%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU750^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:25:28 AM UTC 2026
% Result : Theorem 0.55s 0.51s
% Output : CNFRefutation 0.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU750^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 % Computer : n011.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Tue Sep 29 14:21:32 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.24 Running higher-order theorem proving
% 0.20/0.31 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p
% 0.55/0.51 % Version: 3.5.1-ho
% 0.55/0.51 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.55/0.51 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.55/0.51 % Starting ehoh_best5 with 300s (1) cores
% 0.55/0.51 % Starting almost_fo_3_lam with 300s (1) cores
% 0.55/0.51 % Starting new_bool_5 with 300s (1) cores
% 0.55/0.51 % Starting pre_casc_3 with 300s (1) cores
% 0.55/0.51 % Starting ho_unfolding_8 with 300s (1) cores
% 0.55/0.51 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.55/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.55/0.51 % Starting new_ho_5 with 300s (1) cores
% 0.55/0.51 % new_bool_5 with pid 159143 completed with status 0
% 0.55/0.51 % Result found by new_bool_5
% 0.55/0.51 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.55/0.51 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.55/0.51 % Starting ehoh_best5 with 300s (1) cores
% 0.55/0.51 % Starting almost_fo_3_lam with 300s (1) cores
% 0.55/0.51 % Starting new_bool_5 with 300s (1) cores
% 0.55/0.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 0.55/0.51 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 0.55/0.51 % Search class: HGHSM-FSLM32-MHFMMSBN
% 0.55/0.51 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.55/0.51 % Starting SubtermCWHack with 28s (1) cores
% 0.55/0.51 % SubtermCWHack with pid 159159 completed with status 0
% 0.55/0.51 % Result found by SubtermCWHack
% 0.55/0.51 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.55/0.51 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.55/0.51 % Starting ehoh_best5 with 300s (1) cores
% 0.55/0.51 % Starting almost_fo_3_lam with 300s (1) cores
% 0.55/0.51 % Starting new_bool_5 with 300s (1) cores
% 0.55/0.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 0.55/0.51 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 0.55/0.51 % Search class: HGHSM-FSLM32-MHFMMSBN
% 0.55/0.51 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.55/0.51 % Starting SubtermCWHack with 28s (1) cores
% 0.55/0.51 % Preprocessing time : 0.004 s
% 0.55/0.51
% 0.55/0.51 % Proof found!
% 0.55/0.51 % SZS status Theorem
% 0.55/0.51 % SZS output start CNFRefutation
% 0.55/0.51 thf(decl_23, type, in: $i > $i > $o).
% 0.55/0.51 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.55/0.51 thf(decl_25, type, setextAx: $o).
% 0.55/0.51 thf(decl_26, type, emptyset: $i).
% 0.55/0.51 thf(decl_27, type, emptysetAx: $o).
% 0.55/0.51 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.55/0.51 thf(decl_29, type, setadjoinAx: $o).
% 0.55/0.51 thf(decl_30, type, powerset: $i > $i).
% 0.55/0.51 thf(decl_31, type, powersetAx: $o).
% 0.55/0.51 thf(decl_32, type, setunion: $i > $i).
% 0.55/0.51 thf(decl_33, type, setunionAx: $o).
% 0.55/0.51 thf(decl_34, type, omega: $i).
% 0.55/0.51 thf(decl_35, type, omega0Ax: $o).
% 0.55/0.51 thf(decl_36, type, omegaSAx: $o).
% 0.55/0.51 thf(decl_37, type, omegaIndAx: $o).
% 0.55/0.51 thf(decl_38, type, replAx: $o).
% 0.55/0.51 thf(decl_39, type, foundationAx: $o).
% 0.55/0.51 thf(decl_40, type, wellorderingAx: $o).
% 0.55/0.51 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.55/0.51 thf(decl_42, type, descrp: $o).
% 0.55/0.51 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.55/0.51 thf(decl_44, type, dsetconstrI: $o).
% 0.55/0.51 thf(decl_45, type, dsetconstrEL: $o).
% 0.55/0.51 thf(decl_46, type, dsetconstrER: $o).
% 0.55/0.51 thf(decl_47, type, exuE1: $o).
% 0.55/0.51 thf(decl_48, type, prop2set: $o > $i).
% 0.55/0.51 thf(decl_49, type, prop2setE: $o).
% 0.55/0.51 thf(decl_50, type, emptysetE: $o).
% 0.55/0.51 thf(decl_51, type, emptysetimpfalse: $o).
% 0.55/0.51 thf(decl_52, type, notinemptyset: $o).
% 0.55/0.51 thf(decl_53, type, exuE3e: $o).
% 0.55/0.51 thf(decl_54, type, setext: $o).
% 0.55/0.51 thf(decl_55, type, emptyI: $o).
% 0.55/0.51 thf(decl_56, type, noeltsimpempty: $o).
% 0.55/0.51 thf(decl_57, type, setbeta: $o).
% 0.55/0.51 thf(decl_58, type, nonempty: $i > $o).
% 0.55/0.51 thf(decl_59, type, nonemptyE1: $o).
% 0.55/0.51 thf(decl_60, type, nonemptyI: $o).
% 0.55/0.51 thf(decl_61, type, nonemptyI1: $o).
% 0.55/0.51 thf(decl_62, type, setadjoinIL: $o).
% 0.55/0.51 thf(decl_63, type, emptyinunitempty: $o).
% 0.55/0.51 thf(decl_64, type, setadjoinIR: $o).
% 0.55/0.51 thf(decl_65, type, setadjoinE: $o).
% 0.55/0.51 thf(decl_66, type, setadjoinOr: $o).
% 0.55/0.51 thf(decl_67, type, setoftrueEq: $o).
% 0.55/0.51 thf(decl_68, type, powersetI: $o).
% 0.55/0.51 thf(decl_69, type, emptyinPowerset: $o).
% 0.55/0.51 thf(decl_70, type, emptyInPowerset: $o).
% 0.55/0.51 thf(decl_71, type, powersetE: $o).
% 0.55/0.51 thf(decl_72, type, setunionI: $o).
% 0.55/0.51 thf(decl_73, type, setunionE: $o).
% 0.55/0.51 thf(decl_74, type, subPowSU: $o).
% 0.55/0.51 thf(decl_75, type, exuE2: $o).
% 0.55/0.51 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.55/0.51 thf(decl_77, type, uniqinunit: $o).
% 0.55/0.51 thf(decl_78, type, notinsingleton: $o).
% 0.55/0.51 thf(decl_79, type, eqinunit: $o).
% 0.55/0.51 thf(decl_80, type, singletonsswitch: $o).
% 0.55/0.51 thf(decl_81, type, upairsetE: $o).
% 0.55/0.51 thf(decl_82, type, upairsetIL: $o).
% 0.55/0.51 thf(decl_83, type, upairsetIR: $o).
% 0.55/0.51 thf(decl_84, type, emptyE1: $o).
% 0.55/0.51 thf(decl_85, type, vacuousDall: $o).
% 0.55/0.51 thf(decl_86, type, quantDeMorgan1: $o).
% 0.55/0.51 thf(decl_87, type, quantDeMorgan2: $o).
% 0.55/0.51 thf(decl_88, type, quantDeMorgan3: $o).
% 0.55/0.51 thf(decl_89, type, quantDeMorgan4: $o).
% 0.55/0.51 thf(decl_90, type, prop2setI: $o).
% 0.55/0.51 thf(decl_92, type, prop2set2propI: $o).
% 0.55/0.51 thf(decl_93, type, notdexE: $o).
% 0.55/0.51 thf(decl_94, type, notdallE: $o).
% 0.55/0.51 thf(decl_95, type, exuI1: $o).
% 0.55/0.51 thf(decl_96, type, exuI3: $o).
% 0.55/0.51 thf(decl_97, type, exuI2: $o).
% 0.55/0.51 thf(decl_98, type, inCongP: $o).
% 0.55/0.51 thf(decl_99, type, in__Cong: $o).
% 0.55/0.51 thf(decl_100, type, exuE3u: $o).
% 0.55/0.51 thf(decl_101, type, exu__Cong: $o).
% 0.55/0.51 thf(decl_102, type, emptyset__Cong: $o).
% 0.55/0.51 thf(decl_103, type, setadjoin__Cong: $o).
% 0.55/0.51 thf(decl_104, type, powerset__Cong: $o).
% 0.55/0.51 thf(decl_105, type, setunion__Cong: $o).
% 0.55/0.51 thf(decl_106, type, omega__Cong: $o).
% 0.55/0.51 thf(decl_107, type, exuEu: $o).
% 0.55/0.51 thf(decl_108, type, descr__Cong: $o).
% 0.55/0.51 thf(decl_109, type, dsetconstr__Cong: $o).
% 0.55/0.51 thf(decl_110, type, subset: $i > $i > $o).
% 0.55/0.51 thf(decl_113, type, subsetI1: $o).
% 0.55/0.51 thf(decl_114, type, eqimpsubset2: $o).
% 0.55/0.51 thf(decl_115, type, eqimpsubset1: $o).
% 0.55/0.51 thf(decl_116, type, subsetI2: $o).
% 0.55/0.51 thf(decl_117, type, emptysetsubset: $o).
% 0.55/0.51 thf(decl_118, type, subsetE: $o).
% 0.55/0.51 thf(decl_119, type, subsetE2: $o).
% 0.55/0.51 thf(decl_120, type, notsubsetI: $o).
% 0.55/0.51 thf(decl_121, type, notequalI1: $o).
% 0.55/0.51 thf(decl_122, type, notequalI2: $o).
% 0.55/0.51 thf(decl_123, type, subsetRefl: $o).
% 0.55/0.51 thf(decl_124, type, subsetTrans: $o).
% 0.55/0.51 thf(decl_125, type, setadjoinSub: $o).
% 0.55/0.51 thf(decl_126, type, setadjoinSub2: $o).
% 0.55/0.51 thf(decl_127, type, subset2powerset: $o).
% 0.55/0.51 thf(decl_128, type, setextsub: $o).
% 0.55/0.51 thf(decl_129, type, subsetemptysetimpeq: $o).
% 0.55/0.51 thf(decl_130, type, powersetI1: $o).
% 0.55/0.51 thf(decl_131, type, powersetE1: $o).
% 0.55/0.51 thf(decl_132, type, inPowerset: $o).
% 0.55/0.51 thf(decl_133, type, powersetsubset: $o).
% 0.55/0.51 thf(decl_134, type, sepInPowerset: $o).
% 0.55/0.51 thf(decl_135, type, sepSubset: $o).
% 0.55/0.51 thf(decl_136, type, binunion: $i > $i > $i).
% 0.55/0.51 thf(decl_137, type, binunionIL: $o).
% 0.55/0.51 thf(decl_138, type, upairset2IR: $o).
% 0.55/0.51 thf(decl_139, type, binunionIR: $o).
% 0.55/0.51 thf(decl_140, type, binunionEcases: $o).
% 0.55/0.51 thf(decl_141, type, binunionE: $o).
% 0.55/0.51 thf(decl_142, type, binunionLsub: $o).
% 0.55/0.51 thf(decl_143, type, binunionRsub: $o).
% 0.55/0.51 thf(decl_144, type, binintersect: $i > $i > $i).
% 0.55/0.51 thf(decl_145, type, binintersectI: $o).
% 0.55/0.51 thf(decl_146, type, binintersectSubset5: $o).
% 0.55/0.51 thf(decl_147, type, binintersectEL: $o).
% 0.55/0.51 thf(decl_148, type, binintersectLsub: $o).
% 0.55/0.51 thf(decl_149, type, binintersectSubset2: $o).
% 0.55/0.51 thf(decl_150, type, binintersectSubset3: $o).
% 0.55/0.51 thf(decl_151, type, binintersectER: $o).
% 0.55/0.51 thf(decl_152, type, disjointsetsI1: $o).
% 0.55/0.51 thf(decl_153, type, binintersectRsub: $o).
% 0.55/0.51 thf(decl_154, type, binintersectSubset4: $o).
% 0.55/0.51 thf(decl_155, type, binintersectSubset1: $o).
% 0.55/0.51 thf(decl_156, type, bs114d: $o).
% 0.55/0.51 thf(decl_158, type, setminus: $i > $i > $i).
% 0.55/0.51 thf(decl_159, type, setminusI: $o).
% 0.55/0.51 thf(decl_160, type, setminusEL: $o).
% 0.55/0.51 thf(decl_161, type, setminusER: $o).
% 0.55/0.51 thf(decl_162, type, setminusSubset2: $o).
% 0.55/0.51 thf(decl_163, type, setminusERneg: $o).
% 0.55/0.51 thf(decl_164, type, setminusELneg: $o).
% 0.55/0.51 thf(decl_165, type, setminusILneg: $o).
% 0.55/0.51 thf(decl_166, type, setminusIRneg: $o).
% 0.55/0.51 thf(decl_167, type, setminusLsub: $o).
% 0.55/0.51 thf(decl_168, type, setminusSubset1: $o).
% 0.55/0.51 thf(decl_169, type, symdiff: $i > $i > $i).
% 0.55/0.51 thf(decl_170, type, symdiffE: $o).
% 0.55/0.51 thf(decl_171, type, symdiffI1: $o).
% 0.55/0.51 thf(decl_172, type, symdiffI2: $o).
% 0.55/0.51 thf(decl_173, type, symdiffIneg1: $o).
% 0.55/0.51 thf(decl_174, type, symdiffIneg2: $o).
% 0.55/0.51 thf(decl_175, type, iskpair: $i > $o).
% 0.55/0.51 thf(decl_176, type, secondinupair: $o).
% 0.55/0.51 thf(decl_177, type, setukpairIL: $o).
% 0.55/0.51 thf(decl_178, type, setukpairIR: $o).
% 0.55/0.51 thf(decl_179, type, kpairiskpair: $o).
% 0.55/0.51 thf(decl_180, type, kpair: $i > $i > $i).
% 0.55/0.51 thf(decl_181, type, kpairp: $o).
% 0.55/0.51 thf(decl_182, type, cartprod: $i > $i > $i).
% 0.55/0.51 thf(decl_183, type, singletonsubset: $o).
% 0.55/0.51 thf(decl_184, type, singletoninpowerset: $o).
% 0.55/0.51 thf(decl_185, type, singletoninpowunion: $o).
% 0.55/0.51 thf(decl_186, type, upairset2E: $o).
% 0.55/0.51 thf(decl_187, type, upairsubunion: $o).
% 0.55/0.51 thf(decl_188, type, upairinpowunion: $o).
% 0.55/0.51 thf(decl_189, type, ubforcartprodlem1: $o).
% 0.55/0.51 thf(decl_190, type, ubforcartprodlem2: $o).
% 0.55/0.51 thf(decl_191, type, ubforcartprodlem3: $o).
% 0.55/0.51 thf(decl_192, type, cartprodpairin: $o).
% 0.55/0.51 thf(decl_193, type, cartprodmempair1: $o).
% 0.55/0.51 thf(decl_194, type, cartprodmempair: $o).
% 0.55/0.51 thf(decl_195, type, setunionE2: $o).
% 0.55/0.51 thf(decl_196, type, setunionsingleton1: $o).
% 0.55/0.51 thf(decl_197, type, setunionsingleton2: $o).
% 0.55/0.51 thf(decl_198, type, setunionsingleton: $o).
% 0.55/0.51 thf(decl_199, type, singleton: $i > $o).
% 0.55/0.51 thf(decl_200, type, singletonprop: $o).
% 0.55/0.51 thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 0.55/0.51 thf(decl_202, type, ex1E1: $o).
% 0.55/0.51 thf(decl_203, type, ex1I: $o).
% 0.55/0.51 thf(decl_204, type, ex1I2: $o).
% 0.55/0.51 thf(decl_205, type, singletonsuniq: $o).
% 0.55/0.51 thf(decl_210, type, setukpairinjL1: $o).
% 0.55/0.51 thf(decl_211, type, kfstsingleton: $o).
% 0.55/0.51 thf(decl_212, type, theprop: $o).
% 0.55/0.51 thf(decl_213, type, kfst: $i > $i).
% 0.55/0.51 thf(decl_214, type, kfstpairEq: $o).
% 0.55/0.51 thf(decl_215, type, cartprodfstin: $o).
% 0.55/0.51 thf(decl_216, type, setukpairinjL2: $o).
% 0.55/0.51 thf(decl_217, type, setukpairinjL: $o).
% 0.55/0.51 thf(decl_218, type, setukpairinjR11: $o).
% 0.55/0.51 thf(decl_219, type, setukpairinjR12: $o).
% 0.55/0.51 thf(decl_220, type, setukpairinjR1: $o).
% 0.55/0.51 thf(decl_221, type, upairequniteq: $o).
% 0.55/0.51 thf(decl_222, type, setukpairinjR2: $o).
% 0.55/0.51 thf(decl_223, type, setukpairinjR: $o).
% 0.55/0.51 thf(decl_224, type, ksndsingleton: $o).
% 0.55/0.51 thf(decl_225, type, ksnd: $i > $i).
% 0.55/0.51 thf(decl_226, type, ksndpairEq: $o).
% 0.55/0.51 thf(decl_227, type, kpairsurjEq: $o).
% 0.55/0.51 thf(decl_228, type, cartprodsndin: $o).
% 0.55/0.51 thf(decl_229, type, cartprodpairmemEL: $o).
% 0.55/0.51 thf(decl_230, type, cartprodpairmemER: $o).
% 0.55/0.51 thf(decl_231, type, cartprodmempaircEq: $o).
% 0.55/0.51 thf(decl_232, type, cartprodfstpairEq: $o).
% 0.55/0.51 thf(decl_233, type, cartprodsndpairEq: $o).
% 0.55/0.51 thf(decl_234, type, cartprodpairsurjEq: $o).
% 0.55/0.51 thf(decl_235, type, breln: $i > $i > $i > $o).
% 0.55/0.51 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 0.55/0.51 thf(decl_237, type, dpsetconstrI: $o).
% 0.55/0.51 thf(decl_238, type, dpsetconstrSub: $o).
% 0.55/0.51 thf(decl_239, type, setOfPairsIsBReln: $o).
% 0.55/0.51 thf(decl_240, type, dpsetconstrERa: $o).
% 0.55/0.51 thf(decl_241, type, dpsetconstrEL1: $o).
% 0.55/0.51 thf(decl_242, type, dpsetconstrEL2: $o).
% 0.55/0.51 thf(decl_243, type, dpsetconstrER: $o).
% 0.55/0.51 thf(decl_244, type, func: $i > $i > $i > $o).
% 0.55/0.51 thf(decl_245, type, funcSet: $i > $i > $i).
% 0.55/0.51 thf(decl_246, type, funcImageSingleton: $o).
% 0.55/0.51 thf(decl_247, type, apProp: $o).
% 0.55/0.51 thf(decl_248, type, ap: $i > $i > $i > $i > $i).
% 0.55/0.51 thf(decl_249, type, app: $o).
% 0.55/0.51 thf(decl_250, type, infuncsetfunc: $o).
% 0.55/0.51 thf(decl_251, type, ap2p: $o).
% 0.55/0.51 thf(decl_252, type, funcinfuncset: $o).
% 0.55/0.51 thf(decl_253, type, lamProp: $o).
% 0.55/0.51 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
% 0.55/0.51 thf(decl_255, type, lamp: $o).
% 0.55/0.51 thf(decl_256, type, lam2p: $o).
% 0.55/0.51 thf(decl_257, type, brelnall1: $o).
% 0.55/0.51 thf(decl_258, type, brelnall2: $o).
% 0.55/0.51 thf(decl_259, type, ex1E2: $o).
% 0.55/0.51 thf(decl_260, type, funcGraphProp1: $o).
% 0.55/0.51 thf(decl_261, type, funcGraphProp3: $o).
% 0.55/0.51 thf(decl_262, type, funcGraphProp2: $o).
% 0.55/0.51 thf(decl_263, type, funcextLem: $o).
% 0.55/0.51 thf(decl_264, type, funcGraphProp4: $o).
% 0.55/0.51 thf(decl_265, type, subbreln: $o).
% 0.55/0.51 thf(decl_266, type, eqbreln: $o).
% 0.55/0.51 thf(decl_267, type, funcext: $o).
% 0.55/0.51 thf(decl_268, type, funcext2: $o).
% 0.55/0.51 thf(decl_269, type, ap2apEq1: $o).
% 0.55/0.51 thf(decl_270, type, ap2apEq2: $o).
% 0.55/0.51 thf(decl_271, type, beta1: $o).
% 0.55/0.51 thf(decl_272, type, eta1: $o).
% 0.55/0.51 thf(decl_273, type, lam2lamEq: $o).
% 0.55/0.52 thf(decl_274, type, beta2: $o).
% 0.55/0.52 thf(decl_275, type, eta2: $o).
% 0.55/0.52 thf(decl_276, type, iffalseProp1: $o).
% 0.55/0.52 thf(decl_277, type, iffalseProp2: $o).
% 0.55/0.52 thf(decl_278, type, iftrueProp1: $o).
% 0.55/0.52 thf(decl_279, type, iftrueProp2: $o).
% 0.55/0.52 thf(decl_280, type, ifSingleton: $o).
% 0.55/0.52 thf(decl_281, type, if: $i > $o > $i > $i > $i).
% 0.55/0.52 thf(decl_282, type, ifp: $o).
% 0.55/0.52 thf(decl_283, type, theeq: $o).
% 0.55/0.52 thf(decl_284, type, iftrue: $o).
% 0.55/0.52 thf(decl_285, type, iffalse: $o).
% 0.55/0.52 thf(decl_286, type, iftrueorfalse: $o).
% 0.55/0.52 thf(decl_287, type, binintersectT_lem: $o).
% 0.55/0.52 thf(decl_288, type, binunionT_lem: $o).
% 0.55/0.52 thf(decl_289, type, powersetT_lem: $o).
% 0.55/0.52 thf(decl_290, type, setminusT_lem: $o).
% 0.55/0.52 thf(decl_291, type, complementT_lem: $o).
% 0.55/0.52 thf(decl_292, type, setextT: $o).
% 0.55/0.52 thf(decl_293, type, subsetTI: $o).
% 0.55/0.52 thf(decl_294, type, powersetTI1: $o).
% 0.55/0.52 thf(decl_295, type, powersetTE1: $o).
% 0.55/0.52 thf(decl_296, type, complementTI1: $o).
% 0.55/0.52 thf(decl_297, type, complementTE1: $o).
% 0.55/0.52 thf(decl_298, type, binintersectTELcontra: $o).
% 0.55/0.52 thf(decl_299, type, binintersectTERcontra: $o).
% 0.55/0.52 thf(decl_300, type, contrasubsetT: $o).
% 0.55/0.52 thf(decl_301, type, contrasubsetT1: $o).
% 0.55/0.52 thf(decl_302, type, contrasubsetT2: $o).
% 0.55/0.52 thf(decl_303, type, contrasubsetT3: $o).
% 0.55/0.52 thf(decl_304, type, doubleComplementI1: $o).
% 0.55/0.52 thf(decl_305, type, doubleComplementE1: $o).
% 0.55/0.52 thf(decl_306, type, doubleComplementSub1: $o).
% 0.55/0.52 thf(decl_307, type, doubleComplementSub2: $o).
% 0.55/0.52 thf(decl_308, type, doubleComplementEq: $o).
% 0.55/0.52 thf(decl_309, type, complementTnotintersectT: $o).
% 0.55/0.52 thf(decl_310, type, complementImpComplementIntersect: $o).
% 0.55/0.52 thf(decl_311, type, complementSubsetComplementIntersect: $o).
% 0.55/0.52 thf(decl_312, type, complementInPowersetComplementIntersect: $o).
% 0.55/0.52 thf(decl_313, type, contraSubsetComplement: $o).
% 0.55/0.52 thf(decl_314, type, complementTcontraSubset: $o).
% 0.55/0.52 thf(decl_315, type, binunionTILcontra: $o).
% 0.55/0.52 thf(decl_316, type, binunionTIRcontra: $o).
% 0.55/0.52 thf(decl_317, type, inIntersectImpInUnion: $o).
% 0.55/0.52 thf(decl_318, type, inIntersectImpInUnion2: $o).
% 0.55/0.52 thf(decl_319, type, inIntersectImpInIntersectUnions: $o).
% 0.55/0.52 thf(decl_320, type, intersectInPowersetIntersectUnions: $o).
% 0.55/0.52 thf(decl_321, type, inComplementUnionImpNotIn1: $o).
% 0.55/0.52 thf(decl_322, type, inComplementUnionImpInComplement1: $o).
% 0.55/0.52 thf(decl_323, type, binunionTE: $o).
% 0.55/0.52 thf(decl_324, type, binunionTEcontra: $o).
% 0.55/0.52 thf(decl_325, type, demorgan2a1: $o).
% 0.55/0.52 thf(decl_326, type, complementUnionInPowersetComplement: $o).
% 0.55/0.52 thf(decl_327, type, epred1_0: $o).
% 0.55/0.52 thf(decl_328, type, esk1_2: $i > $i > $i).
% 0.55/0.52 thf(decl_329, type, esk2_2: $i > $i > $i).
% 0.55/0.52 thf(decl_330, type, esk3_2: $i > $i > $i).
% 0.55/0.52 thf(decl_331, type, esk4_1: $i > $i).
% 0.55/0.52 thf(decl_332, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.55/0.52 thf(decl_333, type, esk6_2: ($i > $i > $o) > $i > $i).
% 0.55/0.52 thf(decl_334, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
% 0.55/0.52 thf(decl_335, type, esk8_1: $i > $i).
% 0.55/0.52 thf(decl_336, type, esk9_1: ($i > $o) > $i).
% 0.55/0.52 thf(decl_337, type, esk10_1: ($i > $o) > $i).
% 0.55/0.52 thf(decl_338, type, esk11_2: $i > $i > $i).
% 0.55/0.52 thf(decl_339, type, esk12_2: $i > $i > $i).
% 0.55/0.52 thf(decl_340, type, esk13_1: $i > $i).
% 0.55/0.52 thf(decl_341, type, esk14_1: $i > $i).
% 0.55/0.52 thf(decl_342, type, esk15_1: $i > $i).
% 0.55/0.52 thf(decl_343, type, esk16_2: $i > $i > $i).
% 0.55/0.52 thf(decl_344, type, esk17_3: $i > $i > $o > $i).
% 0.55/0.52 thf(decl_345, type, esk18_1: ($i > $o) > $i).
% 0.55/0.52 thf(decl_346, type, esk19_1: $i > $i).
% 0.55/0.52 thf(decl_347, type, esk20_2: $i > ($i > $o) > $i).
% 0.55/0.52 thf(decl_348, type, esk21_2: $i > ($i > $o) > $i).
% 0.55/0.52 thf(decl_349, type, esk22_2: $i > ($i > $o) > $i).
% 0.55/0.52 thf(decl_350, type, esk23_2: $i > ($i > $o) > $i).
% 0.55/0.52 thf(decl_351, type, esk24_2: $i > ($i > $o) > $i).
% 0.55/0.52 thf(decl_352, type, esk25_2: $i > ($i > $o) > $i).
% 0.55/0.52 thf(decl_353, type, esk26_2: ($i > $o) > $i > $i).
% 0.55/0.52 thf(decl_354, type, esk27_1: ($i > $o) > $i).
% 0.55/0.52 thf(decl_355, type, esk28_1: ($i > $o) > $i).
% 0.55/0.52 thf(decl_356, type, esk29_2: ($i > $o) > $i > $i).
% 0.55/0.52 thf(decl_357, type, esk30_2: ($i > $o) > ($i > $o) > $i).
% 0.55/0.52 thf(decl_358, type, esk31_2: ($i > $o) > ($i > $o) > $i).
% 0.55/0.52 thf(decl_359, type, esk32_2: ($i > $o) > ($i > $o) > $i).
% 0.55/0.52 thf(decl_360, type, esk33_2: ($i > $o) > ($i > $o) > $i).
% 0.55/0.52 thf(decl_361, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.55/0.52 thf(decl_362, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.55/0.52 thf(decl_363, type, esk36_2: $i > $i > $i).
% 0.55/0.52 thf(decl_364, type, esk37_2: $i > $i > $i).
% 0.55/0.52 thf(decl_365, type, esk38_2: $i > $i > $i).
% 0.55/0.52 thf(decl_366, type, esk39_3: $i > $i > $i > $i).
% 0.55/0.52 thf(decl_367, type, esk40_3: $i > $i > $i > $i).
% 0.55/0.52 thf(decl_368, type, esk41_2: $i > $i > $i).
% 0.55/0.52 thf(decl_369, type, esk42_2: $i > ($i > $o) > $i).
% 0.55/0.52 thf(decl_370, type, esk43_2: $i > ($i > $o) > $i).
% 0.55/0.52 thf(decl_371, type, esk44_2: $i > ($i > $o) > $i).
% 0.55/0.52 thf(decl_372, type, esk45_3: $i > ($i > $o) > $i > $i).
% 0.55/0.52 thf(decl_373, type, esk46_2: $i > ($i > $o) > $i).
% 0.55/0.52 thf(decl_374, type, esk47_2: $i > ($i > $o) > $i).
% 0.55/0.52 thf(decl_375, type, esk48_3: $i > $i > ($i > $i) > $i).
% 0.55/0.52 thf(decl_376, type, esk49_3: $i > $i > ($i > $i) > $i).
% 0.55/0.52 thf(decl_377, type, esk50_3: $i > $i > ($i > $i) > $i).
% 0.55/0.52 thf(decl_378, type, esk51_4: $i > $i > $i > ($i > $o) > $i).
% 0.55/0.52 thf(decl_379, type, esk52_4: $i > $i > $i > ($i > $o) > $i).
% 0.55/0.52 thf(decl_380, type, esk53_4: $i > $i > $i > ($i > $o) > $i).
% 0.55/0.52 thf(decl_381, type, esk54_4: $i > $i > $i > ($i > $o) > $i).
% 0.55/0.52 thf(decl_382, type, esk55_4: $i > $i > $i > $i > $i).
% 0.55/0.52 thf(decl_383, type, esk56_4: $i > $i > $i > $i > $i).
% 0.55/0.52 thf(decl_384, type, esk57_4: $i > $i > $i > $i > $i).
% 0.55/0.52 thf(decl_385, type, esk58_4: $i > $i > $i > $i > $i).
% 0.55/0.52 thf(decl_386, type, esk59_4: $i > $i > $i > $i > $i).
% 0.55/0.52 thf(decl_387, type, esk60_4: $i > $i > $i > $i > $i).
% 0.55/0.52 thf(decl_388, type, esk61_4: $i > $i > $i > $i > $i).
% 0.55/0.52 thf(decl_389, type, esk62_4: $i > $i > $i > $i > $i).
% 0.55/0.52 thf(decl_390, type, esk63_4: $i > $i > $i > $i > $i).
% 0.55/0.52 thf(decl_391, type, esk64_3: $i > $i > ($i > $i) > $i).
% 0.55/0.52 thf(decl_392, type, esk65_3: $i > $i > ($i > $i) > $i).
% 0.55/0.52 thf(decl_393, type, esk66_3: $i > $i > ($i > $i) > $i).
% 0.55/0.52 thf(decl_394, type, esk67_3: $i > $i > $i > $i).
% 0.55/0.52 thf(decl_395, type, esk68_3: $i > $i > $i > $i).
% 0.55/0.52 thf(decl_396, type, esk69_3: $i > $i > $i > $i).
% 0.55/0.52 thf(decl_397, type, esk70_3: $i > $i > $i > $i).
% 0.55/0.52 thf(decl_398, type, esk71_0: $i).
% 0.55/0.52 thf(decl_399, type, esk72_0: $i).
% 0.55/0.52 thf(decl_400, type, esk73_0: $i).
% 0.55/0.52 thf(decl_401, type, esk74_0: $i).
% 0.55/0.52 thf(demorgan2a2, 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)=>((inIntersectImpInUnion)=>((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>((binunionTE)=>((binunionTEcontra)=>((demorgan2a1)=>((complementUnionInPowersetComplement)=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', demorgan2a2)).
% 0.55/0.52 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', exuI2)).
% 0.55/0.52 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', exuI3)).
% 0.55/0.52 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', exuI1)).
% 0.55/0.52 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', exu__Cong)).
% 0.55/0.52 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', exuE3u)).
% 0.55/0.52 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', exuEu)).
% 0.55/0.52 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', dsetconstr__Cong)).
% 0.55/0.52 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', descr__Cong)).
% 0.55/0.52 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', sepInPowerset)).
% 0.55/0.52 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', sepSubset)).
% 0.55/0.52 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/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', beta2)).
% 0.55/0.52 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/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', lam2lamEq)).
% 0.55/0.52 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/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', eta1)).
% 0.55/0.52 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/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', beta1)).
% 0.55/0.52 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', kfstsingleton)).
% 0.55/0.52 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', ex1I2)).
% 0.55/0.52 thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', ex1I)).
% 0.55/0.52 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', ex1E1)).
% 0.55/0.52 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', singletonprop)).
% 0.55/0.52 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', ksndsingleton)).
% 0.55/0.52 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setOfPairsIsBReln)).
% 0.55/0.52 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', dpsetconstrSub)).
% 0.55/0.52 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', dpsetconstrI)).
% 0.55/0.52 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', dpsetconstrERa)).
% 0.55/0.52 thf(apProp, axiom, ((apProp)<=>![X4:$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/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', apProp)).
% 0.55/0.52 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', funcImageSingleton)).
% 0.55/0.52 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', dpsetconstrER)).
% 0.55/0.52 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', dpsetconstrEL2)).
% 0.55/0.52 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', dpsetconstrEL1)).
% 0.55/0.52 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', ex1E2)).
% 0.55/0.52 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:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', lam2p)).
% 0.55/0.52 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', lamp)).
% 0.55/0.52 thf(lamProp, axiom, ((lamProp)<=>![X4:$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/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', lamProp)).
% 0.55/0.52 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/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', eta2)).
% 0.55/0.52 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X40))&(((X14)=(X2)))))|(((~((X40)))&(((X14)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', iffalseProp2)).
% 0.55/0.52 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$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/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', iftrueProp1)).
% 0.55/0.52 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X42))&(((X14)=(X2)))))|(((~((X42)))&(((X14)=(X3)))))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', iftrueProp2)).
% 0.55/0.52 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$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/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', ifSingleton)).
% 0.55/0.52 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X39))&(((X14)=(X2)))))|(((~((X39)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', iffalseProp1)).
% 0.55/0.52 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', emptyE1)).
% 0.55/0.52 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', exuE2)).
% 0.55/0.52 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setoftrueEq)).
% 0.55/0.52 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', nonemptyI)).
% 0.55/0.52 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setbeta)).
% 0.55/0.52 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', exuE3e)).
% 0.55/0.52 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', exuE1)).
% 0.55/0.52 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', dsetconstrER)).
% 0.55/0.52 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', dsetconstrEL)).
% 0.55/0.52 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', dsetconstrI)).
% 0.55/0.52 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', descrp)).
% 0.55/0.52 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', replAx)).
% 0.55/0.52 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', theeq)).
% 0.55/0.52 thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', ifp)).
% 0.55/0.52 thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', iftrue)).
% 0.55/0.52 thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', iffalse)).
% 0.55/0.52 thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', iftrueorfalse)).
% 0.55/0.52 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', binintersectT_lem)).
% 0.55/0.52 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', binunionT_lem)).
% 0.55/0.52 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', inCongP)).
% 0.55/0.52 thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', powersetT_lem)).
% 0.55/0.52 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setminusT_lem)).
% 0.55/0.52 thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', complementT_lem)).
% 0.55/0.52 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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setextT)).
% 0.55/0.52 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', notdallE)).
% 0.55/0.52 thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', subsetTI)).
% 0.55/0.52 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', notdexE)).
% 0.55/0.52 thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', powersetTI1)).
% 0.55/0.52 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', prop2setI)).
% 0.55/0.52 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/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', powersetTE1)).
% 0.55/0.52 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', in__Cong)).
% 0.55/0.52 thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', complementTI1)).
% 0.55/0.52 thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', complementTE1)).
% 0.55/0.52 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/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', binintersectTELcontra)).
% 0.55/0.52 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/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', binintersectTERcontra)).
% 0.55/0.52 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/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', contrasubsetT)).
% 0.55/0.52 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/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', contrasubsetT1)).
% 0.55/0.52 thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', contrasubsetT2)).
% 0.55/0.52 thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$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/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', contrasubsetT3)).
% 0.55/0.52 thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', doubleComplementI1)).
% 0.55/0.52 thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$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/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', doubleComplementE1)).
% 0.55/0.52 thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', doubleComplementSub1)).
% 0.55/0.52 thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', doubleComplementSub2)).
% 0.55/0.52 thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', doubleComplementEq)).
% 0.55/0.52 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/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', complementTnotintersectT)).
% 0.55/0.52 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', omega__Cong)).
% 0.55/0.52 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/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', complementImpComplementIntersect)).
% 0.55/0.52 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setunion__Cong)).
% 0.55/0.52 thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', complementSubsetComplementIntersect)).
% 0.55/0.52 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', powerset__Cong)).
% 0.55/0.52 thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$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/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', complementInPowersetComplementIntersect)).
% 0.55/0.52 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setadjoin__Cong)).
% 0.55/0.52 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/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', contraSubsetComplement)).
% 0.55/0.52 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', emptyset__Cong)).
% 0.55/0.52 thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', complementTcontraSubset)).
% 0.55/0.52 thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', binunionTILcontra)).
% 0.55/0.52 thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', binunionTIRcontra)).
% 0.55/0.52 thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$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/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', inIntersectImpInUnion)).
% 0.55/0.52 thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', inIntersectImpInUnion2)).
% 0.55/0.52 thf(inIntersectImpInIntersectUnions, axiom, ((inIntersectImpInIntersectUnions)<=>![X4:$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 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', inIntersectImpInIntersectUnions)).
% 0.55/0.52 thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', intersectInPowersetIntersectUnions)).
% 0.55/0.52 thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', inComplementUnionImpNotIn1)).
% 0.55/0.52 thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', inComplementUnionImpInComplement1)).
% 0.55/0.52 thf(binunionTE, axiom, ((binunionTE)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X50:$o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ X21 @ X48))=>(((in @ X2 @ X21)=>(X50))=>(((in @ X2 @ X48)=>(X50))=>(X50))))))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', binunionTE)).
% 0.55/0.52 thf(binunionTEcontra, axiom, ((binunionTEcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', binunionTEcontra)).
% 0.55/0.52 thf(demorgan2a1, axiom, ((demorgan2a1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', demorgan2a1)).
% 0.55/0.52 thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', complementUnionInPowersetComplement)).
% 0.55/0.52 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', emptysetsubset)).
% 0.55/0.52 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', subsetI2)).
% 0.55/0.52 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', eqimpsubset1)).
% 0.55/0.52 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', eqimpsubset2)).
% 0.55/0.52 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', subsetI1)).
% 0.55/0.52 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', subsetE)).
% 0.55/0.52 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setadjoinSub)).
% 0.55/0.52 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', subsetTrans)).
% 0.55/0.52 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', subsetRefl)).
% 0.55/0.52 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', notequalI2)).
% 0.55/0.52 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', notequalI1)).
% 0.55/0.52 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', notsubsetI)).
% 0.55/0.52 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', subsetE2)).
% 0.55/0.52 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setadjoinSub2)).
% 0.55/0.52 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', powersetsubset)).
% 0.55/0.52 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', inPowerset)).
% 0.55/0.52 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', powersetE1)).
% 0.55/0.52 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', powersetI1)).
% 0.55/0.52 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', subsetemptysetimpeq)).
% 0.55/0.52 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setextsub)).
% 0.55/0.52 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', subset2powerset)).
% 0.55/0.52 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', binunionLsub)).
% 0.55/0.52 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', binunionE)).
% 0.55/0.52 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', binunionEcases)).
% 0.55/0.52 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', binunionIR)).
% 0.55/0.52 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', upairset2IR)).
% 0.55/0.52 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', binunionIL)).
% 0.55/0.52 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', binunionRsub)).
% 0.55/0.52 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', binintersectER)).
% 0.55/0.52 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', binintersectSubset3)).
% 0.55/0.52 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', binintersectSubset2)).
% 0.55/0.52 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', binintersectLsub)).
% 0.55/0.52 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', binintersectEL)).
% 0.55/0.52 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', binintersectSubset5)).
% 0.55/0.52 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', binintersectI)).
% 0.55/0.52 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', disjointsetsI1)).
% 0.55/0.52 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/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', ap2apEq2)).
% 0.55/0.52 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/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', ap2apEq1)).
% 0.55/0.52 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setminusER)).
% 0.55/0.52 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setminusEL)).
% 0.55/0.52 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setminusI)).
% 0.55/0.52 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', bs114d)).
% 0.55/0.52 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', binintersectSubset1)).
% 0.55/0.52 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', binintersectSubset4)).
% 0.55/0.52 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', binintersectRsub)).
% 0.55/0.52 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setminusSubset2)).
% 0.55/0.52 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', symdiffE)).
% 0.55/0.52 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setminusSubset1)).
% 0.55/0.52 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setminusLsub)).
% 0.55/0.52 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setminusIRneg)).
% 0.55/0.52 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setminusILneg)).
% 0.55/0.52 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setminusELneg)).
% 0.55/0.52 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setminusERneg)).
% 0.55/0.52 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', symdiffI1)).
% 0.55/0.52 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', kpairiskpair)).
% 0.55/0.52 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setukpairIR)).
% 0.55/0.52 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setukpairIL)).
% 0.55/0.52 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', secondinupair)).
% 0.55/0.52 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', symdiffIneg2)).
% 0.55/0.52 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', symdiffIneg1)).
% 0.55/0.52 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', symdiffI2)).
% 0.55/0.52 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', kpairp)).
% 0.55/0.52 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', ubforcartprodlem1)).
% 0.55/0.52 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', upairinpowunion)).
% 0.55/0.52 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', upairsubunion)).
% 0.55/0.52 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', upairset2E)).
% 0.55/0.52 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', singletoninpowunion)).
% 0.55/0.52 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', singletoninpowerset)).
% 0.55/0.52 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', singletonsubset)).
% 0.55/0.52 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', ubforcartprodlem2)).
% 0.55/0.52 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setunionsingleton2)).
% 0.55/0.52 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setunionsingleton1)).
% 0.55/0.52 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setunionE2)).
% 0.55/0.52 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', cartprodmempair)).
% 0.55/0.52 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', cartprodmempair1)).
% 0.55/0.52 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', cartprodpairin)).
% 0.55/0.52 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', ubforcartprodlem3)).
% 0.55/0.52 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setunionsingleton)).
% 0.55/0.52 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setukpairinjL1)).
% 0.55/0.52 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', singletonsuniq)).
% 0.55/0.52 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', theprop)).
% 0.55/0.52 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setukpairinjR1)).
% 0.55/0.52 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setukpairinjR12)).
% 0.55/0.52 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setukpairinjR11)).
% 0.55/0.52 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setukpairinjL)).
% 0.55/0.52 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setukpairinjL2)).
% 0.55/0.52 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', cartprodfstin)).
% 0.55/0.52 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', kfstpairEq)).
% 0.55/0.52 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', upairequniteq)).
% 0.55/0.52 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', cartprodpairmemEL)).
% 0.55/0.52 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', cartprodsndin)).
% 0.55/0.52 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', kpairsurjEq)).
% 0.55/0.52 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', ksndpairEq)).
% 0.55/0.52 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setukpairinjR)).
% 0.55/0.52 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setukpairinjR2)).
% 0.55/0.52 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', cartprodpairmemER)).
% 0.55/0.52 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', cartprodpairsurjEq)).
% 0.55/0.52 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', cartprodsndpairEq)).
% 0.55/0.52 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', cartprodfstpairEq)).
% 0.55/0.52 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', cartprodmempaircEq)).
% 0.55/0.52 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', infuncsetfunc)).
% 0.55/0.52 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/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', app)).
% 0.55/0.52 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/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', ap2p)).
% 0.55/0.52 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/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', brelnall2)).
% 0.55/0.52 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/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', brelnall1)).
% 0.55/0.52 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', funcinfuncset)).
% 0.55/0.52 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', funcGraphProp1)).
% 0.55/0.52 thf(funcext, axiom, ((funcext)<=>![X4:$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/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', funcext)).
% 0.55/0.52 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/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', eqbreln)).
% 0.55/0.52 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/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', subbreln)).
% 0.55/0.52 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', funcGraphProp4)).
% 0.55/0.52 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$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/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', funcextLem)).
% 0.55/0.52 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', funcGraphProp2)).
% 0.55/0.52 thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', funcGraphProp3)).
% 0.55/0.52 thf(funcext2, axiom, ((funcext2)<=>![X4:$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/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', funcext2)).
% 0.55/0.52 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', quantDeMorgan4)).
% 0.55/0.52 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', quantDeMorgan3)).
% 0.55/0.52 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', quantDeMorgan2)).
% 0.55/0.52 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', quantDeMorgan1)).
% 0.55/0.52 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', vacuousDall)).
% 0.55/0.52 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', upairsetIR)).
% 0.55/0.52 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', upairsetIL)).
% 0.55/0.52 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', upairsetE)).
% 0.55/0.52 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', singletonsswitch)).
% 0.55/0.52 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', eqinunit)).
% 0.55/0.52 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', notinsingleton)).
% 0.55/0.52 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', uniqinunit)).
% 0.55/0.52 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', nonemptyImpWitness)).
% 0.55/0.52 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', subPowSU)).
% 0.55/0.52 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setunionE)).
% 0.55/0.52 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setunionI)).
% 0.55/0.52 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', powersetE)).
% 0.55/0.52 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', emptyInPowerset)).
% 0.55/0.52 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', emptyinPowerset)).
% 0.55/0.52 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', powersetI)).
% 0.55/0.52 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setadjoinOr)).
% 0.55/0.52 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setadjoinE)).
% 0.55/0.52 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setadjoinIR)).
% 0.55/0.52 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', emptyinunitempty)).
% 0.55/0.52 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setadjoinIL)).
% 0.55/0.52 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', nonemptyI1)).
% 0.55/0.52 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', nonemptyE1)).
% 0.55/0.52 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', noeltsimpempty)).
% 0.55/0.52 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', emptyI)).
% 0.55/0.52 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setext)).
% 0.55/0.52 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', notinemptyset)).
% 0.55/0.52 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', emptysetimpfalse)).
% 0.55/0.52 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', emptysetE)).
% 0.55/0.52 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', prop2setE)).
% 0.55/0.52 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', wellorderingAx)).
% 0.55/0.52 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', foundationAx)).
% 0.55/0.52 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', omegaIndAx)).
% 0.55/0.52 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', omegaSAx)).
% 0.55/0.52 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', omega0Ax)).
% 0.55/0.52 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setunionAx)).
% 0.55/0.52 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', powersetAx)).
% 0.55/0.52 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setadjoinAx)).
% 0.55/0.52 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', emptysetAx)).
% 0.55/0.52 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.iZ1TZCs5Rb/E---3.1_159128.p', setextAx)).
% 0.55/0.52 thf(c_0_266, 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)=>((inIntersectImpInUnion)=>((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>((binunionTE)=>((binunionTEcontra)=>((demorgan2a1)=>((complementUnionInPowersetComplement)=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[demorgan2a2])).
% 0.55/0.52 thf(c_0_267, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.55/0.52 thf(c_0_268, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.55/0.52 thf(c_0_269, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 0.55/0.52 thf(c_0_270, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.55/0.52 thf(c_0_271, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 0.55/0.52 thf(c_0_272, 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])).
% 0.55/0.52 thf(c_0_273, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 0.55/0.52 thf(c_0_274, plain, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 0.55/0.52 thf(c_0_275, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 0.55/0.52 thf(c_0_276, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 0.55/0.52 thf(c_0_277, 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])).
% 0.55/0.52 thf(c_0_278, 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])).
% 0.55/0.52 thf(c_0_279, 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])).
% 0.55/0.52 thf(c_0_280, 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])).
% 0.55/0.52 thf(c_0_281, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 0.55/0.52 thf(c_0_282, plain, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 0.55/0.52 thf(c_0_283, plain, ((ex1I)<=>![X4:$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])).
% 0.55/0.52 thf(c_0_284, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 0.55/0.52 thf(c_0_285, plain, ((singletonprop)<=>![X4:$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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 0.55/0.52 thf(c_0_286, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 0.55/0.52 thf(c_0_287, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 0.55/0.52 thf(c_0_288, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 0.55/0.52 thf(c_0_289, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 0.55/0.52 thf(c_0_290, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 0.55/0.52 thf(c_0_291, plain, ((apProp)<=>![X4:$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])).
% 0.55/0.52 thf(c_0_292, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
% 0.55/0.52 thf(c_0_293, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 0.55/0.52 thf(c_0_294, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 0.55/0.52 thf(c_0_295, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 0.55/0.52 thf(c_0_296, plain, ((ex1E2)<=>![X4:$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])).
% 0.55/0.52 thf(c_0_297, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
% 0.55/0.52 thf(c_0_298, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
% 0.55/0.52 thf(c_0_299, plain, ((lamProp)<=>![X4:$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])).
% 0.55/0.52 thf(c_0_300, 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])).
% 0.55/0.52 thf(c_0_301, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X40))&(((Z0)=(X2)))))|(((~((X40)))&(((Z0)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])).
% 0.55/0.52 thf(c_0_302, plain, ((iftrueProp1)<=>![X4:$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])).
% 0.55/0.52 thf(c_0_303, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X42))&(((Z0)=(X2)))))|(((~((X42)))&(((Z0)=(X3)))))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])).
% 0.55/0.52 thf(c_0_304, plain, ((ifSingleton)<=>![X4:$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])).
% 0.55/0.52 thf(c_0_305, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X39))&(((Z0)=(X2)))))|(((~((X39)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
% 0.55/0.52 thf(c_0_306, plain, ((emptyE1)<=>![X4:$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])).
% 0.55/0.52 thf(c_0_307, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.55/0.52 thf(c_0_308, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.55/0.52 thf(c_0_309, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.55/0.52 thf(c_0_310, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.55/0.52 thf(c_0_311, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.55/0.52 thf(c_0_312, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.55/0.52 thf(c_0_313, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.55/0.52 thf(c_0_314, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.55/0.52 thf(c_0_315, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.55/0.52 thf(c_0_316, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.55/0.52 thf(c_0_317, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.55/0.52 thf(c_0_318, plain, ((epred1_0)<=>![X919:$i]:(?[X920:$i]:((((![X921:$i]:(((in @ X921 @ X920)=>![X922:$i]:(((in @ X922 @ X921)=>(in @ X922 @ X919)))))&![X923:$i, X924:$i]:((((in @ X923 @ X919)&(in @ X924 @ X919))=>(![X925:$i]:(((in @ X925 @ X920)=>((in @ X923 @ X925)<=>(in @ X924 @ X925))))=>((X923)=(X924))))))&![X926:$i, X927:$i]:((((in @ X926 @ X920)&(in @ X927 @ X920))=>(![X928:$i]:(((in @ X928 @ X926)=>(in @ X928 @ X927)))|![X929:$i]:(((in @ X929 @ X927)=>(in @ X929 @ X926)))))))&![X930:$i]:(((![X931:$i]:(((in @ X931 @ X930)=>(in @ X931 @ X919)))&?[X932:$i]:((in @ X932 @ X930)))=>?[X933:$i, X934:$i]:(((((in @ X933 @ X920)&(in @ X934 @ X930))&~(?[X935:$i]:(((in @ X935 @ X933)&(in @ X935 @ X930)))))&![X936:$i]:(((in @ X936 @ X920)=>(![X937:$i]:(((in @ X937 @ X936)=>(in @ X937 @ X933)))|(in @ X934 @ X936)))))))))))), introduced(definition)).
% 0.55/0.52 thf(c_0_319, negated_conjecture, ~((![X892:$i, X893:$i]:((![X894:$i]:(((in @ X894 @ X892)<=>(in @ X894 @ X893)))=>((X892)=(X893))))=>(![X895:$i]:(~(in @ X895 @ emptyset))=>(![X896:$i, X897:$i, X898:$i]:(((in @ X898 @ (setadjoin @ X896 @ X897))<=>(((X898)=(X896))|(in @ X898 @ X897))))=>(![X899:$i, X900:$i]:(((in @ X900 @ (powerset @ X899))<=>![X901:$i]:(((in @ X901 @ X900)=>(in @ X901 @ X899)))))=>(![X902:$i, X903:$i]:(((in @ X903 @ (setunion @ X902))<=>?[X904:$i]:(((in @ X903 @ X904)&(in @ X904 @ X902)))))=>((in @ emptyset @ omega)=>(![X905:$i]:(((in @ X905 @ omega)=>(in @ (setadjoin @ X905 @ X905) @ omega)))=>(![X906:$i]:((((in @ emptyset @ X906)&![X907:$i]:((((in @ X907 @ omega)&(in @ X907 @ X906))=>(in @ (setadjoin @ X907 @ X907) @ X906))))=>![X908:$i]:(((in @ X908 @ omega)=>(in @ X908 @ X906)))))=>(![X909:$i > $i > $o, X910:$i]:((![X911:$i]:(((in @ X911 @ X910)=>(exu @ (X909 @ X911))))=>?[X912:$i]:(![X913:$i]:(((in @ X913 @ X912)<=>?[X914:$i]:(((in @ X914 @ X910)&(X909 @ X914 @ X913))))))))=>(![X915:$i]:((?[X916:$i]:((in @ X916 @ X915))=>?[X917:$i]:(((in @ X917 @ X915)&~(?[X918:$i]:(((in @ X918 @ X917)&(in @ X918 @ X915))))))))=>((epred1_0)=>(![X938:$i > $o]:(((exu @ X938)=>(X938 @ (descr @ (^[Z0:$i]:(X938 @ Z0))))))=>(![X939:$i, X940:$i > $o, X941:$i]:(((in @ X941 @ X939)=>((X940 @ X941)=>(in @ X941 @ (dsetconstr @ X939 @ X940)))))=>(![X942:$i, X943:$i > $o, X944:$i]:(((in @ X944 @ (dsetconstr @ X942 @ X943))=>(in @ X944 @ X942)))=>(![X945:$i, X946:$i > $o, X947:$i]:(((in @ X947 @ (dsetconstr @ X945 @ X946))=>(X946 @ X947)))=>(![X948:$i > $o]:(((exu @ X948)=>?[X949:$i]:(((X948 @ X949)&![X950:$i]:(((X948 @ X950)=>((X949)=(X950))))))))=>(![X951:$o, X952:$i]:(((in @ X952 @ (prop2set @ ((X951))))=>(X951)))=>(![X953:$i]:(((in @ X953 @ emptyset)=>![X954:$o]:((X954))))=>(![X955:$i]:(((in @ X955 @ emptyset)=>~($true)))=>(![X956:$i]:(~(in @ X956 @ emptyset))=>(![X957:$i > $o]:(((exu @ X957)=>?[X958:$i]:((X957 @ X958))))=>(![X959:$i, X960:$i]:((![X961:$i]:(((in @ X961 @ X959)=>(in @ X961 @ X960)))=>(![X962:$i]:(((in @ X962 @ X960)=>(in @ X962 @ X959)))=>((X959)=(X960)))))=>(![X963:$i]:((![X964:$i]:(~(in @ X964 @ X963))=>((X963)=(emptyset))))=>(![X965:$i]:((![X966:$i]:(~(in @ X966 @ X965))=>((X965)=(emptyset))))=>(![X967:$i, X968:$i > $o, X969:$i]:(((in @ X969 @ X967)=>((in @ X969 @ (dsetconstr @ X967 @ X968))<=>(X968 @ X969))))=>(![X970:$i]:(((nonempty @ X970)=>?[X971:$i]:((in @ X971 @ X970))))=>(![X972:$i, X973:$i > $o, X974:$i]:(((in @ X974 @ X972)=>((X973 @ X974)=>(nonempty @ (dsetconstr @ X972 @ X973)))))=>(![X975:$i]:((?[X976:$i]:((in @ X976 @ X975))=>(nonempty @ X975)))=>(![X977:$i, X978:$i]:((in @ X977 @ (setadjoin @ X977 @ X978)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X979:$i, X980:$i, X981:$i]:(((in @ X981 @ X980)=>(in @ X981 @ (setadjoin @ X979 @ X980))))=>(![X982:$i, X983:$i, X984:$i]:(((in @ X984 @ (setadjoin @ X982 @ X983))=>![X985:$o]:(((((X984)=(X982))=>(X985))=>(((in @ X984 @ X983)=>(X985))=>(X985))))))=>(![X986:$i, X987:$i, X988:$i]:(((in @ X988 @ (setadjoin @ X986 @ X987))=>(((X988)=(X986))|(in @ X988 @ X987))))=>(![X989:$i]:(((dsetconstr @ X989 @ (^[Z0:$i]:($true)))=(X989)))=>(![X990:$i, X991:$i]:((![X992:$i]:(((in @ X992 @ X991)=>(in @ X992 @ X990)))=>(in @ X991 @ (powerset @ X990))))=>(![X993:$i]:((in @ emptyset @ (powerset @ X993)))=>(![X994:$i]:((in @ emptyset @ (powerset @ X994)))=>(![X995:$i, X996:$i, X997:$i]:(((in @ X996 @ (powerset @ X995))=>((in @ X997 @ X996)=>(in @ X997 @ X995))))=>(![X998:$i, X999:$i, X1000:$i]:(((in @ X999 @ X1000)=>((in @ X1000 @ X998)=>(in @ X999 @ (setunion @ X998)))))=>(![X1001:$i, X1002:$i]:(((in @ X1002 @ (setunion @ X1001))=>![X1003:$o]:((![X1004:$i]:(((in @ X1002 @ X1004)=>((in @ X1004 @ X1001)=>(X1003))))=>(X1003)))))=>(![X1005:$i, X1006:$i]:(((in @ X1006 @ X1005)=>(in @ X1006 @ (powerset @ (setunion @ X1005)))))=>(![X1007:$i > $o]:(((exu @ X1007)=>?[X1008:$i]:(![X1009:$i]:(((X1007 @ X1009)<=>((X1009)=(X1008)))))))=>(![X1010:$i]:(((nonempty @ X1010)=>?[X1011:$i]:(((in @ X1011 @ X1010)&$true))))=>(![X1012:$i, X1013:$i]:(((in @ X1012 @ (setadjoin @ X1013 @ emptyset))=>((X1012)=(X1013))))=>(![X1014:$i, X1015:$i]:((((X1014)!=(X1015))=>~(in @ X1015 @ (setadjoin @ X1014 @ emptyset))))=>(![X1016:$i, X1017:$i]:((((X1016)=(X1017))=>(in @ X1016 @ (setadjoin @ X1017 @ emptyset))))=>(![X1018:$i, X1019:$i]:(((in @ X1018 @ (setadjoin @ X1019 @ emptyset))=>(in @ X1019 @ (setadjoin @ X1018 @ emptyset))))=>(![X1020:$i, X1021:$i, X1022:$i]:(((in @ X1022 @ (setadjoin @ X1020 @ (setadjoin @ X1021 @ emptyset)))=>(((X1022)=(X1020))|((X1022)=(X1021)))))=>(![X1023:$i, X1024:$i]:((in @ X1023 @ (setadjoin @ X1023 @ (setadjoin @ X1024 @ emptyset))))=>(![X1025:$i, X1026:$i]:((in @ X1026 @ (setadjoin @ X1025 @ (setadjoin @ X1026 @ emptyset))))=>(![X1027:$i, X1028:$i > $o]:((?[X1029:$i]:(((in @ X1029 @ X1027)&(X1028 @ X1029)))=>(((dsetconstr @ X1027 @ X1028)=(emptyset))=>~($true))))=>(![X1030:$i > $o, X1031:$i]:(((in @ X1031 @ emptyset)=>(X1030 @ 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:$i]:(((in @ X1043 @ X1040)=>~((X1041 @ X1043))))))=>(![X1044:$i, X1045:$i > $o]:((?[X1046:$i]:(((in @ X1046 @ X1044)&~((X1045 @ X1046))))=>~(![X1047:$i]:(((in @ X1047 @ X1044)=>(X1045 @ X1047))))))=>(![X1048:$o]:(((X1048)=>(in @ emptyset @ (prop2set @ ((X1048))))))=>((prop2set2propI)=>(![X1049:$i, X1050:$i > $o]:((~(?[X1051:$i]:(((in @ X1051 @ X1049)&(X1050 @ X1051))))=>![X1052:$i]:(((in @ X1052 @ X1049)=>~((X1050 @ X1052))))))=>(![X1053:$i, X1054:$i > $o]:((~(![X1055:$i]:(((in @ X1055 @ X1053)=>(X1054 @ X1055))))=>?[X1056:$i]:(((in @ X1056 @ X1053)&~((X1054 @ X1056))))))=>(![X1057:$i > $o]:((?[X1058:$i]:(((X1057 @ X1058)&![X1059:$i]:(((X1057 @ X1059)=>((X1058)=(X1059))))))=>(exu @ X1057)))=>(![X1060:$i > $o]:((?[X1061:$i]:((X1060 @ X1061))=>(![X1062:$i, X1063:$i]:(((X1060 @ X1062)=>((X1060 @ X1063)=>((X1062)=(X1063)))))=>(exu @ X1060))))=>(![X1064:$i > $o]:((?[X1065:$i]:(![X1066:$i]:(((X1064 @ X1066)<=>((X1066)=(X1065)))))=>(exu @ X1064)))=>(![X1067:$i, X1068:$i]:((((X1067)=(X1068))=>![X1069:$i, X1070:$i]:((((X1069)=(X1070))=>((in @ X1069 @ X1067)=>(in @ X1070 @ X1068))))))=>(![X1071:$i, X1072:$i]:((((X1071)=(X1072))=>![X1073:$i, X1074:$i]:((((X1073)=(X1074))=>((in @ X1073 @ X1071)<=>(in @ X1074 @ X1072))))))=>(![X1075:$i > $o]:(((exu @ X1075)=>![X1076:$i, X1077:$i]:(((X1075 @ X1076)=>((X1075 @ X1077)=>((X1076)=(X1077)))))))=>(![X1078:$i > $o, X1079:$i > $o]:((![X1080:$i, X1081:$i]:((((X1080)=(X1081))=>((X1078 @ X1080)<=>(X1079 @ X1081))))=>((exu @ X1078)<=>(exu @ 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X1669 @ X1670))))))))=>(![X1671:$i, X1672:$i]:(((in @ X1672 @ (powerset @ X1671))=>![X1673:$i]:(((in @ X1673 @ (powerset @ X1671))=>((subset @ X1672 @ (setminus @ X1671 @ X1673))=>![X1674:$i]:(((in @ X1674 @ X1671)=>((in @ X1674 @ X1673)=>(in @ X1674 @ (setminus @ X1671 @ X1672))))))))))=>(![X1675:$i, X1676:$i]:(((in @ X1676 @ (powerset @ X1675))=>![X1677:$i]:(((in @ X1677 @ (powerset @ X1675))=>((subset @ X1676 @ (setminus @ X1675 @ X1677))=>(subset @ X1677 @ (setminus @ X1675 @ X1676)))))))=>(![X1678:$i, X1679:$i]:(((in @ X1679 @ (powerset @ X1678))=>![X1680:$i]:(((in @ X1680 @ (powerset @ X1678))=>![X1681:$i]:(((in @ X1681 @ X1678)=>(~(in @ X1681 @ (binunion @ X1679 @ X1680))=>~(in @ X1681 @ X1679))))))))=>(![X1682:$i, X1683:$i]:(((in @ X1683 @ (powerset @ X1682))=>![X1684:$i]:(((in @ X1684 @ (powerset @ X1682))=>![X1685:$i]:(((in @ X1685 @ X1682)=>(~(in @ X1685 @ (binunion @ X1683 @ X1684))=>~(in @ X1685 @ X1684))))))))=>(![X1686:$i, X1687:$i]:(((in @ X1687 @ (powerset @ X1686))=>![X1688:$i]:(((in @ X1688 @ (powerset @ X1686))=>![X1689:$i]:(((in @ X1689 @ (powerset @ X1686))=>![X1690:$i]:(((in @ X1690 @ X1686)=>((in @ X1690 @ (binintersect @ X1687 @ X1688))=>(in @ X1690 @ (binunion @ X1687 @ X1689)))))))))))=>(![X1691:$i, X1692:$i]:(((in @ X1692 @ (powerset @ X1691))=>![X1693:$i]:(((in @ X1693 @ (powerset @ X1691))=>![X1694:$i]:(((in @ X1694 @ (powerset @ X1691))=>![X1695:$i]:(((in @ X1695 @ X1691)=>((in @ X1695 @ (binintersect @ X1692 @ X1693))=>(in @ X1695 @ (binunion @ X1693 @ X1694)))))))))))=>(![X1696:$i, X1697:$i]:(((in @ X1697 @ (powerset @ X1696))=>![X1698:$i]:(((in @ X1698 @ (powerset @ X1696))=>![X1699:$i]:(((in @ X1699 @ (powerset @ X1696))=>![X1700:$i]:(((in @ X1700 @ X1696)=>((in @ X1700 @ (binintersect @ X1697 @ X1698))=>(in @ X1700 @ (binintersect @ (binunion @ X1697 @ X1699) @ (binunion @ X1698 @ X1699))))))))))))=>(![X1701:$i, X1702:$i]:(((in @ X1702 @ (powerset @ X1701))=>![X1703:$i]:(((in @ X1703 @ (powerset @ X1701))=>![X1704:$i]:(((in @ X1704 @ (powerset @ X1701))=>(in @ (binintersect @ X1702 @ X1703) @ (powerset @ (binintersect @ (binunion @ X1702 @ X1704) @ (binunion @ X1703 @ X1704))))))))))=>(![X1705:$i, X1706:$i]:(((in @ X1706 @ (powerset @ X1705))=>![X1707:$i]:(((in @ X1707 @ (powerset @ X1705))=>![X1708:$i]:(((in @ X1708 @ X1705)=>((in @ X1708 @ (setminus @ X1705 @ (binunion @ X1706 @ X1707)))=>~(in @ X1708 @ X1706))))))))=>(![X1709:$i, X1710:$i]:(((in @ X1710 @ (powerset @ X1709))=>![X1711:$i]:(((in @ X1711 @ (powerset @ X1709))=>![X1712:$i]:(((in @ X1712 @ X1709)=>((in @ X1712 @ (setminus @ X1709 @ (binunion @ X1710 @ X1711)))=>(in @ X1712 @ (setminus @ X1709 @ X1710)))))))))=>(![X1713:$i, X1714:$i]:(((in @ X1714 @ (powerset @ X1713))=>![X1715:$i]:(((in @ X1715 @ (powerset @ X1713))=>![X1716:$o, X1717:$i]:(((in @ X1717 @ X1713)=>((in @ X1717 @ (binunion @ X1714 @ X1715))=>(((in @ X1717 @ X1714)=>(X1716))=>(((in @ X1717 @ X1715)=>(X1716))=>(X1716))))))))))=>(![X1718:$i, X1719:$i]:(((in @ X1719 @ (powerset @ X1718))=>![X1720:$i]:(((in @ X1720 @ (powerset @ X1718))=>![X1721:$i]:(((in @ X1721 @ X1718)=>(~(in @ X1721 @ X1719)=>(~(in @ X1721 @ X1720)=>~(in @ X1721 @ (binunion @ X1719 @ X1720))))))))))=>(![X1722:$i, X1723:$i]:(((in @ X1723 @ (powerset @ X1722))=>![X1724:$i]:(((in @ X1724 @ (powerset @ X1722))=>![X1725:$i]:(((in @ X1725 @ X1722)=>((in @ X1725 @ (setminus @ X1722 @ (binunion @ X1723 @ X1724)))=>(in @ X1725 @ (setminus @ X1722 @ X1723)))))))))=>(![X1726:$i, X1727:$i]:(((in @ X1727 @ (powerset @ X1726))=>![X1728:$i]:(((in @ X1728 @ (powerset @ X1726))=>(in @ (setminus @ X1726 @ (binunion @ X1727 @ X1728)) @ (powerset @ (setminus @ X1726 @ X1727)))))))=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[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)],[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)],[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_266, theeq]), ifp]), iftrue]), iffalse]), iftrueorfalse]), binintersectT_lem]), binunionT_lem]), inCongP]), powersetT_lem]), c_0_267]), setminusT_lem]), c_0_268]), complementT_lem]), c_0_269]), setextT]), notdallE]), subsetTI]), notdexE]), powersetTI1]), prop2setI]), powersetTE1]), in__Cong]), complementTI1]), complementTE1]), binintersectTELcontra]), binintersectTERcontra]), contrasubsetT]), contrasubsetT1]), contrasubsetT2]), contrasubsetT3]), doubleComplementI1]), doubleComplementE1]), doubleComplementSub1]), doubleComplementSub2]), doubleComplementEq]), complementTnotintersectT]), omega__Cong]), complementImpComplementIntersect]), setunion__Cong]), complementSubsetComplementIntersect]), powerset__Cong]), complementInPowersetComplementIntersect]), setadjoin__Cong]), contraSubsetComplement]), emptyset__Cong]), complementTcontraSubset]), c_0_270]), binunionTILcontra]), c_0_271]), binunionTIRcontra]), c_0_272]), inIntersectImpInUnion]), inIntersectImpInUnion2]), inIntersectImpInIntersectUnions]), intersectInPowersetIntersectUnions]), inComplementUnionImpNotIn1]), inComplementUnionImpInComplement1]), binunionTE]), binunionTEcontra]), demorgan2a1]), complementUnionInPowersetComplement]), emptysetsubset]), subsetI2]), eqimpsubset1]), eqimpsubset2]), subsetI1]), c_0_273]), c_0_274]), subsetE]), setadjoinSub]), subsetTrans]), subsetRefl]), notequalI2]), notequalI1]), notsubsetI]), subsetE2]), setadjoinSub2]), powersetsubset]), inPowerset]), powersetE1]), powersetI1]), subsetemptysetimpeq]), setextsub]), subset2powerset]), c_0_275]), binunionLsub]), binunionE]), binunionEcases]), binunionIR]), upairset2IR]), binunionIL]), c_0_276]), binunionRsub]), binintersectER]), binintersectSubset3]), binintersectSubset2]), binintersectLsub]), binintersectEL]), binintersectSubset5]), binintersectI]), disjointsetsI1]), c_0_277]), c_0_278]), c_0_279]), c_0_280]), ap2apEq2]), ap2apEq1]), setminusER]), setminusEL]), setminusI]), bs114d]), binintersectSubset1]), binintersectSubset4]), binintersectRsub]), setminusSubset2]), symdiffE]), setminusSubset1]), setminusLsub]), setminusIRneg]), setminusILneg]), setminusELneg]), setminusERneg]), symdiffI1]), kpairiskpair]), setukpairIR]), setukpairIL]), secondinupair]), symdiffIneg2]), symdiffIneg1]), symdiffI2]), kpairp]), ubforcartprodlem1]), upairinpowunion]), upairsubunion]), upairset2E]), singletoninpowunion]), singletoninpowerset]), singletonsubset]), ubforcartprodlem2]), setunionsingleton2]), setunionsingleton1]), setunionE2]), cartprodmempair]), cartprodmempair1]), cartprodpairin]), ubforcartprodlem3]), setunionsingleton]), c_0_281]), setukpairinjL1]), singletonsuniq]), c_0_282]), c_0_283]), c_0_284]), c_0_285]), theprop]), setukpairinjR1]), setukpairinjR12]), setukpairinjR11]), setukpairinjL]), setukpairinjL2]), cartprodfstin]), kfstpairEq]), upairequniteq]), cartprodpairmemEL]), cartprodsndin]), kpairsurjEq]), ksndpairEq]), c_0_286]), setukpairinjR]), setukpairinjR2]), cartprodpairmemER]), c_0_287]), c_0_288]), c_0_289]), cartprodpairsurjEq]), cartprodsndpairEq]), cartprodfstpairEq]), cartprodmempaircEq]), c_0_290]), infuncsetfunc]), app]), c_0_291]), c_0_292]), c_0_293]), c_0_294]), c_0_295]), ap2p]), c_0_296]), brelnall2]), brelnall1]), c_0_297]), c_0_298]), c_0_299]), funcinfuncset]), funcGraphProp1]), funcext]), eqbreln]), subbreln]), funcGraphProp4]), funcextLem]), funcGraphProp2]), funcGraphProp3]), funcext2]), c_0_300]), c_0_301]), c_0_302]), c_0_303]), c_0_304]), c_0_305]), quantDeMorgan4]), quantDeMorgan3]), quantDeMorgan2]), quantDeMorgan1]), vacuousDall]), c_0_306]), upairsetIR]), upairsetIL]), upairsetE]), singletonsswitch]), eqinunit]), notinsingleton]), uniqinunit]), nonemptyImpWitness]), c_0_307]), subPowSU]), setunionE]), setunionI]), powersetE]), emptyInPowerset]), emptyinPowerset]), powersetI]), c_0_308]), setadjoinOr]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), nonemptyI1]), c_0_309]), nonemptyE1]), c_0_310]), noeltsimpempty]), emptyI]), setext]), c_0_311]), notinemptyset]), emptysetimpfalse]), emptysetE]), prop2setE]), c_0_312]), c_0_313]), c_0_314]), c_0_315]), c_0_316]), wellorderingAx]), foundationAx]), c_0_317]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_318])).
% 0.55/0.52 thf(c_0_320, negated_conjecture, ![X1729:$i, X1730:$i, X1732:$i, X1733:$i, X1734:$i, X1735:$i, X1736:$i, X1737:$i, X1738:$i, X1739:$i, X1740:$i, X1742:$i, X1743:$i, X1745:$i, X1746:$i, X1747:$i, X1748:$i, X1749:$i, X1751:$i, X1752:$i > $i > $o, X1753:$i, X1756:$i, X1758:$i, X1759:$i, X1760:$i, X1761:$i, X1763:$i, X1764:$i > $o, X1765:$i, X1766:$i > $o, X1767:$i, X1768:$i, X1769:$i > $o, X1770:$i, X1771:$i, X1772:$i > $o, X1773:$i, X1774:$i > $o, X1776:$i, X1777:$o, X1778:$i, X1779:$i, X1780:$o, X1781:$i, X1782:$i, X1783:$i > $o, X1785:$i, X1786:$i, X1789:$i, X1791:$i, X1793:$i, X1794:$i > $o, X1795:$i, X1796:$i, X1798:$i, X1799:$i > $o, X1800:$i, X1801:$i, X1802:$i, X1803:$i, X1804:$i, X1805:$i, X1806:$i, X1807:$i, X1808:$i, X1809:$i, X1810:$i, X1811:$o, X1812:$i, X1813:$i, X1814:$i, X1815:$i, X1816:$i, X1817:$i, X1819:$i, X1820:$i, X1821:$i, X1822:$i, X1823:$i, X1824:$i, X1825:$i, X1826:$i, X1827:$i, X1828:$i, X1829:$o, X1831:$i, X1832:$i, X1833:$i > $o, X1835:$i, X1836:$i, X1837:$i, X1839:$i, X1840:$i, X1841:$i, X1842:$i, X1843:$i, X1844:$i, X1845:$i, X1846:$i, X1847:$i, X1848:$i, X1849:$i, X1850:$i, X1851:$i, X1852:$i, X1853:$i, X1854:$i, X1855:$i > $o, X1856:$i, X1857:$i > $o, X1858:$i, X1859:$i, X1860:$i > $o, X1861:$i, X1863:$i, X1864:$i > $o, X1866:$i, X1867:$i, X1868:$i > $o, X1870:$i, X1871:$i, X1872:$i > $o, X1873:$i, X1875:$o, X1876:$i, X1877:$i > $o, X1879:$i, X1880:$i, X1881:$i > $o, X1882:$i, X1884:$i > $o, X1885:$i, X1887:$i > $o, X1888:$i, X1891:$i > $o, X1892:$i, X1894:$i, X1895:$i, X1896:$i, X1897:$i, X1898:$i, X1899:$i, X1900:$i, X1901:$i, X1902:$i > $o, X1903:$i, X1904:$i, X1905:$i > $o, X1906:$i > $o, X1909:$i, X1910:$i, X1911:$i, X1912:$i, X1913:$i, X1914:$i, X1915:$i, X1916:$i, X1917:$i > $o, X1918:$i, X1919:$i, X1920:$i > $o, X1921:$i > $o, X1924:$i, X1925:$i, X1926:$i > $o, X1927:$i > $o, X1930:$i, X1931:$i, X1933:$i, X1934:$i, X1935:$i, X1936:$i, X1937:$i, X1938:$i, X1940:$i, X1941:$i, X1942:$i, X1943:$i, X1944:$i, X1945:$i, X1946:$i, X1947:$i, X1948:$i, X1949:$i, X1950:$i, X1951:$i, X1952:$i, X1953:$i, X1954:$i, X1955:$i, X1956:$i, X1957:$i, X1958:$i, 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 > $o, X1978:$i, X1979:$i > $o, X1980:$i, X1981:$i, X1982:$i, X1983:$i, X1984:$i, X1985:$i, X1986:$i, X1987:$i, X1988:$i, X1989:$i, X1990:$i, X1991:$o, X1992:$i, X1993:$i, X1994:$i, X1995:$i, X1996:$i, 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, X2020:$i, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2025:$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:$i, X2059:$o, X2060:$i, X2061:$i, X2062:$i, X2063:$i, X2064:$i, X2065:$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:$i, X2121:$i, X2122:$i, X2123:$i, X2124:$i, X2125:$i, X2127:$i, X2128:$i, X2129:$i, X2130:$i, X2131:$i > $o, X2134:$i, X2135:$i, X2136:$i > $o, X2138:$i, X2139:$i > $o, X2140:$i, X2142:$i, X2143:$i > $o, X2146:$i, X2147:$i, X2148:$i, X2149:$i, X2150:$i, 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 > $i > $o, X2219:$i, X2220:$i, X2221:$i, X2222:$i, X2223:$i > $i > $o, X2224:$i, X2225:$i, X2226:$i > $i > $o, X2227:$i, X2228:$i, X2229:$i > $i > $o, X2230:$i, X2231:$i, X2232:$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, 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 > $i, X2273:$i, X2274:$i, X2275:$i > $i, X2277:$i, X2278:$i, X2279:$i > $i, X2281:$i, X2282:$i, X2283:$i, X2284:$i > $o, X2287:$i, X2288:$i, X2289:$i, X2290:$i, X2291:$i > $o, X2294:$i, X2295:$i, X2296:$i > $o, X2297:$i, X2298:$i, X2299:$i, X2300:$i, X2301:$i, 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, X2317:$i, X2318:$i, X2319:$i, X2320:$i, X2321:$i, X2322:$i, X2323:$i, X2324:$i, X2325:$i, X2326:$i, X2327:$i, X2330:$i, X2331:$i, X2332:$i, X2333:$i, X2338:$i, X2339:$i, X2340:$i, X2341:$i, X2343:$i, X2344:$i, X2345:$i, X2346:$i, X2348:$i, X2349:$i, X2350:$i, X2351:$i, X2352:$i, X2353:$i, X2354:$i, X2355:$i, X2356:$i, X2357:$i, X2358:$i > $i, X2360:$i, X2361:$i, X2362:$i, X2363:$i, X2364:$i, X2365:$i, X2366:$i > $i, X2368:$i, X2369:$i, X2370:$i > $i, X2372:$i, X2373:$i, X2374:$i, X2375:$i, X2376:$i, X2377:$o, X2378:$i, X2379:$i, X2380:$i, X2381:$o, X2382:$i, X2383:$i, X2384:$i, X2385:$o, X2386:$i, X2387:$i, X2388:$i, X2389:$o, X2390:$i, X2391:$i, X2392:$i, X2393:$o, X2394:$i, X2395:$i, X2396:$i, X2397:$o, X2398:$i, X2399:$i, X2400:$i, X2401:$i, X2402:$i, X2403:$o, X2404:$i, X2405:$i, X2406:$i, X2407:$o, X2408:$i, X2409:$i, X2410:$i, X2411:$o, X2412:$i, X2413:$i, X2414:$i, X2415:$i, X2416:$i, 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:$i, X2432:$i, X2433:$i, X2434:$i, X2436:$i, X2437:$i, X2438:$i, X2440:$i, X2441:$i, X2442:$i, X2443:$i, X2444:$i, X2445:$i, X2446:$i, X2447:$i, X2448:$i, X2449:$i, X2450:$i, X2451:$i, X2452:$i, X2453:$i, X2454:$i, X2455:$i, X2456:$i, X2457:$i, X2458:$i, X2459:$i, X2460:$i, X2461:$i, X2462:$i, X2463:$i, X2464:$i, X2465:$i, X2466:$i, X2467:$i, X2468:$i, X2469:$i, X2470:$i, X2471:$i, X2472:$i, X2473:$i, X2474:$i, X2475:$i, X2476:$i, X2477:$i, X2478:$i, X2479:$i, X2480:$i, X2481:$i, X2482:$i, X2483:$i, X2484:$i, X2485:$i, X2486:$i, X2487:$i, X2488:$i, X2489:$i, X2490:$i, X2491:$i, X2492:$i, X2493:$i, X2494:$i, X2495:$i, X2496:$i, X2497:$i, X2498:$i, X2499:$i, X2500:$i, X2501:$i, X2502:$i, X2503:$i, X2504:$i, X2505:$i, X2506:$i, X2507:$i, X2508:$i, X2509:$i, X2510:$i, X2511:$i, X2512:$i, X2513:$i, X2514:$i, X2515:$i, X2516:$i, X2517:$i, X2518:$i, X2519:$i, X2520:$i, X2521:$i, X2522:$i, X2523:$i, X2524:$i, X2525:$i, X2526:$i, X2527:$i, X2528:$i, X2529:$i, X2530:$i, X2531:$i, X2532:$i, X2533:$i, X2534:$i, X2535:$i, X2536:$i, X2537:$i, X2538:$i, X2539:$i, X2540:$i, X2541:$i, X2542:$i, X2543:$o, X2544:$i, X2545:$i, X2546:$i, X2547:$i, X2548:$i, X2549:$i, X2550:$i, X2551:$i, X2552:$i, X2553:$i, X2554:$i, X2555:$i]:((((~(in @ (esk1_2 @ X1729 @ X1730) @ X1729)|~(in @ (esk1_2 @ X1729 @ X1730) @ X1730)|((X1729)=(X1730)))&((in @ (esk1_2 @ X1729 @ X1730) @ X1729)|(in @ (esk1_2 @ X1729 @ X1730) @ X1730)|((X1729)=(X1730))))&(~(in @ X1732 @ emptyset)&(((~(in @ X1735 @ (setadjoin @ X1733 @ X1734))|(((X1735)=(X1733))|(in @ X1735 @ X1734)))&((((X1735)!=(X1733))|(in @ X1735 @ (setadjoin @ X1733 @ X1734)))&(~(in @ X1735 @ X1734)|(in @ X1735 @ (setadjoin @ X1733 @ X1734)))))&(((~(in @ X1737 @ (powerset @ X1736))|(~(in @ X1738 @ X1737)|(in @ X1738 @ X1736)))&(((in @ (esk2_2 @ X1739 @ X1740) @ X1740)|(in @ X1740 @ (powerset @ X1739)))&(~(in @ (esk2_2 @ X1739 @ X1740) @ X1739)|(in @ X1740 @ (powerset @ X1739)))))&(((((in @ X1743 @ (esk3_2 @ X1742 @ X1743))|~(in @ X1743 @ (setunion @ X1742)))&((in @ (esk3_2 @ X1742 @ X1743) @ X1742)|~(in @ X1743 @ (setunion @ X1742))))&(~(in @ X1746 @ X1747)|~(in @ X1747 @ X1745)|(in @ X1746 @ (setunion @ X1745))))&((in @ emptyset @ omega)&((~(in @ X1748 @ omega)|(in @ (setadjoin @ X1748 @ X1748) @ omega))&(((((in @ (esk4_1 @ X1749) @ omega)|~(in @ emptyset @ X1749)|(~(in @ X1751 @ omega)|(in @ X1751 @ X1749)))&((in @ (esk4_1 @ X1749) @ X1749)|~(in @ emptyset @ X1749)|(~(in @ X1751 @ omega)|(in @ X1751 @ X1749))))&(~(in @ (setadjoin @ (esk4_1 @ X1749) @ (esk4_1 @ X1749)) @ X1749)|~(in @ emptyset @ X1749)|(~(in @ X1751 @ omega)|(in @ X1751 @ X1749))))&((((((in @ (esk7_3 @ X1752 @ X1753 @ X1756) @ X1753)|~(in @ X1756 @ (esk6_2 @ X1752 @ X1753))|(in @ (esk5_2 @ X1752 @ X1753) @ X1753))&((X1752 @ (esk7_3 @ X1752 @ X1753 @ X1756) @ X1756)|~(in @ X1756 @ (esk6_2 @ X1752 @ X1753))|(in @ (esk5_2 @ X1752 @ X1753) @ X1753)))&(~(in @ X1759 @ X1753)|~(X1752 @ X1759 @ X1758)|(in @ X1758 @ (esk6_2 @ X1752 @ X1753))|(in @ (esk5_2 @ X1752 @ X1753) @ X1753)))&((((in @ (esk7_3 @ X1752 @ X1753 @ X1756) @ X1753)|~(in @ X1756 @ (esk6_2 @ X1752 @ X1753))|~(exu @ (X1752 @ (esk5_2 @ X1752 @ X1753))))&((X1752 @ (esk7_3 @ X1752 @ X1753 @ X1756) @ X1756)|~(in @ X1756 @ (esk6_2 @ X1752 @ X1753))|~(exu @ (X1752 @ (esk5_2 @ X1752 @ X1753)))))&(~(in @ X1759 @ X1753)|~(X1752 @ X1759 @ X1758)|(in @ X1758 @ (esk6_2 @ X1752 @ X1753))|~(exu @ (X1752 @ (esk5_2 @ X1752 @ X1753))))))&((((in @ (esk8_1 @ X1760) @ X1760)|~(in @ X1761 @ X1760))&(~(in @ X1763 @ (esk8_1 @ X1760))|~(in @ X1763 @ X1760)|~(in @ X1761 @ X1760)))&((epred1_0)&((~(exu @ X1764)|(X1764 @ (descr @ X1764)))&((~(in @ X1767 @ X1765)|(~(X1766 @ X1767)|(in @ X1767 @ (dsetconstr @ X1765 @ X1766))))&((~(in @ X1770 @ (dsetconstr @ X1768 @ X1769))|(in @ X1770 @ X1768))&((~(in @ X1773 @ (dsetconstr @ X1771 @ X1772))|(X1772 @ X1773))&((((X1774 @ (esk9_1 @ X1774))|~(exu @ X1774))&(~(X1774 @ X1776)|((esk9_1 @ X1774)=(X1776))|~(exu @ X1774)))&((~(in @ X1778 @ (prop2set @ ((X1777))))|(X1777))&((~(in @ X1779 @ emptyset)|(X1780))&((~(in @ X1781 @ emptyset)|~($true))&(~(in @ X1782 @ emptyset)&((~(exu @ X1783)|(X1783 @ (esk10_1 @ X1783)))&(((((in @ (esk12_2 @ X1785 @ X1786) @ X1786)|((X1785)=(X1786))|(in @ (esk11_2 @ X1785 @ X1786) @ X1785))&(~(in @ (esk12_2 @ X1785 @ X1786) @ X1785)|((X1785)=(X1786))|(in @ (esk11_2 @ X1785 @ X1786) @ X1785)))&(((in @ (esk12_2 @ X1785 @ X1786) @ X1786)|((X1785)=(X1786))|~(in @ (esk11_2 @ X1785 @ X1786) @ X1786))&(~(in @ (esk12_2 @ X1785 @ X1786) @ X1785)|((X1785)=(X1786))|~(in @ (esk11_2 @ X1785 @ X1786) @ X1786))))&(((in @ (esk13_1 @ X1789) @ X1789)|((X1789)=(emptyset)))&(((in @ (esk14_1 @ X1791) @ X1791)|((X1791)=(emptyset)))&(((~(in @ X1795 @ (dsetconstr @ X1793 @ X1794))|(X1794 @ X1795)|~(in @ X1795 @ X1793))&(~(X1794 @ X1795)|(in @ X1795 @ (dsetconstr @ X1793 @ X1794))|~(in @ X1795 @ X1793)))&((~(nonempty @ X1796)|(in @ (esk15_1 @ X1796) @ X1796))&((~(in @ X1800 @ X1798)|(~(X1799 @ X1800)|(nonempty @ (dsetconstr @ X1798 @ X1799))))&((~(in @ X1802 @ X1801)|(nonempty @ X1801))&((in @ X1803 @ (setadjoin @ X1803 @ X1804))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X1807 @ X1806)|(in @ X1807 @ (setadjoin @ X1805 @ X1806)))&(((((in @ X1810 @ X1809)|(X1811)|((X1810)=(X1808))|~(in @ X1810 @ (setadjoin @ X1808 @ X1809)))&(~(X1811)|(X1811)|((X1810)=(X1808))|~(in @ X1810 @ (setadjoin @ X1808 @ X1809))))&(((in @ X1810 @ X1809)|(X1811)|~(X1811)|~(in @ X1810 @ (setadjoin @ X1808 @ X1809)))&(~(X1811)|(X1811)|~(X1811)|~(in @ X1810 @ (setadjoin @ X1808 @ X1809)))))&((~(in @ X1814 @ (setadjoin @ X1812 @ X1813))|(((X1814)=(X1812))|(in @ X1814 @ X1813)))&(((dsetconstr @ X1815 @ (^[Z0:$i]:($true)))=(X1815))&((((in @ (esk16_2 @ X1816 @ X1817) @ X1817)|(in @ X1817 @ (powerset @ X1816)))&(~(in @ (esk16_2 @ X1816 @ X1817) @ X1816)|(in @ X1817 @ (powerset @ X1816))))&((in @ emptyset @ (powerset @ X1819))&((in @ emptyset @ (powerset @ X1820))&((~(in @ X1822 @ (powerset @ X1821))|(~(in @ X1823 @ X1822)|(in @ X1823 @ X1821)))&((~(in @ X1825 @ X1826)|(~(in @ X1826 @ X1824)|(in @ X1825 @ (setunion @ X1824))))&((((in @ X1828 @ (esk17_3 @ X1827 @ X1828 @ X1829))|(X1829)|~(in @ X1828 @ (setunion @ X1827)))&(((in @ (esk17_3 @ X1827 @ X1828 @ X1829) @ X1827)|(X1829)|~(in @ X1828 @ (setunion @ X1827)))&(~(X1829)|(X1829)|~(in @ X1828 @ (setunion @ X1827)))))&((~(in @ X1832 @ X1831)|(in @ X1832 @ (powerset @ (setunion @ X1831))))&(((~(X1833 @ X1835)|((X1835)=(esk18_1 @ X1833))|~(exu @ X1833))&(((X1836)!=(esk18_1 @ X1833))|(X1833 @ X1836)|~(exu @ X1833)))&((((in @ (esk19_1 @ X1837) @ X1837)|~(nonempty @ X1837))&(($true)|~(nonempty @ X1837)))&((~(in @ X1839 @ (setadjoin @ X1840 @ emptyset))|((X1839)=(X1840)))&((((X1841)=(X1842))|~(in @ X1842 @ (setadjoin @ X1841 @ emptyset)))&((((X1843)!=(X1844))|(in @ X1843 @ (setadjoin @ X1844 @ emptyset)))&((~(in @ X1845 @ (setadjoin @ X1846 @ emptyset))|(in @ X1846 @ (setadjoin @ X1845 @ emptyset)))&((~(in @ X1849 @ (setadjoin @ X1847 @ (setadjoin @ X1848 @ emptyset)))|(((X1849)=(X1847))|((X1849)=(X1848))))&((in @ X1850 @ (setadjoin @ X1850 @ (setadjoin @ X1851 @ emptyset)))&((in @ X1853 @ (setadjoin @ X1852 @ (setadjoin @ X1853 @ emptyset)))&((~(in @ X1856 @ X1854)|~(X1855 @ X1856)|(((dsetconstr @ X1854 @ 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(^[Z0:$i]:((((((X2385))&(((Z0)=(X2386)))))|(((~((X2385)))&(((Z0)=(X2387)))))))))))))&((~(in @ X2390 @ X2388)|(~(in @ X2391 @ X2388)|(~(X2389)|((dsetconstr @ X2388 @ (^[Z0:$i]:((((((X2389))&(((Z0)=(X2390)))))|(((~((X2389)))&(((Z0)=(X2391)))))))))=(setadjoin @ X2390 @ emptyset)))))&((~(in @ X2394 @ X2392)|(~(in @ X2395 @ X2392)|(singleton @ (dsetconstr @ X2392 @ (^[Z0:$i]:((((((X2393))&(((Z0)=(X2394)))))|(((~((X2393)))&(((Z0)=(X2395))))))))))))&((~(in @ X2398 @ X2396)|(~(in @ X2399 @ X2396)|(in @ (if @ X2396 @ ((X2397)) @ X2398 @ X2399) @ X2396)))&((~(singleton @ X2400)|(~(in @ X2401 @ X2400)|((setunion @ X2400)=(X2401))))&((~(in @ X2404 @ X2402)|(~(in @ X2405 @ X2402)|(~(X2403)|((if @ X2402 @ ((X2403)) @ X2404 @ X2405)=(X2404)))))&((~(in @ X2408 @ X2406)|(~(in @ X2409 @ X2406)|((X2407)|((if @ X2406 @ ((X2407)) @ X2408 @ X2409)=(X2409)))))&((~(in @ X2412 @ X2410)|(~(in @ X2413 @ X2410)|(in @ (if @ X2410 @ ((X2411)) @ X2412 @ X2413) @ (setadjoin @ X2412 @ (setadjoin @ X2413 @ emptyset)))))&((~(in @ X2415 @ (powerset @ X2414))|(~(in @ X2416 @ (powerset @ X2414))|(in @ (binintersect @ X2415 @ X2416) @ (powerset @ X2414))))&((~(in @ X2418 @ (powerset @ X2417))|(~(in @ X2419 @ (powerset @ X2417))|(in @ (binunion @ X2418 @ X2419) @ (powerset @ X2417))))&((~(in @ X2421 @ (powerset @ X2420))|(in @ (powerset @ X2421) @ (powerset @ (powerset @ X2420))))&((~(in @ X2423 @ (powerset @ X2422))|(~(in @ X2424 @ (powerset @ X2422))|(in @ (setminus @ X2423 @ X2424) @ (powerset @ X2422))))&((~(in @ X2426 @ (powerset @ X2425))|(in @ (setminus @ X2425 @ X2426) @ (powerset @ X2425)))&(((((in @ (esk68_3 @ X2427 @ X2428 @ X2429) @ X2427)|((X2428)=(X2429))|(in @ (esk67_3 @ X2427 @ X2428 @ X2429) @ X2427)|~(in @ X2429 @ (powerset @ X2427))|~(in @ X2428 @ (powerset @ X2427)))&(((in @ (esk68_3 @ X2427 @ X2428 @ X2429) @ X2429)|((X2428)=(X2429))|(in @ (esk67_3 @ X2427 @ X2428 @ X2429) @ X2427)|~(in @ X2429 @ (powerset @ X2427))|~(in @ X2428 @ (powerset @ X2427)))&(~(in @ (esk68_3 @ X2427 @ X2428 @ X2429) @ X2428)|((X2428)=(X2429))|(in @ (esk67_3 @ X2427 @ X2428 @ X2429) @ X2427)|~(in @ X2429 @ (powerset @ X2427))|~(in @ X2428 @ (powerset @ X2427)))))&((((in @ (esk68_3 @ X2427 @ X2428 @ X2429) @ X2427)|((X2428)=(X2429))|(in @ (esk67_3 @ X2427 @ X2428 @ X2429) @ X2428)|~(in @ X2429 @ (powerset @ X2427))|~(in @ X2428 @ (powerset @ X2427)))&(((in @ (esk68_3 @ X2427 @ X2428 @ X2429) @ X2429)|((X2428)=(X2429))|(in @ (esk67_3 @ X2427 @ X2428 @ X2429) @ X2428)|~(in @ X2429 @ (powerset @ X2427))|~(in @ X2428 @ (powerset @ X2427)))&(~(in @ (esk68_3 @ X2427 @ X2428 @ X2429) @ X2428)|((X2428)=(X2429))|(in @ (esk67_3 @ X2427 @ X2428 @ X2429) @ X2428)|~(in @ X2429 @ (powerset @ X2427))|~(in @ X2428 @ (powerset @ X2427)))))&(((in @ (esk68_3 @ X2427 @ X2428 @ X2429) @ X2427)|((X2428)=(X2429))|~(in @ (esk67_3 @ X2427 @ X2428 @ X2429) @ X2429)|~(in @ X2429 @ (powerset @ X2427))|~(in @ X2428 @ (powerset @ X2427)))&(((in @ (esk68_3 @ X2427 @ X2428 @ X2429) @ X2429)|((X2428)=(X2429))|~(in @ (esk67_3 @ X2427 @ X2428 @ X2429) @ X2429)|~(in @ X2429 @ (powerset @ X2427))|~(in @ X2428 @ (powerset @ X2427)))&(~(in @ (esk68_3 @ X2427 @ X2428 @ X2429) @ X2428)|((X2428)=(X2429))|~(in @ (esk67_3 @ X2427 @ X2428 @ X2429) @ X2429)|~(in @ X2429 @ (powerset @ X2427))|~(in @ X2428 @ (powerset @ X2427)))))))&((((in @ (esk69_3 @ X2432 @ X2433 @ X2434) @ X2432)|(subset @ X2433 @ X2434)|~(in @ X2434 @ (powerset @ X2432))|~(in @ X2433 @ (powerset @ X2432)))&(((in @ (esk69_3 @ X2432 @ X2433 @ X2434) @ X2433)|(subset @ X2433 @ X2434)|~(in @ X2434 @ (powerset @ X2432))|~(in @ X2433 @ (powerset @ X2432)))&(~(in @ (esk69_3 @ X2432 @ X2433 @ X2434) @ X2434)|(subset @ X2433 @ X2434)|~(in @ X2434 @ (powerset @ X2432))|~(in @ X2433 @ (powerset @ X2432)))))&((((in @ (esk70_3 @ X2436 @ X2437 @ X2438) @ X2436)|(in @ X2437 @ (powerset @ X2438))|~(in @ X2438 @ (powerset @ X2436))|~(in @ X2437 @ (powerset @ X2436)))&(((in @ (esk70_3 @ X2436 @ X2437 @ X2438) @ X2437)|(in @ X2437 @ (powerset @ X2438))|~(in @ X2438 @ (powerset @ X2436))|~(in @ X2437 @ (powerset @ X2436)))&(~(in @ (esk70_3 @ X2436 @ X2437 @ X2438) @ X2438)|(in @ X2437 @ (powerset @ X2438))|~(in @ X2438 @ (powerset @ X2436))|~(in @ X2437 @ (powerset @ X2436)))))&((~(in @ X2441 @ (powerset @ X2440))|(~(in @ X2442 @ (powerset @ X2440))|(~(in @ X2443 @ X2440)|(~(in @ X2441 @ (powerset @ X2442))|(~(in @ X2443 @ X2441)|(in @ X2443 @ X2442))))))&((~(in @ X2445 @ (powerset @ X2444))|(~(in @ X2446 @ X2444)|(~(in @ X2446 @ X2445)|~(in @ X2446 @ (setminus @ X2444 @ X2445)))))&((~(in @ X2448 @ (powerset @ X2447))|(~(in @ X2449 @ X2447)|((in @ X2449 @ (setminus @ X2447 @ X2448))|(in @ X2449 @ X2448))))&((~(in @ X2451 @ (powerset @ X2450))|(~(in @ X2452 @ (powerset @ X2450))|(~(in @ X2453 @ X2450)|((in @ X2453 @ X2451)|~(in @ X2453 @ (binintersect @ X2451 @ X2452))))))&((~(in @ X2455 @ (powerset @ X2454))|(~(in @ X2456 @ (powerset @ X2454))|(~(in @ X2457 @ X2454)|((in @ X2457 @ X2456)|~(in @ X2457 @ (binintersect @ X2455 @ X2456))))))&((~(in @ X2459 @ (powerset @ X2458))|(~(in @ X2460 @ (powerset @ X2458))|(~(in @ X2461 @ X2458)|(~(subset @ X2459 @ (setminus @ X2458 @ X2460))|(~(in @ X2461 @ X2460)|~(in @ X2461 @ X2459))))))&((~(in @ X2463 @ (powerset @ X2462))|(~(in @ X2464 @ (powerset @ X2462))|(~(in @ X2465 @ X2462)|(~(subset @ X2463 @ X2464)|((in @ X2465 @ X2464)|~(in @ X2465 @ X2463))))))&((~(in @ X2467 @ (powerset @ X2466))|(~(in @ X2468 @ (powerset @ X2466))|(~(subset @ X2467 @ X2468)|(subset @ (setminus @ X2466 @ X2468) @ (setminus @ X2466 @ X2467)))))&((~(in @ X2470 @ (powerset @ X2469))|(~(in @ X2471 @ (powerset @ X2469))|(~(subset @ (setminus @ X2469 @ X2471) @ (setminus @ X2469 @ X2470))|(subset @ X2470 @ X2471))))&((~(in @ X2473 @ (powerset @ X2472))|(~(in @ X2474 @ X2472)|(~(in @ X2474 @ X2473)|(in @ X2474 @ (setminus @ X2472 @ (setminus @ X2472 @ X2473))))))&((~(in @ X2476 @ (powerset @ X2475))|(~(in @ X2477 @ X2475)|(~(in @ X2477 @ (setminus @ X2475 @ (setminus @ X2475 @ X2476)))|(in @ X2477 @ X2476))))&((~(in @ X2479 @ (powerset @ X2478))|(subset @ X2479 @ (setminus @ X2478 @ (setminus @ X2478 @ X2479))))&((~(in @ X2481 @ (powerset @ X2480))|(subset @ (setminus @ X2480 @ (setminus @ X2480 @ X2481)) @ X2481))&((~(in @ X2483 @ (powerset @ X2482))|((X2483)=(setminus @ X2482 @ (setminus @ X2482 @ X2483))))&((~(in @ X2485 @ (powerset @ X2484))|(~(in @ X2486 @ (powerset @ X2484))|(~(in @ X2487 @ X2484)|(~(in @ X2487 @ (setminus @ X2484 @ X2485))|~(in @ X2487 @ (binintersect @ X2485 @ X2486))))))&((~(in @ X2489 @ (powerset @ X2488))|(~(in @ X2490 @ (powerset @ X2488))|(~(in @ X2491 @ X2488)|(~(in @ X2491 @ (setminus @ X2488 @ X2489))|(in @ X2491 @ (setminus @ X2488 @ (binintersect @ X2489 @ X2490)))))))&((~(in @ X2493 @ (powerset @ X2492))|(~(in @ X2494 @ (powerset @ X2492))|(subset @ (setminus @ X2492 @ X2493) @ (setminus @ X2492 @ (binintersect @ X2493 @ X2494)))))&((~(in @ X2496 @ (powerset @ X2495))|(~(in @ X2497 @ (powerset @ X2495))|(in @ (setminus @ X2495 @ X2496) @ (powerset @ (setminus @ X2495 @ (binintersect @ X2496 @ X2497))))))&((~(in @ X2499 @ (powerset @ X2498))|(~(in @ X2500 @ (powerset @ X2498))|(~(subset @ X2499 @ (setminus @ X2498 @ X2500))|(~(in @ X2501 @ X2498)|(~(in @ X2501 @ X2500)|(in @ X2501 @ (setminus @ X2498 @ X2499)))))))&((~(in @ X2503 @ (powerset @ X2502))|(~(in @ X2504 @ (powerset @ X2502))|(~(subset @ X2503 @ (setminus @ X2502 @ X2504))|(subset @ X2504 @ (setminus @ X2502 @ X2503)))))&((~(in @ X2506 @ (powerset @ X2505))|(~(in @ X2507 @ (powerset @ X2505))|(~(in @ X2508 @ X2505)|((in @ X2508 @ (binunion @ X2506 @ X2507))|~(in @ X2508 @ X2506)))))&((~(in @ X2510 @ (powerset @ X2509))|(~(in @ X2511 @ (powerset @ X2509))|(~(in @ X2512 @ X2509)|((in @ X2512 @ (binunion @ X2510 @ X2511))|~(in @ X2512 @ X2511)))))&((~(in @ X2514 @ (powerset @ X2513))|(~(in @ X2515 @ (powerset @ X2513))|(~(in @ X2516 @ (powerset @ X2513))|(~(in @ X2517 @ X2513)|(~(in @ X2517 @ (binintersect @ X2514 @ X2515))|(in @ X2517 @ (binunion @ X2514 @ X2516)))))))&((~(in @ X2519 @ (powerset @ X2518))|(~(in @ X2520 @ (powerset @ X2518))|(~(in @ X2521 @ (powerset @ X2518))|(~(in @ X2522 @ X2518)|(~(in @ X2522 @ (binintersect @ X2519 @ X2520))|(in @ X2522 @ (binunion @ X2520 @ X2521)))))))&((~(in @ X2524 @ (powerset @ X2523))|(~(in @ X2525 @ (powerset @ X2523))|(~(in @ X2526 @ (powerset @ X2523))|(~(in @ X2527 @ X2523)|(~(in @ X2527 @ (binintersect @ X2524 @ X2525))|(in @ X2527 @ (binintersect @ (binunion @ X2524 @ X2526) @ (binunion @ X2525 @ X2526))))))))&((~(in @ X2529 @ (powerset @ X2528))|(~(in @ X2530 @ (powerset @ X2528))|(~(in @ X2531 @ (powerset @ X2528))|(in @ (binintersect @ X2529 @ X2530) @ (powerset @ (binintersect @ (binunion @ X2529 @ X2531) @ (binunion @ X2530 @ X2531)))))))&((~(in @ X2533 @ (powerset @ X2532))|(~(in @ X2534 @ (powerset @ X2532))|(~(in @ X2535 @ X2532)|(~(in @ X2535 @ (setminus @ X2532 @ (binunion @ X2533 @ X2534)))|~(in @ X2535 @ X2533)))))&((~(in @ X2537 @ (powerset @ X2536))|(~(in @ X2538 @ (powerset @ X2536))|(~(in @ X2539 @ X2536)|(~(in @ X2539 @ (setminus @ X2536 @ (binunion @ X2537 @ X2538)))|(in @ X2539 @ (setminus @ X2536 @ X2537))))))&(((((in @ X2544 @ X2542)|(X2543)|(in @ X2544 @ X2541)|~(in @ X2544 @ (binunion @ X2541 @ X2542))|~(in @ X2544 @ X2540)|~(in @ X2542 @ (powerset @ X2540))|~(in @ X2541 @ (powerset @ X2540)))&(~(X2543)|(X2543)|(in @ X2544 @ X2541)|~(in @ X2544 @ (binunion @ X2541 @ X2542))|~(in @ X2544 @ X2540)|~(in @ X2542 @ (powerset @ X2540))|~(in @ X2541 @ (powerset @ X2540))))&(((in @ X2544 @ X2542)|(X2543)|~(X2543)|~(in @ X2544 @ (binunion @ X2541 @ X2542))|~(in @ X2544 @ X2540)|~(in @ X2542 @ (powerset @ X2540))|~(in @ X2541 @ (powerset @ X2540)))&(~(X2543)|(X2543)|~(X2543)|~(in @ X2544 @ (binunion @ X2541 @ X2542))|~(in @ X2544 @ X2540)|~(in @ X2542 @ (powerset @ X2540))|~(in @ X2541 @ (powerset @ X2540)))))&((~(in @ X2546 @ (powerset @ X2545))|(~(in @ X2547 @ (powerset @ X2545))|(~(in @ X2548 @ X2545)|((in @ X2548 @ X2546)|((in @ X2548 @ X2547)|~(in @ X2548 @ (binunion @ X2546 @ X2547)))))))&((~(in @ X2550 @ (powerset @ X2549))|(~(in @ X2551 @ (powerset @ X2549))|(~(in @ X2552 @ X2549)|(~(in @ X2552 @ (setminus @ X2549 @ (binunion @ X2550 @ X2551)))|(in @ X2552 @ (setminus @ X2549 @ X2550))))))&((~(in @ X2554 @ (powerset @ X2553))|(~(in @ X2555 @ (powerset @ X2553))|(in @ (setminus @ X2553 @ (binunion @ X2554 @ X2555)) @ (powerset @ (setminus @ X2553 @ X2554)))))&((in @ esk72_0 @ (powerset @ esk71_0))&((in @ esk73_0 @ (powerset @ esk71_0))&((in @ esk74_0 @ esk71_0)&((in @ esk74_0 @ (setminus @ esk71_0 @ (binunion @ esk72_0 @ esk73_0)))&~(in @ esk74_0 @ (setminus @ esk71_0 @ esk73_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_319])])])])])])])).
% 0.55/0.52 thf(c_0_321, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:((~((in @ X2 @ (setminus @ X3 @ X4)))|~((in @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_320])).
% 0.55/0.52 thf(c_0_322, negated_conjecture, (in @ esk74_0 @ (setminus @ esk71_0 @ (binunion @ esk72_0 @ esk73_0))), inference(split_conjunct,[status(thm)],[c_0_320])).
% 0.55/0.52 thf(c_0_323, negated_conjecture, ~((in @ esk74_0 @ (binunion @ esk72_0 @ esk73_0))), inference(spm,[status(thm)],[c_0_321, c_0_322])).
% 0.55/0.52 thf(c_0_324, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (binunion @ X4 @ X3))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_320])).
% 0.55/0.52 thf(c_0_325, negated_conjecture, ~((in @ esk74_0 @ (setminus @ esk71_0 @ esk73_0))), inference(split_conjunct,[status(thm)],[c_0_320])).
% 0.55/0.52 thf(c_0_326, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (setminus @ X3 @ X4))|(in @ X2 @ X4)|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_320])).
% 0.55/0.52 thf(c_0_327, negated_conjecture, (in @ esk74_0 @ esk71_0), inference(split_conjunct,[status(thm)],[c_0_320])).
% 0.55/0.52 thf(c_0_328, negated_conjecture, ~((in @ esk74_0 @ esk73_0)), inference(spm,[status(thm)],[c_0_323, c_0_324])).
% 0.55/0.52 thf(c_0_329, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_325, c_0_326]), c_0_327])]), c_0_328]), ['proof']).
% 0.55/0.52 % SZS output end CNFRefutation
% 0.55/0.52 % Parsed axioms : 575
% 0.55/0.52 % Removed by relevancy pruning/SinE : 309
% 0.55/0.52 % Initial clauses : 431
% 0.55/0.52 % Removed in clause preprocessing : 37
% 0.55/0.52 % Initial clauses in saturation : 394
% 0.55/0.52 % Processed clauses : 704
% 0.55/0.52 % ...of these trivial : 48
% 0.55/0.52 % ...subsumed : 310
% 0.55/0.52 % ...remaining for further processing : 346
% 0.55/0.52 % Other redundant clauses eliminated : 29
% 0.55/0.52 % Clauses deleted for lack of memory : 0
% 0.55/0.52 % Backward-subsumed : 1
% 0.55/0.52 % Backward-rewritten : 13
% 0.55/0.52 % Generated clauses : 2677
% 0.55/0.52 % ...of the previous two non-redundant : 2295
% 0.55/0.52 % ...aggressively subsumed : 0
% 0.55/0.52 % Contextual simplify-reflections : 0
% 0.55/0.52 % Paramodulations : 2644
% 0.55/0.52 % Factorizations : 0
% 0.55/0.52 % NegExts : 0
% 0.55/0.52 % Equation resolutions : 32
% 0.55/0.52 % Disequality decompositions : 0
% 0.55/0.52 % Total rewrite steps : 412
% 0.55/0.52 % ...of those cached : 318
% 0.55/0.52 % Propositional unsat checks : 0
% 0.55/0.52 % Propositional check models : 0
% 0.55/0.52 % Propositional check unsatisfiable : 0
% 0.55/0.52 % Propositional clauses : 0
% 0.55/0.52 % Propositional clauses after purity: 0
% 0.55/0.52 % Propositional unsat core size : 0
% 0.55/0.52 % Propositional preprocessing time : 0.000
% 0.55/0.52 % Propositional encoding time : 0.000
% 0.55/0.52 % Propositional solver time : 0.000
% 0.55/0.52 % Success case prop preproc time : 0.000
% 0.55/0.52 % Success case prop encoding time : 0.000
% 0.55/0.52 % Success case prop solver time : 0.000
% 0.55/0.52 % Current number of processed clauses : 322
% 0.55/0.52 % Positive orientable unit clauses : 75
% 0.55/0.52 % Positive unorientable unit clauses: 0
% 0.55/0.52 % Negative unit clauses : 10
% 0.55/0.52 % Non-unit-clauses : 237
% 0.55/0.52 % Current number of unprocessed clauses: 1918
% 0.55/0.52 % ...number of literals in the above : 5252
% 0.55/0.52 % Current number of archived formulas : 0
% 0.55/0.52 % Current number of archived clauses : 14
% 0.55/0.52 % Clause-clause subsumption calls (NU) : 14039
% 0.55/0.52 % Rec. Clause-clause subsumption calls : 11522
% 0.55/0.52 % Non-unit clause-clause subsumptions : 274
% 0.55/0.52 % Unit Clause-clause subsumption calls : 734
% 0.55/0.52 % Rewrite failures with RHS unbound : 0
% 0.55/0.52 % BW rewrite match attempts : 24
% 0.55/0.52 % BW rewrite match successes : 9
% 0.55/0.52 % Condensation attempts : 0
% 0.55/0.52 % Condensation successes : 0
% 0.55/0.52 % Termbank termtop insertions : 94422
% 0.55/0.52 % Search garbage collected termcells : 26927
% 0.55/0.52
% 0.55/0.52 % -------------------------------------------------
% 0.55/0.52 % User time : 0.144 s
% 0.55/0.52 % System time : 0.022 s
% 0.55/0.52 % Total time : 0.166 s
% 0.55/0.52 % Maximum resident set size: 10424 pages
% 0.55/0.52
% 0.55/0.52 % -------------------------------------------------
% 0.55/0.52 % User time : 0.158 s
% 0.55/0.52 % System time : 0.032 s
% 0.55/0.52 % Total time : 0.190 s
% 0.55/0.52 % Maximum resident set size: 5632 pages
% 0.55/0.52 % E exiting
%------------------------------------------------------------------------------