%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU740^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 08:27:36 AM UTC 2026
% Result : Theorem 0.49s 0.47s
% Output : CNFRefutation 0.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU740^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n005.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 14:19:01 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.20/0.29 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p
% 0.49/0.47 % Version: 3.5.1-ho
% 0.49/0.47 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.49/0.47 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.49/0.47 % Starting ehoh_best5 with 300s (1) cores
% 0.49/0.47 % Starting almost_fo_3_lam with 300s (1) cores
% 0.49/0.47 % Starting new_bool_5 with 300s (1) cores
% 0.49/0.47 % Starting pre_casc_3 with 300s (1) cores
% 0.49/0.47 % Starting ho_unfolding_8 with 300s (1) cores
% 0.49/0.47 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.49/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.49/0.47 % Starting new_ho_5 with 300s (1) cores
% 0.49/0.47 % ho_unfolding_8 with pid 1733611 completed with status 0
% 0.49/0.47 % Result found by ho_unfolding_8
% 0.49/0.47 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.49/0.47 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.49/0.47 % Starting ehoh_best5 with 300s (1) cores
% 0.49/0.47 % Starting almost_fo_3_lam with 300s (1) cores
% 0.49/0.47 % Starting new_bool_5 with 300s (1) cores
% 0.49/0.47 % Starting pre_casc_3 with 300s (1) cores
% 0.49/0.47 % Starting ho_unfolding_8 with 300s (1) cores
% 0.49/0.47 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.49/0.47 % No SInE strategy applied
% 0.49/0.47 % Search class: HGHSM-FSLM32-MHFMMSBN
% 0.49/0.47 % Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 0.49/0.47 % Starting SubtermCWHack with 31s (1) cores
% 0.49/0.47 % SubtermCWHack with pid 1733633 completed with status 0
% 0.49/0.47 % Result found by SubtermCWHack
% 0.49/0.47 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.49/0.47 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.49/0.47 % Starting ehoh_best5 with 300s (1) cores
% 0.49/0.47 % Starting almost_fo_3_lam with 300s (1) cores
% 0.49/0.47 % Starting new_bool_5 with 300s (1) cores
% 0.49/0.47 % Starting pre_casc_3 with 300s (1) cores
% 0.49/0.47 % Starting ho_unfolding_8 with 300s (1) cores
% 0.49/0.47 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.49/0.47 % No SInE strategy applied
% 0.49/0.47 % Search class: HGHSM-FSLM32-MHFMMSBN
% 0.49/0.47 % Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 0.49/0.47 % Starting SubtermCWHack with 31s (1) cores
% 0.49/0.47 % Preprocessing time : 0.004 s
% 0.49/0.47
% 0.49/0.47 % Proof found!
% 0.49/0.47 % SZS status Theorem
% 0.49/0.47 % SZS output start CNFRefutation
% 0.49/0.47 thf(decl_23, type, in: $i > $i > $o).
% 0.49/0.47 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.49/0.47 thf(decl_25, type, setextAx: $o).
% 0.49/0.47 thf(decl_26, type, emptyset: $i).
% 0.49/0.47 thf(decl_27, type, emptysetAx: $o).
% 0.49/0.47 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.49/0.47 thf(decl_29, type, setadjoinAx: $o).
% 0.49/0.47 thf(decl_30, type, powerset: $i > $i).
% 0.49/0.47 thf(decl_31, type, powersetAx: $o).
% 0.49/0.47 thf(decl_32, type, setunion: $i > $i).
% 0.49/0.47 thf(decl_33, type, setunionAx: $o).
% 0.49/0.47 thf(decl_34, type, omega: $i).
% 0.49/0.47 thf(decl_35, type, omega0Ax: $o).
% 0.49/0.47 thf(decl_36, type, omegaSAx: $o).
% 0.49/0.47 thf(decl_37, type, omegaIndAx: $o).
% 0.49/0.47 thf(decl_38, type, replAx: $o).
% 0.49/0.47 thf(decl_39, type, foundationAx: $o).
% 0.49/0.47 thf(decl_40, type, wellorderingAx: $o).
% 0.49/0.47 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.49/0.47 thf(decl_42, type, descrp: $o).
% 0.49/0.47 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.49/0.47 thf(decl_44, type, dsetconstrI: $o).
% 0.49/0.47 thf(decl_45, type, dsetconstrEL: $o).
% 0.49/0.47 thf(decl_46, type, dsetconstrER: $o).
% 0.49/0.47 thf(decl_47, type, exuE1: $o).
% 0.49/0.47 thf(decl_48, type, prop2set: $o > $i).
% 0.49/0.47 thf(decl_49, type, prop2setE: $o).
% 0.49/0.47 thf(decl_50, type, emptysetE: $o).
% 0.49/0.47 thf(decl_51, type, emptysetimpfalse: $o).
% 0.49/0.47 thf(decl_52, type, notinemptyset: $o).
% 0.49/0.47 thf(decl_53, type, exuE3e: $o).
% 0.49/0.47 thf(decl_54, type, setext: $o).
% 0.49/0.47 thf(decl_55, type, emptyI: $o).
% 0.49/0.47 thf(decl_56, type, noeltsimpempty: $o).
% 0.49/0.47 thf(decl_57, type, setbeta: $o).
% 0.49/0.47 thf(decl_58, type, nonempty: $i > $o).
% 0.49/0.47 thf(decl_59, type, nonemptyE1: $o).
% 0.49/0.47 thf(decl_60, type, nonemptyI: $o).
% 0.49/0.47 thf(decl_61, type, nonemptyI1: $o).
% 0.49/0.47 thf(decl_62, type, setadjoinIL: $o).
% 0.49/0.47 thf(decl_63, type, emptyinunitempty: $o).
% 0.49/0.47 thf(decl_64, type, setadjoinIR: $o).
% 0.49/0.47 thf(decl_65, type, setadjoinE: $o).
% 0.49/0.47 thf(decl_66, type, setadjoinOr: $o).
% 0.49/0.47 thf(decl_67, type, setoftrueEq: $o).
% 0.49/0.47 thf(decl_68, type, powersetI: $o).
% 0.49/0.47 thf(decl_69, type, emptyinPowerset: $o).
% 0.49/0.47 thf(decl_70, type, emptyInPowerset: $o).
% 0.49/0.47 thf(decl_71, type, powersetE: $o).
% 0.49/0.47 thf(decl_72, type, setunionI: $o).
% 0.49/0.47 thf(decl_73, type, setunionE: $o).
% 0.49/0.47 thf(decl_74, type, subPowSU: $o).
% 0.49/0.47 thf(decl_75, type, exuE2: $o).
% 0.49/0.47 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.49/0.47 thf(decl_77, type, uniqinunit: $o).
% 0.49/0.47 thf(decl_78, type, notinsingleton: $o).
% 0.49/0.47 thf(decl_79, type, eqinunit: $o).
% 0.49/0.47 thf(decl_80, type, singletonsswitch: $o).
% 0.49/0.47 thf(decl_81, type, upairsetE: $o).
% 0.49/0.47 thf(decl_82, type, upairsetIL: $o).
% 0.49/0.47 thf(decl_83, type, upairsetIR: $o).
% 0.49/0.47 thf(decl_84, type, emptyE1: $o).
% 0.49/0.47 thf(decl_85, type, vacuousDall: $o).
% 0.49/0.47 thf(decl_86, type, quantDeMorgan1: $o).
% 0.49/0.47 thf(decl_87, type, quantDeMorgan2: $o).
% 0.49/0.47 thf(decl_88, type, quantDeMorgan3: $o).
% 0.49/0.47 thf(decl_89, type, quantDeMorgan4: $o).
% 0.49/0.47 thf(decl_90, type, prop2setI: $o).
% 0.49/0.47 thf(decl_91, type, set2prop: $i > $o).
% 0.49/0.47 thf(decl_92, type, prop2set2propI: $o).
% 0.49/0.47 thf(decl_93, type, notdexE: $o).
% 0.49/0.47 thf(decl_94, type, notdallE: $o).
% 0.49/0.47 thf(decl_95, type, exuI1: $o).
% 0.49/0.47 thf(decl_96, type, exuI3: $o).
% 0.49/0.47 thf(decl_97, type, exuI2: $o).
% 0.49/0.47 thf(decl_98, type, inCongP: $o).
% 0.49/0.47 thf(decl_99, type, in__Cong: $o).
% 0.49/0.47 thf(decl_100, type, exuE3u: $o).
% 0.49/0.47 thf(decl_101, type, exu__Cong: $o).
% 0.49/0.47 thf(decl_102, type, emptyset__Cong: $o).
% 0.49/0.47 thf(decl_103, type, setadjoin__Cong: $o).
% 0.49/0.47 thf(decl_104, type, powerset__Cong: $o).
% 0.49/0.47 thf(decl_105, type, setunion__Cong: $o).
% 0.49/0.47 thf(decl_106, type, omega__Cong: $o).
% 0.49/0.47 thf(decl_107, type, exuEu: $o).
% 0.49/0.47 thf(decl_108, type, descr__Cong: $o).
% 0.49/0.47 thf(decl_109, type, dsetconstr__Cong: $o).
% 0.49/0.47 thf(decl_110, type, subset: $i > $i > $o).
% 0.49/0.47 thf(decl_113, type, subsetI1: $o).
% 0.49/0.47 thf(decl_114, type, eqimpsubset2: $o).
% 0.49/0.47 thf(decl_115, type, eqimpsubset1: $o).
% 0.49/0.47 thf(decl_116, type, subsetI2: $o).
% 0.49/0.47 thf(decl_117, type, emptysetsubset: $o).
% 0.49/0.47 thf(decl_118, type, subsetE: $o).
% 0.49/0.47 thf(decl_119, type, subsetE2: $o).
% 0.49/0.47 thf(decl_120, type, notsubsetI: $o).
% 0.49/0.47 thf(decl_121, type, notequalI1: $o).
% 0.49/0.47 thf(decl_122, type, notequalI2: $o).
% 0.49/0.47 thf(decl_123, type, subsetRefl: $o).
% 0.49/0.47 thf(decl_124, type, subsetTrans: $o).
% 0.49/0.47 thf(decl_125, type, setadjoinSub: $o).
% 0.49/0.47 thf(decl_126, type, setadjoinSub2: $o).
% 0.49/0.47 thf(decl_127, type, subset2powerset: $o).
% 0.49/0.47 thf(decl_128, type, setextsub: $o).
% 0.49/0.47 thf(decl_129, type, subsetemptysetimpeq: $o).
% 0.49/0.47 thf(decl_130, type, powersetI1: $o).
% 0.49/0.47 thf(decl_131, type, powersetE1: $o).
% 0.49/0.47 thf(decl_132, type, inPowerset: $o).
% 0.49/0.47 thf(decl_133, type, powersetsubset: $o).
% 0.49/0.47 thf(decl_134, type, sepInPowerset: $o).
% 0.49/0.47 thf(decl_135, type, sepSubset: $o).
% 0.49/0.47 thf(decl_136, type, binunion: $i > $i > $i).
% 0.49/0.47 thf(decl_137, type, binunionIL: $o).
% 0.49/0.47 thf(decl_138, type, upairset2IR: $o).
% 0.49/0.47 thf(decl_139, type, binunionIR: $o).
% 0.49/0.47 thf(decl_140, type, binunionEcases: $o).
% 0.49/0.47 thf(decl_141, type, binunionE: $o).
% 0.49/0.47 thf(decl_142, type, binunionLsub: $o).
% 0.49/0.47 thf(decl_143, type, binunionRsub: $o).
% 0.49/0.47 thf(decl_144, type, binintersect: $i > $i > $i).
% 0.49/0.47 thf(decl_145, type, binintersectI: $o).
% 0.49/0.47 thf(decl_146, type, binintersectSubset5: $o).
% 0.49/0.47 thf(decl_147, type, binintersectEL: $o).
% 0.49/0.47 thf(decl_148, type, binintersectLsub: $o).
% 0.49/0.47 thf(decl_149, type, binintersectSubset2: $o).
% 0.49/0.47 thf(decl_150, type, binintersectSubset3: $o).
% 0.49/0.47 thf(decl_151, type, binintersectER: $o).
% 0.49/0.47 thf(decl_152, type, disjointsetsI1: $o).
% 0.49/0.47 thf(decl_153, type, binintersectRsub: $o).
% 0.49/0.47 thf(decl_154, type, binintersectSubset4: $o).
% 0.49/0.47 thf(decl_155, type, binintersectSubset1: $o).
% 0.49/0.47 thf(decl_156, type, bs114d: $o).
% 0.49/0.47 thf(decl_158, type, setminus: $i > $i > $i).
% 0.49/0.47 thf(decl_159, type, setminusI: $o).
% 0.49/0.47 thf(decl_160, type, setminusEL: $o).
% 0.49/0.47 thf(decl_161, type, setminusER: $o).
% 0.49/0.47 thf(decl_162, type, setminusSubset2: $o).
% 0.49/0.47 thf(decl_163, type, setminusERneg: $o).
% 0.49/0.47 thf(decl_164, type, setminusELneg: $o).
% 0.49/0.47 thf(decl_165, type, setminusILneg: $o).
% 0.49/0.47 thf(decl_166, type, setminusIRneg: $o).
% 0.49/0.47 thf(decl_167, type, setminusLsub: $o).
% 0.49/0.47 thf(decl_168, type, setminusSubset1: $o).
% 0.49/0.47 thf(decl_169, type, symdiff: $i > $i > $i).
% 0.49/0.47 thf(decl_170, type, symdiffE: $o).
% 0.49/0.47 thf(decl_171, type, symdiffI1: $o).
% 0.49/0.47 thf(decl_172, type, symdiffI2: $o).
% 0.49/0.47 thf(decl_173, type, symdiffIneg1: $o).
% 0.49/0.47 thf(decl_174, type, symdiffIneg2: $o).
% 0.49/0.47 thf(decl_175, type, iskpair: $i > $o).
% 0.49/0.47 thf(decl_176, type, secondinupair: $o).
% 0.49/0.47 thf(decl_177, type, setukpairIL: $o).
% 0.49/0.47 thf(decl_178, type, setukpairIR: $o).
% 0.49/0.47 thf(decl_179, type, kpairiskpair: $o).
% 0.49/0.47 thf(decl_180, type, kpair: $i > $i > $i).
% 0.49/0.47 thf(decl_181, type, kpairp: $o).
% 0.49/0.47 thf(decl_182, type, cartprod: $i > $i > $i).
% 0.49/0.47 thf(decl_183, type, singletonsubset: $o).
% 0.49/0.47 thf(decl_184, type, singletoninpowerset: $o).
% 0.49/0.47 thf(decl_185, type, singletoninpowunion: $o).
% 0.49/0.47 thf(decl_186, type, upairset2E: $o).
% 0.49/0.47 thf(decl_187, type, upairsubunion: $o).
% 0.49/0.47 thf(decl_188, type, upairinpowunion: $o).
% 0.49/0.47 thf(decl_189, type, ubforcartprodlem1: $o).
% 0.49/0.47 thf(decl_190, type, ubforcartprodlem2: $o).
% 0.49/0.47 thf(decl_191, type, ubforcartprodlem3: $o).
% 0.49/0.47 thf(decl_192, type, cartprodpairin: $o).
% 0.49/0.47 thf(decl_193, type, cartprodmempair1: $o).
% 0.49/0.47 thf(decl_194, type, cartprodmempair: $o).
% 0.49/0.47 thf(decl_195, type, setunionE2: $o).
% 0.49/0.47 thf(decl_196, type, setunionsingleton1: $o).
% 0.49/0.47 thf(decl_197, type, setunionsingleton2: $o).
% 0.49/0.47 thf(decl_198, type, setunionsingleton: $o).
% 0.49/0.47 thf(decl_199, type, singleton: $i > $o).
% 0.49/0.47 thf(decl_200, type, singletonprop: $o).
% 0.49/0.47 thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 0.49/0.47 thf(decl_202, type, ex1E1: $o).
% 0.49/0.47 thf(decl_203, type, ex1I: $o).
% 0.49/0.47 thf(decl_204, type, ex1I2: $o).
% 0.49/0.47 thf(decl_205, type, singletonsuniq: $o).
% 0.49/0.47 thf(decl_210, type, setukpairinjL1: $o).
% 0.49/0.47 thf(decl_211, type, kfstsingleton: $o).
% 0.49/0.47 thf(decl_212, type, theprop: $o).
% 0.49/0.47 thf(decl_213, type, kfst: $i > $i).
% 0.49/0.47 thf(decl_214, type, kfstpairEq: $o).
% 0.49/0.47 thf(decl_215, type, cartprodfstin: $o).
% 0.49/0.47 thf(decl_216, type, setukpairinjL2: $o).
% 0.49/0.47 thf(decl_217, type, setukpairinjL: $o).
% 0.49/0.47 thf(decl_218, type, setukpairinjR11: $o).
% 0.49/0.47 thf(decl_219, type, setukpairinjR12: $o).
% 0.49/0.47 thf(decl_220, type, setukpairinjR1: $o).
% 0.49/0.47 thf(decl_221, type, upairequniteq: $o).
% 0.49/0.47 thf(decl_222, type, setukpairinjR2: $o).
% 0.49/0.47 thf(decl_223, type, setukpairinjR: $o).
% 0.49/0.47 thf(decl_224, type, ksndsingleton: $o).
% 0.49/0.47 thf(decl_225, type, ksnd: $i > $i).
% 0.49/0.47 thf(decl_226, type, ksndpairEq: $o).
% 0.49/0.47 thf(decl_227, type, kpairsurjEq: $o).
% 0.49/0.47 thf(decl_228, type, cartprodsndin: $o).
% 0.49/0.47 thf(decl_229, type, cartprodpairmemEL: $o).
% 0.49/0.47 thf(decl_230, type, cartprodpairmemER: $o).
% 0.49/0.47 thf(decl_231, type, cartprodmempaircEq: $o).
% 0.49/0.47 thf(decl_232, type, cartprodfstpairEq: $o).
% 0.49/0.47 thf(decl_233, type, cartprodsndpairEq: $o).
% 0.49/0.47 thf(decl_234, type, cartprodpairsurjEq: $o).
% 0.49/0.47 thf(decl_235, type, breln: $i > $i > $i > $o).
% 0.49/0.47 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 0.49/0.47 thf(decl_237, type, dpsetconstrI: $o).
% 0.49/0.47 thf(decl_238, type, dpsetconstrSub: $o).
% 0.49/0.47 thf(decl_239, type, setOfPairsIsBReln: $o).
% 0.49/0.47 thf(decl_240, type, dpsetconstrERa: $o).
% 0.49/0.47 thf(decl_241, type, dpsetconstrEL1: $o).
% 0.49/0.47 thf(decl_242, type, dpsetconstrEL2: $o).
% 0.49/0.47 thf(decl_243, type, dpsetconstrER: $o).
% 0.49/0.47 thf(decl_244, type, func: $i > $i > $i > $o).
% 0.49/0.47 thf(decl_245, type, funcSet: $i > $i > $i).
% 0.49/0.47 thf(decl_246, type, funcImageSingleton: $o).
% 0.49/0.47 thf(decl_247, type, apProp: $o).
% 0.49/0.47 thf(decl_248, type, ap: $i > $i > $i > $i > $i).
% 0.49/0.47 thf(decl_249, type, app: $o).
% 0.49/0.47 thf(decl_250, type, infuncsetfunc: $o).
% 0.49/0.47 thf(decl_251, type, ap2p: $o).
% 0.49/0.47 thf(decl_252, type, funcinfuncset: $o).
% 0.49/0.47 thf(decl_253, type, lamProp: $o).
% 0.49/0.47 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
% 0.49/0.47 thf(decl_255, type, lamp: $o).
% 0.49/0.47 thf(decl_256, type, lam2p: $o).
% 0.49/0.47 thf(decl_257, type, brelnall1: $o).
% 0.49/0.47 thf(decl_258, type, brelnall2: $o).
% 0.49/0.47 thf(decl_259, type, ex1E2: $o).
% 0.49/0.47 thf(decl_260, type, funcGraphProp1: $o).
% 0.49/0.47 thf(decl_261, type, funcGraphProp3: $o).
% 0.49/0.47 thf(decl_262, type, funcGraphProp2: $o).
% 0.49/0.47 thf(decl_263, type, funcextLem: $o).
% 0.49/0.47 thf(decl_264, type, funcGraphProp4: $o).
% 0.49/0.47 thf(decl_265, type, subbreln: $o).
% 0.49/0.47 thf(decl_266, type, eqbreln: $o).
% 0.49/0.47 thf(decl_267, type, funcext: $o).
% 0.49/0.47 thf(decl_268, type, funcext2: $o).
% 0.49/0.47 thf(decl_269, type, ap2apEq1: $o).
% 0.49/0.47 thf(decl_270, type, ap2apEq2: $o).
% 0.49/0.47 thf(decl_271, type, beta1: $o).
% 0.49/0.47 thf(decl_272, type, eta1: $o).
% 0.49/0.47 thf(decl_273, type, lam2lamEq: $o).
% 0.49/0.47 thf(decl_274, type, beta2: $o).
% 0.49/0.47 thf(decl_275, type, eta2: $o).
% 0.49/0.47 thf(decl_276, type, iffalseProp1: $o).
% 0.49/0.47 thf(decl_277, type, iffalseProp2: $o).
% 0.49/0.47 thf(decl_278, type, iftrueProp1: $o).
% 0.49/0.47 thf(decl_279, type, iftrueProp2: $o).
% 0.49/0.47 thf(decl_280, type, ifSingleton: $o).
% 0.49/0.47 thf(decl_281, type, if: $i > $o > $i > $i > $i).
% 0.49/0.47 thf(decl_282, type, ifp: $o).
% 0.49/0.47 thf(decl_283, type, theeq: $o).
% 0.49/0.47 thf(decl_284, type, iftrue: $o).
% 0.49/0.47 thf(decl_285, type, iffalse: $o).
% 0.49/0.47 thf(decl_286, type, iftrueorfalse: $o).
% 0.49/0.47 thf(decl_287, type, binintersectT_lem: $o).
% 0.49/0.47 thf(decl_288, type, binunionT_lem: $o).
% 0.49/0.47 thf(decl_289, type, powersetT_lem: $o).
% 0.49/0.47 thf(decl_290, type, setminusT_lem: $o).
% 0.49/0.47 thf(decl_291, type, complementT_lem: $o).
% 0.49/0.47 thf(decl_292, type, setextT: $o).
% 0.49/0.47 thf(decl_293, type, subsetTI: $o).
% 0.49/0.47 thf(decl_294, type, powersetTI1: $o).
% 0.49/0.47 thf(decl_295, type, powersetTE1: $o).
% 0.49/0.47 thf(decl_296, type, complementTI1: $o).
% 0.49/0.47 thf(decl_297, type, complementTE1: $o).
% 0.49/0.47 thf(decl_298, type, binintersectTELcontra: $o).
% 0.49/0.47 thf(decl_299, type, binintersectTERcontra: $o).
% 0.49/0.47 thf(decl_300, type, contrasubsetT: $o).
% 0.49/0.47 thf(decl_301, type, contrasubsetT1: $o).
% 0.49/0.47 thf(decl_302, type, contrasubsetT2: $o).
% 0.49/0.47 thf(decl_303, type, contrasubsetT3: $o).
% 0.49/0.47 thf(decl_304, type, doubleComplementI1: $o).
% 0.49/0.47 thf(decl_305, type, doubleComplementE1: $o).
% 0.49/0.47 thf(decl_306, type, doubleComplementSub1: $o).
% 0.49/0.47 thf(decl_307, type, doubleComplementSub2: $o).
% 0.49/0.47 thf(decl_308, type, doubleComplementEq: $o).
% 0.49/0.47 thf(decl_309, type, complementTnotintersectT: $o).
% 0.49/0.47 thf(decl_310, type, complementImpComplementIntersect: $o).
% 0.49/0.47 thf(decl_311, type, complementSubsetComplementIntersect: $o).
% 0.49/0.47 thf(decl_312, type, complementInPowersetComplementIntersect: $o).
% 0.49/0.47 thf(decl_313, type, contraSubsetComplement: $o).
% 0.49/0.47 thf(decl_314, type, complementTcontraSubset: $o).
% 0.49/0.47 thf(decl_315, type, binunionTILcontra: $o).
% 0.49/0.47 thf(decl_316, type, binunionTIRcontra: $o).
% 0.49/0.47 thf(decl_317, type, epred1_0: $o).
% 0.49/0.47 thf(decl_318, type, esk1_2: $i > $i > $i).
% 0.49/0.47 thf(decl_319, type, esk2_2: $i > $i > $i).
% 0.49/0.47 thf(decl_320, type, esk3_2: $i > $i > $i).
% 0.49/0.47 thf(decl_321, type, esk4_1: $i > $i).
% 0.49/0.47 thf(decl_322, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.49/0.47 thf(decl_323, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.49/0.47 thf(decl_324, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.49/0.47 thf(decl_325, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.49/0.47 thf(decl_326, type, esk9_1: $i > $i).
% 0.49/0.47 thf(decl_327, type, esk10_2: ($i > $o) > $i > $i).
% 0.49/0.47 thf(decl_328, type, esk11_2: ($i > $o) > $i > $i).
% 0.49/0.47 thf(decl_329, type, esk12_1: ($i > $o) > $i).
% 0.49/0.47 thf(decl_330, type, esk13_2: ($i > $o) > $i > $i).
% 0.49/0.47 thf(decl_331, type, esk14_1: ($i > $o) > $i).
% 0.49/0.47 thf(decl_332, type, esk15_2: $i > $i > $i).
% 0.49/0.47 thf(decl_333, type, esk16_2: $i > $i > $i).
% 0.49/0.47 thf(decl_334, type, esk17_1: $i > $i).
% 0.49/0.47 thf(decl_335, type, esk18_1: $i > $i).
% 0.49/0.47 thf(decl_336, type, esk19_1: $i > $i).
% 0.49/0.47 thf(decl_337, type, esk20_2: $i > $i > $i).
% 0.49/0.47 thf(decl_338, type, esk21_3: $i > $i > $o > $i).
% 0.49/0.47 thf(decl_339, type, esk22_2: ($i > $o) > $i > $i).
% 0.49/0.47 thf(decl_340, type, esk23_1: ($i > $o) > $i).
% 0.49/0.47 thf(decl_341, type, esk24_1: $i > $i).
% 0.49/0.47 thf(decl_342, type, esk25_2: $i > ($i > $o) > $i).
% 0.49/0.47 thf(decl_343, type, esk26_2: $i > ($i > $o) > $i).
% 0.49/0.47 thf(decl_344, type, esk27_2: $i > ($i > $o) > $i).
% 0.49/0.47 thf(decl_345, type, esk28_2: $i > ($i > $o) > $i).
% 0.49/0.47 thf(decl_346, type, esk29_2: $i > ($i > $o) > $i).
% 0.49/0.47 thf(decl_347, type, esk30_2: $i > ($i > $o) > $i).
% 0.49/0.47 thf(decl_348, type, esk31_2: ($i > $o) > $i > $i).
% 0.49/0.47 thf(decl_349, type, esk32_1: ($i > $o) > $i).
% 0.49/0.47 thf(decl_350, type, esk33_1: ($i > $o) > $i).
% 0.49/0.47 thf(decl_351, type, esk34_1: ($i > $o) > $i).
% 0.49/0.47 thf(decl_352, type, esk35_1: ($i > $o) > $i).
% 0.49/0.47 thf(decl_353, type, esk36_2: ($i > $o) > $i > $i).
% 0.49/0.47 thf(decl_354, type, esk37_1: ($i > $o) > $i).
% 0.49/0.47 thf(decl_355, type, esk38_2: ($i > $o) > $i > $i).
% 0.49/0.47 thf(decl_356, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 0.49/0.47 thf(decl_357, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 0.49/0.47 thf(decl_358, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.49/0.47 thf(decl_359, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 0.49/0.47 thf(decl_360, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.49/0.47 thf(decl_361, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 0.49/0.47 thf(decl_362, type, esk45_2: ($i > $o) > $i > $i).
% 0.49/0.47 thf(decl_363, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 0.49/0.47 thf(decl_364, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 0.49/0.47 thf(decl_365, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.49/0.47 thf(decl_366, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.49/0.47 thf(decl_367, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.49/0.47 thf(decl_368, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.49/0.47 thf(decl_369, type, esk52_2: $i > $i > $i).
% 0.49/0.47 thf(decl_370, type, esk53_2: $i > $i > $i).
% 0.49/0.47 thf(decl_371, type, esk54_2: $i > $i > $i).
% 0.49/0.47 thf(decl_372, type, esk55_3: $i > $i > $i > $i).
% 0.49/0.47 thf(decl_373, type, esk56_3: $i > $i > $i > $i).
% 0.49/0.47 thf(decl_374, type, esk57_2: $i > $i > $i).
% 0.49/0.47 thf(decl_375, type, esk58_2: $i > ($i > $o) > $i).
% 0.49/0.47 thf(decl_376, type, esk59_2: $i > ($i > $o) > $i).
% 0.49/0.47 thf(decl_377, type, esk60_2: $i > ($i > $o) > $i).
% 0.49/0.47 thf(decl_378, type, esk61_3: $i > ($i > $o) > $i > $i).
% 0.49/0.47 thf(decl_379, type, esk62_2: $i > ($i > $o) > $i).
% 0.49/0.47 thf(decl_380, type, esk63_2: $i > ($i > $o) > $i).
% 0.49/0.47 thf(decl_381, type, esk64_3: $i > $i > ($i > $i) > $i).
% 0.49/0.47 thf(decl_382, type, esk65_3: $i > $i > ($i > $i) > $i).
% 0.49/0.47 thf(decl_383, type, esk66_3: $i > $i > ($i > $i) > $i).
% 0.49/0.47 thf(decl_384, type, esk67_4: $i > $i > $i > ($i > $o) > $i).
% 0.49/0.47 thf(decl_385, type, esk68_4: $i > $i > $i > ($i > $o) > $i).
% 0.49/0.47 thf(decl_386, type, esk69_4: $i > $i > $i > ($i > $o) > $i).
% 0.49/0.47 thf(decl_387, type, esk70_4: $i > $i > $i > ($i > $o) > $i).
% 0.49/0.47 thf(decl_388, type, esk71_4: $i > $i > $i > $i > $i).
% 0.49/0.47 thf(decl_389, type, esk72_4: $i > $i > $i > $i > $i).
% 0.49/0.47 thf(decl_390, type, esk73_4: $i > $i > $i > $i > $i).
% 0.49/0.47 thf(decl_391, type, esk74_4: $i > $i > $i > $i > $i).
% 0.49/0.47 thf(decl_392, type, esk75_4: $i > $i > $i > $i > $i).
% 0.49/0.47 thf(decl_393, type, esk76_4: $i > $i > $i > $i > $i).
% 0.49/0.47 thf(decl_394, type, esk77_4: $i > $i > $i > $i > $i).
% 0.49/0.47 thf(decl_395, type, esk78_4: $i > $i > $i > $i > $i).
% 0.49/0.47 thf(decl_396, type, esk79_4: $i > $i > $i > $i > $i).
% 0.49/0.47 thf(decl_397, type, esk80_3: $i > $i > ($i > $i) > $i).
% 0.49/0.47 thf(decl_398, type, esk81_3: $i > $i > ($i > $i) > $i).
% 0.49/0.47 thf(decl_399, type, esk82_3: $i > $i > ($i > $i) > $i).
% 0.49/0.47 thf(decl_400, type, esk83_3: $i > $i > $i > $i).
% 0.49/0.47 thf(decl_401, type, esk84_3: $i > $i > $i > $i).
% 0.49/0.47 thf(decl_402, type, esk85_3: $i > $i > $i > $i).
% 0.49/0.47 thf(decl_403, type, esk86_3: $i > $i > $i > $i).
% 0.49/0.47 thf(decl_404, type, esk87_0: $i).
% 0.49/0.47 thf(decl_405, type, esk88_0: $i).
% 0.49/0.47 thf(decl_406, type, esk89_0: $i).
% 0.49/0.47 thf(decl_407, type, esk90_0: $i).
% 0.49/0.47 thf(decl_408, type, esk91_0: $i).
% 0.49/0.47 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', replAx)).
% 0.49/0.47 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', exu)).
% 0.49/0.47 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', descrp)).
% 0.49/0.47 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', exuE1)).
% 0.49/0.47 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', exuE3e)).
% 0.49/0.47 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', nonempty)).
% 0.49/0.47 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', nonemptyI)).
% 0.49/0.47 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', exuE2)).
% 0.49/0.47 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', exuI1)).
% 0.49/0.47 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', exuI3)).
% 0.49/0.47 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', exuI2)).
% 0.49/0.47 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', exuE3u)).
% 0.49/0.47 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', exu__Cong)).
% 0.49/0.47 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', exuEu)).
% 0.49/0.47 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', descr__Cong)).
% 0.49/0.47 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', ex1E1)).
% 0.49/0.47 thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', ex1)).
% 0.49/0.47 thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', ex1I)).
% 0.49/0.47 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', ex1I2)).
% 0.49/0.47 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setOfPairsIsBReln)).
% 0.49/0.47 thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', breln)).
% 0.49/0.47 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', ex1E2)).
% 0.49/0.47 thf(inIntersectImpInUnion, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>((subbreln)=>((eqbreln)=>((funcext)=>((funcext2)=>((ap2apEq1)=>((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>((beta2)=>((eta2)=>((iffalseProp1)=>((iffalseProp2)=>((iftrueProp1)=>((iftrueProp2)=>((ifSingleton)=>((ifp)=>((theeq)=>((iftrue)=>((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>((setminusT_lem)=>((complementT_lem)=>((setextT)=>((subsetTI)=>((powersetTI1)=>((powersetTE1)=>((complementTI1)=>((complementTE1)=>((binintersectTELcontra)=>((binintersectTERcontra)=>((contrasubsetT)=>((contrasubsetT1)=>((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>((doubleComplementE1)=>((doubleComplementSub1)=>((doubleComplementSub2)=>((doubleComplementEq)=>((complementTnotintersectT)=>((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>((complementInPowersetComplementIntersect)=>((contraSubsetComplement)=>((complementTcontraSubset)=>((binunionTILcontra)=>((binunionTIRcontra)=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', inIntersectImpInUnion)).
% 0.49/0.47 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', dsetconstrI)).
% 0.49/0.47 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', dsetconstrEL)).
% 0.49/0.47 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', dsetconstrER)).
% 0.49/0.47 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setbeta)).
% 0.49/0.47 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', nonemptyE1)).
% 0.49/0.47 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', nonemptyI1)).
% 0.49/0.47 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setoftrueEq)).
% 0.49/0.47 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', nonemptyImpWitness)).
% 0.49/0.47 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', emptyE1)).
% 0.49/0.47 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', dsetconstr__Cong)).
% 0.49/0.47 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', sepInPowerset)).
% 0.49/0.47 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', sepSubset)).
% 0.49/0.47 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', singletonprop)).
% 0.49/0.47 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', kfstsingleton)).
% 0.49/0.47 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', ksndsingleton)).
% 0.49/0.47 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', dpsetconstrI)).
% 0.49/0.47 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', dpsetconstrSub)).
% 0.49/0.47 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', dpsetconstrERa)).
% 0.49/0.47 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', dpsetconstrEL1)).
% 0.49/0.47 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', dpsetconstrEL2)).
% 0.49/0.47 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', dpsetconstrER)).
% 0.49/0.47 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', funcImageSingleton)).
% 0.49/0.47 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', apProp)).
% 0.49/0.47 thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X30 @ X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', lamProp)).
% 0.49/0.47 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', lamp)).
% 0.49/0.47 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', lam2p)).
% 0.49/0.47 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', brelnall1)).
% 0.49/0.47 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', brelnall2)).
% 0.49/0.47 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', subbreln)).
% 0.49/0.47 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', eqbreln)).
% 0.49/0.47 thf(beta1, axiom, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X36 @ X3))) @ X2)=(X36 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', beta1)).
% 0.49/0.47 thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', eta1)).
% 0.49/0.47 thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', lam2lamEq)).
% 0.49/0.47 thf(beta2, axiom, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X38 @ X3))) @ X2)=(X38 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', beta2)).
% 0.49/0.47 thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', eta2)).
% 0.49/0.47 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X39))&(((X14)=(X2)))))|(((~((X39)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', iffalseProp1)).
% 0.49/0.47 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X40))&(((X14)=(X2)))))|(((~((X40)))&(((X14)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', iffalseProp2)).
% 0.49/0.47 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X41))&(((X14)=(X2)))))|(((~((X41)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', iftrueProp1)).
% 0.49/0.47 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X42))&(((X14)=(X2)))))|(((~((X42)))&(((X14)=(X3)))))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', iftrueProp2)).
% 0.49/0.47 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X43))&(((X14)=(X2)))))|(((~((X43)))&(((X14)=(X3))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', ifSingleton)).
% 0.49/0.47 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setextAx)).
% 0.49/0.47 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', emptysetAx)).
% 0.49/0.47 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setadjoinAx)).
% 0.49/0.47 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', powersetAx)).
% 0.49/0.47 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setunionAx)).
% 0.49/0.47 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', omega0Ax)).
% 0.49/0.47 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', omegaSAx)).
% 0.49/0.47 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', omegaIndAx)).
% 0.49/0.47 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', foundationAx)).
% 0.49/0.47 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', wellorderingAx)).
% 0.49/0.47 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', prop2setE)).
% 0.49/0.47 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', emptysetE)).
% 0.49/0.47 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', emptysetimpfalse)).
% 0.49/0.47 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', notinemptyset)).
% 0.49/0.47 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setext)).
% 0.49/0.47 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', emptyI)).
% 0.49/0.47 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', noeltsimpempty)).
% 0.49/0.47 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setadjoinIL)).
% 0.49/0.47 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', emptyinunitempty)).
% 0.49/0.47 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setadjoinIR)).
% 0.49/0.47 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setadjoinE)).
% 0.49/0.47 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setadjoinOr)).
% 0.49/0.47 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', powersetI)).
% 0.49/0.47 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', emptyinPowerset)).
% 0.49/0.47 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', emptyInPowerset)).
% 0.49/0.47 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', powersetE)).
% 0.49/0.47 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setunionI)).
% 0.49/0.47 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setunionE)).
% 0.49/0.47 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', subPowSU)).
% 0.49/0.47 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', uniqinunit)).
% 0.49/0.47 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', notinsingleton)).
% 0.49/0.47 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', eqinunit)).
% 0.49/0.47 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', singletonsswitch)).
% 0.49/0.47 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', upairsetE)).
% 0.49/0.47 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', upairsetIL)).
% 0.49/0.47 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', upairsetIR)).
% 0.49/0.47 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', vacuousDall)).
% 0.49/0.47 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', quantDeMorgan1)).
% 0.49/0.47 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', quantDeMorgan2)).
% 0.49/0.47 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', quantDeMorgan3)).
% 0.49/0.47 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', quantDeMorgan4)).
% 0.49/0.47 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', prop2setI)).
% 0.49/0.47 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', prop2set2propI)).
% 0.49/0.47 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', notdexE)).
% 0.49/0.47 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', notdallE)).
% 0.49/0.47 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', inCongP)).
% 0.49/0.47 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', in__Cong)).
% 0.49/0.47 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', emptyset__Cong)).
% 0.49/0.47 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setadjoin__Cong)).
% 0.49/0.47 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', powerset__Cong)).
% 0.49/0.47 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setunion__Cong)).
% 0.49/0.47 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', omega__Cong)).
% 0.49/0.47 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', subsetI1)).
% 0.49/0.47 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', eqimpsubset2)).
% 0.49/0.47 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', eqimpsubset1)).
% 0.49/0.47 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', subsetI2)).
% 0.49/0.47 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', emptysetsubset)).
% 0.49/0.47 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', subsetE)).
% 0.49/0.47 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', subsetE2)).
% 0.49/0.47 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', notsubsetI)).
% 0.49/0.47 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', notequalI1)).
% 0.49/0.47 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', notequalI2)).
% 0.49/0.47 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', subsetRefl)).
% 0.49/0.47 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', subsetTrans)).
% 0.49/0.47 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setadjoinSub)).
% 0.49/0.47 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setadjoinSub2)).
% 0.49/0.47 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', subset2powerset)).
% 0.49/0.47 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setextsub)).
% 0.49/0.47 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', subsetemptysetimpeq)).
% 0.49/0.47 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', powersetI1)).
% 0.49/0.47 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', powersetE1)).
% 0.49/0.47 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', inPowerset)).
% 0.49/0.47 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', powersetsubset)).
% 0.49/0.47 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', binunionIL)).
% 0.49/0.47 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', upairset2IR)).
% 0.49/0.47 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', binunionIR)).
% 0.49/0.47 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', binunionEcases)).
% 0.49/0.47 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', binunionE)).
% 0.49/0.47 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', binunionLsub)).
% 0.49/0.47 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', binunionRsub)).
% 0.49/0.47 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', binintersectI)).
% 0.49/0.47 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', binintersectSubset5)).
% 0.49/0.47 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', binintersectEL)).
% 0.49/0.47 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', binintersectLsub)).
% 0.49/0.47 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', binintersectSubset2)).
% 0.49/0.47 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', binintersectSubset3)).
% 0.49/0.47 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', binintersectER)).
% 0.49/0.47 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', disjointsetsI1)).
% 0.49/0.47 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', binintersectRsub)).
% 0.49/0.47 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', binintersectSubset4)).
% 0.49/0.47 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', binintersectSubset1)).
% 0.49/0.47 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', bs114d)).
% 0.49/0.47 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setminusI)).
% 0.49/0.47 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setminusEL)).
% 0.49/0.47 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setminusER)).
% 0.49/0.47 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setminusSubset2)).
% 0.49/0.47 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setminusERneg)).
% 0.49/0.47 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setminusELneg)).
% 0.49/0.47 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setminusILneg)).
% 0.49/0.47 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setminusIRneg)).
% 0.49/0.47 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setminusLsub)).
% 0.49/0.47 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setminusSubset1)).
% 0.49/0.47 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', symdiffE)).
% 0.49/0.47 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', symdiffI1)).
% 0.49/0.47 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', symdiffI2)).
% 0.49/0.47 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', symdiffIneg1)).
% 0.49/0.47 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', symdiffIneg2)).
% 0.49/0.47 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', secondinupair)).
% 0.49/0.47 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setukpairIL)).
% 0.49/0.47 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setukpairIR)).
% 0.49/0.47 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', kpairiskpair)).
% 0.49/0.47 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', kpairp)).
% 0.49/0.47 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', singletonsubset)).
% 0.49/0.47 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', singletoninpowerset)).
% 0.49/0.47 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', singletoninpowunion)).
% 0.49/0.47 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', upairset2E)).
% 0.49/0.47 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', upairsubunion)).
% 0.49/0.47 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', upairinpowunion)).
% 0.49/0.47 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', ubforcartprodlem1)).
% 0.49/0.47 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', ubforcartprodlem2)).
% 0.49/0.47 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', ubforcartprodlem3)).
% 0.49/0.47 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', cartprodpairin)).
% 0.49/0.47 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', cartprodmempair1)).
% 0.49/0.47 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', cartprodmempair)).
% 0.49/0.47 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setunionE2)).
% 0.49/0.47 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setunionsingleton1)).
% 0.49/0.47 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setunionsingleton2)).
% 0.49/0.47 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setunionsingleton)).
% 0.49/0.47 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', singletonsuniq)).
% 0.49/0.47 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setukpairinjL1)).
% 0.49/0.47 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', theprop)).
% 0.49/0.47 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', kfstpairEq)).
% 0.49/0.47 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', cartprodfstin)).
% 0.49/0.47 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setukpairinjL2)).
% 0.49/0.47 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setukpairinjL)).
% 0.49/0.47 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setukpairinjR11)).
% 0.49/0.47 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setukpairinjR12)).
% 0.49/0.47 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setukpairinjR1)).
% 0.49/0.47 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', upairequniteq)).
% 0.49/0.47 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setukpairinjR2)).
% 0.49/0.47 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setukpairinjR)).
% 0.49/0.47 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', ksndpairEq)).
% 0.49/0.47 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', kpairsurjEq)).
% 0.49/0.47 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', cartprodsndin)).
% 0.49/0.47 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', cartprodpairmemEL)).
% 0.49/0.47 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', cartprodpairmemER)).
% 0.49/0.47 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', cartprodmempaircEq)).
% 0.49/0.47 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', cartprodfstpairEq)).
% 0.49/0.47 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', cartprodsndpairEq)).
% 0.49/0.47 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', cartprodpairsurjEq)).
% 0.49/0.47 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', app)).
% 0.49/0.47 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', infuncsetfunc)).
% 0.49/0.47 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', ap2p)).
% 0.49/0.47 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', funcinfuncset)).
% 0.49/0.47 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', funcGraphProp1)).
% 0.49/0.47 thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', funcGraphProp3)).
% 0.49/0.47 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', funcGraphProp2)).
% 0.49/0.47 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', funcextLem)).
% 0.49/0.47 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', funcGraphProp4)).
% 0.49/0.47 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', funcext)).
% 0.49/0.47 thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', funcext2)).
% 0.49/0.47 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', ap2apEq1)).
% 0.49/0.47 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', ap2apEq2)).
% 0.49/0.47 thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', ifp)).
% 0.49/0.47 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', theeq)).
% 0.49/0.47 thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', iftrue)).
% 0.49/0.47 thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', iffalse)).
% 0.49/0.47 thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', iftrueorfalse)).
% 0.49/0.47 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', binintersectT_lem)).
% 0.49/0.47 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', binunionT_lem)).
% 0.49/0.47 thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', powersetT_lem)).
% 0.49/0.47 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setminusT_lem)).
% 0.49/0.47 thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', complementT_lem)).
% 0.49/0.47 thf(setextT, axiom, ((setextT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', setextT)).
% 0.49/0.47 thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', subsetTI)).
% 0.49/0.47 thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', powersetTI1)).
% 0.49/0.47 thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', powersetTE1)).
% 0.49/0.47 thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', complementTI1)).
% 0.49/0.47 thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', complementTE1)).
% 0.49/0.47 thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', binintersectTELcontra)).
% 0.49/0.47 thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', binintersectTERcontra)).
% 0.49/0.47 thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', contrasubsetT)).
% 0.49/0.47 thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', contrasubsetT1)).
% 0.49/0.47 thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', contrasubsetT2)).
% 0.49/0.47 thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', contrasubsetT3)).
% 0.49/0.47 thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', doubleComplementI1)).
% 0.49/0.47 thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', doubleComplementE1)).
% 0.49/0.47 thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', doubleComplementSub1)).
% 0.49/0.47 thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', doubleComplementSub2)).
% 0.49/0.47 thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', doubleComplementEq)).
% 0.49/0.47 thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', complementTnotintersectT)).
% 0.49/0.47 thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', complementImpComplementIntersect)).
% 0.49/0.47 thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', complementSubsetComplementIntersect)).
% 0.49/0.47 thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', complementInPowersetComplementIntersect)).
% 0.49/0.47 thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', contraSubsetComplement)).
% 0.49/0.47 thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', complementTcontraSubset)).
% 0.49/0.47 thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', binunionTILcontra)).
% 0.49/0.47 thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.jN6CNbvCef/E---3.1_1733594.p', binunionTIRcontra)).
% 0.49/0.47 thf(c_0_261, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.49/0.47 thf(c_0_262, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.49/0.47 thf(c_0_263, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.49/0.47 thf(c_0_264, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.49/0.47 thf(c_0_265, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.49/0.47 thf(c_0_266, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.49/0.47 thf(c_0_267, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.49/0.47 thf(c_0_268, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.49/0.47 thf(c_0_269, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 0.49/0.47 thf(c_0_270, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.49/0.47 thf(c_0_271, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.49/0.47 thf(c_0_272, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 0.49/0.47 thf(c_0_273, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.49/0.47 thf(c_0_274, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 0.49/0.47 thf(c_0_275, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))=>((exu @ (^[Z0:$i]:((X17 @ Z0))))=>((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 0.49/0.47 thf(c_0_276, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 0.49/0.47 thf(c_0_277, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((singleton @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2)))))))), inference(fof_simplification,[status(thm)],[ex1])).
% 0.49/0.47 thf(c_0_278, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])).
% 0.49/0.47 thf(c_0_279, plain, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 0.49/0.47 thf(c_0_280, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 0.49/0.47 thf(c_0_281, plain, ((breln)=(^[Z0:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
% 0.49/0.47 thf(c_0_282, plain, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[ex1E2])).
% 0.49/0.47 thf(c_0_283, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>((subbreln)=>((eqbreln)=>((funcext)=>((funcext2)=>((ap2apEq1)=>((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>((beta2)=>((eta2)=>((iffalseProp1)=>((iffalseProp2)=>((iftrueProp1)=>((iftrueProp2)=>((ifSingleton)=>((ifp)=>((theeq)=>((iftrue)=>((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>((setminusT_lem)=>((complementT_lem)=>((setextT)=>((subsetTI)=>((powersetTI1)=>((powersetTE1)=>((complementTI1)=>((complementTE1)=>((binintersectTELcontra)=>((binintersectTERcontra)=>((contrasubsetT)=>((contrasubsetT1)=>((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>((doubleComplementE1)=>((doubleComplementSub1)=>((doubleComplementSub2)=>((doubleComplementEq)=>((complementTnotintersectT)=>((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>((complementInPowersetComplementIntersect)=>((contraSubsetComplement)=>((complementTcontraSubset)=>((binunionTILcontra)=>((binunionTIRcontra)=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[inIntersectImpInUnion])).
% 0.49/0.47 thf(c_0_284, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X850:$i]:(((((X6 @ X2 @ X850)))&(![X851:$i]:(((((X6 @ X2 @ X851)))=>(((X850)=(X851)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_261, c_0_262])).
% 0.49/0.47 thf(c_0_285, plain, ((descrp)=(![X1:$i > $o]:((((?[X852:$i]:(((((X1 @ X852)))&(![X853:$i]:(((((X1 @ X853)))=>(((X852)=(X853))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_263, c_0_262])).
% 0.49/0.47 thf(c_0_286, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.49/0.47 thf(c_0_287, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.49/0.47 thf(c_0_288, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.49/0.47 thf(c_0_289, plain, ((exuE1)=(![X1:$i > $o]:((((?[X854:$i]:(((((X1 @ X854)))&(![X855:$i]:(((((X1 @ X855)))=>(((X854)=(X855))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_264, c_0_262])).
% 0.49/0.47 thf(c_0_290, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X856:$i]:(((((X1 @ X856)))&(![X857:$i]:(((((X1 @ X857)))=>(((X856)=(X857))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_265, c_0_262])).
% 0.49/0.47 thf(c_0_291, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.49/0.47 thf(c_0_292, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_266])).
% 0.49/0.47 thf(c_0_293, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_267, c_0_266])).
% 0.49/0.47 thf(c_0_294, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_266])).
% 0.49/0.47 thf(c_0_295, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.49/0.47 thf(c_0_296, plain, ((exuE2)=(![X1:$i > $o]:((((?[X858:$i]:(((((X1 @ X858)))&(![X859:$i]:(((((X1 @ X859)))=>(((X858)=(X859))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_268, c_0_262])).
% 0.49/0.47 thf(c_0_297, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_266])).
% 0.49/0.47 thf(c_0_298, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
% 0.49/0.47 thf(c_0_299, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X860:$i]:(((((X1 @ X860)))&(![X861:$i]:(((((X1 @ X861)))=>(((X860)=(X861)))))))))))))), inference(apply_def,[status(thm)],[c_0_269, c_0_262])).
% 0.49/0.47 thf(c_0_300, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X862:$i]:(((((X1 @ X862)))&(![X863:$i]:(((((X1 @ X863)))=>(((X862)=(X863)))))))))))))))), inference(apply_def,[status(thm)],[c_0_270, c_0_262])).
% 0.49/0.47 thf(c_0_301, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X864:$i]:(((((X1 @ X864)))&(![X865:$i]:(((((X1 @ X865)))=>(((X864)=(X865)))))))))))))), inference(apply_def,[status(thm)],[c_0_271, c_0_262])).
% 0.49/0.47 thf(c_0_302, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X866:$i]:(((((X1 @ X866)))&(![X867:$i]:(((((X1 @ X867)))=>(((X866)=(X867))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_272, c_0_262])).
% 0.49/0.47 thf(c_0_303, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X868:$i]:(((((X1 @ X868)))&(![X869:$i]:(((((X1 @ X869)))=>(((X868)=(X869))))))))))<=>((?[X870:$i]:(((((X17 @ X870)))&(![X871:$i]:(((((X17 @ X871)))=>(((X870)=(X871)))))))))))))))), inference(apply_def,[status(thm)],[c_0_273, c_0_262])).
% 0.49/0.47 thf(c_0_304, plain, ((exuEu)=(![X1:$i > $o]:((((?[X872:$i]:(((((X1 @ X872)))&(![X873:$i]:(((((X1 @ X873)))=>(((X872)=(X873))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_274, c_0_262])).
% 0.49/0.47 thf(c_0_305, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X874:$i]:(((((X1 @ X874)))&(![X875:$i]:(((((X1 @ X875)))=>(((X874)=(X875))))))))))=>((((?[X876:$i]:(((((X17 @ X876)))&(![X877:$i]:(((((X17 @ X877)))=>(((X876)=(X877))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_275, c_0_262])).
% 0.49/0.47 thf(c_0_306, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 0.49/0.47 thf(c_0_307, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 0.49/0.47 thf(c_0_308, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 0.49/0.47 thf(c_0_309, plain, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 0.49/0.47 thf(c_0_310, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:(((((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0))))))))=>(?[X2:$i]:((((in @ X2 @ X4))&((X1 @ X2))))))))), inference(apply_def,[status(thm)],[c_0_276, c_0_277])).
% 0.49/0.47 thf(c_0_311, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>(((![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X3))=>(((X3)=(X2))))))))=>(((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))))))))))), inference(apply_def,[status(thm)],[c_0_278, c_0_277])).
% 0.49/0.47 thf(c_0_312, 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)))))=>(((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_279, c_0_277])).
% 0.49/0.47 thf(c_0_313, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 0.49/0.47 thf(c_0_314, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 0.49/0.47 thf(c_0_315, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 0.49/0.47 thf(c_0_316, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 0.49/0.47 thf(c_0_317, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_280, c_0_281])).
% 0.49/0.47 thf(c_0_318, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 0.49/0.47 thf(c_0_319, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 0.49/0.47 thf(c_0_320, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 0.49/0.47 thf(c_0_321, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 0.49/0.47 thf(c_0_322, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
% 0.49/0.47 thf(c_0_323, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
% 0.49/0.47 thf(c_0_324, plain, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:(((X30 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])).
% 0.49/0.47 thf(c_0_325, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
% 0.49/0.47 thf(c_0_326, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
% 0.49/0.47 thf(c_0_327, axiom, ((brelnall1)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((X1 @ (kpair @ X2 @ X3)))))))))))=>(![X2:$i]:((((in @ X2 @ X33))=>((X1 @ X2)))))))))))), inference(apply_def,[status(thm)],[brelnall1, c_0_281])).
% 0.49/0.47 thf(c_0_328, axiom, ((brelnall2)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((X1 @ (kpair @ X2 @ X3)))))))))))=>(![X2:$i]:((((in @ X2 @ X33))=>((X1 @ X2)))))))))))), inference(apply_def,[status(thm)],[brelnall2, c_0_281])).
% 0.49/0.47 thf(c_0_329, plain, ((ex1E2)=(![X4:$i, X1:$i > $o]:(((((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0))))))))=>(![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))))))))))), inference(apply_def,[status(thm)],[c_0_282, c_0_277])).
% 0.49/0.47 thf(c_0_330, axiom, ((subbreln)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X35:$i]:(((((subset @ X35 @ (cartprod @ X4 @ X5))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((in @ (kpair @ X2 @ X3) @ X35))))))))))=>((subset @ X33 @ X35))))))))))), inference(apply_def,[status(thm)],[subbreln, c_0_281])).
% 0.49/0.47 thf(c_0_331, axiom, ((eqbreln)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X35:$i]:(((((subset @ X35 @ (cartprod @ X4 @ X5))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((in @ (kpair @ X2 @ X3) @ X35))))))))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X35))=>((in @ (kpair @ X2 @ X3) @ X33))))))))))=>(((X33)=(X35)))))))))))))), inference(apply_def,[status(thm)],[eqbreln, c_0_281])).
% 0.49/0.47 thf(c_0_332, plain, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X36 @ Z0))) @ X2)=(X36 @ X2))))))), inference(fof_simplification,[status(thm)],[beta1])).
% 0.49/0.47 thf(c_0_333, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])).
% 0.49/0.47 thf(c_0_334, plain, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[Z0:$i]:(X37 @ Z0)))=(lam @ X4 @ X5 @ (^[Z0:$i]:(X37 @ Z0))))))), inference(fof_simplification,[status(thm)],[lam2lamEq])).
% 0.49/0.47 thf(c_0_335, plain, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X38 @ Z0))) @ X2)=(X38 @ X2))))))), inference(fof_simplification,[status(thm)],[beta2])).
% 0.49/0.47 thf(c_0_336, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])).
% 0.49/0.47 thf(c_0_337, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X39))&(((Z0)=(X2)))))|(((~((X39)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
% 0.49/0.47 thf(c_0_338, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X40))&(((Z0)=(X2)))))|(((~((X40)))&(((Z0)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])).
% 0.49/0.47 thf(c_0_339, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X41))&(((Z0)=(X2)))))|(((~((X41)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
% 0.49/0.47 thf(c_0_340, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X42))&(((Z0)=(X2)))))|(((~((X42)))&(((Z0)=(X3)))))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])).
% 0.49/0.47 thf(c_0_341, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X43))&(((Z0)=(X2)))))|(((~((X43)))&(((Z0)=(X3))))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
% 0.49/0.47 thf(c_0_342, plain, ((epred1_0)<=>![X907:$i]:(?[X908:$i]:((((![X909:$i]:(((in @ X909 @ X908)=>![X910:$i]:(((in @ X910 @ X909)=>(in @ X910 @ X907)))))&![X911:$i, X912:$i]:((((in @ X911 @ X907)&(in @ X912 @ X907))=>(![X913:$i]:(((in @ X913 @ X908)=>((in @ X911 @ X913)<=>(in @ X912 @ X913))))=>((X911)=(X912))))))&![X914:$i, X915:$i]:((((in @ X914 @ X908)&(in @ X915 @ X908))=>(![X916:$i]:(((in @ X916 @ X914)=>(in @ X916 @ X915)))|![X917:$i]:(((in @ X917 @ X915)=>(in @ X917 @ X914)))))))&![X918:$i]:(((![X919:$i]:(((in @ X919 @ X918)=>(in @ X919 @ X907)))&?[X920:$i]:((in @ X920 @ X918)))=>?[X921:$i, X922:$i]:(((((in @ X921 @ X908)&(in @ X922 @ X918))&~(?[X923:$i]:(((in @ X923 @ X921)&(in @ X923 @ X918)))))&![X924:$i]:(((in @ X924 @ X908)=>(![X925:$i]:(((in @ X925 @ X924)=>(in @ X925 @ X921)))|(in @ X922 @ X924)))))))))))), introduced(definition)).
% 0.49/0.47 thf(c_0_343, negated_conjecture, ~((![X878:$i, X879:$i]:((![X880:$i]:(((in @ X880 @ X878)<=>(in @ X880 @ X879)))=>((X878)=(X879))))=>(![X881:$i]:(~(in @ X881 @ emptyset))=>(![X882:$i, X883:$i, X884:$i]:(((in @ X884 @ (setadjoin @ X882 @ X883))<=>(((X884)=(X882))|(in @ X884 @ X883))))=>(![X885:$i, X886:$i]:(((in @ X886 @ (powerset @ X885))<=>![X887:$i]:(((in @ X887 @ X886)=>(in @ X887 @ X885)))))=>(![X888:$i, X889:$i]:(((in @ X889 @ (setunion @ X888))<=>?[X890:$i]:(((in @ X889 @ X890)&(in @ X890 @ X888)))))=>((in @ emptyset @ omega)=>(![X891:$i]:(((in @ X891 @ omega)=>(in @ (setadjoin @ X891 @ X891) @ omega)))=>(![X892:$i]:((((in @ emptyset @ X892)&![X893:$i]:((((in @ X893 @ omega)&(in @ X893 @ X892))=>(in @ (setadjoin @ X893 @ X893) @ X892))))=>![X894:$i]:(((in @ X894 @ omega)=>(in @ X894 @ X892)))))=>(![X895:$i > $i > $o, X896:$i]:((![X897:$i]:(((in @ X897 @ X896)=>?[X898:$i]:(((X895 @ X897 @ X898)&![X899:$i]:(((X895 @ X897 @ X899)=>((X898)=(X899))))))))=>?[X900:$i]:(![X901:$i]:(((in @ X901 @ X900)<=>?[X902:$i]:(((in @ X902 @ X896)&(X895 @ X902 @ X901))))))))=>(![X903:$i]:((?[X904:$i]:((in @ X904 @ X903))=>?[X905:$i]:(((in @ X905 @ X903)&~(?[X906:$i]:(((in @ X906 @ X905)&(in @ X906 @ X903))))))))=>((epred1_0)=>(![X926:$i > $o]:((?[X927:$i]:(((X926 @ X927)&![X928:$i]:(((X926 @ X928)=>((X927)=(X928))))))=>(X926 @ (descr @ (^[Z0:$i]:(X926 @ Z0))))))=>(![X929:$i, X930:$i > $o, X931:$i]:(((in @ X931 @ X929)=>((X930 @ X931)=>(in @ X931 @ (dsetconstr @ X929 @ X930)))))=>(![X932:$i, X933:$i > $o, X934:$i]:(((in @ X934 @ (dsetconstr @ X932 @ X933))=>(in @ X934 @ X932)))=>(![X935:$i, X936:$i > $o, X937:$i]:(((in @ X937 @ (dsetconstr @ X935 @ X936))=>(X936 @ X937)))=>(![X938:$i > $o]:((?[X939:$i]:(((X938 @ X939)&![X940:$i]:(((X938 @ X940)=>((X939)=(X940))))))=>?[X941:$i]:(((X938 @ X941)&![X942:$i]:(((X938 @ X942)=>((X941)=(X942))))))))=>(![X943:$o, X944:$i]:(((in @ X944 @ (prop2set @ ((X943))))=>(X943)))=>(![X945:$i]:(((in @ X945 @ emptyset)=>![X946:$o]:((X946))))=>(![X947:$i]:(((in @ X947 @ emptyset)=>~($true)))=>(![X948:$i]:(~(in @ X948 @ emptyset))=>(![X949:$i > $o]:((?[X950:$i]:(((X949 @ X950)&![X951:$i]:(((X949 @ X951)=>((X950)=(X951))))))=>?[X952:$i]:((X949 @ X952))))=>(![X953:$i, X954:$i]:((![X955:$i]:(((in @ X955 @ X953)=>(in @ X955 @ X954)))=>(![X956:$i]:(((in @ X956 @ X954)=>(in @ X956 @ X953)))=>((X953)=(X954)))))=>(![X957:$i]:((![X958:$i]:(~(in @ X958 @ X957))=>((X957)=(emptyset))))=>(![X959:$i]:((![X960:$i]:(~(in @ X960 @ X959))=>((X959)=(emptyset))))=>(![X961:$i, X962:$i > $o, X963:$i]:(((in @ X963 @ X961)=>((in @ X963 @ (dsetconstr @ X961 @ X962))<=>(X962 @ X963))))=>(![X964:$i]:((((X964)!=(emptyset))=>?[X965:$i]:((in @ X965 @ X964))))=>(![X966:$i, X967:$i > $o, X968:$i]:(((in @ X968 @ X966)=>((X967 @ X968)=>((dsetconstr @ X966 @ X967)!=(emptyset)))))=>(![X969:$i]:((?[X970:$i]:((in @ X970 @ X969))=>((X969)!=(emptyset))))=>(![X971:$i, X972:$i]:((in @ X971 @ (setadjoin @ X971 @ X972)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X973:$i, X974:$i, X975:$i]:(((in @ X975 @ X974)=>(in @ X975 @ (setadjoin @ X973 @ X974))))=>(![X976:$i, X977:$i, X978:$i]:(((in @ X978 @ (setadjoin @ X976 @ X977))=>![X979:$o]:(((((X978)=(X976))=>(X979))=>(((in @ X978 @ X977)=>(X979))=>(X979))))))=>(![X980:$i, X981:$i, X982:$i]:(((in @ X982 @ (setadjoin @ X980 @ X981))=>(((X982)=(X980))|(in @ X982 @ X981))))=>(![X983:$i]:(((dsetconstr @ X983 @ (^[Z0:$i]:($true)))=(X983)))=>(![X984:$i, X985:$i]:((![X986:$i]:(((in @ X986 @ X985)=>(in @ X986 @ X984)))=>(in @ X985 @ (powerset @ X984))))=>(![X987:$i]:((in @ emptyset @ (powerset @ X987)))=>(![X988:$i]:((in @ emptyset @ (powerset @ X988)))=>(![X989:$i, X990:$i, X991:$i]:(((in @ X990 @ (powerset @ X989))=>((in @ X991 @ X990)=>(in @ X991 @ X989))))=>(![X992:$i, X993:$i, X994:$i]:(((in @ X993 @ X994)=>((in @ X994 @ X992)=>(in @ X993 @ (setunion @ X992)))))=>(![X995:$i, X996:$i]:(((in @ X996 @ (setunion @ X995))=>![X997:$o]:((![X998:$i]:(((in @ X996 @ X998)=>((in @ X998 @ X995)=>(X997))))=>(X997)))))=>(![X999:$i, X1000:$i]:(((in @ X1000 @ X999)=>(in @ X1000 @ (powerset @ (setunion @ X999)))))=>(![X1001:$i > $o]:((?[X1002:$i]:(((X1001 @ X1002)&![X1003:$i]:(((X1001 @ X1003)=>((X1002)=(X1003))))))=>?[X1004:$i]:(![X1005:$i]:(((X1001 @ X1005)<=>((X1005)=(X1004)))))))=>(![X1006:$i]:((((X1006)!=(emptyset))=>?[X1007:$i]:(((in @ X1007 @ X1006)&$true))))=>(![X1008:$i, X1009:$i]:(((in @ X1008 @ (setadjoin @ X1009 @ emptyset))=>((X1008)=(X1009))))=>(![X1010:$i, X1011:$i]:((((X1010)!=(X1011))=>~(in @ X1011 @ (setadjoin @ X1010 @ emptyset))))=>(![X1012:$i, X1013:$i]:((((X1012)=(X1013))=>(in @ X1012 @ (setadjoin @ X1013 @ emptyset))))=>(![X1014:$i, X1015:$i]:(((in @ X1014 @ (setadjoin @ X1015 @ emptyset))=>(in @ X1015 @ (setadjoin @ X1014 @ emptyset))))=>(![X1016:$i, X1017:$i, X1018:$i]:(((in @ X1018 @ (setadjoin @ X1016 @ (setadjoin @ X1017 @ emptyset)))=>(((X1018)=(X1016))|((X1018)=(X1017)))))=>(![X1019:$i, X1020:$i]:((in @ X1019 @ (setadjoin @ X1019 @ (setadjoin @ X1020 @ emptyset))))=>(![X1021:$i, X1022:$i]:((in @ X1022 @ (setadjoin @ X1021 @ (setadjoin @ X1022 @ emptyset))))=>(![X1023:$i, X1024:$i > $o]:((?[X1025:$i]:(((in @ X1025 @ X1023)&(X1024 @ X1025)))=>(((dsetconstr @ X1023 @ X1024)=(emptyset))=>~($true))))=>(![X1026:$i > $o, X1027:$i]:(((in @ X1027 @ emptyset)=>(X1026 @ X1027)))=>(![X1028:$i, X1029:$i > $o]:((~(![X1030:$i]:(((in @ X1030 @ X1028)=>(X1029 @ X1030))))=>?[X1031:$i]:(((in @ X1031 @ X1028)&~((X1029 @ X1031))))))=>(![X1032:$i, X1033:$i > $o]:((![X1034:$i]:(((in @ X1034 @ X1032)=>~((X1033 @ X1034))))=>~(?[X1035:$i]:(((in @ X1035 @ X1032)&(X1033 @ X1035))))))=>(![X1036:$i, X1037:$i > $o]:((~(?[X1038:$i]:(((in @ X1038 @ X1036)&(X1037 @ X1038))))=>![X1039:$i]:(((in @ X1039 @ X1036)=>~((X1037 @ X1039))))))=>(![X1040:$i, X1041:$i > $o]:((?[X1042:$i]:(((in @ X1042 @ X1040)&~((X1041 @ X1042))))=>~(![X1043:$i]:(((in @ X1043 @ X1040)=>(X1041 @ X1043))))))=>(![X1044:$o]:(((X1044)=>(in @ emptyset @ (prop2set @ ((X1044))))))=>(![X1045:$o]:(((X1045)=>(set2prop @ (prop2set @ ((X1045))))))=>(![X1046:$i, X1047:$i > $o]:((~(?[X1048:$i]:(((in @ X1048 @ X1046)&(X1047 @ X1048))))=>![X1049:$i]:(((in @ X1049 @ X1046)=>~((X1047 @ X1049))))))=>(![X1050:$i, X1051:$i > $o]:((~(![X1052:$i]:(((in @ X1052 @ X1050)=>(X1051 @ X1052))))=>?[X1053:$i]:(((in @ X1053 @ X1050)&~((X1051 @ X1053))))))=>(![X1054:$i > $o]:((?[X1055:$i]:(((X1054 @ X1055)&![X1056:$i]:(((X1054 @ X1056)=>((X1055)=(X1056))))))=>?[X1057:$i]:(((X1054 @ X1057)&![X1058:$i]:(((X1054 @ X1058)=>((X1057)=(X1058))))))))=>(![X1059:$i > $o]:((?[X1060:$i]:((X1059 @ X1060))=>(![X1061:$i, X1062:$i]:(((X1059 @ X1061)=>((X1059 @ X1062)=>((X1061)=(X1062)))))=>?[X1063:$i]:(((X1059 @ X1063)&![X1064:$i]:(((X1059 @ X1064)=>((X1063)=(X1064)))))))))=>(![X1065:$i > $o]:((?[X1066:$i]:(![X1067:$i]:(((X1065 @ X1067)<=>((X1067)=(X1066)))))=>?[X1068:$i]:(((X1065 @ X1068)&![X1069:$i]:(((X1065 @ X1069)=>((X1068)=(X1069))))))))=>(![X1070:$i, X1071:$i]:((((X1070)=(X1071))=>![X1072:$i, X1073:$i]:((((X1072)=(X1073))=>((in @ X1072 @ X1070)=>(in @ X1073 @ X1071))))))=>(![X1074:$i, X1075:$i]:((((X1074)=(X1075))=>![X1076:$i, X1077:$i]:((((X1076)=(X1077))=>((in @ X1076 @ X1074)<=>(in @ X1077 @ X1075))))))=>(![X1078:$i > $o]:((?[X1079:$i]:(((X1078 @ X1079)&![X1080:$i]:(((X1078 @ X1080)=>((X1079)=(X1080))))))=>![X1081:$i, X1082:$i]:(((X1078 @ X1081)=>((X1078 @ X1082)=>((X1081)=(X1082)))))))=>(![X1083:$i > $o, X1084:$i > $o]:((![X1085:$i, X1086:$i]:((((X1085)=(X1086))=>((X1083 @ X1085)<=>(X1084 @ X1086))))=>(?[X1087:$i]:(((X1083 @ X1087)&![X1088:$i]:(((X1083 @ X1088)=>((X1087)=(X1088))))))<=>?[X1089:$i]:(((X1084 @ X1089)&![X1090:$i]:(((X1084 @ X1090)=>((X1089)=(X1090)))))))))=>(((emptyset)=(emptyset))=>(![X1091:$i, X1092:$i]:((((X1091)=(X1092))=>![X1093:$i, X1094:$i]:((((X1093)=(X1094))=>((setadjoin @ X1091 @ X1093)=(setadjoin @ X1092 @ X1094))))))=>(![X1095:$i, X1096:$i]:((((X1095)=(X1096))=>((powerset @ X1095)=(powerset @ X1096))))=>(![X1097:$i, X1098:$i]:((((X1097)=(X1098))=>((setunion @ X1097)=(setunion @ X1098))))=>(((omega)=(omega))=>(![X1099:$i > $o]:((?[X1100:$i]:(((X1099 @ X1100)&![X1101:$i]:(((X1099 @ X1101)=>((X1100)=(X1101))))))=>![X1102:$i, X1103:$i]:(((X1099 @ X1102)=>((X1099 @ X1103)=>((X1102)=(X1103)))))))=>(![X1104:$i > $o, X1105:$i > $o]:((![X1106:$i, X1107:$i]:((((X1106)=(X1107))=>((X1104 @ X1106)<=>(X1105 @ X1107))))=>(?[X1108:$i]:(((X1104 @ X1108)&![X1109:$i]:(((X1104 @ X1109)=>((X1108)=(X1109))))))=>(?[X1110:$i]:(((X1105 @ X1110)&![X1111:$i]:(((X1105 @ X1111)=>((X1110)=(X1111))))))=>((descr @ X1104)=(descr @ X1105))))))=>(![X1112:$i, X1113:$i]:((((X1112)=(X1113))=>![X1114:$i > $o, X1115:$i > $o]:((![X1116:$i]:(((in @ X1116 @ X1112)=>![X1117:$i]:(((in @ X1117 @ X1113)=>(((X1116)=(X1117))=>((X1114 @ X1116)<=>(X1115 @ X1117)))))))=>((dsetconstr @ X1112 @ X1114)=(dsetconstr @ X1113 @ X1115))))))=>(![X1118:$i, X1119:$i]:((![X1120:$i]:(((in @ X1120 @ X1118)=>(in @ X1120 @ X1119)))=>(subset @ X1118 @ X1119)))=>(![X1121:$i, X1122:$i]:((((X1121)=(X1122))=>(subset @ X1122 @ X1121)))=>(![X1123:$i, X1124:$i]:((((X1123)=(X1124))=>(subset @ X1123 @ X1124)))=>(![X1125:$i, X1126:$i]:((![X1127:$i]:(((in @ X1127 @ X1125)=>(in @ X1127 @ X1126)))=>(subset @ X1125 @ X1126)))=>(![X1128:$i]:((subset @ emptyset @ X1128))=>(![X1129:$i, X1130:$i, X1131:$i]:(((subset @ X1129 @ X1130)=>((in @ X1131 @ X1129)=>(in @ X1131 @ X1130))))=>(![X1132:$i, X1133:$i, X1134:$i]:(((subset @ X1132 @ X1133)=>(~(in @ X1134 @ X1133)=>~(in @ X1134 @ X1132))))=>(![X1135:$i, X1136:$i, X1137:$i]:(((in @ X1137 @ X1135)=>(~(in @ X1137 @ X1136)=>~(subset @ X1135 @ X1136))))=>(![X1138:$i, X1139:$i]:((~(subset @ X1138 @ X1139)=>((X1138)!=(X1139))))=>(![X1140:$i, X1141:$i, X1142:$i]:(((in @ X1142 @ X1140)=>(~(in @ X1142 @ X1141)=>((X1140)!=(X1141)))))=>(![X1143:$i]:((subset @ X1143 @ X1143))=>(![X1144:$i, X1145:$i, X1146:$i]:(((subset @ X1144 @ X1145)=>((subset @ X1145 @ X1146)=>(subset @ X1144 @ X1146))))=>(![X1147:$i, X1148:$i]:((subset @ X1148 @ (setadjoin @ X1147 @ X1148)))=>(![X1149:$i, X1150:$i, X1151:$i]:(((subset @ X1149 @ X1151)=>(subset @ X1149 @ (setadjoin @ X1150 @ X1151))))=>(![X1152:$i, X1153:$i]:(((subset @ X1152 @ X1153)=>(in @ X1152 @ (powerset @ X1153))))=>(![X1154:$i, X1155:$i]:(((subset @ X1154 @ X1155)=>((subset @ X1155 @ X1154)=>((X1154)=(X1155)))))=>(![X1156:$i]:(((subset @ X1156 @ emptyset)=>((X1156)=(emptyset))))=>(![X1157:$i, X1158:$i]:(((subset @ X1158 @ X1157)=>(in @ X1158 @ (powerset @ X1157))))=>(![X1159:$i, X1160:$i]:(((in @ X1160 @ (powerset @ X1159))=>(subset @ X1160 @ X1159)))=>(![X1161:$i]:((in @ X1161 @ (powerset @ X1161)))=>(![X1162:$i, X1163:$i]:(((subset @ X1162 @ X1163)=>(subset @ (powerset @ X1162) @ (powerset @ X1163))))=>(![X1164:$i, X1165:$i > $o]:((in @ (dsetconstr @ X1164 @ X1165) @ (powerset @ X1164)))=>(![X1166:$i, X1167:$i > $o]:((subset @ (dsetconstr @ X1166 @ X1167) @ X1166))=>(![X1168:$i, X1169:$i, X1170:$i]:(((in @ X1170 @ X1168)=>(in @ X1170 @ (binunion @ X1168 @ X1169))))=>(![X1171:$i, X1172:$i]:((in @ X1172 @ (setadjoin @ X1171 @ (setadjoin @ X1172 @ emptyset))))=>(![X1173:$i, X1174:$i, X1175:$i]:(((in @ X1175 @ X1174)=>(in @ X1175 @ (binunion @ X1173 @ X1174))))=>(![X1176:$i, X1177:$i, X1178:$i, X1179:$o]:(((in @ X1178 @ (binunion @ X1176 @ X1177))=>(((in @ X1178 @ X1176)=>(X1179))=>(((in @ X1178 @ X1177)=>(X1179))=>(X1179)))))=>(![X1180:$i, X1181:$i, X1182:$i]:(((in @ X1182 @ (binunion @ X1180 @ X1181))=>((in @ X1182 @ X1180)|(in @ X1182 @ X1181))))=>(![X1183:$i, X1184:$i]:((subset @ X1183 @ (binunion @ X1183 @ X1184)))=>(![X1185:$i, X1186:$i]:((subset @ X1186 @ (binunion @ X1185 @ X1186)))=>(![X1187:$i, X1188:$i, X1189:$i]:(((in @ X1189 @ X1187)=>((in @ X1189 @ X1188)=>(in @ X1189 @ (binintersect @ X1187 @ X1188)))))=>(![X1190:$i, X1191:$i, X1192:$i]:(((subset @ X1192 @ X1190)=>((subset @ X1192 @ X1191)=>(subset @ X1192 @ (binintersect @ X1190 @ X1191)))))=>(![X1193:$i, X1194:$i, X1195:$i]:(((in @ X1195 @ (binintersect @ X1193 @ X1194))=>(in @ X1195 @ X1193)))=>(![X1196:$i, X1197:$i]:((subset @ (binintersect @ X1196 @ X1197) @ X1196))=>(![X1198:$i, X1199:$i]:(((subset @ X1198 @ X1199)=>((binintersect @ X1198 @ X1199)=(X1198))))=>(![X1200:$i, X1201:$i]:((((binintersect @ X1200 @ X1201)=(X1201))=>(subset @ X1201 @ X1200)))=>(![X1202:$i, X1203:$i, X1204:$i]:(((in @ X1204 @ (binintersect @ X1202 @ X1203))=>(in @ X1204 @ X1203)))=>(![X1205:$i, X1206:$i]:((~(?[X1207:$i]:(((in @ X1207 @ X1205)&(in @ X1207 @ X1206))))=>((binintersect @ X1205 @ X1206)=(emptyset))))=>(![X1208:$i, X1209:$i]:((subset @ (binintersect @ X1208 @ X1209) @ X1209))=>(![X1210:$i, X1211:$i]:(((subset @ X1211 @ X1210)=>((binintersect @ X1210 @ X1211)=(X1211))))=>(![X1212:$i, X1213:$i]:((((binintersect @ X1212 @ X1213)=(X1212))=>(subset @ X1212 @ X1213)))=>(![X1214:$i, X1215:$i, 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X1698 @ X1699))=>~(in @ X1700 @ X1699))))))))=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_283, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_284]), foundationAx]), wellorderingAx]), c_0_285]), c_0_286]), c_0_287]), c_0_288]), c_0_289]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_290]), setext]), emptyI]), noeltsimpempty]), c_0_291]), c_0_292]), c_0_293]), c_0_294]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_295]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_296]), c_0_297]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_298]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_299]), c_0_300]), c_0_301]), inCongP]), in__Cong]), c_0_302]), c_0_303]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_304]), c_0_305]), c_0_306]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_307]), c_0_308]), binunionIL]), upairset2IR]), binunionIR]), binunionEcases]), binunionE]), binunionLsub]), binunionRsub]), binintersectI]), binintersectSubset5]), binintersectEL]), binintersectLsub]), binintersectSubset2]), binintersectSubset3]), binintersectER]), disjointsetsI1]), binintersectRsub]), binintersectSubset4]), binintersectSubset1]), bs114d]), setminusI]), setminusEL]), setminusER]), setminusSubset2]), setminusERneg]), setminusELneg]), setminusILneg]), setminusIRneg]), setminusLsub]), setminusSubset1]), symdiffE]), symdiffI1]), symdiffI2]), symdiffIneg1]), symdiffIneg2]), secondinupair]), setukpairIL]), setukpairIR]), kpairiskpair]), kpairp]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1]), cartprodmempair]), setunionE2]), setunionsingleton1]), setunionsingleton2]), setunionsingleton]), c_0_309]), c_0_310]), c_0_311]), c_0_312]), singletonsuniq]), setukpairinjL1]), c_0_313]), theprop]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_314]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_315]), c_0_316]), c_0_317]), c_0_318]), c_0_319]), c_0_320]), c_0_321]), c_0_322]), c_0_323]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_324]), c_0_325]), c_0_326]), c_0_327]), c_0_328]), c_0_329]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), c_0_330]), c_0_331]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_332]), c_0_333]), c_0_334]), c_0_335]), c_0_336]), c_0_337]), c_0_338]), c_0_339]), c_0_340]), c_0_341]), ifp]), theeq]), iftrue]), iffalse]), iftrueorfalse]), binintersectT_lem]), binunionT_lem]), powersetT_lem]), setminusT_lem]), complementT_lem]), setextT]), subsetTI]), powersetTI1]), powersetTE1]), complementTI1]), complementTE1]), binintersectTELcontra]), binintersectTERcontra]), contrasubsetT]), contrasubsetT1]), contrasubsetT2]), contrasubsetT3]), doubleComplementI1]), doubleComplementE1]), doubleComplementSub1]), doubleComplementSub2]), doubleComplementEq]), complementTnotintersectT]), complementImpComplementIntersect]), complementSubsetComplementIntersect]), complementInPowersetComplementIntersect]), contraSubsetComplement]), complementTcontraSubset]), binunionTILcontra]), binunionTIRcontra])])]), c_0_342])).
% 0.49/0.47 thf(c_0_344, negated_conjecture, ![X1701:$i, X1702:$i, X1704:$i, X1705:$i, X1706:$i, X1707:$i, X1708:$i, X1709:$i, X1710:$i, X1711:$i, X1712:$i, X1714:$i, X1715:$i, X1717:$i, X1718:$i, X1719:$i, X1720:$i, X1721:$i, X1723:$i, X1724:$i > $i > $o, X1725:$i, X1727:$i, X1730:$i, X1732:$i, X1733:$i, X1734:$i, X1735:$i, X1737:$i, X1738:$i > $o, X1739:$i, X1741:$i, X1742:$i > $o, X1743:$i, X1744:$i, X1745:$i > $o, X1746:$i, X1747:$i, X1748:$i > $o, X1749:$i, X1750:$i > $o, X1751:$i, X1754:$i, X1755:$o, X1756:$i, X1757:$i, X1758:$o, X1759:$i, X1760:$i, X1761:$i > $o, X1762:$i, X1765:$i, X1766:$i, X1769:$i, X1771:$i, X1773:$i, X1774:$i > $o, X1775:$i, X1776:$i, X1778:$i, X1779:$i > $o, X1780:$i, X1781:$i, X1782:$i, X1783:$i, X1784:$i, X1785:$i, X1786:$i, X1787:$i, X1788:$i, X1789:$i, X1790:$i, X1791:$o, X1792:$i, X1793:$i, X1794:$i, X1795:$i, X1796:$i, X1797:$i, X1799:$i, X1800:$i, X1801:$i, X1802:$i, X1803:$i, X1804:$i, X1805:$i, X1806:$i, X1807:$i, X1808:$i, X1809:$o, X1811:$i, X1812:$i, X1813:$i > $o, X1814:$i, X1817:$i, X1818:$i, X1819:$i, X1821:$i, X1822:$i, X1823:$i, X1824:$i, X1825:$i, X1826:$i, X1827:$i, X1828:$i, X1829:$i, X1830:$i, X1831:$i, X1832:$i, X1833:$i, X1834:$i, X1835:$i, X1836:$i, X1837:$i > $o, X1838:$i, X1839:$i > $o, X1840:$i, X1841:$i, X1842:$i > $o, X1843:$i, X1845:$i, X1846:$i > $o, X1848:$i, X1849:$i, X1850:$i > $o, X1852:$i, X1853:$i, X1854:$i > $o, X1855:$i, X1857:$o, X1858:$o, X1859:$i, X1860:$i > $o, X1862:$i, X1863:$i, X1864:$i > $o, X1865:$i, X1867:$i > $o, X1868:$i, X1871:$i, X1872:$i > $o, X1873:$i, X1877:$i, X1878:$i > $o, X1879:$i, X1882:$i, X1883:$i, X1884:$i, X1885:$i, X1886:$i, X1887:$i, X1888:$i, X1889:$i, X1890:$i, X1891:$i > $o, X1892:$i, X1894:$i, X1895:$i, X1896:$i > $o, X1897:$i > $o, X1900:$i, X1903:$i, X1904:$i, X1907:$i, X1908:$i, X1909:$i, X1910:$i, X1911:$i, X1912:$i, X1913:$i, X1914:$i, X1915:$i, X1916:$i > $o, X1917:$i, X1919:$i, X1920:$i, X1921:$i > $o, X1922:$i > $o, X1925:$i, X1927:$i, X1929:$i, X1930:$i, X1931:$i > $o, X1932:$i > $o, X1935:$i, X1936:$i, X1938:$i, X1939:$i, X1940:$i, X1941:$i, X1942:$i, X1943:$i, X1945:$i, X1946:$i, X1947:$i, X1948:$i, X1949:$i, X1950:$i, X1951:$i, X1952:$i, X1953:$i, X1954:$i, X1955:$i, X1956:$i, X1957:$i, X1958:$i, X1959:$i, X1960:$i, X1961:$i, X1962:$i, X1963:$i, X1964:$i, X1965:$i, X1966:$i, X1967:$i, X1968:$i, X1969:$i, X1970:$i, X1971:$i, X1972:$i, X1973:$i, X1974:$i, X1975:$i, X1976:$i, X1977:$i, X1978:$i, X1979:$i, X1980:$i, X1981:$i, X1982:$i > $o, X1983:$i, X1984:$i > $o, X1985:$i, X1986:$i, X1987:$i, X1988:$i, X1989:$i, X1990:$i, X1991:$i, X1992:$i, X1993:$i, X1994:$i, X1995:$i, X1996:$o, X1997:$i, X1998:$i, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$i, X2004:$i, X2005:$i, X2006:$i, X2007:$i, X2008:$i, X2009:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2015:$i, X2016:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$i, X2021:$i, X2022:$i, X2023:$i, X2025:$i, X2026:$i, X2027:$i, X2028:$i, X2029:$i, X2030:$i, X2031:$i, X2032:$i, X2033:$i, X2034:$i, X2035:$i, X2036:$i, X2037:$i, X2038:$i, X2039:$i, X2040:$i, X2041:$i, X2042:$i, X2043:$i, X2044:$i, X2045:$i, X2046:$i, X2047:$i, X2048:$i, X2049:$i, X2050:$i, X2051:$i, X2052:$i, X2053:$i, X2054:$i, X2055:$i, X2056:$i, X2057:$i, X2058:$i, X2059:$i, X2060:$i, X2061:$i, X2062:$i, X2063:$i, X2064:$o, X2065:$i, X2066:$i, X2067:$i, X2068:$i, X2069:$i, X2070:$i, X2071:$i, X2072:$i, X2073:$i, X2074:$i, X2075:$i, X2076:$i, X2077:$i, X2078:$i, X2079:$i, X2080:$i, X2081:$i, X2082:$i, X2083:$i, X2084:$i, X2085:$i, X2086:$i, X2087:$i, X2088:$i, X2089:$i, X2090:$i, X2091:$i, X2092:$i, X2093:$i, X2094:$i, X2095:$i, X2096:$i, X2097:$i, X2098:$i, X2099:$i, X2100:$i, X2101:$i, X2102:$i, X2103:$i, X2104:$i, X2105:$i, X2106:$i, X2107:$i, X2108:$i, X2109:$i, X2110:$i, X2111:$i, X2112:$i, X2113:$i, X2114:$i, X2115:$i, X2116:$i, X2117:$i, X2118:$i, X2119:$i, X2120:$i, X2121:$i, X2122:$i, X2123:$i, X2126:$i, X2127:$i, X2128:$i, X2129:$i, X2130:$i, X2132:$i, X2133:$i, X2134:$i, X2135:$i, X2136:$i > $o, X2139:$i, X2140:$i, X2141:$i > $o, X2143:$i, X2144:$i > $o, X2145:$i, X2147:$i, X2148:$i > $o, X2151:$i, X2152:$i, X2153:$i, X2154:$i, X2155:$i, X2156:$i, X2157:$i, X2158:$i, X2159:$i, X2160:$i, X2161:$i, X2162:$i, X2163:$i, X2164:$i, X2165:$i, X2166:$i, X2167:$i, X2168:$i, X2169:$i, X2170:$i, X2171:$i, X2172:$i, X2173:$i, X2174:$i, X2175:$i, X2176:$i, X2177:$i, X2178:$i, X2179:$i, X2180:$i, X2181:$i, X2182:$i, X2183:$i, X2184:$i, X2185:$i, X2186:$i, X2187:$i, X2188:$i, X2189:$i, X2190:$i, X2191:$i, X2192:$i, X2193:$i, X2194:$i, X2195:$i, X2196:$i, X2197:$i, X2198:$i, X2199:$i, X2200:$i, X2201:$i, X2202:$i, X2203:$i, X2204:$i, X2205:$i, X2206:$i, X2207:$i, X2208:$i, X2209:$i, X2210:$i, X2211:$i, X2212:$i, X2213:$i, X2214:$i, X2215:$i, X2216:$i, X2217:$i, X2218:$i, X2219:$i, X2220:$i, X2221:$i, X2222:$i, X2223:$i > $i > $o, X2224:$i, X2225:$i, X2226:$i, X2227:$i, X2228:$i > $i > $o, X2229:$i, X2230:$i, X2231:$i > $i > $o, X2232:$i, X2233:$i, X2234:$i > $i > $o, X2235:$i, X2236:$i, X2237:$i, X2238:$i, X2239:$i > $i > $o, X2240:$i, X2241:$i, X2242:$i, X2243:$i, X2244:$i > $i > $o, X2245:$i, X2246:$i, X2247:$i, X2248:$i, X2249:$i > $i > $o, X2250:$i, X2251:$i, X2252:$i, X2253:$i, X2254:$i, X2255:$i, X2256:$i, X2257:$i, X2258:$i, X2259:$i, X2260:$i, X2261:$i, X2262:$i, X2263:$i, X2264:$i, X2265:$i, X2266:$i, X2267:$i, X2268:$i, X2269:$i, X2270:$i, X2271:$i, X2272:$i, X2273:$i, X2274:$i, X2275:$i, X2276:$i > $i, X2278:$i, X2279:$i, X2280:$i > $i, X2282:$i, X2283:$i, X2284:$i > $i, X2286:$i, X2287:$i, X2288:$i, X2289:$i > $o, X2292:$i, X2293:$i, X2294:$i, X2295:$i, X2296:$i > $o, X2299:$i, X2300:$i, X2301:$i > $o, X2302:$i, X2303:$i, X2304:$i, X2305:$i, X2306:$i, X2307:$i, X2308:$i, X2309:$i, X2310:$i, X2311:$i, X2312:$i, X2313:$i, X2314:$i, X2315:$i, X2316:$i, X2317:$i, X2318:$i, X2319:$i, X2320:$i, X2322:$i, X2323:$i, X2324:$i, X2325:$i, X2326:$i, X2327:$i, X2328:$i, X2329:$i, X2330:$i, X2331:$i, X2332:$i, X2335:$i, X2336:$i, X2337:$i, X2338:$i, X2343:$i, X2344:$i, X2345:$i, X2346:$i, X2348:$i, X2349:$i, X2350:$i, X2351:$i, X2353:$i, X2354:$i, X2355:$i, X2356:$i, X2357:$i, X2358:$i, X2359:$i, X2360:$i, X2361:$i, X2362:$i, X2363:$i > $i, X2365:$i, X2366:$i, X2367:$i, X2368:$i, X2369:$i, X2370:$i, X2371:$i > $i, X2373:$i, X2374:$i, X2375:$i > $i, X2377:$i, X2378:$i, X2379:$i, X2380:$i, X2381:$i, X2382:$o, X2383:$i, X2384:$i, X2385:$i, X2386:$o, X2387:$i, X2388:$i, X2389:$i, X2390:$o, X2391:$i, X2392:$i, X2393:$i, X2394:$o, X2395:$i, X2396:$i, X2397:$i, X2398:$o, X2399:$i, X2400:$i, X2401:$i, X2402:$o, X2403:$i, X2404:$i, X2405:$i, X2406:$i, X2407:$i, X2408:$o, X2409:$i, X2410:$i, X2411:$i, X2412:$o, X2413:$i, X2414:$i, X2415:$i, X2416:$o, X2417:$i, X2418:$i, X2419:$i, X2420:$i, X2421:$i, X2422:$i, X2423:$i, X2424:$i, X2425:$i, X2426:$i, X2427:$i, X2428:$i, X2429:$i, X2430:$i, X2431:$i, X2432:$i, X2433:$i, X2434:$i, X2437:$i, X2438:$i, X2439:$i, X2441:$i, X2442:$i, X2443:$i, X2445:$i, X2446:$i, X2447:$i, X2448:$i, X2449:$i, X2450:$i, X2451:$i, 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(kpair @ (esk76_4 @ X2335 @ X2336 @ X2337 @ X2338) @ (esk77_4 @ X2335 @ X2336 @ X2337 @ X2338)) @ X2337)|((X2337)=(X2338))|(in @ (esk75_4 @ X2335 @ X2336 @ X2337 @ X2338) @ X2336)|~(subset @ X2338 @ (cartprod @ X2335 @ X2336))|~(subset @ X2337 @ (cartprod @ X2335 @ X2336))))))&((((in @ (esk76_4 @ X2335 @ X2336 @ X2337 @ X2338) @ X2335)|((X2337)=(X2338))|(in @ (kpair @ (esk74_4 @ X2335 @ X2336 @ X2337 @ X2338) @ (esk75_4 @ X2335 @ X2336 @ X2337 @ X2338)) @ X2337)|~(subset @ X2338 @ (cartprod @ X2335 @ X2336))|~(subset @ X2337 @ (cartprod @ X2335 @ X2336)))&(((in @ (esk77_4 @ X2335 @ X2336 @ X2337 @ X2338) @ X2336)|((X2337)=(X2338))|(in @ (kpair @ (esk74_4 @ X2335 @ X2336 @ X2337 @ X2338) @ (esk75_4 @ X2335 @ X2336 @ X2337 @ X2338)) @ X2337)|~(subset @ X2338 @ (cartprod @ X2335 @ X2336))|~(subset @ X2337 @ (cartprod @ X2335 @ X2336)))&(((in @ (kpair @ (esk76_4 @ X2335 @ X2336 @ X2337 @ X2338) @ (esk77_4 @ X2335 @ X2336 @ X2337 @ X2338)) @ X2338)|((X2337)=(X2338))|(in @ (kpair @ (esk74_4 @ X2335 @ X2336 @ X2337 @ X2338) @ (esk75_4 @ X2335 @ X2336 @ X2337 @ X2338)) @ X2337)|~(subset @ X2338 @ (cartprod @ X2335 @ X2336))|~(subset @ X2337 @ (cartprod @ X2335 @ X2336)))&(~(in @ (kpair @ (esk76_4 @ X2335 @ X2336 @ X2337 @ X2338) @ (esk77_4 @ X2335 @ X2336 @ X2337 @ X2338)) @ X2337)|((X2337)=(X2338))|(in @ (kpair @ (esk74_4 @ X2335 @ X2336 @ X2337 @ X2338) @ (esk75_4 @ X2335 @ X2336 @ X2337 @ X2338)) @ X2337)|~(subset @ X2338 @ (cartprod @ X2335 @ X2336))|~(subset @ X2337 @ (cartprod @ X2335 @ X2336))))))&(((in @ (esk76_4 @ X2335 @ X2336 @ X2337 @ X2338) @ X2335)|((X2337)=(X2338))|~(in @ (kpair @ (esk74_4 @ X2335 @ X2336 @ X2337 @ X2338) @ (esk75_4 @ X2335 @ X2336 @ X2337 @ X2338)) @ X2338)|~(subset @ X2338 @ (cartprod @ X2335 @ X2336))|~(subset @ X2337 @ (cartprod @ X2335 @ X2336)))&(((in @ (esk77_4 @ X2335 @ X2336 @ X2337 @ X2338) @ X2336)|((X2337)=(X2338))|~(in @ (kpair @ (esk74_4 @ X2335 @ X2336 @ X2337 @ X2338) @ (esk75_4 @ X2335 @ X2336 @ X2337 @ X2338)) @ X2338)|~(subset @ X2338 @ (cartprod @ X2335 @ X2336))|~(subset @ X2337 @ (cartprod @ X2335 @ X2336)))&(((in @ (kpair @ (esk76_4 @ X2335 @ X2336 @ X2337 @ X2338) @ (esk77_4 @ X2335 @ X2336 @ X2337 @ X2338)) @ X2338)|((X2337)=(X2338))|~(in @ (kpair @ (esk74_4 @ X2335 @ X2336 @ X2337 @ X2338) @ (esk75_4 @ X2335 @ X2336 @ X2337 @ X2338)) @ X2338)|~(subset @ X2338 @ (cartprod @ X2335 @ X2336))|~(subset @ X2337 @ (cartprod @ X2335 @ X2336)))&(~(in @ (kpair @ (esk76_4 @ X2335 @ X2336 @ X2337 @ X2338) @ (esk77_4 @ X2335 @ X2336 @ X2337 @ X2338)) @ X2337)|((X2337)=(X2338))|~(in @ (kpair @ (esk74_4 @ X2335 @ X2336 @ X2337 @ X2338) @ (esk75_4 @ X2335 @ X2336 @ X2337 @ X2338)) @ X2338)|~(subset @ X2338 @ (cartprod @ X2335 @ X2336))|~(subset @ X2337 @ (cartprod @ X2335 @ X2336)))))))))&((((in @ (esk78_4 @ X2343 @ X2344 @ X2345 @ X2346) @ X2343)|((X2345)=(X2346))|~(func @ X2343 @ X2344 @ X2346)|~(func @ X2343 @ X2344 @ X2345))&(((ap @ X2343 @ X2344 @ X2345 @ (esk78_4 @ X2343 @ X2344 @ X2345 @ X2346))!=(ap @ X2343 @ X2344 @ X2346 @ (esk78_4 @ X2343 @ X2344 @ X2345 @ X2346)))|((X2345)=(X2346))|~(func @ X2343 @ X2344 @ X2346)|~(func @ X2343 @ X2344 @ X2345)))&((((in @ (esk79_4 @ X2348 @ X2349 @ X2350 @ X2351) @ X2348)|((X2350)=(X2351))|~(in @ X2351 @ (funcSet @ X2348 @ X2349))|~(in @ X2350 @ (funcSet @ X2348 @ X2349)))&(((ap @ X2348 @ X2349 @ X2350 @ (esk79_4 @ X2348 @ X2349 @ X2350 @ X2351))!=(ap @ X2348 @ X2349 @ X2351 @ (esk79_4 @ X2348 @ X2349 @ X2350 @ X2351)))|((X2350)=(X2351))|~(in @ X2351 @ (funcSet @ X2348 @ X2349))|~(in @ X2350 @ (funcSet @ X2348 @ X2349))))&((~(in @ X2355 @ (funcSet @ X2353 @ X2354))|(~(in @ X2356 @ X2353)|((ap @ X2353 @ X2354 @ X2355 @ X2356)=(ap @ X2353 @ X2354 @ X2355 @ X2356))))&((~(func @ X2357 @ X2358 @ X2359)|(~(in @ X2360 @ X2357)|((ap @ X2357 @ X2358 @ X2359 @ X2360)=(ap @ X2357 @ X2358 @ X2359 @ X2360))))&((((in @ (esk80_3 @ X2361 @ X2362 @ X2363) @ X2361)|(~(in @ X2365 @ X2361)|((ap @ X2361 @ X2362 @ (lam @ X2361 @ X2362 @ X2363) @ X2365)=(X2363 @ X2365))))&(~(in @ (X2363 @ (esk80_3 @ X2361 @ X2362 @ X2363)) @ X2362)|(~(in @ X2365 @ X2361)|((ap @ X2361 @ X2362 @ (lam @ X2361 @ X2362 @ X2363) @ X2365)=(X2363 @ X2365)))))&((~(func @ X2366 @ X2367 @ X2368)|((lam @ X2366 @ X2367 @ (ap @ X2366 @ X2367 @ X2368))=(X2368)))&((((in @ (esk81_3 @ X2369 @ X2370 @ X2371) @ X2369)|((lam @ X2369 @ X2370 @ X2371)=(lam @ X2369 @ X2370 @ X2371)))&(~(in @ (X2371 @ (esk81_3 @ X2369 @ X2370 @ X2371)) @ X2370)|((lam @ X2369 @ X2370 @ X2371)=(lam @ X2369 @ X2370 @ X2371))))&((((in @ (esk82_3 @ X2373 @ X2374 @ X2375) @ X2373)|(~(in @ X2377 @ X2373)|((ap @ X2373 @ X2374 @ (lam @ X2373 @ X2374 @ X2375) @ X2377)=(X2375 @ X2377))))&(~(in @ (X2375 @ (esk82_3 @ X2373 @ X2374 @ X2375)) @ X2374)|(~(in @ X2377 @ X2373)|((ap @ X2373 @ X2374 @ (lam @ X2373 @ X2374 @ X2375) @ X2377)=(X2375 @ X2377)))))&((~(in @ X2380 @ (funcSet @ X2378 @ X2379))|((lam @ X2378 @ X2379 @ (ap @ X2378 @ X2379 @ X2380))=(X2380)))&((~(in @ X2383 @ X2381)|(~(in @ X2384 @ X2381)|((X2382)|(in @ X2384 @ (dsetconstr @ X2381 @ (^[Z0:$i]:((((((X2382))&(((Z0)=(X2383)))))|(((~((X2382)))&(((Z0)=(X2384)))))))))))))&((~(in @ X2387 @ X2385)|(~(in @ X2388 @ X2385)|((X2386)|((dsetconstr @ X2385 @ (^[Z0:$i]:((((((X2386))&(((Z0)=(X2387)))))|(((~((X2386)))&(((Z0)=(X2388)))))))))=(setadjoin @ X2388 @ emptyset)))))&((~(in @ X2391 @ X2389)|(~(in @ X2392 @ X2389)|(~(X2390)|(in @ X2391 @ (dsetconstr @ X2389 @ (^[Z0:$i]:((((((X2390))&(((Z0)=(X2391)))))|(((~((X2390)))&(((Z0)=(X2392)))))))))))))&((~(in @ X2395 @ X2393)|(~(in @ X2396 @ X2393)|(~(X2394)|((dsetconstr @ X2393 @ (^[Z0:$i]:((((((X2394))&(((Z0)=(X2395)))))|(((~((X2394)))&(((Z0)=(X2396)))))))))=(setadjoin @ X2395 @ emptyset)))))&((~(in @ X2399 @ X2397)|(~(in @ X2400 @ X2397)|(singleton @ (dsetconstr @ X2397 @ (^[Z0:$i]:((((((X2398))&(((Z0)=(X2399)))))|(((~((X2398)))&(((Z0)=(X2400))))))))))))&((~(in @ X2403 @ X2401)|(~(in @ X2404 @ X2401)|(in @ (if @ X2401 @ ((X2402)) @ X2403 @ X2404) @ X2401)))&((~(singleton @ X2405)|(~(in @ X2406 @ X2405)|((setunion @ X2405)=(X2406))))&((~(in @ X2409 @ X2407)|(~(in @ X2410 @ X2407)|(~(X2408)|((if @ X2407 @ ((X2408)) @ X2409 @ X2410)=(X2409)))))&((~(in @ X2413 @ X2411)|(~(in @ X2414 @ X2411)|((X2412)|((if @ X2411 @ ((X2412)) @ X2413 @ X2414)=(X2414)))))&((~(in @ X2417 @ X2415)|(~(in @ X2418 @ X2415)|(in @ (if @ X2415 @ ((X2416)) @ X2417 @ X2418) @ (setadjoin @ X2417 @ (setadjoin @ X2418 @ emptyset)))))&((~(in @ X2420 @ (powerset @ X2419))|(~(in @ X2421 @ (powerset @ X2419))|(in @ (binintersect @ X2420 @ X2421) @ (powerset @ X2419))))&((~(in @ X2423 @ (powerset @ X2422))|(~(in @ X2424 @ (powerset @ X2422))|(in @ (binunion @ X2423 @ X2424) @ (powerset @ X2422))))&((~(in @ X2426 @ (powerset @ X2425))|(in @ (powerset @ X2426) @ (powerset @ (powerset @ X2425))))&((~(in @ X2428 @ (powerset @ X2427))|(~(in @ X2429 @ (powerset @ X2427))|(in @ (setminus @ X2428 @ X2429) @ (powerset @ X2427))))&((~(in @ X2431 @ (powerset @ X2430))|(in @ (setminus @ X2430 @ X2431) @ (powerset @ X2430)))&(((((in @ (esk84_3 @ X2432 @ X2433 @ X2434) @ X2432)|((X2433)=(X2434))|(in @ (esk83_3 @ X2432 @ X2433 @ X2434) @ X2432)|~(in @ X2434 @ (powerset @ X2432))|~(in @ X2433 @ (powerset @ X2432)))&(((in @ (esk84_3 @ X2432 @ X2433 @ X2434) @ X2434)|((X2433)=(X2434))|(in @ (esk83_3 @ X2432 @ X2433 @ X2434) @ X2432)|~(in @ X2434 @ (powerset @ X2432))|~(in @ X2433 @ (powerset @ X2432)))&(~(in @ (esk84_3 @ X2432 @ X2433 @ X2434) @ X2433)|((X2433)=(X2434))|(in @ (esk83_3 @ X2432 @ X2433 @ X2434) @ X2432)|~(in @ X2434 @ (powerset @ X2432))|~(in @ X2433 @ (powerset @ X2432)))))&((((in @ (esk84_3 @ X2432 @ X2433 @ X2434) @ X2432)|((X2433)=(X2434))|(in @ (esk83_3 @ X2432 @ X2433 @ X2434) @ X2433)|~(in @ X2434 @ (powerset @ X2432))|~(in @ X2433 @ (powerset @ X2432)))&(((in @ (esk84_3 @ X2432 @ X2433 @ X2434) @ X2434)|((X2433)=(X2434))|(in @ (esk83_3 @ X2432 @ X2433 @ X2434) @ X2433)|~(in @ X2434 @ (powerset @ X2432))|~(in @ X2433 @ (powerset @ X2432)))&(~(in @ (esk84_3 @ X2432 @ X2433 @ X2434) @ X2433)|((X2433)=(X2434))|(in @ (esk83_3 @ X2432 @ X2433 @ X2434) @ X2433)|~(in @ X2434 @ (powerset @ X2432))|~(in @ X2433 @ (powerset @ X2432)))))&(((in @ (esk84_3 @ X2432 @ X2433 @ X2434) @ X2432)|((X2433)=(X2434))|~(in @ (esk83_3 @ X2432 @ X2433 @ X2434) @ X2434)|~(in @ X2434 @ (powerset @ X2432))|~(in @ X2433 @ (powerset @ X2432)))&(((in @ (esk84_3 @ X2432 @ X2433 @ X2434) @ X2434)|((X2433)=(X2434))|~(in @ (esk83_3 @ X2432 @ X2433 @ X2434) @ X2434)|~(in @ X2434 @ (powerset @ X2432))|~(in @ X2433 @ (powerset @ X2432)))&(~(in @ (esk84_3 @ X2432 @ X2433 @ X2434) @ X2433)|((X2433)=(X2434))|~(in @ (esk83_3 @ X2432 @ X2433 @ X2434) @ X2434)|~(in @ X2434 @ (powerset @ X2432))|~(in @ X2433 @ (powerset @ X2432)))))))&((((in @ (esk85_3 @ X2437 @ X2438 @ X2439) @ X2437)|(subset @ X2438 @ X2439)|~(in @ X2439 @ (powerset @ X2437))|~(in @ X2438 @ (powerset @ X2437)))&(((in @ (esk85_3 @ X2437 @ X2438 @ X2439) @ X2438)|(subset @ X2438 @ X2439)|~(in @ X2439 @ (powerset @ X2437))|~(in @ X2438 @ (powerset @ X2437)))&(~(in @ (esk85_3 @ X2437 @ X2438 @ X2439) @ X2439)|(subset @ X2438 @ X2439)|~(in @ X2439 @ (powerset @ X2437))|~(in @ X2438 @ (powerset @ X2437)))))&((((in @ (esk86_3 @ X2441 @ X2442 @ X2443) @ X2441)|(in @ X2442 @ (powerset @ X2443))|~(in @ X2443 @ (powerset @ X2441))|~(in @ X2442 @ (powerset @ X2441)))&(((in @ (esk86_3 @ X2441 @ X2442 @ X2443) @ X2442)|(in @ X2442 @ (powerset @ X2443))|~(in @ X2443 @ (powerset @ X2441))|~(in @ X2442 @ (powerset @ X2441)))&(~(in @ (esk86_3 @ X2441 @ X2442 @ X2443) @ X2443)|(in @ X2442 @ (powerset @ X2443))|~(in @ X2443 @ (powerset @ X2441))|~(in @ X2442 @ (powerset @ X2441)))))&((~(in @ X2446 @ (powerset @ X2445))|(~(in @ X2447 @ (powerset @ X2445))|(~(in @ X2448 @ X2445)|(~(in @ X2446 @ (powerset @ X2447))|(~(in @ X2448 @ X2446)|(in @ X2448 @ X2447))))))&((~(in @ X2450 @ (powerset @ X2449))|(~(in @ X2451 @ X2449)|(~(in @ X2451 @ X2450)|~(in @ X2451 @ (setminus @ X2449 @ X2450)))))&((~(in @ X2453 @ (powerset @ X2452))|(~(in @ X2454 @ X2452)|((in @ X2454 @ (setminus @ X2452 @ X2453))|(in @ X2454 @ X2453))))&((~(in @ X2456 @ (powerset @ X2455))|(~(in @ X2457 @ (powerset @ X2455))|(~(in @ X2458 @ X2455)|((in @ X2458 @ X2456)|~(in @ X2458 @ (binintersect @ X2456 @ X2457))))))&((~(in @ X2460 @ (powerset @ X2459))|(~(in @ X2461 @ (powerset @ X2459))|(~(in @ X2462 @ X2459)|((in @ X2462 @ X2461)|~(in @ X2462 @ (binintersect @ X2460 @ X2461))))))&((~(in @ X2464 @ (powerset @ X2463))|(~(in @ X2465 @ (powerset @ X2463))|(~(in @ X2466 @ X2463)|(~(subset @ X2464 @ (setminus @ X2463 @ X2465))|(~(in @ X2466 @ X2465)|~(in @ X2466 @ X2464))))))&((~(in @ X2468 @ (powerset @ X2467))|(~(in @ X2469 @ (powerset @ X2467))|(~(in @ X2470 @ X2467)|(~(subset @ X2468 @ X2469)|((in @ X2470 @ X2469)|~(in @ X2470 @ X2468))))))&((~(in @ X2472 @ (powerset @ X2471))|(~(in @ X2473 @ (powerset @ X2471))|(~(subset @ X2472 @ X2473)|(subset @ (setminus @ X2471 @ X2473) @ (setminus @ X2471 @ X2472)))))&((~(in @ X2475 @ (powerset @ X2474))|(~(in @ X2476 @ (powerset @ X2474))|(~(subset @ (setminus @ X2474 @ X2476) @ (setminus @ X2474 @ X2475))|(subset @ X2475 @ X2476))))&((~(in @ X2478 @ (powerset @ X2477))|(~(in @ X2479 @ X2477)|(~(in @ X2479 @ X2478)|(in @ X2479 @ (setminus @ X2477 @ (setminus @ X2477 @ X2478))))))&((~(in @ X2481 @ (powerset @ X2480))|(~(in @ X2482 @ X2480)|(~(in @ X2482 @ (setminus @ X2480 @ (setminus @ X2480 @ X2481)))|(in @ X2482 @ X2481))))&((~(in @ X2484 @ (powerset @ X2483))|(subset @ X2484 @ (setminus @ X2483 @ (setminus @ X2483 @ X2484))))&((~(in @ X2486 @ (powerset @ X2485))|(subset @ (setminus @ X2485 @ (setminus @ X2485 @ X2486)) @ X2486))&((~(in @ X2488 @ (powerset @ X2487))|((X2488)=(setminus @ X2487 @ (setminus @ X2487 @ X2488))))&((~(in @ X2490 @ (powerset @ X2489))|(~(in @ X2491 @ (powerset @ X2489))|(~(in @ X2492 @ X2489)|(~(in @ X2492 @ (setminus @ X2489 @ X2490))|~(in @ X2492 @ (binintersect @ X2490 @ X2491))))))&((~(in @ X2494 @ (powerset @ X2493))|(~(in @ X2495 @ (powerset @ X2493))|(~(in @ X2496 @ X2493)|(~(in @ X2496 @ (setminus @ X2493 @ X2494))|(in @ X2496 @ (setminus @ X2493 @ (binintersect @ X2494 @ X2495)))))))&((~(in @ X2498 @ (powerset @ X2497))|(~(in @ X2499 @ (powerset @ X2497))|(subset @ (setminus @ X2497 @ X2498) @ (setminus @ X2497 @ (binintersect @ X2498 @ X2499)))))&((~(in @ X2501 @ (powerset @ X2500))|(~(in @ X2502 @ (powerset @ X2500))|(in @ (setminus @ X2500 @ X2501) @ (powerset @ (setminus @ X2500 @ (binintersect @ X2501 @ X2502))))))&((~(in @ X2504 @ (powerset @ X2503))|(~(in @ X2505 @ (powerset @ X2503))|(~(subset @ X2504 @ (setminus @ X2503 @ X2505))|(~(in @ X2506 @ X2503)|(~(in @ X2506 @ X2505)|(in @ X2506 @ (setminus @ X2503 @ X2504)))))))&((~(in @ X2508 @ (powerset @ X2507))|(~(in @ X2509 @ (powerset @ X2507))|(~(subset @ X2508 @ (setminus @ X2507 @ X2509))|(subset @ X2509 @ (setminus @ X2507 @ X2508)))))&((~(in @ X2511 @ (powerset @ X2510))|(~(in @ X2512 @ (powerset @ X2510))|(~(in @ X2513 @ X2510)|((in @ X2513 @ (binunion @ X2511 @ X2512))|~(in @ X2513 @ X2511)))))&((~(in @ X2515 @ (powerset @ X2514))|(~(in @ X2516 @ (powerset @ X2514))|(~(in @ X2517 @ X2514)|((in @ X2517 @ (binunion @ X2515 @ X2516))|~(in @ X2517 @ X2516)))))&((in @ esk88_0 @ (powerset @ esk87_0))&((in @ esk89_0 @ (powerset @ esk87_0))&((in @ esk90_0 @ (powerset @ esk87_0))&((in @ esk91_0 @ esk87_0)&((in @ esk91_0 @ (binintersect @ esk88_0 @ esk89_0))&~(in @ esk91_0 @ (binunion @ esk88_0 @ esk90_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_343])])])])])])])).
% 0.49/0.47 thf(c_0_345, negated_conjecture, ~((in @ esk91_0 @ (binunion @ esk88_0 @ esk90_0))), inference(split_conjunct,[status(thm)],[c_0_344])).
% 0.49/0.47 thf(c_0_346, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (binunion @ X3 @ X4))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_344])).
% 0.49/0.47 thf(c_0_347, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ X2 @ X3)|~((in @ X2 @ (binintersect @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_344])).
% 0.49/0.47 thf(c_0_348, negated_conjecture, (in @ esk91_0 @ (binintersect @ esk88_0 @ esk89_0)), inference(split_conjunct,[status(thm)],[c_0_344])).
% 0.49/0.47 thf(c_0_349, negated_conjecture, ~((in @ esk91_0 @ esk88_0)), inference(spm,[status(thm)],[c_0_345, c_0_346])).
% 0.49/0.47 thf(c_0_350, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_347, c_0_348]), c_0_349]), ['proof']).
% 0.49/0.47 % SZS output end CNFRefutation
% 0.49/0.47 % Parsed axioms : 555
% 0.49/0.47 % Removed by relevancy pruning/SinE : 0
% 0.49/0.47 % Initial clauses : 737
% 0.49/0.47 % Removed in clause preprocessing : 323
% 0.49/0.47 % Initial clauses in saturation : 414
% 0.49/0.47 % Processed clauses : 169
% 0.49/0.47 % ...of these trivial : 10
% 0.49/0.47 % ...subsumed : 41
% 0.49/0.47 % ...remaining for further processing : 118
% 0.49/0.47 % Other redundant clauses eliminated : 15
% 0.49/0.47 % Clauses deleted for lack of memory : 0
% 0.49/0.47 % Backward-subsumed : 2
% 0.49/0.47 % Backward-rewritten : 5
% 0.49/0.47 % Generated clauses : 396
% 0.49/0.47 % ...of the previous two non-redundant : 305
% 0.49/0.47 % ...aggressively subsumed : 0
% 0.49/0.47 % Contextual simplify-reflections : 0
% 0.49/0.47 % Paramodulations : 378
% 0.49/0.47 % Factorizations : 0
% 0.49/0.47 % NegExts : 0
% 0.49/0.47 % Equation resolutions : 18
% 0.49/0.47 % Disequality decompositions : 0
% 0.49/0.47 % Total rewrite steps : 85
% 0.49/0.47 % ...of those cached : 50
% 0.49/0.47 % Propositional unsat checks : 0
% 0.49/0.47 % Propositional check models : 0
% 0.49/0.47 % Propositional check unsatisfiable : 0
% 0.49/0.47 % Propositional clauses : 0
% 0.49/0.47 % Propositional clauses after purity: 0
% 0.49/0.47 % Propositional unsat core size : 0
% 0.49/0.47 % Propositional preprocessing time : 0.000
% 0.49/0.47 % Propositional encoding time : 0.000
% 0.49/0.47 % Propositional solver time : 0.000
% 0.49/0.47 % Success case prop preproc time : 0.000
% 0.49/0.47 % Success case prop encoding time : 0.000
% 0.49/0.47 % Success case prop solver time : 0.000
% 0.49/0.47 % Current number of processed clauses : 104
% 0.49/0.47 % Positive orientable unit clauses : 44
% 0.49/0.47 % Positive unorientable unit clauses: 0
% 0.49/0.47 % Negative unit clauses : 5
% 0.49/0.47 % Non-unit-clauses : 55
% 0.49/0.47 % Current number of unprocessed clauses: 548
% 0.49/0.47 % ...number of literals in the above : 1713
% 0.49/0.47 % Current number of archived formulas : 0
% 0.49/0.47 % Current number of archived clauses : 7
% 0.49/0.47 % Clause-clause subsumption calls (NU) : 402
% 0.49/0.47 % Rec. Clause-clause subsumption calls : 344
% 0.49/0.47 % Non-unit clause-clause subsumptions : 32
% 0.49/0.47 % Unit Clause-clause subsumption calls : 98
% 0.49/0.47 % Rewrite failures with RHS unbound : 0
% 0.49/0.47 % BW rewrite match attempts : 11
% 0.49/0.47 % BW rewrite match successes : 4
% 0.49/0.47 % Condensation attempts : 0
% 0.49/0.47 % Condensation successes : 0
% 0.49/0.47 % Termbank termtop insertions : 74206
% 0.49/0.47 % Search garbage collected termcells : 26615
% 0.49/0.47
% 0.49/0.47 % -------------------------------------------------
% 0.49/0.47 % User time : 0.099 s
% 0.49/0.47 % System time : 0.013 s
% 0.49/0.47 % Total time : 0.112 s
% 0.49/0.47 % Maximum resident set size: 9624 pages
% 0.49/0.47
% 0.49/0.47 % -------------------------------------------------
% 0.49/0.47 % User time : 0.110 s
% 0.49/0.47 % System time : 0.024 s
% 0.49/0.47 % Total time : 0.135 s
% 0.49/0.47 % Maximum resident set size: 5632 pages
% 0.49/0.47 % E exiting
%------------------------------------------------------------------------------