%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU760^1 : 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 : n014.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 08:25:31 AM UTC 2026
% Result : Theorem 1.65s 0.67s
% Output : CNFRefutation 1.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU760^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 % Computer : n014.cluster.edu
% 0.08/0.21 % Model : x86_64 x86_64
% 0.08/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.21 % Memory : 8046.5625MB
% 0.08/0.21 % OS : Linux 6.8.0-71-generic
% 0.08/0.21 % CPULimit : 300
% 0.08/0.21 % WCLimit : 300
% 0.08/0.21 % DateTime : Tue Sep 29 14:22:29 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.28 Running higher-order theorem proving
% 0.33/0.40 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.2lTjKz3Vio/E---3.1_2739412.p
% 1.65/0.67 % Version: 3.5.1-ho
% 1.65/0.67 % Preprocessing class: HSLMSLSSLLLCHFA.
% 1.65/0.67 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.65/0.67 % Starting ehoh_best5 with 300s (1) cores
% 1.65/0.67 % Starting almost_fo_3_lam with 300s (1) cores
% 1.65/0.67 % Starting new_bool_5 with 300s (1) cores
% 1.65/0.67 % Starting pre_casc_3 with 300s (1) cores
% 1.65/0.67 % Starting ho_unfolding_8 with 300s (1) cores
% 1.65/0.67 % Starting new_ho_10_cnf2 with 300s (1) cores
% 1.65/0.67 % Starting new_bool_3 with 300s (1) cores
% 1.65/0.67 % Starting new_ho_5 with 300s (1) cores
% 1.65/0.67 % new_bool_5 with pid 2739427 completed with status 0
% 1.65/0.67 % Result found by new_bool_5
% 1.65/0.67 % Preprocessing class: HSLMSLSSLLLCHFA.
% 1.65/0.67 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.65/0.67 % Starting ehoh_best5 with 300s (1) cores
% 1.65/0.67 % Starting almost_fo_3_lam with 300s (1) cores
% 1.65/0.67 % Starting new_bool_5 with 300s (1) cores
% 1.65/0.67 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 1.65/0.67 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 1.65/0.67 % Search class: HGHSM-FSLM32-MHFMMSBN
% 1.65/0.67 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 1.65/0.67 % Starting SubtermCWHack with 28s (1) cores
% 1.65/0.67 % SubtermCWHack with pid 2739439 completed with status 0
% 1.65/0.67 % Result found by SubtermCWHack
% 1.65/0.67 % Preprocessing class: HSLMSLSSLLLCHFA.
% 1.65/0.67 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.65/0.67 % Starting ehoh_best5 with 300s (1) cores
% 1.65/0.67 % Starting almost_fo_3_lam with 300s (1) cores
% 1.65/0.67 % Starting new_bool_5 with 300s (1) cores
% 1.65/0.67 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 1.65/0.67 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 1.65/0.67 % Search class: HGHSM-FSLM32-MHFMMSBN
% 1.65/0.67 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 1.65/0.67 % Starting SubtermCWHack with 28s (1) cores
% 1.65/0.67 % Preprocessing time : 0.009 s
% 1.65/0.67
% 1.65/0.67 % Proof found!
% 1.65/0.67 % SZS status Theorem
% 1.65/0.67 % SZS output start CNFRefutation
% 1.65/0.67 thf(decl_23, type, in: $i > $i > $o).
% 1.65/0.67 thf(decl_24, type, exu: ($i > $o) > $o).
% 1.65/0.67 thf(decl_25, type, setextAx: $o).
% 1.65/0.67 thf(decl_26, type, emptyset: $i).
% 1.65/0.67 thf(decl_27, type, emptysetAx: $o).
% 1.65/0.67 thf(decl_28, type, setadjoin: $i > $i > $i).
% 1.65/0.67 thf(decl_29, type, setadjoinAx: $o).
% 1.65/0.67 thf(decl_30, type, powerset: $i > $i).
% 1.65/0.67 thf(decl_31, type, powersetAx: $o).
% 1.65/0.67 thf(decl_32, type, setunion: $i > $i).
% 1.65/0.67 thf(decl_33, type, setunionAx: $o).
% 1.65/0.67 thf(decl_34, type, omega: $i).
% 1.65/0.67 thf(decl_35, type, omega0Ax: $o).
% 1.65/0.67 thf(decl_36, type, omegaSAx: $o).
% 1.65/0.67 thf(decl_37, type, omegaIndAx: $o).
% 1.65/0.67 thf(decl_38, type, replAx: $o).
% 1.65/0.67 thf(decl_39, type, foundationAx: $o).
% 1.65/0.67 thf(decl_40, type, wellorderingAx: $o).
% 1.65/0.67 thf(decl_41, type, descr: ($i > $o) > $i).
% 1.65/0.67 thf(decl_42, type, descrp: $o).
% 1.65/0.67 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 1.65/0.67 thf(decl_44, type, dsetconstrI: $o).
% 1.65/0.67 thf(decl_45, type, dsetconstrEL: $o).
% 1.65/0.67 thf(decl_46, type, dsetconstrER: $o).
% 1.65/0.67 thf(decl_47, type, exuE1: $o).
% 1.65/0.67 thf(decl_48, type, prop2set: $o > $i).
% 1.65/0.67 thf(decl_49, type, prop2setE: $o).
% 1.65/0.67 thf(decl_50, type, emptysetE: $o).
% 1.65/0.67 thf(decl_51, type, emptysetimpfalse: $o).
% 1.65/0.67 thf(decl_52, type, notinemptyset: $o).
% 1.65/0.67 thf(decl_53, type, exuE3e: $o).
% 1.65/0.67 thf(decl_54, type, setext: $o).
% 1.65/0.67 thf(decl_55, type, emptyI: $o).
% 1.65/0.67 thf(decl_56, type, noeltsimpempty: $o).
% 1.65/0.67 thf(decl_57, type, setbeta: $o).
% 1.65/0.67 thf(decl_58, type, nonempty: $i > $o).
% 1.65/0.67 thf(decl_59, type, nonemptyE1: $o).
% 1.65/0.67 thf(decl_60, type, nonemptyI: $o).
% 1.65/0.67 thf(decl_61, type, nonemptyI1: $o).
% 1.65/0.67 thf(decl_62, type, setadjoinIL: $o).
% 1.65/0.67 thf(decl_63, type, emptyinunitempty: $o).
% 1.65/0.67 thf(decl_64, type, setadjoinIR: $o).
% 1.65/0.67 thf(decl_65, type, setadjoinE: $o).
% 1.65/0.67 thf(decl_66, type, setadjoinOr: $o).
% 1.65/0.67 thf(decl_67, type, setoftrueEq: $o).
% 1.65/0.67 thf(decl_68, type, powersetI: $o).
% 1.65/0.67 thf(decl_69, type, emptyinPowerset: $o).
% 1.65/0.67 thf(decl_70, type, emptyInPowerset: $o).
% 1.65/0.67 thf(decl_71, type, powersetE: $o).
% 1.65/0.67 thf(decl_72, type, setunionI: $o).
% 1.65/0.67 thf(decl_73, type, setunionE: $o).
% 1.65/0.67 thf(decl_74, type, subPowSU: $o).
% 1.65/0.67 thf(decl_75, type, exuE2: $o).
% 1.65/0.67 thf(decl_76, type, nonemptyImpWitness: $o).
% 1.65/0.67 thf(decl_77, type, uniqinunit: $o).
% 1.65/0.67 thf(decl_78, type, notinsingleton: $o).
% 1.65/0.67 thf(decl_79, type, eqinunit: $o).
% 1.65/0.67 thf(decl_80, type, singletonsswitch: $o).
% 1.65/0.67 thf(decl_81, type, upairsetE: $o).
% 1.65/0.67 thf(decl_82, type, upairsetIL: $o).
% 1.65/0.67 thf(decl_83, type, upairsetIR: $o).
% 1.65/0.67 thf(decl_84, type, emptyE1: $o).
% 1.65/0.67 thf(decl_85, type, vacuousDall: $o).
% 1.65/0.67 thf(decl_86, type, quantDeMorgan1: $o).
% 1.65/0.67 thf(decl_87, type, quantDeMorgan2: $o).
% 1.65/0.67 thf(decl_88, type, quantDeMorgan3: $o).
% 1.65/0.67 thf(decl_89, type, quantDeMorgan4: $o).
% 1.65/0.67 thf(decl_90, type, prop2setI: $o).
% 1.65/0.67 thf(decl_92, type, prop2set2propI: $o).
% 1.65/0.67 thf(decl_93, type, notdexE: $o).
% 1.65/0.67 thf(decl_94, type, notdallE: $o).
% 1.65/0.67 thf(decl_95, type, exuI1: $o).
% 1.65/0.67 thf(decl_96, type, exuI3: $o).
% 1.65/0.67 thf(decl_97, type, exuI2: $o).
% 1.65/0.67 thf(decl_98, type, inCongP: $o).
% 1.65/0.67 thf(decl_99, type, in__Cong: $o).
% 1.65/0.67 thf(decl_100, type, exuE3u: $o).
% 1.65/0.67 thf(decl_101, type, exu__Cong: $o).
% 1.65/0.67 thf(decl_102, type, emptyset__Cong: $o).
% 1.65/0.67 thf(decl_103, type, setadjoin__Cong: $o).
% 1.65/0.67 thf(decl_104, type, powerset__Cong: $o).
% 1.65/0.67 thf(decl_105, type, setunion__Cong: $o).
% 1.65/0.67 thf(decl_106, type, omega__Cong: $o).
% 1.65/0.67 thf(decl_107, type, exuEu: $o).
% 1.65/0.67 thf(decl_108, type, descr__Cong: $o).
% 1.65/0.67 thf(decl_109, type, dsetconstr__Cong: $o).
% 1.65/0.67 thf(decl_110, type, subset: $i > $i > $o).
% 1.65/0.67 thf(decl_113, type, subsetI1: $o).
% 1.65/0.67 thf(decl_114, type, eqimpsubset2: $o).
% 1.65/0.67 thf(decl_115, type, eqimpsubset1: $o).
% 1.65/0.67 thf(decl_116, type, subsetI2: $o).
% 1.65/0.67 thf(decl_117, type, emptysetsubset: $o).
% 1.65/0.67 thf(decl_118, type, subsetE: $o).
% 1.65/0.67 thf(decl_119, type, subsetE2: $o).
% 1.65/0.67 thf(decl_120, type, notsubsetI: $o).
% 1.65/0.67 thf(decl_121, type, notequalI1: $o).
% 1.65/0.67 thf(decl_122, type, notequalI2: $o).
% 1.65/0.67 thf(decl_123, type, subsetRefl: $o).
% 1.65/0.67 thf(decl_124, type, subsetTrans: $o).
% 1.65/0.67 thf(decl_125, type, setadjoinSub: $o).
% 1.65/0.67 thf(decl_126, type, setadjoinSub2: $o).
% 1.65/0.67 thf(decl_127, type, subset2powerset: $o).
% 1.65/0.67 thf(decl_128, type, setextsub: $o).
% 1.65/0.67 thf(decl_129, type, subsetemptysetimpeq: $o).
% 1.65/0.67 thf(decl_130, type, powersetI1: $o).
% 1.65/0.67 thf(decl_131, type, powersetE1: $o).
% 1.65/0.67 thf(decl_132, type, inPowerset: $o).
% 1.65/0.67 thf(decl_133, type, powersetsubset: $o).
% 1.65/0.67 thf(decl_134, type, sepInPowerset: $o).
% 1.65/0.67 thf(decl_135, type, sepSubset: $o).
% 1.65/0.67 thf(decl_136, type, binunion: $i > $i > $i).
% 1.65/0.67 thf(decl_137, type, binunionIL: $o).
% 1.65/0.67 thf(decl_138, type, upairset2IR: $o).
% 1.65/0.67 thf(decl_139, type, binunionIR: $o).
% 1.65/0.67 thf(decl_140, type, binunionEcases: $o).
% 1.65/0.67 thf(decl_141, type, binunionE: $o).
% 1.65/0.67 thf(decl_142, type, binunionLsub: $o).
% 1.65/0.67 thf(decl_143, type, binunionRsub: $o).
% 1.65/0.67 thf(decl_144, type, binintersect: $i > $i > $i).
% 1.65/0.67 thf(decl_145, type, binintersectI: $o).
% 1.65/0.67 thf(decl_146, type, binintersectSubset5: $o).
% 1.65/0.67 thf(decl_147, type, binintersectEL: $o).
% 1.65/0.67 thf(decl_148, type, binintersectLsub: $o).
% 1.65/0.67 thf(decl_149, type, binintersectSubset2: $o).
% 1.65/0.67 thf(decl_150, type, binintersectSubset3: $o).
% 1.65/0.67 thf(decl_151, type, binintersectER: $o).
% 1.65/0.67 thf(decl_152, type, disjointsetsI1: $o).
% 1.65/0.67 thf(decl_153, type, binintersectRsub: $o).
% 1.65/0.67 thf(decl_154, type, binintersectSubset4: $o).
% 1.65/0.67 thf(decl_155, type, binintersectSubset1: $o).
% 1.65/0.67 thf(decl_156, type, bs114d: $o).
% 1.65/0.67 thf(decl_158, type, setminus: $i > $i > $i).
% 1.65/0.67 thf(decl_159, type, setminusI: $o).
% 1.65/0.67 thf(decl_160, type, setminusEL: $o).
% 1.65/0.67 thf(decl_161, type, setminusER: $o).
% 1.65/0.67 thf(decl_162, type, setminusSubset2: $o).
% 1.65/0.67 thf(decl_163, type, setminusERneg: $o).
% 1.65/0.67 thf(decl_164, type, setminusELneg: $o).
% 1.65/0.67 thf(decl_165, type, setminusILneg: $o).
% 1.65/0.67 thf(decl_166, type, setminusIRneg: $o).
% 1.65/0.67 thf(decl_167, type, setminusLsub: $o).
% 1.65/0.67 thf(decl_168, type, setminusSubset1: $o).
% 1.65/0.67 thf(decl_169, type, symdiff: $i > $i > $i).
% 1.65/0.67 thf(decl_170, type, symdiffE: $o).
% 1.65/0.67 thf(decl_171, type, symdiffI1: $o).
% 1.65/0.67 thf(decl_172, type, symdiffI2: $o).
% 1.65/0.67 thf(decl_173, type, symdiffIneg1: $o).
% 1.65/0.67 thf(decl_174, type, symdiffIneg2: $o).
% 1.65/0.67 thf(decl_175, type, iskpair: $i > $o).
% 1.65/0.67 thf(decl_176, type, secondinupair: $o).
% 1.65/0.67 thf(decl_177, type, setukpairIL: $o).
% 1.65/0.67 thf(decl_178, type, setukpairIR: $o).
% 1.65/0.67 thf(decl_179, type, kpairiskpair: $o).
% 1.65/0.67 thf(decl_180, type, kpair: $i > $i > $i).
% 1.65/0.67 thf(decl_181, type, kpairp: $o).
% 1.65/0.67 thf(decl_182, type, cartprod: $i > $i > $i).
% 1.65/0.67 thf(decl_183, type, singletonsubset: $o).
% 1.65/0.67 thf(decl_184, type, singletoninpowerset: $o).
% 1.65/0.67 thf(decl_185, type, singletoninpowunion: $o).
% 1.65/0.67 thf(decl_186, type, upairset2E: $o).
% 1.65/0.67 thf(decl_187, type, upairsubunion: $o).
% 1.65/0.67 thf(decl_188, type, upairinpowunion: $o).
% 1.65/0.67 thf(decl_189, type, ubforcartprodlem1: $o).
% 1.65/0.67 thf(decl_190, type, ubforcartprodlem2: $o).
% 1.65/0.67 thf(decl_191, type, ubforcartprodlem3: $o).
% 1.65/0.67 thf(decl_192, type, cartprodpairin: $o).
% 1.65/0.67 thf(decl_193, type, cartprodmempair1: $o).
% 1.65/0.67 thf(decl_194, type, cartprodmempair: $o).
% 1.65/0.67 thf(decl_195, type, setunionE2: $o).
% 1.65/0.67 thf(decl_196, type, setunionsingleton1: $o).
% 1.65/0.67 thf(decl_197, type, setunionsingleton2: $o).
% 1.65/0.67 thf(decl_198, type, setunionsingleton: $o).
% 1.65/0.67 thf(decl_199, type, singleton: $i > $o).
% 1.65/0.67 thf(decl_200, type, singletonprop: $o).
% 1.65/0.67 thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 1.65/0.67 thf(decl_202, type, ex1E1: $o).
% 1.65/0.67 thf(decl_203, type, ex1I: $o).
% 1.65/0.67 thf(decl_204, type, ex1I2: $o).
% 1.65/0.67 thf(decl_205, type, singletonsuniq: $o).
% 1.65/0.67 thf(decl_210, type, setukpairinjL1: $o).
% 1.65/0.67 thf(decl_211, type, kfstsingleton: $o).
% 1.65/0.67 thf(decl_212, type, theprop: $o).
% 1.65/0.67 thf(decl_213, type, kfst: $i > $i).
% 1.65/0.67 thf(decl_214, type, kfstpairEq: $o).
% 1.65/0.67 thf(decl_215, type, cartprodfstin: $o).
% 1.65/0.67 thf(decl_216, type, setukpairinjL2: $o).
% 1.65/0.67 thf(decl_217, type, setukpairinjL: $o).
% 1.65/0.67 thf(decl_218, type, setukpairinjR11: $o).
% 1.65/0.67 thf(decl_219, type, setukpairinjR12: $o).
% 1.65/0.67 thf(decl_220, type, setukpairinjR1: $o).
% 1.65/0.67 thf(decl_221, type, upairequniteq: $o).
% 1.65/0.67 thf(decl_222, type, setukpairinjR2: $o).
% 1.65/0.67 thf(decl_223, type, setukpairinjR: $o).
% 1.65/0.67 thf(decl_224, type, ksndsingleton: $o).
% 1.65/0.67 thf(decl_225, type, ksnd: $i > $i).
% 1.65/0.67 thf(decl_226, type, ksndpairEq: $o).
% 1.65/0.67 thf(decl_227, type, kpairsurjEq: $o).
% 1.65/0.67 thf(decl_228, type, cartprodsndin: $o).
% 1.65/0.67 thf(decl_229, type, cartprodpairmemEL: $o).
% 1.65/0.67 thf(decl_230, type, cartprodpairmemER: $o).
% 1.65/0.67 thf(decl_231, type, cartprodmempaircEq: $o).
% 1.65/0.67 thf(decl_232, type, cartprodfstpairEq: $o).
% 1.65/0.67 thf(decl_233, type, cartprodsndpairEq: $o).
% 1.65/0.67 thf(decl_234, type, cartprodpairsurjEq: $o).
% 1.65/0.67 thf(decl_235, type, breln: $i > $i > $i > $o).
% 1.65/0.67 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 1.65/0.67 thf(decl_237, type, dpsetconstrI: $o).
% 1.65/0.67 thf(decl_238, type, dpsetconstrSub: $o).
% 1.65/0.67 thf(decl_239, type, setOfPairsIsBReln: $o).
% 1.65/0.67 thf(decl_240, type, dpsetconstrERa: $o).
% 1.65/0.67 thf(decl_241, type, dpsetconstrEL1: $o).
% 1.65/0.67 thf(decl_242, type, dpsetconstrEL2: $o).
% 1.65/0.67 thf(decl_243, type, dpsetconstrER: $o).
% 1.65/0.67 thf(decl_244, type, func: $i > $i > $i > $o).
% 1.65/0.67 thf(decl_245, type, funcSet: $i > $i > $i).
% 1.65/0.67 thf(decl_246, type, funcImageSingleton: $o).
% 1.65/0.67 thf(decl_247, type, apProp: $o).
% 1.65/0.67 thf(decl_248, type, ap: $i > $i > $i > $i > $i).
% 1.65/0.67 thf(decl_249, type, app: $o).
% 1.65/0.67 thf(decl_250, type, infuncsetfunc: $o).
% 1.65/0.67 thf(decl_251, type, ap2p: $o).
% 1.65/0.67 thf(decl_252, type, funcinfuncset: $o).
% 1.65/0.67 thf(decl_253, type, lamProp: $o).
% 1.65/0.67 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
% 1.65/0.67 thf(decl_255, type, lamp: $o).
% 1.65/0.67 thf(decl_256, type, lam2p: $o).
% 1.65/0.67 thf(decl_257, type, brelnall1: $o).
% 1.65/0.67 thf(decl_258, type, brelnall2: $o).
% 1.65/0.67 thf(decl_259, type, ex1E2: $o).
% 1.65/0.67 thf(decl_260, type, funcGraphProp1: $o).
% 1.65/0.67 thf(decl_261, type, funcGraphProp3: $o).
% 1.65/0.67 thf(decl_262, type, funcGraphProp2: $o).
% 1.65/0.67 thf(decl_263, type, funcextLem: $o).
% 1.65/0.67 thf(decl_264, type, funcGraphProp4: $o).
% 1.65/0.67 thf(decl_265, type, subbreln: $o).
% 1.65/0.67 thf(decl_266, type, eqbreln: $o).
% 1.65/0.67 thf(decl_267, type, funcext: $o).
% 1.65/0.67 thf(decl_268, type, funcext2: $o).
% 1.65/0.67 thf(decl_269, type, ap2apEq1: $o).
% 1.65/0.67 thf(decl_270, type, ap2apEq2: $o).
% 1.65/0.67 thf(decl_271, type, beta1: $o).
% 1.65/0.67 thf(decl_272, type, eta1: $o).
% 1.65/0.67 thf(decl_273, type, lam2lamEq: $o).
% 1.65/0.67 thf(decl_274, type, beta2: $o).
% 1.65/0.67 thf(decl_275, type, eta2: $o).
% 1.65/0.67 thf(decl_276, type, iffalseProp1: $o).
% 1.65/0.67 thf(decl_277, type, iffalseProp2: $o).
% 1.65/0.67 thf(decl_278, type, iftrueProp1: $o).
% 1.65/0.67 thf(decl_279, type, iftrueProp2: $o).
% 1.65/0.67 thf(decl_280, type, ifSingleton: $o).
% 1.65/0.67 thf(decl_281, type, if: $i > $o > $i > $i > $i).
% 1.65/0.67 thf(decl_282, type, ifp: $o).
% 1.65/0.67 thf(decl_283, type, theeq: $o).
% 1.65/0.67 thf(decl_284, type, iftrue: $o).
% 1.65/0.67 thf(decl_285, type, iffalse: $o).
% 1.65/0.67 thf(decl_286, type, iftrueorfalse: $o).
% 1.65/0.67 thf(decl_287, type, binintersectT_lem: $o).
% 1.65/0.67 thf(decl_288, type, binunionT_lem: $o).
% 1.65/0.67 thf(decl_289, type, powersetT_lem: $o).
% 1.65/0.67 thf(decl_290, type, setminusT_lem: $o).
% 1.65/0.67 thf(decl_291, type, complementT_lem: $o).
% 1.65/0.67 thf(decl_292, type, setextT: $o).
% 1.65/0.67 thf(decl_293, type, subsetTI: $o).
% 1.65/0.67 thf(decl_294, type, powersetTI1: $o).
% 1.65/0.67 thf(decl_295, type, powersetTE1: $o).
% 1.65/0.67 thf(decl_296, type, complementTI1: $o).
% 1.65/0.67 thf(decl_297, type, complementTE1: $o).
% 1.65/0.67 thf(decl_298, type, binintersectTELcontra: $o).
% 1.65/0.67 thf(decl_299, type, binintersectTERcontra: $o).
% 1.65/0.67 thf(decl_300, type, contrasubsetT: $o).
% 1.65/0.67 thf(decl_301, type, contrasubsetT1: $o).
% 1.65/0.67 thf(decl_302, type, contrasubsetT2: $o).
% 1.65/0.67 thf(decl_303, type, contrasubsetT3: $o).
% 1.65/0.67 thf(decl_304, type, doubleComplementI1: $o).
% 1.65/0.67 thf(decl_305, type, doubleComplementE1: $o).
% 1.65/0.67 thf(decl_306, type, doubleComplementSub1: $o).
% 1.65/0.67 thf(decl_307, type, doubleComplementSub2: $o).
% 1.65/0.67 thf(decl_308, type, doubleComplementEq: $o).
% 1.65/0.67 thf(decl_309, type, complementTnotintersectT: $o).
% 1.65/0.67 thf(decl_310, type, complementImpComplementIntersect: $o).
% 1.65/0.67 thf(decl_311, type, complementSubsetComplementIntersect: $o).
% 1.65/0.67 thf(decl_312, type, complementInPowersetComplementIntersect: $o).
% 1.65/0.67 thf(decl_313, type, contraSubsetComplement: $o).
% 1.65/0.67 thf(decl_314, type, complementTcontraSubset: $o).
% 1.65/0.67 thf(decl_315, type, binunionTILcontra: $o).
% 1.65/0.67 thf(decl_316, type, binunionTIRcontra: $o).
% 1.65/0.67 thf(decl_317, type, inIntersectImpInUnion: $o).
% 1.65/0.67 thf(decl_318, type, inIntersectImpInUnion2: $o).
% 1.65/0.67 thf(decl_319, type, inIntersectImpInIntersectUnions: $o).
% 1.65/0.67 thf(decl_320, type, intersectInPowersetIntersectUnions: $o).
% 1.65/0.67 thf(decl_321, type, inComplementUnionImpNotIn1: $o).
% 1.65/0.67 thf(decl_322, type, inComplementUnionImpInComplement1: $o).
% 1.65/0.67 thf(decl_323, type, binunionTE: $o).
% 1.65/0.67 thf(decl_324, type, binunionTEcontra: $o).
% 1.65/0.67 thf(decl_325, type, demorgan2a1: $o).
% 1.65/0.67 thf(decl_326, type, complementUnionInPowersetComplement: $o).
% 1.65/0.67 thf(decl_327, type, demorgan2a2: $o).
% 1.65/0.67 thf(decl_328, type, demorgan1a: $o).
% 1.65/0.67 thf(decl_329, type, demorgan1b: $o).
% 1.65/0.67 thf(decl_330, type, demorgan1: $o).
% 1.65/0.67 thf(decl_331, type, demorgan2a: $o).
% 1.65/0.67 thf(decl_332, type, demorgan2b2: $o).
% 1.65/0.67 thf(decl_333, type, demorgan2b: $o).
% 1.65/0.67 thf(decl_334, type, demorgan2: $o).
% 1.65/0.67 thf(decl_335, type, woz13rule0: $o).
% 1.65/0.67 thf(decl_336, type, woz13rule1: $o).
% 1.65/0.67 thf(decl_337, type, epred1_0: $o).
% 1.65/0.67 thf(decl_338, type, esk1_2: $i > $i > $i).
% 1.65/0.67 thf(decl_339, type, esk2_2: $i > $i > $i).
% 1.65/0.67 thf(decl_340, type, esk3_2: $i > $i > $i).
% 1.65/0.67 thf(decl_341, type, esk4_1: $i > $i).
% 1.65/0.67 thf(decl_342, type, esk5_2: ($i > $i > $o) > $i > $i).
% 1.65/0.67 thf(decl_343, type, esk6_2: ($i > $i > $o) > $i > $i).
% 1.65/0.67 thf(decl_344, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
% 1.65/0.67 thf(decl_345, type, esk8_1: $i > $i).
% 1.65/0.67 thf(decl_346, type, esk9_1: ($i > $o) > $i).
% 1.65/0.67 thf(decl_347, type, esk10_1: ($i > $o) > $i).
% 1.65/0.67 thf(decl_348, type, esk11_2: $i > $i > $i).
% 1.65/0.67 thf(decl_349, type, esk12_2: $i > $i > $i).
% 1.65/0.67 thf(decl_350, type, esk13_1: $i > $i).
% 1.65/0.67 thf(decl_351, type, esk14_1: $i > $i).
% 1.65/0.67 thf(decl_352, type, esk15_1: $i > $i).
% 1.65/0.67 thf(decl_353, type, esk16_2: $i > $i > $i).
% 1.65/0.67 thf(decl_354, type, esk17_3: $i > $i > $o > $i).
% 1.65/0.67 thf(decl_355, type, esk18_1: ($i > $o) > $i).
% 1.65/0.67 thf(decl_356, type, esk19_1: $i > $i).
% 1.65/0.67 thf(decl_357, type, esk20_2: $i > ($i > $o) > $i).
% 1.65/0.67 thf(decl_358, type, esk21_2: $i > ($i > $o) > $i).
% 1.65/0.67 thf(decl_359, type, esk22_2: $i > ($i > $o) > $i).
% 1.65/0.67 thf(decl_360, type, esk23_2: $i > ($i > $o) > $i).
% 1.65/0.67 thf(decl_361, type, esk24_2: $i > ($i > $o) > $i).
% 1.65/0.67 thf(decl_362, type, esk25_2: $i > ($i > $o) > $i).
% 1.65/0.67 thf(decl_363, type, esk26_2: ($i > $o) > $i > $i).
% 1.65/0.67 thf(decl_364, type, esk27_1: ($i > $o) > $i).
% 1.65/0.67 thf(decl_365, type, esk28_1: ($i > $o) > $i).
% 1.65/0.67 thf(decl_366, type, esk29_2: ($i > $o) > $i > $i).
% 1.65/0.67 thf(decl_367, type, esk30_2: ($i > $o) > ($i > $o) > $i).
% 1.65/0.67 thf(decl_368, type, esk31_2: ($i > $o) > ($i > $o) > $i).
% 1.65/0.67 thf(decl_369, type, esk32_2: ($i > $o) > ($i > $o) > $i).
% 1.65/0.67 thf(decl_370, type, esk33_2: ($i > $o) > ($i > $o) > $i).
% 1.65/0.67 thf(decl_371, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 1.65/0.67 thf(decl_372, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 1.65/0.67 thf(decl_373, type, esk36_2: $i > $i > $i).
% 1.65/0.67 thf(decl_374, type, esk37_2: $i > $i > $i).
% 1.65/0.67 thf(decl_375, type, esk38_2: $i > $i > $i).
% 1.65/0.67 thf(decl_376, type, esk39_3: $i > $i > $i > $i).
% 1.65/0.67 thf(decl_377, type, esk40_3: $i > $i > $i > $i).
% 1.65/0.67 thf(decl_378, type, esk41_2: $i > $i > $i).
% 1.65/0.67 thf(decl_379, type, esk42_2: $i > ($i > $o) > $i).
% 1.65/0.67 thf(decl_380, type, esk43_2: $i > ($i > $o) > $i).
% 1.65/0.67 thf(decl_381, type, esk44_2: $i > ($i > $o) > $i).
% 1.65/0.67 thf(decl_382, type, esk45_3: $i > ($i > $o) > $i > $i).
% 1.65/0.67 thf(decl_383, type, esk46_2: $i > ($i > $o) > $i).
% 1.65/0.67 thf(decl_384, type, esk47_2: $i > ($i > $o) > $i).
% 1.65/0.67 thf(decl_385, type, esk48_3: $i > $i > ($i > $i) > $i).
% 1.65/0.67 thf(decl_386, type, esk49_3: $i > $i > ($i > $i) > $i).
% 1.65/0.67 thf(decl_387, type, esk50_3: $i > $i > ($i > $i) > $i).
% 1.65/0.67 thf(decl_388, type, esk51_4: $i > $i > $i > ($i > $o) > $i).
% 1.65/0.67 thf(decl_389, type, esk52_4: $i > $i > $i > ($i > $o) > $i).
% 1.65/0.67 thf(decl_390, type, esk53_4: $i > $i > $i > ($i > $o) > $i).
% 1.65/0.67 thf(decl_391, type, esk54_4: $i > $i > $i > ($i > $o) > $i).
% 1.65/0.67 thf(decl_392, type, esk55_4: $i > $i > $i > $i > $i).
% 1.65/0.67 thf(decl_393, type, esk56_4: $i > $i > $i > $i > $i).
% 1.65/0.67 thf(decl_394, type, esk57_4: $i > $i > $i > $i > $i).
% 1.65/0.67 thf(decl_395, type, esk58_4: $i > $i > $i > $i > $i).
% 1.65/0.67 thf(decl_396, type, esk59_4: $i > $i > $i > $i > $i).
% 1.65/0.67 thf(decl_397, type, esk60_4: $i > $i > $i > $i > $i).
% 1.65/0.67 thf(decl_398, type, esk61_4: $i > $i > $i > $i > $i).
% 1.65/0.67 thf(decl_399, type, esk62_4: $i > $i > $i > $i > $i).
% 1.65/0.67 thf(decl_400, type, esk63_4: $i > $i > $i > $i > $i).
% 1.65/0.67 thf(decl_401, type, esk64_3: $i > $i > ($i > $i) > $i).
% 1.65/0.67 thf(decl_402, type, esk65_3: $i > $i > ($i > $i) > $i).
% 1.65/0.67 thf(decl_403, type, esk66_3: $i > $i > ($i > $i) > $i).
% 1.65/0.67 thf(decl_404, type, esk67_3: $i > $i > $i > $i).
% 1.65/0.67 thf(decl_405, type, esk68_3: $i > $i > $i > $i).
% 1.65/0.67 thf(decl_406, type, esk69_3: $i > $i > $i > $i).
% 1.65/0.67 thf(decl_407, type, esk70_3: $i > $i > $i > $i).
% 1.65/0.67 thf(decl_408, type, esk71_0: $i).
% 1.65/0.67 thf(decl_409, type, esk72_0: $i).
% 1.65/0.67 thf(decl_410, type, esk73_0: $i).
% 1.65/0.67 thf(decl_411, type, esk74_0: $i).
% 1.65/0.67 thf(woz13rule2, 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)=>((demorgan2a2)=>((demorgan1a)=>((demorgan1b)=>((demorgan1)=>((demorgan2a)=>((demorgan2b2)=>((demorgan2b)=>((demorgan2)=>((woz13rule0)=>((woz13rule1)=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X48 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', woz13rule2)).
% 1.65/0.67 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', exuE3u)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', exuI2)).
% 1.65/0.67 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', exuI3)).
% 1.65/0.67 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', exuI1)).
% 1.65/0.67 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', exu__Cong)).
% 1.65/0.67 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', descr__Cong)).
% 1.65/0.67 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', exuEu)).
% 1.65/0.67 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', dsetconstr__Cong)).
% 1.65/0.67 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', sepSubset)).
% 1.65/0.67 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', sepInPowerset)).
% 1.65/0.67 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X40))&(((X14)=(X2)))))|(((~((X40)))&(((X14)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', iffalseProp2)).
% 1.65/0.67 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$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.2lTjKz3Vio/E---3.1_2739412.p', iffalseProp1)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', eta2)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', beta2)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', lam2lamEq)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', eta1)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', beta1)).
% 1.65/0.67 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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', singletonprop)).
% 1.65/0.67 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', ex1E1)).
% 1.65/0.67 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', kfstsingleton)).
% 1.65/0.67 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', ex1I2)).
% 1.65/0.67 thf(ex1I, axiom, ((ex1I)<=>![X4:$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.2lTjKz3Vio/E---3.1_2739412.p', ex1I)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', ksndsingleton)).
% 1.65/0.67 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:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', dpsetconstrEL1)).
% 1.65/0.67 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', dpsetconstrERa)).
% 1.65/0.67 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', setOfPairsIsBReln)).
% 1.65/0.67 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', dpsetconstrSub)).
% 1.65/0.67 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', dpsetconstrI)).
% 1.65/0.67 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', dpsetconstrEL2)).
% 1.65/0.67 thf(apProp, axiom, ((apProp)<=>![X4:$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.2lTjKz3Vio/E---3.1_2739412.p', apProp)).
% 1.65/0.67 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', funcImageSingleton)).
% 1.65/0.67 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', dpsetconstrER)).
% 1.65/0.67 thf(lamProp, axiom, ((lamProp)<=>![X4:$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.2lTjKz3Vio/E---3.1_2739412.p', lamProp)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', ex1E2)).
% 1.65/0.67 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:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', lam2p)).
% 1.65/0.67 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', lamp)).
% 1.65/0.67 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$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.2lTjKz3Vio/E---3.1_2739412.p', iftrueProp1)).
% 1.65/0.67 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X43))&(((X14)=(X2)))))|(((~((X43)))&(((X14)=(X3))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', ifSingleton)).
% 1.65/0.67 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$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.2lTjKz3Vio/E---3.1_2739412.p', iftrueProp2)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', emptyE1)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', exuE2)).
% 1.65/0.67 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', setoftrueEq)).
% 1.65/0.67 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', nonemptyI)).
% 1.65/0.67 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', setbeta)).
% 1.65/0.67 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', exuE3e)).
% 1.65/0.67 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', exuE1)).
% 1.65/0.67 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', dsetconstrER)).
% 1.65/0.67 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', dsetconstrEL)).
% 1.65/0.67 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', dsetconstrI)).
% 1.65/0.67 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', descrp)).
% 1.65/0.67 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', replAx)).
% 1.65/0.67 thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', subsetTI)).
% 1.65/0.67 thf(setextT, axiom, ((setextT)<=>![X4:$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.2lTjKz3Vio/E---3.1_2739412.p', setextT)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', powersetTI1)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', powersetTE1)).
% 1.65/0.67 thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', complementTI1)).
% 1.65/0.67 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', in__Cong)).
% 1.65/0.67 thf(complementTE1, axiom, ((complementTE1)<=>![X4:$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.2lTjKz3Vio/E---3.1_2739412.p', complementTE1)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', inCongP)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', binintersectTELcontra)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', binintersectTERcontra)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', contrasubsetT)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', contrasubsetT1)).
% 1.65/0.67 thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', contrasubsetT2)).
% 1.65/0.67 thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$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.2lTjKz3Vio/E---3.1_2739412.p', contrasubsetT3)).
% 1.65/0.67 thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', doubleComplementI1)).
% 1.65/0.67 thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$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.2lTjKz3Vio/E---3.1_2739412.p', doubleComplementE1)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', doubleComplementSub1)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', doubleComplementSub2)).
% 1.65/0.67 thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', doubleComplementEq)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', complementTnotintersectT)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', complementImpComplementIntersect)).
% 1.65/0.67 thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', complementSubsetComplementIntersect)).
% 1.65/0.67 thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$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.2lTjKz3Vio/E---3.1_2739412.p', complementInPowersetComplementIntersect)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', contraSubsetComplement)).
% 1.65/0.67 thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', complementTcontraSubset)).
% 1.65/0.67 thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', binunionTILcontra)).
% 1.65/0.67 thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', binunionTIRcontra)).
% 1.65/0.67 thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$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.2lTjKz3Vio/E---3.1_2739412.p', inIntersectImpInUnion)).
% 1.65/0.67 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', omega__Cong)).
% 1.65/0.67 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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', inIntersectImpInUnion2)).
% 1.65/0.67 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', setunion__Cong)).
% 1.65/0.67 thf(inIntersectImpInIntersectUnions, axiom, ((inIntersectImpInIntersectUnions)<=>![X4:$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.2lTjKz3Vio/E---3.1_2739412.p', inIntersectImpInIntersectUnions)).
% 1.65/0.67 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', powerset__Cong)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', intersectInPowersetIntersectUnions)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', setadjoin__Cong)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', inComplementUnionImpNotIn1)).
% 1.65/0.67 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', emptyset__Cong)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', inComplementUnionImpInComplement1)).
% 1.65/0.67 thf(binunionTE, axiom, ((binunionTE)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X50:$o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ X21 @ X48))=>(((in @ X2 @ X21)=>(X50))=>(((in @ X2 @ X48)=>(X50))=>(X50))))))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', binunionTE)).
% 1.65/0.67 thf(binunionTEcontra, axiom, ((binunionTEcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', binunionTEcontra)).
% 1.65/0.67 thf(demorgan2a1, axiom, ((demorgan2a1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', demorgan2a1)).
% 1.65/0.67 thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$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.2lTjKz3Vio/E---3.1_2739412.p', complementUnionInPowersetComplement)).
% 1.65/0.67 thf(demorgan2a2, axiom, ((demorgan2a2)<=>![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.2lTjKz3Vio/E---3.1_2739412.p', demorgan2a2)).
% 1.65/0.67 thf(demorgan1a, axiom, ((demorgan1a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', demorgan1a)).
% 1.65/0.67 thf(demorgan1b, axiom, ((demorgan1b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', demorgan1b)).
% 1.65/0.67 thf(demorgan1, axiom, ((demorgan1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ X21 @ X48))=(binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', demorgan1)).
% 1.65/0.67 thf(demorgan2a, axiom, ((demorgan2a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', demorgan2a)).
% 1.65/0.67 thf(demorgan2b2, axiom, ((demorgan2b2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>((in @ X2 @ (setminus @ X4 @ X48))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', demorgan2b2)).
% 1.65/0.67 thf(demorgan2b, axiom, ((demorgan2b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', demorgan2b)).
% 1.65/0.67 thf(demorgan2, axiom, ((demorgan2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binunion @ X21 @ X48))=(binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', demorgan2)).
% 1.65/0.67 thf(woz13rule0, axiom, ((woz13rule0)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ X4)))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', woz13rule0)).
% 1.65/0.67 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', subsetE2)).
% 1.65/0.67 thf(woz13rule1, axiom, ((woz13rule1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', woz13rule1)).
% 1.65/0.67 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', subsetE)).
% 1.65/0.67 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', emptysetsubset)).
% 1.65/0.67 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', subsetI2)).
% 1.65/0.67 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', eqimpsubset1)).
% 1.65/0.67 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', eqimpsubset2)).
% 1.65/0.67 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', subsetI1)).
% 1.65/0.67 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', notsubsetI)).
% 1.65/0.67 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', setminusERneg)).
% 1.65/0.67 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', setminusSubset2)).
% 1.65/0.67 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', subset2powerset)).
% 1.65/0.67 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', setadjoinSub2)).
% 1.65/0.67 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', setadjoinSub)).
% 1.65/0.67 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', subsetTrans)).
% 1.65/0.67 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', subsetRefl)).
% 1.65/0.67 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', notequalI2)).
% 1.65/0.67 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', notequalI1)).
% 1.65/0.67 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', setextsub)).
% 1.65/0.67 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', powersetsubset)).
% 1.65/0.67 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', inPowerset)).
% 1.65/0.67 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', powersetE1)).
% 1.65/0.67 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', powersetI1)).
% 1.65/0.67 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', subsetemptysetimpeq)).
% 1.65/0.67 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', binunionIL)).
% 1.65/0.67 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', binintersectI)).
% 1.65/0.67 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', binunionRsub)).
% 1.65/0.67 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', binunionLsub)).
% 1.65/0.67 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', binunionE)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', binunionEcases)).
% 1.65/0.67 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', binunionIR)).
% 1.65/0.67 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', upairset2IR)).
% 1.65/0.67 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', binintersectSubset5)).
% 1.65/0.67 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', binintersectRsub)).
% 1.65/0.67 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', disjointsetsI1)).
% 1.65/0.67 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', binintersectER)).
% 1.65/0.67 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', binintersectSubset3)).
% 1.65/0.67 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', binintersectSubset2)).
% 1.65/0.67 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', binintersectLsub)).
% 1.65/0.67 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', binintersectEL)).
% 1.65/0.67 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', binintersectSubset4)).
% 1.65/0.67 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', ap2apEq2)).
% 1.65/0.67 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', setminusER)).
% 1.65/0.67 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', setminusEL)).
% 1.65/0.67 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', setminusI)).
% 1.65/0.67 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', bs114d)).
% 1.65/0.67 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', binintersectSubset1)).
% 1.65/0.67 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', setminusELneg)).
% 1.65/0.67 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', symdiffI2)).
% 1.65/0.67 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', symdiffI1)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', symdiffE)).
% 1.65/0.67 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', setminusSubset1)).
% 1.65/0.67 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', setminusLsub)).
% 1.65/0.67 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', setminusIRneg)).
% 1.65/0.67 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', setminusILneg)).
% 1.65/0.67 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', symdiffIneg1)).
% 1.65/0.67 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', singletonsubset)).
% 1.65/0.67 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', kpairp)).
% 1.65/0.67 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', kpairiskpair)).
% 1.65/0.67 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', setukpairIR)).
% 1.65/0.67 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', setukpairIL)).
% 1.65/0.67 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', secondinupair)).
% 1.65/0.67 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', symdiffIneg2)).
% 1.65/0.67 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', singletoninpowerset)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', ubforcartprodlem3)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', ubforcartprodlem2)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', ubforcartprodlem1)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', upairinpowunion)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', upairsubunion)).
% 1.65/0.67 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', upairset2E)).
% 1.65/0.67 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', singletoninpowunion)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', cartprodpairin)).
% 1.65/0.67 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', setunionsingleton)).
% 1.65/0.67 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', setunionsingleton2)).
% 1.65/0.67 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', setunionsingleton1)).
% 1.65/0.67 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', setunionE2)).
% 1.65/0.67 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', cartprodmempair)).
% 1.65/0.67 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.2lTjKz3Vio/E---3.1_2739412.p', cartprodmempair1)).
% 1.65/0.67 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', kfstpairEq)).
% 1.65/0.67 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', theprop)).
% 1.65/0.67 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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.2lTjKz3Vio/E---3.1_2739412.p', setukpairinjL1)).
% 1.65/0.67 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', singletonsuniq)).
% 1.65/0.67 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', cartprodfstin)).
% 1.65/0.67 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', setukpairinjR2)).
% 1.65/0.67 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', upairequniteq)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', setukpairinjR1)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', setukpairinjR12)).
% 1.65/0.67 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', setukpairinjR11)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', setukpairinjL)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', setukpairinjL2)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', setukpairinjR)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', cartprodmempaircEq)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', cartprodpairmemER)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', cartprodpairmemEL)).
% 1.65/0.67 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', cartprodsndin)).
% 1.65/0.67 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', kpairsurjEq)).
% 1.65/0.67 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', ksndpairEq)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', cartprodfstpairEq)).
% 1.65/0.67 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', cartprodpairsurjEq)).
% 1.65/0.67 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', cartprodsndpairEq)).
% 1.65/0.67 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', funcinfuncset)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', ap2p)).
% 1.65/0.67 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', infuncsetfunc)).
% 1.65/0.67 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', app)).
% 1.65/0.67 thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', funcGraphProp3)).
% 1.65/0.67 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', funcGraphProp1)).
% 1.65/0.67 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$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.2lTjKz3Vio/E---3.1_2739412.p', brelnall2)).
% 1.65/0.67 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.2lTjKz3Vio/E---3.1_2739412.p', brelnall1)).
% 1.65/0.67 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', funcGraphProp2)).
% 1.65/0.67 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', ap2apEq1)).
% 1.65/0.67 thf(funcext2, axiom, ((funcext2)<=>![X4:$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.2lTjKz3Vio/E---3.1_2739412.p', funcext2)).
% 1.65/0.68 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', funcext)).
% 1.65/0.68 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', eqbreln)).
% 1.65/0.68 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', subbreln)).
% 1.65/0.68 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$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.2lTjKz3Vio/E---3.1_2739412.p', funcGraphProp4)).
% 1.65/0.68 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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', funcextLem)).
% 1.65/0.68 thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', iftrueorfalse)).
% 1.65/0.68 thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', iffalse)).
% 1.65/0.68 thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', iftrue)).
% 1.65/0.68 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', theeq)).
% 1.65/0.68 thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', ifp)).
% 1.65/0.68 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$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.2lTjKz3Vio/E---3.1_2739412.p', binunionT_lem)).
% 1.65/0.68 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.2lTjKz3Vio/E---3.1_2739412.p', powersetT_lem)).
% 1.65/0.68 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', setminusT_lem)).
% 1.65/0.68 thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', complementT_lem)).
% 1.65/0.68 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$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.2lTjKz3Vio/E---3.1_2739412.p', binintersectT_lem)).
% 1.65/0.68 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', notdallE)).
% 1.65/0.68 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', notdexE)).
% 1.65/0.68 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', prop2setI)).
% 1.65/0.68 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', quantDeMorgan4)).
% 1.65/0.68 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', quantDeMorgan3)).
% 1.65/0.68 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', quantDeMorgan2)).
% 1.65/0.68 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', quantDeMorgan1)).
% 1.65/0.68 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', vacuousDall)).
% 1.65/0.68 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', upairsetIR)).
% 1.65/0.68 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', upairsetIL)).
% 1.65/0.68 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', upairsetE)).
% 1.65/0.68 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', singletonsswitch)).
% 1.65/0.68 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', eqinunit)).
% 1.65/0.68 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', notinsingleton)).
% 1.65/0.68 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', uniqinunit)).
% 1.65/0.68 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', nonemptyImpWitness)).
% 1.65/0.68 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', subPowSU)).
% 1.65/0.68 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.2lTjKz3Vio/E---3.1_2739412.p', setunionE)).
% 1.65/0.68 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', setunionI)).
% 1.65/0.68 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', powersetE)).
% 1.65/0.68 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', emptyInPowerset)).
% 1.65/0.68 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', emptyinPowerset)).
% 1.65/0.68 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', powersetI)).
% 1.65/0.68 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', setadjoinOr)).
% 1.65/0.68 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.2lTjKz3Vio/E---3.1_2739412.p', setadjoinE)).
% 1.65/0.68 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', setadjoinIR)).
% 1.65/0.68 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', emptyinunitempty)).
% 1.65/0.68 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', setadjoinIL)).
% 1.65/0.68 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', nonemptyI1)).
% 1.65/0.68 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', nonemptyE1)).
% 1.65/0.68 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', noeltsimpempty)).
% 1.65/0.68 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', emptyI)).
% 1.65/0.68 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', setext)).
% 1.65/0.68 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', notinemptyset)).
% 1.65/0.68 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', emptysetimpfalse)).
% 1.65/0.68 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', emptysetE)).
% 1.65/0.68 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', prop2setE)).
% 1.65/0.68 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', wellorderingAx)).
% 1.65/0.68 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', foundationAx)).
% 1.65/0.68 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.2lTjKz3Vio/E---3.1_2739412.p', omegaIndAx)).
% 1.65/0.68 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', omegaSAx)).
% 1.65/0.68 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', omega0Ax)).
% 1.65/0.68 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', setunionAx)).
% 1.65/0.68 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', powersetAx)).
% 1.65/0.68 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', setadjoinAx)).
% 1.65/0.68 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', emptysetAx)).
% 1.65/0.68 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.2lTjKz3Vio/E---3.1_2739412.p', setextAx)).
% 1.65/0.68 thf(c_0_276, 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)=>((demorgan2a2)=>((demorgan1a)=>((demorgan1b)=>((demorgan1)=>((demorgan2a)=>((demorgan2b2)=>((demorgan2b)=>((demorgan2)=>((woz13rule0)=>((woz13rule1)=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X48 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[woz13rule2])).
% 1.65/0.68 thf(c_0_277, 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])).
% 1.65/0.68 thf(c_0_278, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 1.65/0.68 thf(c_0_279, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 1.65/0.68 thf(c_0_280, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 1.65/0.68 thf(c_0_281, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 1.65/0.68 thf(c_0_282, plain, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 1.65/0.68 thf(c_0_283, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 1.65/0.68 thf(c_0_284, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 1.65/0.68 thf(c_0_285, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 1.65/0.68 thf(c_0_286, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 1.65/0.68 thf(c_0_287, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X40))&(((Z0)=(X2)))))|(((~((X40)))&(((Z0)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])).
% 1.65/0.68 thf(c_0_288, plain, ((iffalseProp1)<=>![X4:$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])).
% 1.65/0.68 thf(c_0_289, 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])).
% 1.65/0.68 thf(c_0_290, 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])).
% 1.65/0.68 thf(c_0_291, 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])).
% 1.65/0.68 thf(c_0_292, 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])).
% 1.65/0.68 thf(c_0_293, 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])).
% 1.65/0.68 thf(c_0_294, 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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 1.65/0.68 thf(c_0_295, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 1.65/0.68 thf(c_0_296, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 1.65/0.68 thf(c_0_297, plain, ((ex1I2)<=>![X4:$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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 1.65/0.68 thf(c_0_298, plain, ((ex1I)<=>![X4:$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])).
% 1.65/0.68 thf(c_0_299, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 1.65/0.68 thf(c_0_300, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 1.65/0.68 thf(c_0_301, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 1.65/0.68 thf(c_0_302, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 1.65/0.68 thf(c_0_303, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 1.65/0.68 thf(c_0_304, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 1.65/0.68 thf(c_0_305, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 1.65/0.68 thf(c_0_306, plain, ((apProp)<=>![X4:$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])).
% 1.65/0.68 thf(c_0_307, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
% 1.65/0.68 thf(c_0_308, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 1.65/0.68 thf(c_0_309, plain, ((lamProp)<=>![X4:$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])).
% 1.65/0.68 thf(c_0_310, 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])).
% 1.65/0.68 thf(c_0_311, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
% 1.65/0.68 thf(c_0_312, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
% 1.65/0.68 thf(c_0_313, plain, ((iftrueProp1)<=>![X4:$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])).
% 1.65/0.68 thf(c_0_314, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X43))&(((Z0)=(X2)))))|(((~((X43)))&(((Z0)=(X3))))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
% 1.65/0.68 thf(c_0_315, plain, ((iftrueProp2)<=>![X4:$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])).
% 1.65/0.68 thf(c_0_316, 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])).
% 1.65/0.68 thf(c_0_317, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 1.65/0.68 thf(c_0_318, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 1.65/0.68 thf(c_0_319, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 1.65/0.68 thf(c_0_320, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 1.65/0.68 thf(c_0_321, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 1.65/0.68 thf(c_0_322, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 1.65/0.68 thf(c_0_323, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 1.65/0.68 thf(c_0_324, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 1.65/0.68 thf(c_0_325, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 1.65/0.68 thf(c_0_326, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 1.65/0.68 thf(c_0_327, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 1.65/0.68 thf(c_0_328, plain, ((epred1_0)<=>![X957:$i]:(?[X958:$i]:((((![X959:$i]:(((in @ X959 @ X958)=>![X960:$i]:(((in @ X960 @ X959)=>(in @ X960 @ X957)))))&![X961:$i, X962:$i]:((((in @ X961 @ X957)&(in @ X962 @ X957))=>(![X963:$i]:(((in @ X963 @ X958)=>((in @ X961 @ X963)<=>(in @ X962 @ X963))))=>((X961)=(X962))))))&![X964:$i, X965:$i]:((((in @ X964 @ X958)&(in @ X965 @ X958))=>(![X966:$i]:(((in @ X966 @ X964)=>(in @ X966 @ X965)))|![X967:$i]:(((in @ X967 @ X965)=>(in @ X967 @ X964)))))))&![X968:$i]:(((![X969:$i]:(((in @ X969 @ X968)=>(in @ X969 @ X957)))&?[X970:$i]:((in @ X970 @ X968)))=>?[X971:$i, X972:$i]:(((((in @ X971 @ X958)&(in @ X972 @ X968))&~(?[X973:$i]:(((in @ X973 @ X971)&(in @ X973 @ X968)))))&![X974:$i]:(((in @ X974 @ X958)=>(![X975:$i]:(((in @ X975 @ X974)=>(in @ X975 @ X971)))|(in @ X972 @ X974)))))))))))), introduced(definition)).
% 1.65/0.68 thf(c_0_329, negated_conjecture, ~((![X930:$i, X931:$i]:((![X932:$i]:(((in @ X932 @ X930)<=>(in @ X932 @ X931)))=>((X930)=(X931))))=>(![X933:$i]:(~(in @ X933 @ emptyset))=>(![X934:$i, X935:$i, X936:$i]:(((in @ X936 @ (setadjoin @ X934 @ X935))<=>(((X936)=(X934))|(in @ X936 @ X935))))=>(![X937:$i, X938:$i]:(((in @ X938 @ (powerset @ X937))<=>![X939:$i]:(((in @ X939 @ X938)=>(in @ X939 @ X937)))))=>(![X940:$i, X941:$i]:(((in @ X941 @ (setunion @ X940))<=>?[X942:$i]:(((in @ X941 @ X942)&(in @ X942 @ X940)))))=>((in @ emptyset @ omega)=>(![X943:$i]:(((in @ X943 @ omega)=>(in @ (setadjoin @ X943 @ X943) @ omega)))=>(![X944:$i]:((((in @ emptyset @ X944)&![X945:$i]:((((in @ X945 @ omega)&(in @ X945 @ X944))=>(in @ (setadjoin @ X945 @ X945) @ X944))))=>![X946:$i]:(((in @ X946 @ omega)=>(in @ X946 @ X944)))))=>(![X947:$i > $i > $o, X948:$i]:((![X949:$i]:(((in @ X949 @ X948)=>(exu @ (X947 @ X949))))=>?[X950:$i]:(![X951:$i]:(((in @ X951 @ X950)<=>?[X952:$i]:(((in @ X952 @ X948)&(X947 @ X952 @ X951))))))))=>(![X953:$i]:((?[X954:$i]:((in @ X954 @ X953))=>?[X955:$i]:(((in @ X955 @ X953)&~(?[X956:$i]:(((in @ X956 @ X955)&(in @ X956 @ X953))))))))=>((epred1_0)=>(![X976:$i > $o]:(((exu @ X976)=>(X976 @ (descr @ (^[Z0:$i]:(X976 @ Z0))))))=>(![X977:$i, X978:$i > $o, X979:$i]:(((in @ X979 @ X977)=>((X978 @ X979)=>(in @ X979 @ (dsetconstr @ X977 @ X978)))))=>(![X980:$i, X981:$i > $o, X982:$i]:(((in @ X982 @ (dsetconstr @ X980 @ X981))=>(in @ X982 @ X980)))=>(![X983:$i, X984:$i > $o, X985:$i]:(((in @ X985 @ (dsetconstr @ X983 @ X984))=>(X984 @ X985)))=>(![X986:$i > $o]:(((exu @ X986)=>?[X987:$i]:(((X986 @ X987)&![X988:$i]:(((X986 @ X988)=>((X987)=(X988))))))))=>(![X989:$o, X990:$i]:(((in @ X990 @ (prop2set @ ((X989))))=>(X989)))=>(![X991:$i]:(((in @ X991 @ emptyset)=>![X992:$o]:((X992))))=>(![X993:$i]:(((in @ X993 @ emptyset)=>~($true)))=>(![X994:$i]:(~(in @ X994 @ emptyset))=>(![X995:$i > $o]:(((exu @ X995)=>?[X996:$i]:((X995 @ X996))))=>(![X997:$i, X998:$i]:((![X999:$i]:(((in @ X999 @ X997)=>(in @ X999 @ X998)))=>(![X1000:$i]:(((in @ X1000 @ X998)=>(in @ X1000 @ X997)))=>((X997)=(X998)))))=>(![X1001:$i]:((![X1002:$i]:(~(in @ X1002 @ X1001))=>((X1001)=(emptyset))))=>(![X1003:$i]:((![X1004:$i]:(~(in @ X1004 @ X1003))=>((X1003)=(emptyset))))=>(![X1005:$i, X1006:$i > $o, X1007:$i]:(((in @ X1007 @ X1005)=>((in @ X1007 @ (dsetconstr @ X1005 @ X1006))<=>(X1006 @ X1007))))=>(![X1008:$i]:(((nonempty @ X1008)=>?[X1009:$i]:((in @ X1009 @ X1008))))=>(![X1010:$i, X1011:$i > $o, X1012:$i]:(((in @ X1012 @ X1010)=>((X1011 @ X1012)=>(nonempty @ (dsetconstr @ X1010 @ X1011)))))=>(![X1013:$i]:((?[X1014:$i]:((in @ X1014 @ X1013))=>(nonempty @ X1013)))=>(![X1015:$i, X1016:$i]:((in @ X1015 @ (setadjoin @ X1015 @ X1016)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1017:$i, X1018:$i, X1019:$i]:(((in @ X1019 @ X1018)=>(in @ X1019 @ (setadjoin @ X1017 @ X1018))))=>(![X1020:$i, X1021:$i, X1022:$i]:(((in @ X1022 @ (setadjoin @ X1020 @ X1021))=>![X1023:$o]:(((((X1022)=(X1020))=>(X1023))=>(((in @ X1022 @ X1021)=>(X1023))=>(X1023))))))=>(![X1024:$i, X1025:$i, X1026:$i]:(((in @ X1026 @ (setadjoin @ X1024 @ X1025))=>(((X1026)=(X1024))|(in @ X1026 @ X1025))))=>(![X1027:$i]:(((dsetconstr @ X1027 @ (^[Z0:$i]:($true)))=(X1027)))=>(![X1028:$i, X1029:$i]:((![X1030:$i]:(((in @ X1030 @ X1029)=>(in @ X1030 @ X1028)))=>(in @ X1029 @ (powerset @ X1028))))=>(![X1031:$i]:((in @ emptyset @ (powerset @ X1031)))=>(![X1032:$i]:((in @ emptyset @ (powerset @ X1032)))=>(![X1033:$i, X1034:$i, X1035:$i]:(((in @ X1034 @ (powerset @ X1033))=>((in @ X1035 @ X1034)=>(in @ X1035 @ X1033))))=>(![X1036:$i, X1037:$i, X1038:$i]:(((in @ X1037 @ X1038)=>((in @ X1038 @ X1036)=>(in @ X1037 @ (setunion @ X1036)))))=>(![X1039:$i, X1040:$i]:(((in @ X1040 @ (setunion @ X1039))=>![X1041:$o]:((![X1042:$i]:(((in @ X1040 @ X1042)=>((in @ X1042 @ X1039)=>(X1041))))=>(X1041)))))=>(![X1043:$i, X1044:$i]:(((in @ X1044 @ X1043)=>(in @ X1044 @ (powerset @ (setunion @ X1043)))))=>(![X1045:$i > $o]:(((exu @ X1045)=>?[X1046:$i]:(![X1047:$i]:(((X1045 @ X1047)<=>((X1047)=(X1046)))))))=>(![X1048:$i]:(((nonempty @ X1048)=>?[X1049:$i]:(((in @ X1049 @ X1048)&$true))))=>(![X1050:$i, X1051:$i]:(((in @ X1050 @ (setadjoin @ X1051 @ emptyset))=>((X1050)=(X1051))))=>(![X1052:$i, X1053:$i]:((((X1052)!=(X1053))=>~(in @ X1053 @ (setadjoin @ X1052 @ emptyset))))=>(![X1054:$i, X1055:$i]:((((X1054)=(X1055))=>(in @ X1054 @ (setadjoin @ X1055 @ emptyset))))=>(![X1056:$i, X1057:$i]:(((in @ X1056 @ (setadjoin @ X1057 @ emptyset))=>(in @ X1057 @ (setadjoin @ X1056 @ emptyset))))=>(![X1058:$i, X1059:$i, X1060:$i]:(((in @ X1060 @ (setadjoin @ X1058 @ (setadjoin @ X1059 @ emptyset)))=>(((X1060)=(X1058))|((X1060)=(X1059)))))=>(![X1061:$i, X1062:$i]:((in @ X1061 @ (setadjoin @ X1061 @ (setadjoin @ X1062 @ emptyset))))=>(![X1063:$i, X1064:$i]:((in @ X1064 @ (setadjoin @ X1063 @ (setadjoin @ X1064 @ emptyset))))=>(![X1065:$i, X1066:$i > $o]:((?[X1067:$i]:(((in @ X1067 @ X1065)&(X1066 @ X1067)))=>(((dsetconstr @ X1065 @ X1066)=(emptyset))=>~($true))))=>(![X1068:$i > $o, X1069:$i]:(((in @ X1069 @ emptyset)=>(X1068 @ X1069)))=>(![X1070:$i, X1071:$i > $o]:((~(![X1072:$i]:(((in @ X1072 @ X1070)=>(X1071 @ X1072))))=>?[X1073:$i]:(((in @ X1073 @ X1070)&~((X1071 @ X1073))))))=>(![X1074:$i, X1075:$i > $o]:((![X1076:$i]:(((in @ X1076 @ X1074)=>~((X1075 @ X1076))))=>~(?[X1077:$i]:(((in @ X1077 @ X1074)&(X1075 @ X1077))))))=>(![X1078:$i, X1079:$i > $o]:((~(?[X1080:$i]:(((in @ X1080 @ X1078)&(X1079 @ X1080))))=>![X1081:$i]:(((in @ X1081 @ X1078)=>~((X1079 @ X1081))))))=>(![X1082:$i, X1083:$i > $o]:((?[X1084:$i]:(((in @ X1084 @ X1082)&~((X1083 @ X1084))))=>~(![X1085:$i]:(((in @ X1085 @ X1082)=>(X1083 @ X1085))))))=>(![X1086:$o]:(((X1086)=>(in @ emptyset @ (prop2set @ ((X1086))))))=>((prop2set2propI)=>(![X1087:$i, X1088:$i > $o]:((~(?[X1089:$i]:(((in @ X1089 @ X1087)&(X1088 @ X1089))))=>![X1090:$i]:(((in @ X1090 @ X1087)=>~((X1088 @ X1090))))))=>(![X1091:$i, X1092:$i > $o]:((~(![X1093:$i]:(((in @ X1093 @ X1091)=>(X1092 @ X1093))))=>?[X1094:$i]:(((in @ X1094 @ X1091)&~((X1092 @ X1094))))))=>(![X1095:$i > $o]:((?[X1096:$i]:(((X1095 @ X1096)&![X1097:$i]:(((X1095 @ X1097)=>((X1096)=(X1097))))))=>(exu @ X1095)))=>(![X1098:$i > $o]:((?[X1099:$i]:((X1098 @ X1099))=>(![X1100:$i, X1101:$i]:(((X1098 @ X1100)=>((X1098 @ X1101)=>((X1100)=(X1101)))))=>(exu @ X1098))))=>(![X1102:$i > $o]:((?[X1103:$i]:(![X1104:$i]:(((X1102 @ X1104)<=>((X1104)=(X1103)))))=>(exu @ X1102)))=>(![X1105:$i, X1106:$i]:((((X1105)=(X1106))=>![X1107:$i, X1108:$i]:((((X1107)=(X1108))=>((in @ X1107 @ X1105)=>(in @ X1108 @ X1106))))))=>(![X1109:$i, X1110:$i]:((((X1109)=(X1110))=>![X1111:$i, X1112:$i]:((((X1111)=(X1112))=>((in @ X1111 @ X1109)<=>(in @ X1112 @ X1110))))))=>(![X1113:$i > $o]:(((exu @ X1113)=>![X1114:$i, X1115:$i]:(((X1113 @ X1114)=>((X1113 @ X1115)=>((X1114)=(X1115)))))))=>(![X1116:$i > $o, X1117:$i > $o]:((![X1118:$i, X1119:$i]:((((X1118)=(X1119))=>((X1116 @ X1118)<=>(X1117 @ X1119))))=>((exu @ X1116)<=>(exu @ X1117))))=>(((emptyset)=(emptyset))=>(![X1120:$i, X1121:$i]:((((X1120)=(X1121))=>![X1122:$i, X1123:$i]:((((X1122)=(X1123))=>((setadjoin @ X1120 @ X1122)=(setadjoin @ X1121 @ X1123))))))=>(![X1124:$i, X1125:$i]:((((X1124)=(X1125))=>((powerset @ X1124)=(powerset @ X1125))))=>(![X1126:$i, X1127:$i]:((((X1126)=(X1127))=>((setunion @ X1126)=(setunion @ X1127))))=>(((omega)=(omega))=>(![X1128:$i > $o]:(((exu @ X1128)=>![X1129:$i, X1130:$i]:(((X1128 @ X1129)=>((X1128 @ X1130)=>((X1129)=(X1130)))))))=>(![X1131:$i > $o, X1132:$i > $o]:((![X1133:$i, X1134:$i]:((((X1133)=(X1134))=>((X1131 @ X1133)<=>(X1132 @ X1134))))=>((exu @ X1131)=>((exu @ X1132)=>((descr @ X1131)=(descr @ X1132))))))=>(![X1135:$i, X1136:$i]:((((X1135)=(X1136))=>![X1137:$i > $o, X1138:$i > $o]:((![X1139:$i]:(((in @ X1139 @ X1135)=>![X1140:$i]:(((in @ X1140 @ X1136)=>(((X1139)=(X1140))=>((X1137 @ X1139)<=>(X1138 @ X1140)))))))=>((dsetconstr @ X1135 @ X1137)=(dsetconstr @ X1136 @ X1138))))))=>(![X1141:$i, X1142:$i]:((![X1143:$i]:(((in @ X1143 @ X1141)=>(in @ X1143 @ X1142)))=>(subset @ X1141 @ X1142)))=>(![X1144:$i, X1145:$i]:((((X1144)=(X1145))=>(subset @ X1145 @ X1144)))=>(![X1146:$i, X1147:$i]:((((X1146)=(X1147))=>(subset @ X1146 @ X1147)))=>(![X1148:$i, X1149:$i]:((![X1150:$i]:(((in @ X1150 @ X1148)=>(in @ X1150 @ X1149)))=>(subset @ X1148 @ X1149)))=>(![X1151:$i]:((subset @ emptyset @ X1151))=>(![X1152:$i, X1153:$i, X1154:$i]:(((subset @ X1152 @ X1153)=>((in @ X1154 @ X1152)=>(in @ X1154 @ X1153))))=>(![X1155:$i, X1156:$i, X1157:$i]:(((subset @ X1155 @ X1156)=>(~(in @ X1157 @ X1156)=>~(in @ X1157 @ X1155))))=>(![X1158:$i, X1159:$i, X1160:$i]:(((in @ X1160 @ X1158)=>(~(in @ X1160 @ X1159)=>~(subset @ X1158 @ X1159))))=>(![X1161:$i, X1162:$i]:((~(subset @ X1161 @ X1162)=>((X1161)!=(X1162))))=>(![X1163:$i, X1164:$i, X1165:$i]:(((in @ X1165 @ X1163)=>(~(in @ X1165 @ X1164)=>((X1163)!=(X1164)))))=>(![X1166:$i]:((subset @ X1166 @ X1166))=>(![X1167:$i, X1168:$i, X1169:$i]:(((subset @ X1167 @ X1168)=>((subset @ X1168 @ X1169)=>(subset @ X1167 @ X1169))))=>(![X1170:$i, X1171:$i]:((subset @ X1171 @ (setadjoin @ X1170 @ X1171)))=>(![X1172:$i, X1173:$i, X1174:$i]:(((subset @ X1172 @ X1174)=>(subset @ X1172 @ (setadjoin @ X1173 @ X1174))))=>(![X1175:$i, X1176:$i]:(((subset @ X1175 @ X1176)=>(in @ X1175 @ (powerset @ X1176))))=>(![X1177:$i, X1178:$i]:(((subset @ X1177 @ X1178)=>((subset @ X1178 @ X1177)=>((X1177)=(X1178)))))=>(![X1179:$i]:(((subset @ X1179 @ emptyset)=>((X1179)=(emptyset))))=>(![X1180:$i, X1181:$i]:(((subset @ X1181 @ X1180)=>(in @ X1181 @ (powerset @ X1180))))=>(![X1182:$i, X1183:$i]:(((in @ X1183 @ (powerset @ X1182))=>(subset @ X1183 @ X1182)))=>(![X1184:$i]:((in @ X1184 @ (powerset @ X1184)))=>(![X1185:$i, X1186:$i]:(((subset @ X1185 @ X1186)=>(subset @ (powerset @ X1185) @ (powerset @ X1186))))=>(![X1187:$i, X1188:$i > $o]:((in @ (dsetconstr @ X1187 @ X1188) @ (powerset @ X1187)))=>(![X1189:$i, X1190:$i > $o]:((subset @ (dsetconstr @ X1189 @ X1190) @ X1189))=>(![X1191:$i, X1192:$i, X1193:$i]:(((in @ X1193 @ X1191)=>(in @ X1193 @ (binunion @ X1191 @ X1192))))=>(![X1194:$i, X1195:$i]:((in @ X1195 @ (setadjoin @ X1194 @ (setadjoin @ X1195 @ emptyset))))=>(![X1196:$i, X1197:$i, X1198:$i]:(((in @ X1198 @ X1197)=>(in @ X1198 @ (binunion @ X1196 @ X1197))))=>(![X1199:$i, X1200:$i, X1201:$i, X1202:$o]:(((in @ X1201 @ (binunion @ X1199 @ X1200))=>(((in @ X1201 @ X1199)=>(X1202))=>(((in @ X1201 @ X1200)=>(X1202))=>(X1202)))))=>(![X1203:$i, X1204:$i, X1205:$i]:(((in @ X1205 @ (binunion @ X1203 @ X1204))=>((in @ X1205 @ X1203)|(in @ X1205 @ X1204))))=>(![X1206:$i, X1207:$i]:((subset @ X1206 @ (binunion @ X1206 @ X1207)))=>(![X1208:$i, X1209:$i]:((subset @ X1209 @ (binunion @ X1208 @ X1209)))=>(![X1210:$i, X1211:$i, X1212:$i]:(((in @ X1212 @ X1210)=>((in @ X1212 @ X1211)=>(in @ X1212 @ (binintersect @ X1210 @ X1211)))))=>(![X1213:$i, X1214:$i, X1215:$i]:(((subset @ X1215 @ X1213)=>((subset @ X1215 @ X1214)=>(subset @ X1215 @ (binintersect @ X1213 @ X1214)))))=>(![X1216:$i, X1217:$i, X1218:$i]:(((in @ X1218 @ (binintersect @ X1216 @ X1217))=>(in @ X1218 @ X1216)))=>(![X1219:$i, X1220:$i]:((subset @ (binintersect @ X1219 @ X1220) @ X1219))=>(![X1221:$i, X1222:$i]:(((subset @ X1221 @ X1222)=>((binintersect @ X1221 @ X1222)=(X1221))))=>(![X1223:$i, X1224:$i]:((((binintersect @ X1223 @ X1224)=(X1224))=>(subset @ X1224 @ X1223)))=>(![X1225:$i, X1226:$i, X1227:$i]:(((in @ X1227 @ (binintersect @ X1225 @ X1226))=>(in @ X1227 @ X1226)))=>(![X1228:$i, X1229:$i]:((~(?[X1230:$i]:(((in @ X1230 @ X1228)&(in @ X1230 @ X1229))))=>((binintersect @ X1228 @ X1229)=(emptyset))))=>(![X1231:$i, X1232:$i]:((subset @ (binintersect @ X1231 @ X1232) @ X1232))=>(![X1233:$i, X1234:$i]:(((subset @ X1234 @ X1233)=>((binintersect @ X1233 @ X1234)=(X1234))))=>(![X1235:$i, X1236:$i]:((((binintersect @ X1235 @ X1236)=(X1235))=>(subset @ X1235 @ X1236)))=>(![X1237:$i, X1238:$i, X1239:$i]:(((binintersect @ X1237 @ 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X1798:$i]:(((in @ X1798 @ (powerset @ X1797))=>![X1799:$i]:(((in @ X1799 @ (powerset @ X1797))=>![X1800:$i]:(((in @ X1800 @ (binintersect @ X1798 @ X1799))=>(in @ X1800 @ X1797)))))))=>(![X1801:$i, X1802:$i]:(((in @ X1802 @ (powerset @ X1801))=>![X1803:$i]:(((in @ X1803 @ (powerset @ X1801))=>![X1804:$i]:(((in @ X1804 @ (powerset @ X1801))=>((subset @ X1802 @ X1804)=>(subset @ (binintersect @ X1802 @ X1803) @ X1804))))))))=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X48 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(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_276, subsetTI]), setextT]), powersetTI1]), powersetTE1]), c_0_277]), complementTI1]), in__Cong]), complementTE1]), inCongP]), binintersectTELcontra]), c_0_278]), binintersectTERcontra]), c_0_279]), contrasubsetT]), c_0_280]), contrasubsetT1]), c_0_281]), contrasubsetT2]), contrasubsetT3]), doubleComplementI1]), doubleComplementE1]), doubleComplementSub1]), doubleComplementSub2]), doubleComplementEq]), complementTnotintersectT]), complementImpComplementIntersect]), complementSubsetComplementIntersect]), complementInPowersetComplementIntersect]), contraSubsetComplement]), complementTcontraSubset]), binunionTILcontra]), c_0_282]), binunionTIRcontra]), c_0_283]), inIntersectImpInUnion]), omega__Cong]), inIntersectImpInUnion2]), setunion__Cong]), inIntersectImpInIntersectUnions]), powerset__Cong]), intersectInPowersetIntersectUnions]), setadjoin__Cong]), inComplementUnionImpNotIn1]), emptyset__Cong]), inComplementUnionImpInComplement1]), c_0_284]), binunionTE]), binunionTEcontra]), demorgan2a1]), complementUnionInPowersetComplement]), demorgan2a2]), demorgan1a]), demorgan1b]), demorgan1]), demorgan2a]), demorgan2b2]), demorgan2b]), demorgan2]), woz13rule0]), subsetE2]), woz13rule1]), subsetE]), emptysetsubset]), subsetI2]), eqimpsubset1]), eqimpsubset2]), subsetI1]), notsubsetI]), setminusERneg]), setminusSubset2]), subset2powerset]), setadjoinSub2]), setadjoinSub]), subsetTrans]), subsetRefl]), notequalI2]), notequalI1]), setextsub]), c_0_285]), c_0_286]), powersetsubset]), inPowerset]), powersetE1]), powersetI1]), subsetemptysetimpeq]), binunionIL]), binintersectI]), binunionRsub]), binunionLsub]), binunionE]), binunionEcases]), binunionIR]), upairset2IR]), binintersectSubset5]), binintersectRsub]), disjointsetsI1]), binintersectER]), binintersectSubset3]), binintersectSubset2]), binintersectLsub]), binintersectEL]), binintersectSubset4]), ap2apEq2]), c_0_287]), c_0_288]), c_0_289]), c_0_290]), c_0_291]), c_0_292]), c_0_293]), setminusER]), setminusEL]), setminusI]), bs114d]), binintersectSubset1]), setminusELneg]), symdiffI2]), symdiffI1]), symdiffE]), setminusSubset1]), setminusLsub]), setminusIRneg]), setminusILneg]), symdiffIneg1]), singletonsubset]), kpairp]), kpairiskpair]), setukpairIR]), setukpairIL]), secondinupair]), symdiffIneg2]), singletoninpowerset]), ubforcartprodlem3]), ubforcartprodlem2]), ubforcartprodlem1]), upairinpowunion]), upairsubunion]), upairset2E]), singletoninpowunion]), cartprodpairin]), c_0_294]), setunionsingleton]), setunionsingleton2]), setunionsingleton1]), setunionE2]), cartprodmempair]), cartprodmempair1]), c_0_295]), kfstpairEq]), theprop]), c_0_296]), setukpairinjL1]), singletonsuniq]), c_0_297]), c_0_298]), cartprodfstin]), setukpairinjR2]), upairequniteq]), setukpairinjR1]), setukpairinjR12]), setukpairinjR11]), setukpairinjL]), setukpairinjL2]), setukpairinjR]), cartprodmempaircEq]), cartprodpairmemER]), cartprodpairmemEL]), cartprodsndin]), kpairsurjEq]), ksndpairEq]), c_0_299]), cartprodfstpairEq]), c_0_300]), c_0_301]), c_0_302]), c_0_303]), c_0_304]), cartprodpairsurjEq]), cartprodsndpairEq]), c_0_305]), funcinfuncset]), ap2p]), infuncsetfunc]), app]), c_0_306]), c_0_307]), c_0_308]), c_0_309]), funcGraphProp3]), funcGraphProp1]), c_0_310]), brelnall2]), brelnall1]), c_0_311]), c_0_312]), funcGraphProp2]), ap2apEq1]), funcext2]), funcext]), eqbreln]), subbreln]), funcGraphProp4]), funcextLem]), c_0_313]), iftrueorfalse]), iffalse]), iftrue]), theeq]), ifp]), c_0_314]), c_0_315]), binunionT_lem]), powersetT_lem]), setminusT_lem]), complementT_lem]), binintersectT_lem]), notdallE]), notdexE]), prop2setI]), quantDeMorgan4]), quantDeMorgan3]), quantDeMorgan2]), quantDeMorgan1]), vacuousDall]), c_0_316]), upairsetIR]), upairsetIL]), upairsetE]), singletonsswitch]), eqinunit]), notinsingleton]), uniqinunit]), nonemptyImpWitness]), c_0_317]), subPowSU]), setunionE]), setunionI]), powersetE]), emptyInPowerset]), emptyinPowerset]), powersetI]), c_0_318]), setadjoinOr]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), nonemptyI1]), c_0_319]), nonemptyE1]), c_0_320]), noeltsimpempty]), emptyI]), setext]), c_0_321]), notinemptyset]), emptysetimpfalse]), emptysetE]), prop2setE]), c_0_322]), c_0_323]), c_0_324]), c_0_325]), c_0_326]), wellorderingAx]), foundationAx]), c_0_327]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_328])).
% 1.65/0.68 thf(c_0_330, negated_conjecture, ![X1805:$i, X1806:$i, X1808:$i, X1809:$i, X1810:$i, X1811:$i, X1812:$i, X1813:$i, X1814:$i, X1815:$i, X1816:$i, X1818:$i, X1819:$i, X1821:$i, X1822:$i, X1823:$i, X1824:$i, X1825:$i, X1827:$i, X1828:$i > $i > $o, X1829:$i, X1832:$i, X1834:$i, X1835:$i, X1836:$i, X1837:$i, X1839:$i, X1840:$i > $o, X1841:$i, X1842:$i > $o, X1843:$i, X1844:$i, X1845:$i > $o, X1846:$i, X1847:$i, X1848:$i > $o, X1849:$i, X1850:$i > $o, X1852:$i, X1853:$o, X1854:$i, X1855:$i, X1856:$o, X1857:$i, X1858:$i, X1859:$i > $o, X1861:$i, X1862:$i, X1865:$i, X1867:$i, X1869:$i, X1870:$i > $o, X1871:$i, X1872:$i, X1874:$i, X1875:$i > $o, X1876:$i, X1877:$i, X1878:$i, X1879:$i, X1880:$i, X1881:$i, X1882:$i, X1883:$i, X1884:$i, X1885:$i, X1886:$i, X1887:$o, X1888:$i, X1889:$i, X1890:$i, X1891:$i, X1892:$i, X1893:$i, X1895:$i, X1896:$i, X1897:$i, X1898:$i, X1899:$i, X1900:$i, X1901:$i, X1902:$i, X1903:$i, X1904:$i, X1905:$o, X1907:$i, X1908:$i, X1909:$i > $o, X1911:$i, X1912:$i, X1913:$i, X1915:$i, X1916:$i, X1917:$i, X1918:$i, X1919:$i, X1920:$i, X1921:$i, X1922:$i, X1923:$i, X1924:$i, X1925:$i, X1926:$i, X1927:$i, X1928:$i, X1929:$i, X1930:$i, X1931:$i > $o, X1932:$i, X1933:$i > $o, X1934:$i, X1935:$i, X1936:$i > $o, X1937:$i, X1939:$i, X1940:$i > $o, X1942:$i, X1943:$i, X1944:$i > $o, X1946:$i, X1947:$i, X1948:$i > $o, X1949:$i, X1951:$o, X1952:$i, X1953:$i > $o, X1955:$i, X1956:$i, X1957:$i > $o, X1958:$i, X1960:$i > $o, X1961:$i, X1963:$i > $o, X1964:$i, X1967:$i > $o, X1968:$i, X1970:$i, X1971:$i, X1972:$i, X1973:$i, X1974:$i, X1975:$i, X1976:$i, X1977:$i, X1978:$i > $o, X1979:$i, X1980:$i, X1981:$i > $o, X1982:$i > $o, X1985:$i, X1986:$i, X1987:$i, X1988:$i, X1989:$i, X1990:$i, X1991:$i, X1992:$i, X1993:$i > $o, X1994:$i, X1995:$i, X1996:$i > $o, X1997:$i > $o, X2000:$i, X2001:$i, X2002:$i > $o, X2003:$i > $o, X2006:$i, X2007:$i, X2009:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2016:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$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 > $o, X2054:$i, X2055:$i > $o, X2056:$i, X2057:$i, X2058:$i, X2059:$i, X2060:$i, X2061:$i, X2062:$i, X2063:$i, X2064:$i, X2065:$i, X2066:$i, X2067:$o, X2068:$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, X2096:$i, X2097:$i, X2098:$i, X2099:$i, X2100:$i, X2101:$i, X2102:$i, X2103:$i, X2104:$i, X2105:$i, X2106:$i, X2107:$i, X2108:$i, X2109:$i, X2110:$i, X2111:$i, X2112:$i, X2113:$i, X2114:$i, X2115:$i, X2116:$i, X2117:$i, X2118:$i, X2119:$i, X2120:$i, 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X2504)|((X2504)=(X2505))|(in @ (esk67_3 @ X2503 @ X2504 @ X2505) @ X2504)|~(in @ X2505 @ (powerset @ X2503))|~(in @ X2504 @ (powerset @ X2503)))))&(((in @ (esk68_3 @ X2503 @ X2504 @ X2505) @ X2503)|((X2504)=(X2505))|~(in @ (esk67_3 @ X2503 @ X2504 @ X2505) @ X2505)|~(in @ X2505 @ (powerset @ X2503))|~(in @ X2504 @ (powerset @ X2503)))&(((in @ (esk68_3 @ X2503 @ X2504 @ X2505) @ X2505)|((X2504)=(X2505))|~(in @ (esk67_3 @ X2503 @ X2504 @ X2505) @ X2505)|~(in @ X2505 @ (powerset @ X2503))|~(in @ X2504 @ (powerset @ X2503)))&(~(in @ (esk68_3 @ X2503 @ X2504 @ X2505) @ X2504)|((X2504)=(X2505))|~(in @ (esk67_3 @ X2503 @ X2504 @ X2505) @ X2505)|~(in @ X2505 @ (powerset @ X2503))|~(in @ X2504 @ (powerset @ X2503)))))))&((((in @ (esk69_3 @ X2508 @ X2509 @ X2510) @ X2508)|(subset @ X2509 @ X2510)|~(in @ X2510 @ (powerset @ X2508))|~(in @ X2509 @ (powerset @ X2508)))&(((in @ (esk69_3 @ X2508 @ X2509 @ X2510) @ X2509)|(subset @ X2509 @ X2510)|~(in @ X2510 @ (powerset @ X2508))|~(in @ X2509 @ (powerset @ X2508)))&(~(in @ (esk69_3 @ X2508 @ X2509 @ X2510) @ X2510)|(subset @ X2509 @ X2510)|~(in @ X2510 @ (powerset @ X2508))|~(in @ X2509 @ (powerset @ X2508)))))&((((in @ (esk70_3 @ X2512 @ X2513 @ X2514) @ X2512)|(in @ X2513 @ (powerset @ X2514))|~(in @ X2514 @ (powerset @ X2512))|~(in @ X2513 @ (powerset @ X2512)))&(((in @ (esk70_3 @ X2512 @ X2513 @ X2514) @ X2513)|(in @ X2513 @ (powerset @ X2514))|~(in @ X2514 @ (powerset @ X2512))|~(in @ X2513 @ (powerset @ X2512)))&(~(in @ (esk70_3 @ X2512 @ X2513 @ X2514) @ X2514)|(in @ X2513 @ (powerset @ X2514))|~(in @ X2514 @ (powerset @ X2512))|~(in @ X2513 @ (powerset @ X2512)))))&((~(in @ X2517 @ (powerset @ X2516))|(~(in @ X2518 @ (powerset @ X2516))|(~(in @ X2519 @ X2516)|(~(in @ X2517 @ (powerset @ X2518))|(~(in @ X2519 @ X2517)|(in @ X2519 @ X2518))))))&((~(in @ X2521 @ (powerset @ X2520))|(~(in @ X2522 @ X2520)|(~(in @ X2522 @ X2521)|~(in @ X2522 @ (setminus @ X2520 @ X2521)))))&((~(in @ X2524 @ (powerset @ X2523))|(~(in @ X2525 @ X2523)|((in @ X2525 @ (setminus @ X2523 @ X2524))|(in @ X2525 @ X2524))))&((~(in @ X2527 @ (powerset @ X2526))|(~(in @ X2528 @ (powerset @ X2526))|(~(in @ X2529 @ X2526)|((in @ X2529 @ X2527)|~(in @ X2529 @ (binintersect @ X2527 @ X2528))))))&((~(in @ X2531 @ (powerset @ X2530))|(~(in @ X2532 @ (powerset @ X2530))|(~(in @ X2533 @ X2530)|((in @ X2533 @ X2532)|~(in @ X2533 @ (binintersect @ X2531 @ X2532))))))&((~(in @ X2535 @ (powerset @ X2534))|(~(in @ X2536 @ (powerset @ X2534))|(~(in @ X2537 @ X2534)|(~(subset @ X2535 @ (setminus @ X2534 @ X2536))|(~(in @ X2537 @ X2536)|~(in @ X2537 @ X2535))))))&((~(in @ X2539 @ (powerset @ X2538))|(~(in @ X2540 @ (powerset @ X2538))|(~(in @ X2541 @ X2538)|(~(subset @ X2539 @ X2540)|((in @ X2541 @ X2540)|~(in @ X2541 @ X2539))))))&((~(in @ X2543 @ (powerset @ X2542))|(~(in @ X2544 @ (powerset @ X2542))|(~(subset @ X2543 @ X2544)|(subset @ (setminus @ X2542 @ X2544) @ (setminus @ X2542 @ X2543)))))&((~(in @ X2546 @ (powerset @ X2545))|(~(in @ X2547 @ (powerset @ X2545))|(~(subset @ (setminus @ X2545 @ X2547) @ (setminus @ X2545 @ X2546))|(subset @ X2546 @ X2547))))&((~(in @ X2549 @ (powerset @ X2548))|(~(in @ X2550 @ X2548)|(~(in @ X2550 @ X2549)|(in @ X2550 @ (setminus @ X2548 @ (setminus @ X2548 @ X2549))))))&((~(in @ X2552 @ (powerset @ X2551))|(~(in @ X2553 @ X2551)|(~(in @ X2553 @ (setminus @ X2551 @ (setminus @ X2551 @ X2552)))|(in @ X2553 @ X2552))))&((~(in @ X2555 @ (powerset @ X2554))|(subset @ X2555 @ (setminus @ X2554 @ (setminus @ X2554 @ X2555))))&((~(in @ X2557 @ (powerset @ X2556))|(subset @ (setminus @ X2556 @ (setminus @ X2556 @ X2557)) @ X2557))&((~(in @ X2559 @ (powerset @ X2558))|((X2559)=(setminus @ X2558 @ (setminus @ X2558 @ X2559))))&((~(in @ X2561 @ (powerset @ X2560))|(~(in @ X2562 @ (powerset @ X2560))|(~(in @ X2563 @ X2560)|(~(in @ X2563 @ (setminus @ X2560 @ X2561))|~(in @ X2563 @ (binintersect @ X2561 @ X2562))))))&((~(in @ X2565 @ (powerset @ X2564))|(~(in @ X2566 @ (powerset @ X2564))|(~(in @ X2567 @ X2564)|(~(in @ X2567 @ (setminus @ X2564 @ X2565))|(in @ X2567 @ (setminus @ X2564 @ (binintersect @ X2565 @ X2566)))))))&((~(in @ X2569 @ (powerset @ X2568))|(~(in @ X2570 @ (powerset @ X2568))|(subset @ (setminus @ X2568 @ X2569) @ (setminus @ X2568 @ (binintersect @ X2569 @ X2570)))))&((~(in @ X2572 @ (powerset @ X2571))|(~(in @ X2573 @ (powerset @ X2571))|(in @ (setminus @ X2571 @ X2572) @ (powerset @ (setminus @ X2571 @ (binintersect @ X2572 @ X2573))))))&((~(in @ X2575 @ (powerset @ X2574))|(~(in @ X2576 @ (powerset @ X2574))|(~(subset @ X2575 @ (setminus @ X2574 @ X2576))|(~(in @ X2577 @ X2574)|(~(in @ X2577 @ X2576)|(in @ X2577 @ (setminus @ X2574 @ X2575)))))))&((~(in @ X2579 @ (powerset @ X2578))|(~(in @ X2580 @ (powerset @ X2578))|(~(subset @ X2579 @ (setminus @ X2578 @ X2580))|(subset @ X2580 @ (setminus @ X2578 @ X2579)))))&((~(in @ X2582 @ (powerset @ X2581))|(~(in @ X2583 @ (powerset @ X2581))|(~(in @ X2584 @ X2581)|((in @ X2584 @ (binunion @ X2582 @ X2583))|~(in @ X2584 @ X2582)))))&((~(in @ X2586 @ (powerset @ X2585))|(~(in @ X2587 @ (powerset @ X2585))|(~(in @ X2588 @ X2585)|((in @ X2588 @ (binunion @ X2586 @ X2587))|~(in @ X2588 @ X2587)))))&((~(in @ X2590 @ (powerset @ X2589))|(~(in @ X2591 @ (powerset @ X2589))|(~(in @ X2592 @ (powerset @ X2589))|(~(in @ X2593 @ X2589)|(~(in @ X2593 @ (binintersect @ X2590 @ X2591))|(in @ X2593 @ (binunion @ X2590 @ X2592)))))))&((~(in @ X2595 @ (powerset @ X2594))|(~(in @ X2596 @ (powerset @ X2594))|(~(in @ X2597 @ (powerset @ X2594))|(~(in @ X2598 @ X2594)|(~(in @ X2598 @ (binintersect @ X2595 @ X2596))|(in @ X2598 @ (binunion @ X2596 @ X2597)))))))&((~(in @ X2600 @ (powerset @ X2599))|(~(in @ X2601 @ (powerset @ X2599))|(~(in @ X2602 @ (powerset @ X2599))|(~(in @ X2603 @ X2599)|(~(in @ X2603 @ (binintersect @ X2600 @ X2601))|(in @ X2603 @ (binintersect @ (binunion @ X2600 @ X2602) @ (binunion @ X2601 @ X2602))))))))&((~(in @ X2605 @ (powerset @ X2604))|(~(in @ X2606 @ (powerset @ X2604))|(~(in @ X2607 @ (powerset @ X2604))|(in @ (binintersect @ X2605 @ X2606) @ (powerset @ (binintersect @ (binunion @ X2605 @ X2607) @ (binunion @ X2606 @ X2607)))))))&((~(in @ X2609 @ (powerset @ X2608))|(~(in @ X2610 @ (powerset @ X2608))|(~(in @ X2611 @ X2608)|(~(in @ X2611 @ (setminus @ X2608 @ (binunion @ X2609 @ X2610)))|~(in @ X2611 @ X2609)))))&((~(in @ X2613 @ (powerset @ X2612))|(~(in @ X2614 @ (powerset @ X2612))|(~(in @ X2615 @ X2612)|(~(in @ X2615 @ (setminus @ X2612 @ (binunion @ X2613 @ X2614)))|(in @ X2615 @ (setminus @ X2612 @ X2613))))))&(((((in @ X2620 @ X2618)|(X2619)|(in @ X2620 @ X2617)|~(in @ X2620 @ (binunion @ X2617 @ X2618))|~(in @ X2620 @ X2616)|~(in @ X2618 @ (powerset @ X2616))|~(in @ X2617 @ (powerset @ X2616)))&(~(X2619)|(X2619)|(in @ X2620 @ X2617)|~(in @ X2620 @ (binunion @ X2617 @ X2618))|~(in @ X2620 @ X2616)|~(in @ X2618 @ (powerset @ X2616))|~(in @ X2617 @ (powerset @ X2616))))&(((in @ X2620 @ X2618)|(X2619)|~(X2619)|~(in @ X2620 @ (binunion @ X2617 @ X2618))|~(in @ X2620 @ X2616)|~(in @ X2618 @ (powerset @ X2616))|~(in @ X2617 @ (powerset @ X2616)))&(~(X2619)|(X2619)|~(X2619)|~(in @ X2620 @ (binunion @ X2617 @ X2618))|~(in @ X2620 @ X2616)|~(in @ X2618 @ (powerset @ X2616))|~(in @ X2617 @ (powerset @ X2616)))))&((~(in @ X2622 @ (powerset @ X2621))|(~(in @ X2623 @ (powerset @ X2621))|(~(in @ X2624 @ X2621)|((in @ X2624 @ X2622)|((in @ X2624 @ X2623)|~(in @ X2624 @ (binunion @ X2622 @ X2623)))))))&((~(in @ X2626 @ (powerset @ X2625))|(~(in @ X2627 @ (powerset @ X2625))|(~(in @ X2628 @ X2625)|(~(in @ X2628 @ (setminus @ X2625 @ (binunion @ X2626 @ X2627)))|(in @ X2628 @ (setminus @ X2625 @ X2626))))))&((~(in @ X2630 @ (powerset @ X2629))|(~(in @ X2631 @ (powerset @ X2629))|(in @ (setminus @ X2629 @ (binunion @ X2630 @ X2631)) @ (powerset @ (setminus @ X2629 @ X2630)))))&((~(in @ X2633 @ (powerset @ X2632))|(~(in @ X2634 @ (powerset @ X2632))|(~(in @ X2635 @ X2632)|(~(in @ X2635 @ (setminus @ X2632 @ (binunion @ X2633 @ X2634)))|(in @ X2635 @ (setminus @ X2632 @ X2634))))))&((~(in @ X2637 @ (powerset @ X2636))|(~(in @ X2638 @ (powerset @ X2636))|(~(in @ X2639 @ X2636)|(~(in @ X2639 @ (setminus @ X2636 @ (binintersect @ X2637 @ X2638)))|(in @ X2639 @ (binunion @ (setminus @ X2636 @ X2637) @ (setminus @ X2636 @ X2638)))))))&((~(in @ X2641 @ (powerset @ X2640))|(~(in @ X2642 @ (powerset @ X2640))|(~(in @ X2643 @ X2640)|(~(in @ X2643 @ (binunion @ (setminus @ X2640 @ X2641) @ (setminus @ X2640 @ X2642)))|(in @ X2643 @ (setminus @ X2640 @ (binintersect @ X2641 @ X2642)))))))&((~(in @ X2645 @ (powerset @ X2644))|(~(in @ X2646 @ (powerset @ X2644))|((setminus @ X2644 @ (binintersect @ X2645 @ X2646))=(binunion @ (setminus @ X2644 @ X2645) @ (setminus @ X2644 @ X2646)))))&((~(in @ X2648 @ (powerset @ X2647))|(~(in @ X2649 @ (powerset @ X2647))|(~(in @ X2650 @ X2647)|(~(in @ X2650 @ (setminus @ X2647 @ (binunion @ X2648 @ X2649)))|(in @ X2650 @ (binintersect @ (setminus @ X2647 @ X2648) @ (setminus @ X2647 @ X2649)))))))&((~(in @ X2652 @ (powerset @ X2651))|(~(in @ X2653 @ (powerset @ X2651))|(~(in @ X2654 @ X2651)|(~(in @ X2654 @ (setminus @ X2651 @ X2652))|(~(in @ X2654 @ (setminus @ X2651 @ X2653))|(in @ X2654 @ (setminus @ X2651 @ (binunion @ X2652 @ X2653))))))))&((~(in @ X2656 @ (powerset @ X2655))|(~(in @ X2657 @ (powerset @ X2655))|(~(in @ X2658 @ X2655)|(~(in @ X2658 @ (binintersect @ (setminus @ X2655 @ X2656) @ (setminus @ X2655 @ X2657)))|(in @ X2658 @ (setminus @ X2655 @ (binunion @ X2656 @ X2657)))))))&((~(in @ X2660 @ (powerset @ X2659))|(~(in @ X2661 @ (powerset @ X2659))|((setminus @ X2659 @ (binunion @ X2660 @ X2661))=(binintersect @ (setminus @ X2659 @ X2660) @ (setminus @ X2659 @ X2661)))))&((~(in @ X2663 @ (powerset @ X2662))|(~(in @ X2664 @ (powerset @ X2662))|(~(in @ X2665 @ (binintersect @ X2663 @ X2664))|(in @ X2665 @ X2662))))&((~(in @ X2667 @ (powerset @ X2666))|(~(in @ X2668 @ (powerset @ X2666))|(~(in @ X2669 @ (powerset @ X2666))|(~(subset @ X2667 @ X2669)|(subset @ (binintersect @ X2667 @ X2668) @ X2669)))))&((in @ esk72_0 @ (powerset @ esk71_0))&((in @ esk73_0 @ (powerset @ esk71_0))&((in @ esk74_0 @ (powerset @ esk71_0))&((subset @ esk73_0 @ esk74_0)&~(subset @ (binintersect @ esk72_0 @ esk73_0) @ esk74_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_329])])])])])])])).
% 1.65/0.68 thf(c_0_331, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((subset @ X2 @ X4)|~((subset @ X2 @ X3))|~((subset @ X3 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_330])).
% 1.65/0.68 thf(c_0_332, negated_conjecture, (subset @ esk73_0 @ esk74_0), inference(split_conjunct,[status(thm)],[c_0_330])).
% 1.65/0.68 thf(c_0_333, negated_conjecture, ~((subset @ (binintersect @ esk72_0 @ esk73_0) @ esk74_0)), inference(split_conjunct,[status(thm)],[c_0_330])).
% 1.65/0.68 thf(c_0_334, negated_conjecture, ![X2:$i]:(((subset @ X2 @ esk74_0)|~((subset @ X2 @ esk73_0)))), inference(spm,[status(thm)],[c_0_331, c_0_332])).
% 1.65/0.68 thf(c_0_335, negated_conjecture, ![X2:$i, X3:$i]:((subset @ (binintersect @ X2 @ X3) @ X3)), inference(split_conjunct,[status(thm)],[c_0_330])).
% 1.65/0.68 thf(c_0_336, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_333, c_0_334]), c_0_335])]), ['proof']).
% 1.65/0.68 % SZS output end CNFRefutation
% 1.65/0.68 % Parsed axioms : 595
% 1.65/0.68 % Removed by relevancy pruning/SinE : 319
% 1.65/0.68 % Initial clauses : 441
% 1.65/0.68 % Removed in clause preprocessing : 37
% 1.65/0.68 % Initial clauses in saturation : 404
% 1.65/0.68 % Processed clauses : 430
% 1.65/0.68 % ...of these trivial : 47
% 1.65/0.68 % ...subsumed : 160
% 1.65/0.68 % ...remaining for further processing : 223
% 1.65/0.68 % Other redundant clauses eliminated : 24
% 1.65/0.68 % Clauses deleted for lack of memory : 0
% 1.65/0.68 % Backward-subsumed : 1
% 1.65/0.68 % Backward-rewritten : 10
% 1.65/0.68 % Generated clauses : 1245
% 1.65/0.68 % ...of the previous two non-redundant : 1034
% 1.65/0.68 % ...aggressively subsumed : 0
% 1.65/0.68 % Contextual simplify-reflections : 0
% 1.65/0.68 % Paramodulations : 1217
% 1.65/0.68 % Factorizations : 0
% 1.65/0.68 % NegExts : 0
% 1.65/0.68 % Equation resolutions : 27
% 1.65/0.68 % Disequality decompositions : 0
% 1.65/0.68 % Total rewrite steps : 229
% 1.65/0.68 % ...of those cached : 154
% 1.65/0.68 % Propositional unsat checks : 0
% 1.65/0.68 % Propositional check models : 0
% 1.65/0.68 % Propositional check unsatisfiable : 0
% 1.65/0.68 % Propositional clauses : 0
% 1.65/0.68 % Propositional clauses after purity: 0
% 1.65/0.68 % Propositional unsat core size : 0
% 1.65/0.68 % Propositional preprocessing time : 0.000
% 1.65/0.68 % Propositional encoding time : 0.000
% 1.65/0.68 % Propositional solver time : 0.000
% 1.65/0.68 % Success case prop preproc time : 0.000
% 1.65/0.68 % Success case prop encoding time : 0.000
% 1.65/0.68 % Success case prop solver time : 0.000
% 1.65/0.68 % Current number of processed clauses : 204
% 1.65/0.68 % Positive orientable unit clauses : 65
% 1.65/0.68 % Positive unorientable unit clauses: 0
% 1.65/0.68 % Negative unit clauses : 6
% 1.65/0.68 % Non-unit-clauses : 133
% 1.65/0.68 % Current number of unprocessed clauses: 954
% 1.65/0.68 % ...number of literals in the above : 2630
% 1.65/0.68 % Current number of archived formulas : 0
% 1.65/0.68 % Current number of archived clauses : 11
% 1.65/0.68 % Clause-clause subsumption calls (NU) : 4888
% 1.65/0.68 % Rec. Clause-clause subsumption calls : 4093
% 1.65/0.68 % Non-unit clause-clause subsumptions : 150
% 1.65/0.68 % Unit Clause-clause subsumption calls : 270
% 1.65/0.68 % Rewrite failures with RHS unbound : 0
% 1.65/0.68 % BW rewrite match attempts : 22
% 1.65/0.68 % BW rewrite match successes : 10
% 1.65/0.68 % Condensation attempts : 0
% 1.65/0.68 % Condensation successes : 0
% 1.65/0.68 % Termbank termtop insertions : 82900
% 1.65/0.68 % Search garbage collected termcells : 28125
% 1.65/0.68
% 1.65/0.68 % -------------------------------------------------
% 1.65/0.68 % User time : 0.173 s
% 1.65/0.68 % System time : 0.018 s
% 1.65/0.68 % Total time : 0.191 s
% 1.65/0.68 % Maximum resident set size: 10960 pages
% 1.65/0.68
% 1.65/0.68 % -------------------------------------------------
% 1.65/0.68 % User time : 0.192 s
% 1.65/0.68 % System time : 0.025 s
% 1.65/0.68 % Total time : 0.217 s
% 1.65/0.68 % Maximum resident set size: 5888 pages
% 1.65/0.68 % E exiting
%------------------------------------------------------------------------------