ (dsetconstr @ X898 @ X899) @ (powerset @ X898)))=>(![X900:$i, X901:$i > $o]:((subset @ (dsetconstr @ X900 @ X901) @ X900))=>(![X902:$i, X903:$i, X904:$i]:(((in @ X904 @ X902)=>(in @ X904 @ (binunion @ X902 @ X903))))=>(![X905:$i, X906:$i]:((in @ X906 @ (setadjoin @ X905 @ (setadjoin @ X906 @ emptyset))))=>(![X907:$i, X908:$i, X909:$i]:(((in @ X909 @ X908)=>(in @ X909 @ (binunion @ X907 @ X908))))=>(![X910:$i, X911:$i, X912:$i, X913:$o]:(((in @ X912 @ (binunion @ X910 @ X911))=>(((in @ X912 @ X910)=>(X913))=>(((in @ X912 @ X911)=>(X913))=>(X913)))))=>(![X914:$i, X915:$i, X916:$i]:(((in @ X916 @ (binunion @ X914 @ X915))=>((in @ X916 @ X914)|(in @ X916 @ X915))))=>(![X917:$i, X918:$i]:((subset @ X917 @ (binunion @ X917 @ X918)))=>(![X919:$i, X920:$i]:((subset @ X920 @ (binunion @ X919 @ X920)))=>(![X921:$i, X922:$i, X923:$i]:(((in @ X923 @ X921)=>((in @ X923 @ X922)=>(in @ X923 @ (binintersect @ X921 @ X922)))))=>(![X924:$i, X925:$i, X926:$i]:(((subset @ X926 @ X924)=>((subset @ X926 @ X925)=>(subset @ X926 @ (binintersect @ X924 @ X925)))))=>(![X927:$i, X928:$i, X929:$i]:(((in @ X929 @ (binintersect @ X927 @ X928))=>(in @ X929 @ X927)))=>(![X930:$i, X931:$i]:((subset @ (binintersect @ X930 @ X931) @ X930))=>(![X932:$i, X933:$i]:(((subset @ X932 @ X933)=>((binintersect @ X932 @ X933)=(X932))))=>(![X934:$i, X935:$i]:((((binintersect @ X934 @ X935)=(X935))=>(subset @ X935 @ X934)))=>(![X936:$i, X937:$i, X938:$i]:(((in @ X938 @ (binintersect @ X936 @ X937))=>(in @ X938 @ X937)))=>(![X939:$i, X940:$i]:((~(?[X941:$i]:(((in @ X941 @ X939)&(in @ X941 @ X940))))=>((binintersect @ X939 @ X940)=(emptyset))))=>(![X942:$i, X943:$i]:((subset @ (binintersect @ X942 @ X943) @ X943))=>(![X944:$i, X945:$i]:(((subset @ X945 @ X944)=>((binintersect @ X944 @ X945)=(X945))))=>(![X946:$i, X947:$i]:((((binintersect @ X946 @ X947)=(X946))=>(subset @ X946 @ X947)))=>(![X948:$i, X949:$i, X950:$i]:(((binintersect @ X948 @ (binunion @ X949 @ X950))=(binunion @ (binintersect @ X948 @ X949) @ (binintersect @ X948 @ X950))))=>(![X951:$i, X952:$i, X953:$i]:(((in @ X953 @ X951)=>(~(in @ X953 @ X952)=>(in @ X953 @ (setminus @ X951 @ X952)))))=>(![X954:$i, X955:$i, X956:$i]:(((in @ X956 @ (setminus @ X954 @ X955))=>(in @ X956 @ X954)))=>(![X957:$i, X958:$i, X959:$i]:(((in @ X959 @ (setminus @ X957 @ X958))=>~(in @ X959 @ X958)))=>(![X960:$i, X961:$i]:(((subset @ X960 @ X961)=>((setminus @ X960 @ X961)=(emptyset))))=>(![X962:$i, X963:$i, X964:$i]:((~(in @ X964 @ (setminus @ X962 @ X963))=>((in @ X964 @ X962)=>(in @ X964 @ X963))))=>(![X965:$i, X966:$i, X967:$i]:((~(in @ X967 @ (setminus @ X965 @ X966))=>(~(in @ X967 @ X966)=>~(in @ X967 @ X965))))=>(![X968:$i, X969:$i, X970:$i]:((~(in @ X970 @ X968)=>~(in @ X970 @ (setminus @ X968 @ X969))))=>(![X971:$i, X972:$i, X973:$i]:(((in @ X973 @ X972)=>~(in @ X973 @ (setminus @ X971 @ X972))))=>(![X974:$i, X975:$i]:((subset @ (setminus @ X974 @ X975) @ X974))=>(![X976:$i, X977:$i]:((((setminus @ X976 @ X977)=(emptyset))=>(subset @ X976 @ X977)))=>(![X978:$i, X979:$i, X980:$i]:(((in @ X980 @ (symdiff @ X978 @ X979))=>![X981:$o]:((((in @ X980 @ X978)=>(~(in @ X980 @ X979)=>(X981)))=>((~(in @ X980 @ X978)=>((in @ X980 @ X979)=>(X981)))=>(X981))))))=>(![X982:$i, X983:$i, X984:$i]:(((in @ X984 @ X982)=>(~(in @ X984 @ X983)=>(in @ X984 @ (symdiff @ X982 @ X983)))))=>(![X985:$i, X986:$i, X987:$i]:((~(in @ X987 @ X985)=>((in @ X987 @ X986)=>(in @ X987 @ (symdiff @ X985 @ X986)))))=>(![X988:$i, X989:$i, X990:$i]:(((in @ X990 @ X988)=>((in @ X990 @ X989)=>~(in @ X990 @ (symdiff @ X988 @ X989)))))=>(![X991:$i, X992:$i, X993:$i]:((~(in @ X993 @ X991)=>(~(in @ X993 @ X992)=>~(in @ X993 @ (symdiff @ X991 @ X992)))))=>(![X994:$i, X995:$i]:((in @ X995 @ (setadjoin @ X994 @ (setadjoin @ X995 @ emptyset))))=>(![X996:$i, X997:$i]:((in @ X996 @ (setunion @ (setadjoin @ (setadjoin @ X996 @ emptyset) @ (setadjoin @ (setadjoin @ X996 @ (setadjoin @ X997 @ emptyset)) @ emptyset)))))=>(![X998:$i, X999:$i]:((in @ X999 @ (setunion @ (setadjoin @ (setadjoin @ X998 @ emptyset) @ (setadjoin @ (setadjoin @ X998 @ (setadjoin @ X999 @ emptyset)) @ emptyset)))))=>(![X1000:$i, X1001:$i]:((iskpair @ (setadjoin @ (setadjoin @ X1000 @ emptyset) @ (setadjoin @ (setadjoin @ X1000 @ (setadjoin @ X1001 @ emptyset)) @ emptyset))))=>(![X1002:$i, X1003:$i]:((iskpair @ (kpair @ X1002 @ X1003)))=>(![X1004:$i, X1005:$i]:(((in @ X1005 @ X1004)=>(subset @ (setadjoin @ X1005 @ emptyset) @ X1004)))=>(![X1006:$i, X1007:$i]:(((in @ X1007 @ X1006)=>(in @ (setadjoin @ X1007 @ emptyset) @ (powerset @ X1006))))=>(![X1008:$i, X1009:$i, X1010:$i]:(((in @ X1010 @ 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emptyInPowerset]), setukpairinjL1]), singletonsuniq]), c_0_205]), theprop]), setadjoinIR]), kfstpairEq]), setadjoinE]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_206]), ksndpairEq]), setadjoinIL]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), setunionI]), cartprodpairmemER]), powersetE]), cartprodmempaircEq]), quantDeMorgan1]), vacuousDall]), cartprodfstpairEq]), emptyinPowerset]), cartprodsndpairEq]), powersetI]), cartprodpairsurjEq]), c_0_207]), c_0_208]), setadjoinOr]), c_0_209]), setunionE]), c_0_210]), c_0_211]), c_0_212]), c_0_213]), c_0_214]), c_0_215]), c_0_216]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_217]), c_0_218]), singletonsswitch]), c_0_219]), eqinunit]), brelnall1]), notinsingleton]), brelnall2]), uniqinunit]), c_0_220]), nonemptyImpWitness]), funcGraphProp1]), c_0_221]), funcGraphProp3]), funcGraphProp2]), subPowSU]), funcextLem]), upairsetE]), quantDeMorgan3]), quantDeMorgan2]), subsetTrans]), subsetRefl]), notequalI2]), notequalI1]), notsubsetI]), subsetE2]), c_0_222]), upairsetIR]), upairsetIL]), quantDeMorgan4]), inCongP]), c_0_223]), c_0_224]), c_0_225]), notdallE]), emptyinunitempty]), notdexE]), prop2setI]), in__Cong]), omega__Cong]), setunion__Cong]), powerset__Cong]), setadjoin__Cong]), emptyset__Cong]), c_0_226]), c_0_227]), c_0_228]), emptysetsubset]), subsetI2]), eqimpsubset1]), eqimpsubset2]), subsetI1]), c_0_229]), c_0_230]), subsetE]), setadjoinSub]), setadjoinSub2]), powersetsubset]), inPowerset]), powersetE1]), powersetI1]), subsetemptysetimpeq]), setextsub]), subset2powerset]), c_0_231]), binunionLsub]), binunionE]), binunionEcases]), binunionIR]), upairset2IR]), binunionIL]), c_0_232]), binunionRsub]), binintersectER]), binintersectSubset3]), binintersectSubset2]), binintersectLsub]), binintersectEL]), binintersectSubset5]), binintersectI]), disjointsetsI1]), setminusER]), setminusEL]), setminusI]), bs114d]), binintersectSubset1]), binintersectSubset4]), binintersectRsub]), setminusSubset2]), symdiffE]), setminusSubset1]), setminusLsub]), setminusIRneg]), setminusILneg]), setminusELneg]), setminusERneg]), symdiffI1]), kpairiskpair]), setukpairIR]), setukpairIL]), secondinupair]), symdiffIneg2]), symdiffIneg1]), symdiffI2]), kpairp]), ubforcartprodlem1]), upairinpowunion]), upairsubunion]), upairset2E]), singletoninpowunion]), singletoninpowerset]), singletonsubset]), ubforcartprodlem2]), setunionsingleton2]), setunionsingleton1]), setunionE2]), cartprodmempair]), cartprodmempair1]), cartprodpairin]), ubforcartprodlem3]), c_0_233]), c_0_234]), c_0_235]), c_0_236]), setunionsingleton]), nonemptyI1]), c_0_237]), nonemptyE1]), c_0_238]), noeltsimpempty]), emptyI]), setext]), c_0_239]), notinemptyset]), emptysetimpfalse]), emptysetE]), prop2setE]), c_0_240]), c_0_241]), c_0_242]), c_0_243]), c_0_244]), wellorderingAx]), foundationAx]), c_0_245]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_246])).
% 205.15/30.12 thf(c_0_248, negated_conjecture, ![X1241:$i, X1242:$i, X1244:$i, X1245:$i, X1246:$i, X1247:$i, X1248:$i, X1249:$i, X1250:$i, X1251:$i, X1252:$i, X1254:$i, X1255:$i, X1257:$i, X1258:$i, X1259:$i, X1260:$i, X1261:$i, X1263:$i, X1264:$i > $i > $o, X1265:$i, X1268:$i, X1270:$i, X1271:$i, X1272:$i, X1273:$i, X1275:$i, X1276:$i > $o, X1277:$i, X1278:$i > $o, X1279:$i, X1280:$i, X1281:$i > $o, X1282:$i, X1283:$i, X1284:$i > $o, X1285:$i, X1286:$i > $o, X1288:$i, X1289:$o, X1290:$i, X1291:$i, X1292:$o, X1293:$i, X1294:$i, X1295:$i > $o, X1297:$i, X1298:$i, X1301:$i, X1303:$i, X1305:$i, X1306:$i > $o, X1307:$i, X1308:$i, X1310:$i, X1311:$i > $o, X1312:$i, X1313:$i, X1314:$i, X1315:$i, X1316:$i, X1317:$i, X1318:$i, X1319:$i, X1320:$i, X1321:$i, X1322:$i, X1323:$o, X1324:$i, X1325:$i, X1326:$i, X1327:$i, X1328:$i, X1329:$i, X1331:$i, X1332:$i, X1333:$i, X1334:$i, X1335:$i, X1336:$i, X1337:$i, X1338:$i, X1339:$i, X1340:$i, X1341:$o, X1343:$i, X1344:$i, X1345:$i > $o, X1347:$i, X1348:$i, X1349:$i, X1351:$i, X1352:$i, X1353:$i, X1354:$i, X1355:$i, X1356:$i, X1357:$i, X1358:$i, X1359:$i, X1360:$i, X1361:$i, X1362:$i, X1363:$i, X1364:$i, X1365:$i, X1366:$i, X1367:$i > $o, X1368:$i, X1369:$i > $o, X1370:$i, X1371:$i, X1372:$i > $o, X1373:$i, X1375:$i, X1376:$i > $o, X1378:$i, X1379:$i, X1380:$i > $o, X1382:$i, X1383:$i, X1384:$i > $o, X1385:$i, X1387:$o, X1388:$i, X1389:$i > $o, X1391:$i, X1392:$i, X1393:$i > $o, X1394:$i, X1396:$i > $o, X1397:$i, X1399:$i > $o, X1400:$i, X1403:$i > $o, X1404:$i, X1406:$i, X1407:$i, X1408:$i, X1409:$i, X1410:$i, X1411:$i, X1412:$i, X1413:$i, X1414:$i > $o, X1415:$i, X1416:$i, X1417:$i > $o, X1418:$i > $o, X1421:$i, X1422:$i, X1423:$i, X1424:$i, X1425:$i, X1426:$i, X1427:$i, X1428:$i, X1429:$i > $o, X1430:$i, X1431:$i, X1432:$i > $o, X1433:$i > $o, X1436:$i, X1437:$i, X1438:$i > $o, X1439:$i > $o, X1442:$i, X1443:$i, X1445:$i, X1446:$i, X1447:$i, X1448:$i, X1449:$i, X1450:$i, X1452:$i, X1453:$i, X1454:$i, X1455:$i, X1456:$i, X1457:$i, X1458:$i, X1459:$i, X1460:$i, X1461:$i, X1462:$i, X1463:$i, X1464:$i, X1465:$i, X1466:$i, X1467:$i, X1468:$i, X1469:$i, X1470:$i, X1471:$i, X1472:$i, X1473:$i, X1474:$i, X1475:$i, X1476:$i, X1477:$i, X1478:$i, X1479:$i, X1480:$i, X1481:$i, X1482:$i, X1483:$i, X1484:$i, X1485:$i, X1486:$i, X1487:$i, X1488:$i, X1489:$i > $o, X1490:$i, X1491:$i > $o, X1492:$i, X1493:$i, X1494:$i, X1495:$i, X1496:$i, X1497:$i, X1498:$i, X1499:$i, X1500:$i, X1501:$i, X1502:$i, X1503:$o, X1504:$i, X1505:$i, X1506:$i, X1507:$i, X1508:$i, X1509:$i, X1510:$i, X1511:$i, X1512:$i, X1513:$i, X1514:$i, X1515:$i, X1516:$i, X1517:$i, X1518:$i, X1519:$i, X1520:$i, X1521:$i, X1522:$i, X1523:$i, X1524:$i, X1525:$i, X1526:$i, X1527:$i, X1528:$i, X1529:$i, X1530:$i, X1532:$i, X1533:$i, X1534:$i, X1535:$i, X1536:$i, X1537:$i, X1538:$i, X1539:$i, X1540:$i, X1541:$i, X1542:$i, X1543:$i, X1544:$i, X1545:$i, X1546:$i, X1547:$i, X1548:$i, X1549:$i, X1550:$i, X1551:$i, X1552:$i, X1553:$i, X1554:$i, X1555:$i, X1556:$i, X1557:$i, X1558:$i, X1559:$i, X1560:$i, X1561:$i, X1562:$i, X1563:$i, X1564:$i, X1565:$i, X1566:$i, X1567:$i, X1568:$i, X1569:$i, X1570:$i, X1571:$o, 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:$i, X1603:$i, X1604:$i, X1605:$i, X1606:$i, X1607:$i, X1608:$i, X1609:$i, X1610:$i, X1611:$i, X1612:$i, X1613:$i, X1614:$i, X1615:$i, X1616:$i, X1617:$i, X1618:$i, X1619:$i, X1620:$i, X1621:$i, X1622:$i, X1623:$i, X1624:$i, X1625:$i, X1626:$i, X1627:$i, X1628:$i, X1629:$i, X1630:$i, X1633:$i, X1634:$i, X1635:$i, X1636:$i, X1637:$i, X1639:$i, X1640:$i, X1641:$i, X1642:$i, X1643:$i > $o, X1646:$i, X1647:$i, X1648:$i > $o, X1650:$i, X1651:$i > $o, X1652:$i, X1654:$i, X1655:$i > $o, X1658:$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:$i, X1684:$i, 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 > $i > $o, X1731:$i, X1732:$i, X1733:$i, X1734:$i, X1735:$i > $i > $o, X1736:$i, X1737:$i, X1738:$i > $i > $o, X1739:$i, X1740:$i, X1741:$i > $i > $o, X1742:$i, X1743:$i, X1744:$i, X1745:$i, X1746:$i > $i > $o, X1747:$i, X1748:$i, X1749:$i, X1750:$i, X1751:$i > $i > $o, X1752:$i, X1753:$i, X1754:$i, X1755:$i, X1756:$i > $i > $o, X1757:$i, X1758:$i, X1759:$i, X1760:$i, X1761:$i, X1762:$i, X1763:$i, X1764:$i, X1765:$i, X1766:$i, X1767:$i, X1768:$i, X1769:$i, X1770:$i, X1771:$i, X1772:$i, X1773:$i, X1774:$i, X1775:$i, X1776:$i, X1777:$i, X1778:$i, X1779:$i, X1780:$i, X1781:$i, X1782:$i, X1783:$i > $i, X1785:$i, X1786:$i, X1787:$i > $i, X1789:$i, X1790:$i, X1791:$i > $i, X1793:$i, X1794:$i, X1795:$i, X1796:$i > $o, X1799:$i, X1800:$i, X1801:$i, X1802:$i, X1803:$i > $o, X1806:$i, X1807:$i, X1808:$i > $o, X1809:$i, X1810:$i, X1811:$i, X1812:$i, X1813:$i, X1814:$i, X1815:$i, X1816:$i, X1817:$i, X1818:$i, X1819:$i, X1820:$i, X1821:$i, X1822:$i, X1823:$i, X1824:$i, X1825:$i, X1826:$i, X1827:$i, X1829:$i, X1830:$i]:((((~(in @ (esk1_2 @ X1241 @ X1242) @ X1241)|~(in @ (esk1_2 @ X1241 @ X1242) @ X1242)|((X1241)=(X1242)))&((in @ (esk1_2 @ X1241 @ X1242) @ X1241)|(in @ (esk1_2 @ X1241 @ X1242) @ X1242)|((X1241)=(X1242))))&(~(in @ X1244 @ emptyset)&(((~(in @ X1247 @ (setadjoin @ X1245 @ X1246))|(((X1247)=(X1245))|(in @ X1247 @ X1246)))&((((X1247)!=(X1245))|(in @ X1247 @ (setadjoin @ X1245 @ X1246)))&(~(in @ X1247 @ X1246)|(in @ X1247 @ (setadjoin @ X1245 @ X1246)))))&(((~(in @ X1249 @ (powerset @ X1248))|(~(in @ X1250 @ X1249)|(in @ X1250 @ X1248)))&(((in @ (esk2_2 @ X1251 @ X1252) @ X1252)|(in @ X1252 @ (powerset @ X1251)))&(~(in @ (esk2_2 @ X1251 @ X1252) @ X1251)|(in @ X1252 @ (powerset @ X1251)))))&(((((in @ X1255 @ (esk3_2 @ X1254 @ X1255))|~(in @ X1255 @ (setunion @ X1254)))&((in @ (esk3_2 @ X1254 @ X1255) @ X1254)|~(in @ X1255 @ (setunion @ X1254))))&(~(in @ X1258 @ X1259)|~(in @ X1259 @ X1257)|(in @ X1258 @ (setunion @ X1257))))&((in @ emptyset @ omega)&((~(in @ X1260 @ omega)|(in @ (setadjoin @ X1260 @ X1260) @ omega))&(((((in @ (esk4_1 @ X1261) @ omega)|~(in @ emptyset @ X1261)|(~(in @ X1263 @ omega)|(in @ X1263 @ X1261)))&((in @ (esk4_1 @ X1261) @ X1261)|~(in @ emptyset @ X1261)|(~(in @ X1263 @ omega)|(in @ X1263 @ X1261))))&(~(in @ (setadjoin @ (esk4_1 @ X1261) @ (esk4_1 @ X1261)) @ X1261)|~(in @ emptyset @ X1261)|(~(in @ X1263 @ omega)|(in @ X1263 @ X1261))))&((((((in @ (esk7_3 @ X1264 @ X1265 @ X1268) @ X1265)|~(in @ X1268 @ (esk6_2 @ X1264 @ X1265))|(in @ (esk5_2 @ X1264 @ X1265) @ X1265))&((X1264 @ (esk7_3 @ X1264 @ X1265 @ X1268) @ X1268)|~(in @ X1268 @ (esk6_2 @ X1264 @ X1265))|(in @ (esk5_2 @ X1264 @ X1265) @ X1265)))&(~(in @ X1271 @ X1265)|~(X1264 @ X1271 @ X1270)|(in @ X1270 @ (esk6_2 @ X1264 @ X1265))|(in @ (esk5_2 @ X1264 @ X1265) @ X1265)))&((((in @ (esk7_3 @ X1264 @ X1265 @ X1268) @ X1265)|~(in @ X1268 @ (esk6_2 @ X1264 @ X1265))|~(exu @ (X1264 @ (esk5_2 @ X1264 @ X1265))))&((X1264 @ (esk7_3 @ X1264 @ X1265 @ X1268) @ X1268)|~(in @ X1268 @ (esk6_2 @ X1264 @ X1265))|~(exu @ (X1264 @ (esk5_2 @ X1264 @ X1265)))))&(~(in @ X1271 @ X1265)|~(X1264 @ X1271 @ X1270)|(in @ X1270 @ (esk6_2 @ X1264 @ X1265))|~(exu @ (X1264 @ (esk5_2 @ X1264 @ X1265))))))&((((in @ (esk8_1 @ X1272) @ X1272)|~(in @ X1273 @ X1272))&(~(in @ X1275 @ (esk8_1 @ X1272))|~(in @ X1275 @ X1272)|~(in @ 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X1570 @ X1568)|~(in @ X1570 @ (symdiff @ X1568 @ X1569)))&(~(X1571)|(X1571)|(in @ X1570 @ X1568)|~(in @ X1570 @ (symdiff @ X1568 @ X1569)))))&(((~(in @ X1570 @ X1568)|(X1571)|~(in @ X1570 @ X1569)|~(in @ X1570 @ (symdiff @ X1568 @ X1569)))&(((in @ X1570 @ X1569)|(X1571)|~(in @ X1570 @ X1569)|~(in @ X1570 @ (symdiff @ X1568 @ X1569)))&(~(X1571)|(X1571)|~(in @ X1570 @ X1569)|~(in @ X1570 @ (symdiff @ X1568 @ X1569)))))&((~(in @ X1570 @ X1568)|(X1571)|~(X1571)|~(in @ X1570 @ (symdiff @ X1568 @ X1569)))&(((in @ X1570 @ X1569)|(X1571)|~(X1571)|~(in @ X1570 @ (symdiff @ X1568 @ X1569)))&(~(X1571)|(X1571)|~(X1571)|~(in @ X1570 @ (symdiff @ X1568 @ X1569)))))))&((~(in @ X1574 @ X1572)|((in @ X1574 @ X1573)|(in @ X1574 @ (symdiff @ X1572 @ X1573))))&(((in @ X1577 @ X1575)|(~(in @ X1577 @ X1576)|(in @ X1577 @ (symdiff @ X1575 @ X1576))))&((~(in @ X1580 @ X1578)|(~(in @ X1580 @ X1579)|~(in @ X1580 @ (symdiff @ X1578 @ X1579))))&(((in @ X1583 @ X1581)|((in @ X1583 @ X1582)|~(in @ X1583 @ (symdiff @ X1581 @ X1582))))&((in @ X1585 @ (setadjoin @ X1584 @ (setadjoin @ X1585 @ emptyset)))&((in @ X1586 @ (setunion @ (setadjoin @ (setadjoin @ X1586 @ emptyset) @ (setadjoin @ (setadjoin @ X1586 @ (setadjoin @ X1587 @ emptyset)) @ emptyset))))&((in @ X1589 @ (setunion @ (setadjoin @ (setadjoin @ X1588 @ emptyset) @ (setadjoin @ (setadjoin @ X1588 @ (setadjoin @ X1589 @ emptyset)) @ emptyset))))&((iskpair @ (setadjoin @ (setadjoin @ X1590 @ emptyset) @ (setadjoin @ (setadjoin @ X1590 @ (setadjoin @ X1591 @ emptyset)) @ emptyset)))&((iskpair @ (kpair @ X1592 @ X1593))&((~(in @ X1595 @ X1594)|(subset @ (setadjoin @ X1595 @ emptyset) @ X1594))&((~(in @ X1597 @ X1596)|(in @ (setadjoin @ X1597 @ emptyset) @ (powerset @ X1596)))&((~(in @ X1600 @ X1598)|(in @ (setadjoin @ X1600 @ emptyset) @ (powerset @ (binunion @ X1598 @ X1599))))&((~(in @ X1603 @ (setadjoin @ X1601 @ (setadjoin @ X1602 @ emptyset)))|(((X1603)=(X1601))|((X1603)=(X1602))))&((~(in @ X1606 @ X1604)|(~(in @ X1607 @ X1605)|(subset @ (setadjoin @ X1606 @ (setadjoin @ X1607 @ emptyset)) @ (binunion @ X1604 @ X1605))))&((~(in @ X1610 @ X1608)|(~(in @ X1611 @ X1609)|(in @ (setadjoin @ X1610 @ (setadjoin @ X1611 @ emptyset)) @ (powerset @ (binunion @ X1608 @ X1609)))))&((~(in @ X1614 @ X1612)|(~(in @ X1615 @ X1613)|(subset @ (setadjoin @ (setadjoin @ X1614 @ emptyset) @ (setadjoin @ (setadjoin @ X1614 @ (setadjoin @ X1615 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X1612 @ X1613)))))&((~(in @ X1618 @ X1616)|(~(in @ X1619 @ X1617)|(in @ (setadjoin @ (setadjoin @ X1618 @ emptyset) @ (setadjoin @ (setadjoin @ X1618 @ (setadjoin @ X1619 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1616 @ X1617))))))&((~(in @ X1622 @ X1620)|(~(in @ X1623 @ X1621)|(in @ (kpair @ X1622 @ X1623) @ (powerset @ (powerset @ (binunion @ X1620 @ X1621))))))&((~(in @ X1626 @ X1624)|(~(in @ X1627 @ X1625)|(in @ (kpair @ X1626 @ X1627) @ (cartprod @ X1624 @ X1625))))&((((in @ (esk39_3 @ X1628 @ X1629 @ X1630) @ X1628)|~(in @ X1630 @ (cartprod @ X1628 @ X1629)))&(((in @ (esk40_3 @ X1628 @ X1629 @ X1630) @ X1629)|~(in @ X1630 @ (cartprod @ X1628 @ X1629)))&(((X1630)=(kpair @ (esk39_3 @ X1628 @ X1629 @ X1630) @ (esk40_3 @ X1628 @ X1629 @ X1630)))|~(in @ X1630 @ (cartprod @ X1628 @ X1629)))))&((~(in @ X1635 @ (cartprod @ X1633 @ X1634))|(iskpair @ X1635))&((((in @ (esk41_2 @ X1636 @ X1637) @ X1636)|~(in @ X1637 @ (setunion @ X1636)))&((in @ X1637 @ (esk41_2 @ X1636 @ X1637))|~(in @ X1637 @ (setunion @ X1636))))&((subset @ (setunion @ (setadjoin @ X1639 @ emptyset)) @ X1639)&((subset @ X1640 @ (setunion @ (setadjoin @ X1640 @ emptyset)))&(((setunion @ (setadjoin @ X1641 @ emptyset))=(X1641))&((((in @ (esk42_2 @ X1642 @ X1643) @ X1642)|(~(in @ X1646 @ X1642)|~(X1643 @ X1646)|(singleton @ (dsetconstr @ X1642 @ X1643))))&(((in @ (esk43_2 @ X1642 @ X1643) @ X1642)|(~(in @ X1646 @ X1642)|~(X1643 @ X1646)|(singleton @ (dsetconstr @ X1642 @ X1643))))&(((X1643 @ (esk42_2 @ X1642 @ X1643))|(~(in @ X1646 @ X1642)|~(X1643 @ X1646)|(singleton @ (dsetconstr @ X1642 @ X1643))))&(((X1643 @ (esk43_2 @ X1642 @ X1643))|(~(in @ X1646 @ X1642)|~(X1643 @ X1646)|(singleton @ (dsetconstr @ X1642 @ X1643))))&(((esk42_2 @ X1642 @ X1643)!=(esk43_2 @ X1642 @ X1643))|(~(in @ X1646 @ X1642)|~(X1643 @ X1646)|(singleton @ (dsetconstr @ X1642 @ X1643))))))))&((((in @ (esk44_2 @ X1647 @ X1648) @ X1647)|~(ex1 @ X1647 @ X1648))&((X1648 @ (esk44_2 @ X1647 @ X1648))|~(ex1 @ X1647 @ X1648)))&((((in @ (esk45_3 @ X1650 @ X1651 @ X1652) @ X1650)|(ex1 @ X1650 @ X1651)|~(X1651 @ X1652)|~(in @ X1652 @ X1650))&(((X1651 @ (esk45_3 @ X1650 @ X1651 @ X1652))|(ex1 @ X1650 @ X1651)|~(X1651 @ X1652)|~(in @ X1652 @ X1650))&(((esk45_3 @ X1650 @ X1651 @ X1652)!=(X1652))|(ex1 @ X1650 @ X1651)|~(X1651 @ X1652)|~(in @ X1652 @ X1650))))&((((in @ (esk46_2 @ X1654 @ X1655) @ X1654)|(~(in @ X1658 @ X1654)|~(X1655 @ X1658)|(ex1 @ X1654 @ X1655)))&(((in @ (esk47_2 @ X1654 @ X1655) @ X1654)|(~(in @ X1658 @ X1654)|~(X1655 @ X1658)|(ex1 @ X1654 @ X1655)))&(((X1655 @ (esk46_2 @ X1654 @ X1655))|(~(in @ X1658 @ X1654)|~(X1655 @ X1658)|(ex1 @ X1654 @ X1655)))&(((X1655 @ (esk47_2 @ X1654 @ X1655))|(~(in @ X1658 @ X1654)|~(X1655 @ X1658)|(ex1 @ X1654 @ X1655)))&(((esk46_2 @ X1654 @ X1655)!=(esk47_2 @ X1654 @ X1655))|(~(in @ X1658 @ X1654)|~(X1655 @ X1658)|(ex1 @ X1654 @ X1655)))))))&((((setadjoin @ X1659 @ emptyset)!=(setadjoin @ X1660 @ emptyset))|((X1659)=(X1660)))&((~(in @ (setadjoin @ X1663 @ emptyset) @ (setadjoin @ (setadjoin @ X1661 @ emptyset) @ (setadjoin @ (setadjoin @ X1661 @ (setadjoin @ X1662 @ emptyset)) @ emptyset)))|((X1661)=(X1663)))&((~(iskpair @ X1664)|(singleton @ (dsetconstr @ (setunion @ X1664) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1664))))))&((~(singleton @ X1665)|(in @ (setunion @ X1665) @ X1665))&(((kfst @ (kpair @ X1666 @ X1667))=(X1666))&((~(in @ X1670 @ (cartprod @ X1668 @ X1669))|(in @ (kfst @ X1670) @ X1668))&((((setadjoin @ (setadjoin @ X1671 @ emptyset) @ (setadjoin @ (setadjoin @ X1671 @ (setadjoin @ X1672 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1673 @ emptyset) @ (setadjoin @ (setadjoin @ X1673 @ (setadjoin @ X1674 @ emptyset)) @ emptyset)))|((X1671)=(X1673)))&((((kpair @ X1675 @ X1676)!=(kpair @ X1677 @ X1678))|((X1675)=(X1677)))&((((X1679)!=(X1680))|((setadjoin @ X1679 @ (setadjoin @ X1680 @ emptyset))=(setadjoin @ X1679 @ emptyset)))&((((X1681)!=(X1682))|((setadjoin @ (setadjoin @ X1681 @ emptyset) @ (setadjoin @ (setadjoin @ X1681 @ (setadjoin @ X1682 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X1681 @ emptyset) @ emptyset)))&((((setadjoin @ (setadjoin @ X1683 @ emptyset) @ (setadjoin @ (setadjoin @ X1683 @ (setadjoin @ X1684 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1685 @ emptyset) @ (setadjoin @ (setadjoin @ X1685 @ (setadjoin @ X1686 @ emptyset)) @ emptyset)))|(((X1685)!=(X1686))|((X1684)=(X1686))))&((((setadjoin @ X1687 @ (setadjoin @ X1688 @ emptyset))!=(setadjoin @ X1689 @ emptyset))|((X1687)=(X1688)))&((((setadjoin @ (setadjoin @ X1690 @ emptyset) @ (setadjoin @ (setadjoin @ X1690 @ (setadjoin @ X1691 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1692 @ emptyset) @ (setadjoin @ (setadjoin @ X1692 @ (setadjoin @ X1693 @ emptyset)) @ emptyset)))|((X1691)=(X1693)))&((((kpair @ X1694 @ X1695)!=(kpair @ X1696 @ X1697))|((X1695)=(X1697)))&((~(iskpair @ X1698)|(singleton @ (dsetconstr @ (setunion @ X1698) @ (^[Z0:$i]:(((X1698)=(kpair @ (kfst @ X1698) @ Z0)))))))&(((ksnd @ (kpair @ X1699 @ X1700))=(X1700))&((~(iskpair @ X1701)|((kpair @ (kfst @ X1701) @ (ksnd @ X1701))=(X1701)))&((~(in @ X1704 @ (cartprod @ X1702 @ X1703))|(in @ (ksnd @ X1704) @ X1703))&((~(in @ (kpair @ X1707 @ X1708) @ (cartprod @ X1705 @ X1706))|(in @ X1707 @ X1705))&((~(in @ (kpair @ X1711 @ X1712) @ (cartprod @ X1709 @ X1710))|(in @ X1712 @ X1710))&((~(in @ X1715 @ X1713)|(~(in @ X1716 @ X1714)|((kpair @ X1715 @ X1716)=(kpair @ X1715 @ X1716))))&((~(in @ X1719 @ X1717)|(~(in @ X1720 @ X1718)|((kfst @ (kpair @ X1719 @ X1720))=(X1719))))&((~(in @ X1723 @ X1721)|(~(in @ X1724 @ X1722)|((ksnd @ (kpair @ X1723 @ X1724))=(X1724))))&((~(in @ X1727 @ (cartprod @ X1725 @ X1726))|((kpair @ (kfst @ X1727) @ (ksnd @ X1727))=(X1727)))&((~(in @ X1731 @ X1728)|(~(in @ X1732 @ X1729)|(~(X1730 @ X1731 @ X1732)|(in @ (kpair @ X1731 @ X1732) @ (dpsetconstr @ X1728 @ X1729 @ X1730)))))&((subset @ (dpsetconstr @ X1733 @ X1734 @ X1735) @ (cartprod @ X1733 @ X1734))&((breln @ X1736 @ X1737 @ (dpsetconstr @ X1736 @ X1737 @ X1738))&((~(in @ X1742 @ X1739)|(~(in @ X1743 @ X1740)|(~(in @ (kpair @ X1742 @ X1743) @ (dpsetconstr @ X1739 @ X1740 @ X1741))|(X1741 @ X1742 @ X1743))))&((~(in @ (kpair @ X1747 @ X1748) @ (dpsetconstr @ X1744 @ X1745 @ X1746))|(in @ X1747 @ X1744))&((~(in @ (kpair @ X1752 @ X1753) @ (dpsetconstr @ X1749 @ X1750 @ X1751))|(in @ X1753 @ X1750))&((~(in @ (kpair @ X1757 @ X1758) @ (dpsetconstr @ X1754 @ X1755 @ X1756))|(X1756 @ X1757 @ X1758))&((~(func @ X1759 @ X1760 @ X1761)|(~(in @ X1762 @ X1759)|(singleton @ (dsetconstr @ X1760 @ (^[Z0:$i]:((in @ (kpair @ X1762 @ Z0) @ X1761)))))))&((~(func @ X1763 @ X1764 @ X1765)|(~(in @ X1766 @ X1763)|(in @ (setunion @ (dsetconstr @ X1764 @ (^[Z0:$i]:((in @ (kpair @ X1766 @ Z0) @ X1765))))) @ X1764)))&((~(func @ X1767 @ X1768 @ X1769)|(~(in @ X1770 @ X1767)|(in @ (ap @ X1767 @ X1768 @ X1769 @ X1770) @ X1768)))&((~(in @ X1773 @ (funcSet @ X1771 @ X1772))|(func @ X1771 @ X1772 @ X1773))&((~(in @ X1776 @ (funcSet @ X1774 @ X1775))|(~(in @ X1777 @ X1774)|(in @ (ap @ X1774 @ X1775 @ X1776 @ X1777) @ X1775)))&((~(func @ X1778 @ X1779 @ X1780)|(in @ X1780 @ (funcSet @ X1778 @ X1779)))&((((in @ (esk48_3 @ X1781 @ X1782 @ X1783) @ X1781)|(func @ X1781 @ X1782 @ (dpsetconstr @ X1781 @ X1782 @ (^[Z0:$i]:($eq @ (X1783 @ Z0))))))&(~(in @ (X1783 @ (esk48_3 @ X1781 @ X1782 @ X1783)) @ X1782)|(func @ X1781 @ X1782 @ (dpsetconstr @ X1781 @ X1782 @ (^[Z0:$i]:($eq @ (X1783 @ Z0)))))))&((((in @ (esk49_3 @ X1785 @ X1786 @ X1787) @ X1785)|(func @ X1785 @ X1786 @ (lam @ X1785 @ X1786 @ X1787)))&(~(in @ (X1787 @ (esk49_3 @ X1785 @ X1786 @ X1787)) @ X1786)|(func @ X1785 @ X1786 @ (lam @ X1785 @ X1786 @ X1787))))&((((in @ (esk50_3 @ X1789 @ X1790 @ X1791) @ X1789)|(in @ (lam @ X1789 @ X1790 @ X1791) @ (funcSet @ X1789 @ X1790)))&(~(in @ (X1791 @ (esk50_3 @ X1789 @ X1790 @ X1791)) @ X1790)|(in @ (lam @ X1789 @ X1790 @ X1791) @ (funcSet @ X1789 @ X1790))))&((((in @ (esk51_4 @ X1793 @ X1794 @ X1795 @ X1796) @ X1793)|(~(in @ X1799 @ X1795)|(X1796 @ X1799))|~(breln @ X1793 @ X1794 @ X1795))&(((in @ (esk52_4 @ X1793 @ X1794 @ X1795 @ X1796) @ X1794)|(~(in @ X1799 @ X1795)|(X1796 @ X1799))|~(breln @ X1793 @ X1794 @ X1795))&(((in @ (kpair @ (esk51_4 @ X1793 @ X1794 @ X1795 @ X1796) @ (esk52_4 @ X1793 @ X1794 @ X1795 @ X1796)) @ X1795)|(~(in @ X1799 @ X1795)|(X1796 @ X1799))|~(breln @ X1793 @ X1794 @ X1795))&(~(X1796 @ (kpair @ (esk51_4 @ X1793 @ X1794 @ X1795 @ X1796) @ (esk52_4 @ X1793 @ X1794 @ X1795 @ X1796)))|(~(in @ X1799 @ X1795)|(X1796 @ X1799))|~(breln @ X1793 @ X1794 @ X1795)))))&((((in @ (esk53_4 @ X1800 @ X1801 @ X1802 @ X1803) @ X1800)|(~(in @ X1806 @ X1802)|(X1803 @ X1806))|~(breln @ X1800 @ X1801 @ X1802))&(((in @ (esk54_4 @ X1800 @ X1801 @ X1802 @ X1803) @ X1801)|(~(in @ X1806 @ X1802)|(X1803 @ X1806))|~(breln @ X1800 @ X1801 @ X1802))&(((in @ (kpair @ (esk53_4 @ X1800 @ X1801 @ X1802 @ X1803) @ (esk54_4 @ X1800 @ X1801 @ X1802 @ X1803)) @ X1802)|(~(in @ X1806 @ X1802)|(X1803 @ X1806))|~(breln @ X1800 @ X1801 @ X1802))&(~(X1803 @ (kpair @ (esk53_4 @ X1800 @ X1801 @ X1802 @ X1803) @ (esk54_4 @ X1800 @ X1801 @ X1802 @ X1803)))|(~(in @ X1806 @ X1802)|(X1803 @ X1806))|~(breln @ X1800 @ X1801 @ X1802)))))&((~(ex1 @ X1807 @ X1808)|(~(in @ X1809 @ X1807)|(~(in @ X1810 @ X1807)|(~(X1808 @ X1809)|(~(X1808 @ X1810)|((X1809)=(X1810)))))))&((~(func @ X1811 @ X1812 @ X1813)|(~(in @ X1814 @ X1811)|(in @ (kpair @ X1814 @ (ap @ X1811 @ X1812 @ X1813 @ X1814)) @ X1813)))&((~(in @ X1817 @ (funcSet @ X1815 @ X1816))|(~(in @ X1818 @ X1815)|(in @ (kpair @ X1818 @ (ap @ X1815 @ X1816 @ X1817 @ X1818)) @ X1817)))&((~(func @ X1819 @ X1820 @ X1821)|(~(in @ X1822 @ X1819)|(~(in @ X1823 @ X1820)|(~(in @ (kpair @ X1822 @ X1823) @ X1821)|((ap @ X1819 @ X1820 @ X1821 @ X1822)=(X1823))))))&((((in @ (esk55_4 @ X1824 @ X1825 @ X1826 @ X1827) @ X1824)|(~(in @ X1829 @ X1824)|(~(in @ X1830 @ X1825)|(~(in @ (kpair @ X1829 @ X1830) @ X1827)|(in @ (kpair @ X1829 @ X1830) @ X1826))))|~(func @ X1824 @ X1825 @ X1827)|~(func @ X1824 @ X1825 @ X1826))&(((ap @ X1824 @ X1825 @ X1826 @ (esk55_4 @ X1824 @ X1825 @ X1826 @ X1827))!=(ap @ X1824 @ X1825 @ X1827 @ (esk55_4 @ X1824 @ X1825 @ X1826 @ X1827)))|(~(in @ X1829 @ X1824)|(~(in @ X1830 @ X1825)|(~(in @ (kpair @ X1829 @ X1830) @ X1827)|(in @ (kpair @ X1829 @ X1830) @ X1826))))|~(func @ X1824 @ X1825 @ X1827)|~(func @ X1824 @ X1825 @ X1826)))&((in @ esk58_0 @ (funcSet @ esk56_0 @ esk57_0))&((in @ esk59_0 @ esk56_0)&((in @ esk60_0 @ esk57_0)&((in @ (kpair @ esk59_0 @ esk60_0) @ esk58_0)&((ap @ esk56_0 @ esk57_0 @ esk58_0 @ esk59_0)!=(esk60_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_247])])])])])])])).
% 205.15/30.12 thf(c_0_249, negated_conjecture, ![X3:$i, X2:$i, X7:$i, X5:$i, X4:$i]:((((ap @ X2 @ X3 @ X4 @ X5)=(X7))|~((func @ X2 @ X3 @ X4))|~((in @ X5 @ X2))|~((in @ X7 @ X3))|~((in @ (kpair @ X5 @ X7) @ X4)))), inference(split_conjunct,[status(thm)],[c_0_248])).
% 205.15/30.12 thf(c_0_250, negated_conjecture, (in @ (kpair @ esk59_0 @ esk60_0) @ esk58_0), inference(split_conjunct,[status(thm)],[c_0_248])).
% 205.15/30.12 thf(c_0_251, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((func @ X3 @ X4 @ X2)|~((in @ X2 @ (funcSet @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_248])).
% 205.15/30.12 thf(c_0_252, negated_conjecture, (in @ esk58_0 @ (funcSet @ esk56_0 @ esk57_0)), inference(split_conjunct,[status(thm)],[c_0_248])).
% 205.15/30.12 thf(c_0_253, negated_conjecture, ((ap @ esk56_0 @ esk57_0 @ esk58_0 @ esk59_0)!=(esk60_0)), inference(split_conjunct,[status(thm)],[c_0_248])).
% 205.15/30.12 thf(c_0_254, negated_conjecture, ![X3:$i, X2:$i]:((((ap @ X2 @ X3 @ esk58_0 @ esk59_0)=(esk60_0))|~((func @ X2 @ X3 @ esk58_0))|~((in @ esk60_0 @ X3))|~((in @ esk59_0 @ X2)))), inference(spm,[status(thm)],[c_0_249, c_0_250])).
% 205.15/30.12 thf(c_0_255, negated_conjecture, (func @ esk56_0 @ esk57_0 @ esk58_0), inference(spm,[status(thm)],[c_0_251, c_0_252])).
% 205.15/30.12 thf(c_0_256, negated_conjecture, (in @ esk60_0 @ esk57_0), inference(split_conjunct,[status(thm)],[c_0_248])).
% 205.15/30.12 thf(c_0_257, negated_conjecture, (in @ esk59_0 @ esk56_0), inference(split_conjunct,[status(thm)],[c_0_248])).
% 205.15/30.12 thf(c_0_258, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_253, c_0_254]), c_0_255]), c_0_256]), c_0_257])]), ['proof']).
% 205.15/30.12 % SZS output end CNFRefutation
% 205.15/30.12 % Parsed axioms : 453
% 205.15/30.12 % Removed by relevancy pruning/SinE : 249
% 205.15/30.12 % Initial clauses : 319
% 205.15/30.12 % Removed in clause preprocessing : 26
% 205.15/30.12 % Initial clauses in saturation : 293
% 205.15/30.12 % Processed clauses : 2084
% 205.15/30.12 % ...of these trivial : 35
% 205.15/30.12 % ...subsumed : 635
% 205.15/30.12 % ...remaining for further processing : 1414
% 205.15/30.12 % Other redundant clauses eliminated : 83
% 205.15/30.12 % Clauses deleted for lack of memory : 0
% 205.15/30.12 % Backward-subsumed : 48
% 205.15/30.12 % Backward-rewritten : 19
% 205.15/30.12 % Generated clauses : 45922
% 205.15/30.12 % ...of the previous two non-redundant : 44694
% 205.15/30.12 % ...aggressively subsumed : 0
% 205.15/30.12 % Contextual simplify-reflections : 3
% 205.15/30.12 % Paramodulations : 45820
% 205.15/30.12 % Factorizations : 2
% 205.15/30.12 % NegExts : 2
% 205.15/30.12 % Equation resolutions : 88
% 205.15/30.12 % Disequality decompositions : 0
% 205.15/30.12 % Total rewrite steps : 1917
% 205.15/30.12 % ...of those cached : 1676
% 205.15/30.12 % Propositional unsat checks : 0
% 205.15/30.12 % Propositional check models : 0
% 205.15/30.12 % Propositional check unsatisfiable : 0
% 205.15/30.12 % Propositional clauses : 0
% 205.15/30.12 % Propositional clauses after purity: 0
% 205.15/30.12 % Propositional unsat core size : 0
% 205.15/30.12 % Propositional preprocessing time : 0.000
% 205.15/30.12 % Propositional encoding time : 0.000
% 205.15/30.12 % Propositional solver time : 0.000
% 205.15/30.12 % Success case prop preproc time : 0.000
% 205.15/30.12 % Success case prop encoding time : 0.000
% 205.15/30.12 % Success case prop solver time : 0.000
% 205.15/30.12 % Current number of processed clauses : 1079
% 205.15/30.12 % Positive orientable unit clauses : 104
% 205.15/30.12 % Positive unorientable unit clauses: 0
% 205.15/30.12 % Negative unit clauses : 41
% 205.15/30.12 % Non-unit-clauses : 934
% 205.15/30.12 % Current number of unprocessed clauses: 42998
% 205.15/30.12 % ...number of literals in the above : 141060
% 205.15/30.12 % Current number of archived formulas : 0
% 205.15/30.12 % Current number of archived clauses : 322
% 205.15/30.12 % Clause-clause subsumption calls (NU) : 96307
% 205.15/30.12 % Rec. Clause-clause subsumption calls : 72416
% 205.15/30.12 % Non-unit clause-clause subsumptions : 304
% 205.15/30.12 % Unit Clause-clause subsumption calls : 7559
% 205.15/30.12 % Rewrite failures with RHS unbound : 0
% 205.15/30.12 % BW rewrite match attempts : 38
% 205.15/30.12 % BW rewrite match successes : 13
% 205.15/30.12 % Condensation attempts : 2084
% 205.15/30.12 % Condensation successes : 14
% 205.15/30.12 % Termbank termtop insertions : 777736
% 205.15/30.12 % Search garbage collected termcells : 18804
% 205.15/30.12
% 205.15/30.12 % -------------------------------------------------
% 205.15/30.12 % User time : 28.473 s
% 205.15/30.12 % System time : 0.865 s
% 205.15/30.12 % Total time : 29.338 s
% 205.15/30.12 % Maximum resident set size: 7896 pages
% 205.15/30.12
% 205.15/30.12 % -------------------------------------------------
% 205.15/30.12 % User time : 28.497 s
% 205.15/30.12 % System time : 0.874 s
% 205.15/30.12 % Total time : 29.371 s
% 205.15/30.12 % Maximum resident set size: 5376 pages
% 205.15/30.12 % E exiting
%------------------------------------------------------------------------------