%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU738^1 : 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 08:25:25 AM UTC 2026
% Result : Theorem 0.75s 0.43s
% Output : CNFRefutation 0.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU738^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n014.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 14:18:44 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.21/0.29 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.HvOPs3palg/E---3.1_2731752.p
% 0.75/0.43 % Version: 3.5.1-ho
% 0.75/0.43 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.75/0.43 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.75/0.43 % Starting ehoh_best5 with 300s (1) cores
% 0.75/0.43 % Starting almost_fo_3_lam with 300s (1) cores
% 0.75/0.43 % Starting new_bool_5 with 300s (1) cores
% 0.75/0.43 % Starting pre_casc_3 with 300s (1) cores
% 0.75/0.43 % Starting ho_unfolding_8 with 300s (1) cores
% 0.75/0.43 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.75/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.75/0.43 % Starting new_ho_5 with 300s (1) cores
% 0.75/0.43 % new_bool_5 with pid 2731805 completed with status 0
% 0.75/0.43 % Result found by new_bool_5
% 0.75/0.43 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.75/0.43 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.75/0.43 % Starting ehoh_best5 with 300s (1) cores
% 0.75/0.43 % Starting almost_fo_3_lam with 300s (1) cores
% 0.75/0.43 % Starting new_bool_5 with 300s (1) cores
% 0.75/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 0.75/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 0.75/0.43 % Search class: HGHSM-FSLM32-MHFMMSBN
% 0.75/0.43 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.75/0.43 % Starting SubtermCWHack with 28s (1) cores
% 0.75/0.43 % SubtermCWHack with pid 2731834 completed with status 0
% 0.75/0.43 % Result found by SubtermCWHack
% 0.75/0.43 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.75/0.43 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.75/0.43 % Starting ehoh_best5 with 300s (1) cores
% 0.75/0.43 % Starting almost_fo_3_lam with 300s (1) cores
% 0.75/0.43 % Starting new_bool_5 with 300s (1) cores
% 0.75/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 0.75/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 0.75/0.43 % Search class: HGHSM-FSLM32-MHFMMSBN
% 0.75/0.43 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.75/0.43 % Starting SubtermCWHack with 28s (1) cores
% 0.75/0.43 % Preprocessing time : 0.004 s
% 0.75/0.43
% 0.75/0.43 % Proof found!
% 0.75/0.43 % SZS status Theorem
% 0.75/0.43 % SZS output start CNFRefutation
% 0.75/0.43 thf(decl_23, type, in: $i > $i > $o).
% 0.75/0.43 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.75/0.43 thf(decl_25, type, setextAx: $o).
% 0.75/0.43 thf(decl_26, type, emptyset: $i).
% 0.75/0.43 thf(decl_27, type, emptysetAx: $o).
% 0.75/0.43 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.75/0.43 thf(decl_29, type, setadjoinAx: $o).
% 0.75/0.43 thf(decl_30, type, powerset: $i > $i).
% 0.75/0.43 thf(decl_31, type, powersetAx: $o).
% 0.75/0.43 thf(decl_32, type, setunion: $i > $i).
% 0.75/0.43 thf(decl_33, type, setunionAx: $o).
% 0.75/0.43 thf(decl_34, type, omega: $i).
% 0.75/0.43 thf(decl_35, type, omega0Ax: $o).
% 0.75/0.43 thf(decl_36, type, omegaSAx: $o).
% 0.75/0.43 thf(decl_37, type, omegaIndAx: $o).
% 0.75/0.43 thf(decl_38, type, replAx: $o).
% 0.75/0.43 thf(decl_39, type, foundationAx: $o).
% 0.75/0.43 thf(decl_40, type, wellorderingAx: $o).
% 0.75/0.43 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.75/0.43 thf(decl_42, type, descrp: $o).
% 0.75/0.43 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.75/0.43 thf(decl_44, type, dsetconstrI: $o).
% 0.75/0.43 thf(decl_45, type, dsetconstrEL: $o).
% 0.75/0.43 thf(decl_46, type, dsetconstrER: $o).
% 0.75/0.43 thf(decl_47, type, exuE1: $o).
% 0.75/0.43 thf(decl_48, type, prop2set: $o > $i).
% 0.75/0.43 thf(decl_49, type, prop2setE: $o).
% 0.75/0.43 thf(decl_50, type, emptysetE: $o).
% 0.75/0.43 thf(decl_51, type, emptysetimpfalse: $o).
% 0.75/0.43 thf(decl_52, type, notinemptyset: $o).
% 0.75/0.43 thf(decl_53, type, exuE3e: $o).
% 0.75/0.43 thf(decl_54, type, setext: $o).
% 0.75/0.43 thf(decl_55, type, emptyI: $o).
% 0.75/0.43 thf(decl_56, type, noeltsimpempty: $o).
% 0.75/0.43 thf(decl_57, type, setbeta: $o).
% 0.75/0.43 thf(decl_58, type, nonempty: $i > $o).
% 0.75/0.43 thf(decl_59, type, nonemptyE1: $o).
% 0.75/0.43 thf(decl_60, type, nonemptyI: $o).
% 0.75/0.43 thf(decl_61, type, nonemptyI1: $o).
% 0.75/0.43 thf(decl_62, type, setadjoinIL: $o).
% 0.75/0.43 thf(decl_63, type, emptyinunitempty: $o).
% 0.75/0.43 thf(decl_64, type, setadjoinIR: $o).
% 0.75/0.43 thf(decl_65, type, setadjoinE: $o).
% 0.75/0.43 thf(decl_66, type, setadjoinOr: $o).
% 0.75/0.43 thf(decl_67, type, setoftrueEq: $o).
% 0.75/0.43 thf(decl_68, type, powersetI: $o).
% 0.75/0.43 thf(decl_69, type, emptyinPowerset: $o).
% 0.75/0.43 thf(decl_70, type, emptyInPowerset: $o).
% 0.75/0.43 thf(decl_71, type, powersetE: $o).
% 0.75/0.43 thf(decl_72, type, setunionI: $o).
% 0.75/0.43 thf(decl_73, type, setunionE: $o).
% 0.75/0.43 thf(decl_74, type, subPowSU: $o).
% 0.75/0.43 thf(decl_75, type, exuE2: $o).
% 0.75/0.43 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.75/0.43 thf(decl_77, type, uniqinunit: $o).
% 0.75/0.43 thf(decl_78, type, notinsingleton: $o).
% 0.75/0.43 thf(decl_79, type, eqinunit: $o).
% 0.75/0.43 thf(decl_80, type, singletonsswitch: $o).
% 0.75/0.43 thf(decl_81, type, upairsetE: $o).
% 0.75/0.43 thf(decl_82, type, upairsetIL: $o).
% 0.75/0.43 thf(decl_83, type, upairsetIR: $o).
% 0.75/0.43 thf(decl_84, type, emptyE1: $o).
% 0.75/0.43 thf(decl_85, type, vacuousDall: $o).
% 0.75/0.43 thf(decl_86, type, quantDeMorgan1: $o).
% 0.75/0.43 thf(decl_87, type, quantDeMorgan2: $o).
% 0.75/0.43 thf(decl_88, type, quantDeMorgan3: $o).
% 0.75/0.43 thf(decl_89, type, quantDeMorgan4: $o).
% 0.75/0.43 thf(decl_90, type, prop2setI: $o).
% 0.75/0.43 thf(decl_92, type, prop2set2propI: $o).
% 0.75/0.43 thf(decl_93, type, notdexE: $o).
% 0.75/0.43 thf(decl_94, type, notdallE: $o).
% 0.75/0.43 thf(decl_95, type, exuI1: $o).
% 0.75/0.43 thf(decl_96, type, exuI3: $o).
% 0.75/0.43 thf(decl_97, type, exuI2: $o).
% 0.75/0.43 thf(decl_98, type, inCongP: $o).
% 0.75/0.43 thf(decl_99, type, in__Cong: $o).
% 0.75/0.43 thf(decl_100, type, exuE3u: $o).
% 0.75/0.43 thf(decl_101, type, exu__Cong: $o).
% 0.75/0.43 thf(decl_102, type, emptyset__Cong: $o).
% 0.75/0.43 thf(decl_103, type, setadjoin__Cong: $o).
% 0.75/0.43 thf(decl_104, type, powerset__Cong: $o).
% 0.75/0.43 thf(decl_105, type, setunion__Cong: $o).
% 0.75/0.43 thf(decl_106, type, omega__Cong: $o).
% 0.75/0.43 thf(decl_107, type, exuEu: $o).
% 0.75/0.43 thf(decl_108, type, descr__Cong: $o).
% 0.75/0.43 thf(decl_109, type, dsetconstr__Cong: $o).
% 0.75/0.43 thf(decl_110, type, subset: $i > $i > $o).
% 0.75/0.43 thf(decl_113, type, subsetI1: $o).
% 0.75/0.43 thf(decl_114, type, eqimpsubset2: $o).
% 0.75/0.43 thf(decl_115, type, eqimpsubset1: $o).
% 0.75/0.43 thf(decl_116, type, subsetI2: $o).
% 0.75/0.43 thf(decl_117, type, emptysetsubset: $o).
% 0.75/0.43 thf(decl_118, type, subsetE: $o).
% 0.75/0.43 thf(decl_119, type, subsetE2: $o).
% 0.75/0.43 thf(decl_120, type, notsubsetI: $o).
% 0.75/0.43 thf(decl_121, type, notequalI1: $o).
% 0.75/0.43 thf(decl_122, type, notequalI2: $o).
% 0.75/0.43 thf(decl_123, type, subsetRefl: $o).
% 0.75/0.43 thf(decl_124, type, subsetTrans: $o).
% 0.75/0.43 thf(decl_125, type, setadjoinSub: $o).
% 0.75/0.43 thf(decl_126, type, setadjoinSub2: $o).
% 0.75/0.43 thf(decl_127, type, subset2powerset: $o).
% 0.75/0.43 thf(decl_128, type, setextsub: $o).
% 0.75/0.43 thf(decl_129, type, subsetemptysetimpeq: $o).
% 0.75/0.43 thf(decl_130, type, powersetI1: $o).
% 0.75/0.43 thf(decl_131, type, powersetE1: $o).
% 0.75/0.43 thf(decl_132, type, inPowerset: $o).
% 0.75/0.43 thf(decl_133, type, powersetsubset: $o).
% 0.75/0.43 thf(decl_134, type, sepInPowerset: $o).
% 0.75/0.43 thf(decl_135, type, sepSubset: $o).
% 0.75/0.43 thf(decl_136, type, binunion: $i > $i > $i).
% 0.75/0.43 thf(decl_137, type, binunionIL: $o).
% 0.75/0.43 thf(decl_138, type, upairset2IR: $o).
% 0.75/0.43 thf(decl_139, type, binunionIR: $o).
% 0.75/0.43 thf(decl_140, type, binunionEcases: $o).
% 0.75/0.43 thf(decl_141, type, binunionE: $o).
% 0.75/0.43 thf(decl_142, type, binunionLsub: $o).
% 0.75/0.43 thf(decl_143, type, binunionRsub: $o).
% 0.75/0.43 thf(decl_144, type, binintersect: $i > $i > $i).
% 0.75/0.43 thf(decl_145, type, binintersectI: $o).
% 0.75/0.43 thf(decl_146, type, binintersectSubset5: $o).
% 0.75/0.43 thf(decl_147, type, binintersectEL: $o).
% 0.75/0.43 thf(decl_148, type, binintersectLsub: $o).
% 0.75/0.43 thf(decl_149, type, binintersectSubset2: $o).
% 0.75/0.43 thf(decl_150, type, binintersectSubset3: $o).
% 0.75/0.43 thf(decl_151, type, binintersectER: $o).
% 0.75/0.43 thf(decl_152, type, disjointsetsI1: $o).
% 0.75/0.43 thf(decl_153, type, binintersectRsub: $o).
% 0.75/0.43 thf(decl_154, type, binintersectSubset4: $o).
% 0.75/0.43 thf(decl_155, type, binintersectSubset1: $o).
% 0.75/0.43 thf(decl_156, type, bs114d: $o).
% 0.75/0.43 thf(decl_158, type, setminus: $i > $i > $i).
% 0.75/0.43 thf(decl_159, type, setminusI: $o).
% 0.75/0.43 thf(decl_160, type, setminusEL: $o).
% 0.75/0.43 thf(decl_161, type, setminusER: $o).
% 0.75/0.43 thf(decl_162, type, setminusSubset2: $o).
% 0.75/0.43 thf(decl_163, type, setminusERneg: $o).
% 0.75/0.43 thf(decl_164, type, setminusELneg: $o).
% 0.75/0.43 thf(decl_165, type, setminusILneg: $o).
% 0.75/0.43 thf(decl_166, type, setminusIRneg: $o).
% 0.75/0.43 thf(decl_167, type, setminusLsub: $o).
% 0.75/0.43 thf(decl_168, type, setminusSubset1: $o).
% 0.75/0.43 thf(decl_169, type, symdiff: $i > $i > $i).
% 0.75/0.43 thf(decl_170, type, symdiffE: $o).
% 0.75/0.43 thf(decl_171, type, symdiffI1: $o).
% 0.75/0.43 thf(decl_172, type, symdiffI2: $o).
% 0.75/0.43 thf(decl_173, type, symdiffIneg1: $o).
% 0.75/0.43 thf(decl_174, type, symdiffIneg2: $o).
% 0.75/0.43 thf(decl_175, type, iskpair: $i > $o).
% 0.75/0.43 thf(decl_176, type, secondinupair: $o).
% 0.75/0.43 thf(decl_177, type, setukpairIL: $o).
% 0.75/0.43 thf(decl_178, type, setukpairIR: $o).
% 0.75/0.43 thf(decl_179, type, kpairiskpair: $o).
% 0.75/0.43 thf(decl_180, type, kpair: $i > $i > $i).
% 0.75/0.43 thf(decl_181, type, kpairp: $o).
% 0.75/0.43 thf(decl_182, type, cartprod: $i > $i > $i).
% 0.75/0.43 thf(decl_183, type, singletonsubset: $o).
% 0.75/0.43 thf(decl_184, type, singletoninpowerset: $o).
% 0.75/0.43 thf(decl_185, type, singletoninpowunion: $o).
% 0.75/0.43 thf(decl_186, type, upairset2E: $o).
% 0.75/0.43 thf(decl_187, type, upairsubunion: $o).
% 0.75/0.43 thf(decl_188, type, upairinpowunion: $o).
% 0.75/0.43 thf(decl_189, type, ubforcartprodlem1: $o).
% 0.75/0.43 thf(decl_190, type, ubforcartprodlem2: $o).
% 0.75/0.43 thf(decl_191, type, ubforcartprodlem3: $o).
% 0.75/0.43 thf(decl_192, type, cartprodpairin: $o).
% 0.75/0.43 thf(decl_193, type, cartprodmempair1: $o).
% 0.75/0.43 thf(decl_194, type, cartprodmempair: $o).
% 0.75/0.43 thf(decl_195, type, setunionE2: $o).
% 0.75/0.43 thf(decl_196, type, setunionsingleton1: $o).
% 0.75/0.43 thf(decl_197, type, setunionsingleton2: $o).
% 0.75/0.43 thf(decl_198, type, setunionsingleton: $o).
% 0.75/0.43 thf(decl_199, type, singleton: $i > $o).
% 0.75/0.43 thf(decl_200, type, singletonprop: $o).
% 0.75/0.43 thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 0.75/0.43 thf(decl_202, type, ex1E1: $o).
% 0.75/0.43 thf(decl_203, type, ex1I: $o).
% 0.75/0.43 thf(decl_204, type, ex1I2: $o).
% 0.75/0.43 thf(decl_205, type, singletonsuniq: $o).
% 0.75/0.43 thf(decl_210, type, setukpairinjL1: $o).
% 0.75/0.43 thf(decl_211, type, kfstsingleton: $o).
% 0.75/0.43 thf(decl_212, type, theprop: $o).
% 0.75/0.43 thf(decl_213, type, kfst: $i > $i).
% 0.75/0.43 thf(decl_214, type, kfstpairEq: $o).
% 0.75/0.43 thf(decl_215, type, cartprodfstin: $o).
% 0.75/0.43 thf(decl_216, type, setukpairinjL2: $o).
% 0.75/0.43 thf(decl_217, type, setukpairinjL: $o).
% 0.75/0.43 thf(decl_218, type, setukpairinjR11: $o).
% 0.75/0.43 thf(decl_219, type, setukpairinjR12: $o).
% 0.75/0.43 thf(decl_220, type, setukpairinjR1: $o).
% 0.75/0.43 thf(decl_221, type, upairequniteq: $o).
% 0.75/0.43 thf(decl_222, type, setukpairinjR2: $o).
% 0.75/0.43 thf(decl_223, type, setukpairinjR: $o).
% 0.75/0.43 thf(decl_224, type, ksndsingleton: $o).
% 0.75/0.43 thf(decl_225, type, ksnd: $i > $i).
% 0.75/0.43 thf(decl_226, type, ksndpairEq: $o).
% 0.75/0.43 thf(decl_227, type, kpairsurjEq: $o).
% 0.75/0.43 thf(decl_228, type, cartprodsndin: $o).
% 0.75/0.43 thf(decl_229, type, cartprodpairmemEL: $o).
% 0.75/0.43 thf(decl_230, type, cartprodpairmemER: $o).
% 0.75/0.43 thf(decl_231, type, cartprodmempaircEq: $o).
% 0.75/0.43 thf(decl_232, type, cartprodfstpairEq: $o).
% 0.75/0.43 thf(decl_233, type, cartprodsndpairEq: $o).
% 0.75/0.43 thf(decl_234, type, cartprodpairsurjEq: $o).
% 0.75/0.43 thf(decl_235, type, breln: $i > $i > $i > $o).
% 0.75/0.43 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 0.75/0.43 thf(decl_237, type, dpsetconstrI: $o).
% 0.75/0.43 thf(decl_238, type, dpsetconstrSub: $o).
% 0.75/0.43 thf(decl_239, type, setOfPairsIsBReln: $o).
% 0.75/0.43 thf(decl_240, type, dpsetconstrERa: $o).
% 0.75/0.43 thf(decl_241, type, dpsetconstrEL1: $o).
% 0.75/0.43 thf(decl_242, type, dpsetconstrEL2: $o).
% 0.75/0.43 thf(decl_243, type, dpsetconstrER: $o).
% 0.75/0.43 thf(decl_244, type, func: $i > $i > $i > $o).
% 0.75/0.43 thf(decl_245, type, funcSet: $i > $i > $i).
% 0.75/0.43 thf(decl_246, type, funcImageSingleton: $o).
% 0.75/0.43 thf(decl_247, type, apProp: $o).
% 0.75/0.43 thf(decl_248, type, ap: $i > $i > $i > $i > $i).
% 0.75/0.43 thf(decl_249, type, app: $o).
% 0.75/0.43 thf(decl_250, type, infuncsetfunc: $o).
% 0.75/0.43 thf(decl_251, type, ap2p: $o).
% 0.75/0.43 thf(decl_252, type, funcinfuncset: $o).
% 0.75/0.43 thf(decl_253, type, lamProp: $o).
% 0.75/0.43 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
% 0.75/0.43 thf(decl_255, type, lamp: $o).
% 0.75/0.43 thf(decl_256, type, lam2p: $o).
% 0.75/0.43 thf(decl_257, type, brelnall1: $o).
% 0.75/0.43 thf(decl_258, type, brelnall2: $o).
% 0.75/0.43 thf(decl_259, type, ex1E2: $o).
% 0.75/0.43 thf(decl_260, type, funcGraphProp1: $o).
% 0.75/0.43 thf(decl_261, type, funcGraphProp3: $o).
% 0.75/0.43 thf(decl_262, type, funcGraphProp2: $o).
% 0.75/0.43 thf(decl_263, type, funcextLem: $o).
% 0.75/0.43 thf(decl_264, type, funcGraphProp4: $o).
% 0.75/0.43 thf(decl_265, type, subbreln: $o).
% 0.75/0.43 thf(decl_266, type, eqbreln: $o).
% 0.75/0.43 thf(decl_267, type, funcext: $o).
% 0.75/0.43 thf(decl_268, type, funcext2: $o).
% 0.75/0.43 thf(decl_269, type, ap2apEq1: $o).
% 0.75/0.43 thf(decl_270, type, ap2apEq2: $o).
% 0.75/0.43 thf(decl_271, type, beta1: $o).
% 0.75/0.43 thf(decl_272, type, eta1: $o).
% 0.75/0.43 thf(decl_273, type, lam2lamEq: $o).
% 0.75/0.43 thf(decl_274, type, beta2: $o).
% 0.75/0.43 thf(decl_275, type, eta2: $o).
% 0.75/0.43 thf(decl_276, type, iffalseProp1: $o).
% 0.75/0.43 thf(decl_277, type, iffalseProp2: $o).
% 0.75/0.43 thf(decl_278, type, iftrueProp1: $o).
% 0.75/0.43 thf(decl_279, type, iftrueProp2: $o).
% 0.75/0.43 thf(decl_280, type, ifSingleton: $o).
% 0.75/0.43 thf(decl_281, type, if: $i > $o > $i > $i > $i).
% 0.75/0.43 thf(decl_282, type, ifp: $o).
% 0.75/0.43 thf(decl_283, type, theeq: $o).
% 0.75/0.43 thf(decl_284, type, iftrue: $o).
% 0.75/0.43 thf(decl_285, type, iffalse: $o).
% 0.75/0.43 thf(decl_286, type, iftrueorfalse: $o).
% 0.75/0.43 thf(decl_287, type, binintersectT_lem: $o).
% 0.75/0.43 thf(decl_288, type, binunionT_lem: $o).
% 0.75/0.43 thf(decl_289, type, powersetT_lem: $o).
% 0.75/0.43 thf(decl_290, type, setminusT_lem: $o).
% 0.75/0.43 thf(decl_291, type, complementT_lem: $o).
% 0.75/0.43 thf(decl_292, type, setextT: $o).
% 0.75/0.43 thf(decl_293, type, subsetTI: $o).
% 0.75/0.43 thf(decl_294, type, powersetTI1: $o).
% 0.75/0.43 thf(decl_295, type, powersetTE1: $o).
% 0.75/0.43 thf(decl_296, type, complementTI1: $o).
% 0.75/0.43 thf(decl_297, type, complementTE1: $o).
% 0.75/0.43 thf(decl_298, type, binintersectTELcontra: $o).
% 0.75/0.43 thf(decl_299, type, binintersectTERcontra: $o).
% 0.75/0.43 thf(decl_300, type, contrasubsetT: $o).
% 0.75/0.43 thf(decl_301, type, contrasubsetT1: $o).
% 0.75/0.43 thf(decl_302, type, contrasubsetT2: $o).
% 0.75/0.43 thf(decl_303, type, contrasubsetT3: $o).
% 0.75/0.43 thf(decl_304, type, doubleComplementI1: $o).
% 0.75/0.43 thf(decl_305, type, doubleComplementE1: $o).
% 0.75/0.43 thf(decl_306, type, doubleComplementSub1: $o).
% 0.75/0.43 thf(decl_307, type, doubleComplementSub2: $o).
% 0.75/0.43 thf(decl_308, type, doubleComplementEq: $o).
% 0.75/0.43 thf(decl_309, type, complementTnotintersectT: $o).
% 0.75/0.43 thf(decl_310, type, complementImpComplementIntersect: $o).
% 0.75/0.43 thf(decl_311, type, complementSubsetComplementIntersect: $o).
% 0.75/0.43 thf(decl_312, type, complementInPowersetComplementIntersect: $o).
% 0.75/0.43 thf(decl_313, type, contraSubsetComplement: $o).
% 0.75/0.43 thf(decl_314, type, complementTcontraSubset: $o).
% 0.75/0.43 thf(decl_315, type, epred1_0: $o).
% 0.75/0.43 thf(decl_316, type, esk1_2: $i > $i > $i).
% 0.75/0.43 thf(decl_317, type, esk2_2: $i > $i > $i).
% 0.75/0.43 thf(decl_318, type, esk3_2: $i > $i > $i).
% 0.75/0.43 thf(decl_319, type, esk4_1: $i > $i).
% 0.75/0.43 thf(decl_320, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.75/0.43 thf(decl_321, type, esk6_2: ($i > $i > $o) > $i > $i).
% 0.75/0.43 thf(decl_322, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
% 0.75/0.43 thf(decl_323, type, esk8_1: $i > $i).
% 0.75/0.43 thf(decl_324, type, esk9_1: ($i > $o) > $i).
% 0.75/0.43 thf(decl_325, type, esk10_1: ($i > $o) > $i).
% 0.75/0.43 thf(decl_326, type, esk11_2: $i > $i > $i).
% 0.75/0.43 thf(decl_327, type, esk12_2: $i > $i > $i).
% 0.75/0.43 thf(decl_328, type, esk13_1: $i > $i).
% 0.75/0.43 thf(decl_329, type, esk14_1: $i > $i).
% 0.75/0.43 thf(decl_330, type, esk15_1: $i > $i).
% 0.75/0.43 thf(decl_331, type, esk16_2: $i > $i > $i).
% 0.75/0.43 thf(decl_332, type, esk17_3: $i > $i > $o > $i).
% 0.75/0.43 thf(decl_333, type, esk18_1: ($i > $o) > $i).
% 0.75/0.43 thf(decl_334, type, esk19_1: $i > $i).
% 0.75/0.43 thf(decl_335, type, esk20_2: $i > ($i > $o) > $i).
% 0.75/0.43 thf(decl_336, type, esk21_2: $i > ($i > $o) > $i).
% 0.75/0.43 thf(decl_337, type, esk22_2: $i > ($i > $o) > $i).
% 0.75/0.43 thf(decl_338, type, esk23_2: $i > ($i > $o) > $i).
% 0.75/0.43 thf(decl_339, type, esk24_2: $i > ($i > $o) > $i).
% 0.75/0.43 thf(decl_340, type, esk25_2: $i > ($i > $o) > $i).
% 0.75/0.43 thf(decl_341, type, esk26_2: ($i > $o) > $i > $i).
% 0.75/0.43 thf(decl_342, type, esk27_1: ($i > $o) > $i).
% 0.75/0.43 thf(decl_343, type, esk28_1: ($i > $o) > $i).
% 0.75/0.43 thf(decl_344, type, esk29_2: ($i > $o) > $i > $i).
% 0.75/0.43 thf(decl_345, type, esk30_2: ($i > $o) > ($i > $o) > $i).
% 0.75/0.43 thf(decl_346, type, esk31_2: ($i > $o) > ($i > $o) > $i).
% 0.75/0.43 thf(decl_347, type, esk32_2: ($i > $o) > ($i > $o) > $i).
% 0.75/0.43 thf(decl_348, type, esk33_2: ($i > $o) > ($i > $o) > $i).
% 0.75/0.43 thf(decl_349, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.75/0.43 thf(decl_350, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.75/0.43 thf(decl_351, type, esk36_2: $i > $i > $i).
% 0.75/0.43 thf(decl_352, type, esk37_2: $i > $i > $i).
% 0.75/0.43 thf(decl_353, type, esk38_2: $i > $i > $i).
% 0.75/0.43 thf(decl_354, type, esk39_3: $i > $i > $i > $i).
% 0.75/0.43 thf(decl_355, type, esk40_3: $i > $i > $i > $i).
% 0.75/0.43 thf(decl_356, type, esk41_2: $i > $i > $i).
% 0.75/0.43 thf(decl_357, type, esk42_2: $i > ($i > $o) > $i).
% 0.75/0.43 thf(decl_358, type, esk43_2: $i > ($i > $o) > $i).
% 0.75/0.43 thf(decl_359, type, esk44_2: $i > ($i > $o) > $i).
% 0.75/0.43 thf(decl_360, type, esk45_3: $i > ($i > $o) > $i > $i).
% 0.75/0.43 thf(decl_361, type, esk46_2: $i > ($i > $o) > $i).
% 0.75/0.43 thf(decl_362, type, esk47_2: $i > ($i > $o) > $i).
% 0.75/0.43 thf(decl_363, type, esk48_3: $i > $i > ($i > $i) > $i).
% 0.75/0.43 thf(decl_364, type, esk49_3: $i > $i > ($i > $i) > $i).
% 0.75/0.43 thf(decl_365, type, esk50_3: $i > $i > ($i > $i) > $i).
% 0.75/0.43 thf(decl_366, type, esk51_4: $i > $i > $i > ($i > $o) > $i).
% 0.75/0.43 thf(decl_367, type, esk52_4: $i > $i > $i > ($i > $o) > $i).
% 0.75/0.43 thf(decl_368, type, esk53_4: $i > $i > $i > ($i > $o) > $i).
% 0.75/0.43 thf(decl_369, type, esk54_4: $i > $i > $i > ($i > $o) > $i).
% 0.75/0.43 thf(decl_370, type, esk55_4: $i > $i > $i > $i > $i).
% 0.75/0.43 thf(decl_371, type, esk56_4: $i > $i > $i > $i > $i).
% 0.75/0.43 thf(decl_372, type, esk57_4: $i > $i > $i > $i > $i).
% 0.75/0.43 thf(decl_373, type, esk58_4: $i > $i > $i > $i > $i).
% 0.75/0.43 thf(decl_374, type, esk59_4: $i > $i > $i > $i > $i).
% 0.75/0.43 thf(decl_375, type, esk60_4: $i > $i > $i > $i > $i).
% 0.75/0.43 thf(decl_376, type, esk61_4: $i > $i > $i > $i > $i).
% 0.75/0.43 thf(decl_377, type, esk62_4: $i > $i > $i > $i > $i).
% 0.75/0.43 thf(decl_378, type, esk63_4: $i > $i > $i > $i > $i).
% 0.75/0.43 thf(decl_379, type, esk64_3: $i > $i > ($i > $i) > $i).
% 0.75/0.43 thf(decl_380, type, esk65_3: $i > $i > ($i > $i) > $i).
% 0.75/0.43 thf(decl_381, type, esk66_3: $i > $i > ($i > $i) > $i).
% 0.75/0.43 thf(decl_382, type, esk67_3: $i > $i > $i > $i).
% 0.75/0.43 thf(decl_383, type, esk68_3: $i > $i > $i > $i).
% 0.75/0.43 thf(decl_384, type, esk69_3: $i > $i > $i > $i).
% 0.75/0.43 thf(decl_385, type, esk70_3: $i > $i > $i > $i).
% 0.75/0.43 thf(decl_386, type, esk71_0: $i).
% 0.75/0.43 thf(decl_387, type, esk72_0: $i).
% 0.75/0.43 thf(decl_388, type, esk73_0: $i).
% 0.75/0.43 thf(decl_389, type, esk74_0: $i).
% 0.75/0.43 thf(binunionTILcontra, 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)=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', binunionTILcontra)).
% 0.75/0.43 thf(beta1, axiom, ((beta1)<=>![X4:$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.HvOPs3palg/E---3.1_2731752.p', beta1)).
% 0.75/0.43 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.HvOPs3palg/E---3.1_2731752.p', eta1)).
% 0.75/0.43 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.HvOPs3palg/E---3.1_2731752.p', lam2lamEq)).
% 0.75/0.43 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.HvOPs3palg/E---3.1_2731752.p', beta2)).
% 0.75/0.43 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.HvOPs3palg/E---3.1_2731752.p', eta2)).
% 0.75/0.43 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X39))&(((X14)=(X2)))))|(((~((X39)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', iffalseProp1)).
% 0.75/0.43 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$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.HvOPs3palg/E---3.1_2731752.p', iffalseProp2)).
% 0.75/0.43 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X41))&(((X14)=(X2)))))|(((~((X41)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', iftrueProp1)).
% 0.75/0.43 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$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.HvOPs3palg/E---3.1_2731752.p', iftrueProp2)).
% 0.75/0.43 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X43))&(((X14)=(X2)))))|(((~((X43)))&(((X14)=(X3))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', ifSingleton)).
% 0.75/0.43 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', exuI1)).
% 0.75/0.43 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', exu__Cong)).
% 0.75/0.43 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', exuE3u)).
% 0.75/0.43 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.HvOPs3palg/E---3.1_2731752.p', exuI2)).
% 0.75/0.43 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', exuI3)).
% 0.75/0.43 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', dsetconstr__Cong)).
% 0.75/0.43 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', descr__Cong)).
% 0.75/0.43 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', exuEu)).
% 0.75/0.43 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', sepSubset)).
% 0.75/0.43 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', sepInPowerset)).
% 0.75/0.43 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.HvOPs3palg/E---3.1_2731752.p', ex1I)).
% 0.75/0.43 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', ex1E1)).
% 0.75/0.43 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', singletonprop)).
% 0.75/0.43 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', ex1I2)).
% 0.75/0.43 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', kfstsingleton)).
% 0.75/0.43 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', ksndsingleton)).
% 0.75/0.43 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', dpsetconstrER)).
% 0.75/0.43 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', dpsetconstrEL2)).
% 0.75/0.43 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', dpsetconstrEL1)).
% 0.75/0.43 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', dpsetconstrERa)).
% 0.75/0.43 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setOfPairsIsBReln)).
% 0.75/0.43 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', dpsetconstrSub)).
% 0.75/0.43 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', dpsetconstrI)).
% 0.75/0.43 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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.HvOPs3palg/E---3.1_2731752.p', funcImageSingleton)).
% 0.75/0.43 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:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', lamp)).
% 0.75/0.43 thf(lamProp, axiom, ((lamProp)<=>![X4:$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.HvOPs3palg/E---3.1_2731752.p', lamProp)).
% 0.75/0.43 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', apProp)).
% 0.75/0.43 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', lam2p)).
% 0.75/0.43 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$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.HvOPs3palg/E---3.1_2731752.p', ex1E2)).
% 0.75/0.43 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.HvOPs3palg/E---3.1_2731752.p', emptyE1)).
% 0.75/0.43 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.HvOPs3palg/E---3.1_2731752.p', exuE2)).
% 0.75/0.43 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setoftrueEq)).
% 0.75/0.43 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', nonemptyI)).
% 0.75/0.43 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setbeta)).
% 0.75/0.43 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', exuE3e)).
% 0.75/0.43 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', exuE1)).
% 0.75/0.43 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', dsetconstrER)).
% 0.75/0.43 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', dsetconstrEL)).
% 0.75/0.43 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', dsetconstrI)).
% 0.75/0.43 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', descrp)).
% 0.75/0.43 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', replAx)).
% 0.75/0.43 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', ap2apEq2)).
% 0.75/0.43 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', ap2apEq1)).
% 0.75/0.43 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', notdallE)).
% 0.75/0.43 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', notdexE)).
% 0.75/0.43 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', prop2setI)).
% 0.75/0.43 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.HvOPs3palg/E---3.1_2731752.p', ifp)).
% 0.75/0.43 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', quantDeMorgan4)).
% 0.75/0.43 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', theeq)).
% 0.75/0.43 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', quantDeMorgan3)).
% 0.75/0.43 thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', iftrue)).
% 0.75/0.43 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', quantDeMorgan2)).
% 0.75/0.43 thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', iffalse)).
% 0.75/0.43 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', vacuousDall)).
% 0.75/0.43 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.HvOPs3palg/E---3.1_2731752.p', iftrueorfalse)).
% 0.75/0.43 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', quantDeMorgan1)).
% 0.75/0.43 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$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.HvOPs3palg/E---3.1_2731752.p', binintersectT_lem)).
% 0.75/0.43 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', binunionT_lem)).
% 0.75/0.43 thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', powersetT_lem)).
% 0.75/0.43 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$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.HvOPs3palg/E---3.1_2731752.p', setminusT_lem)).
% 0.75/0.43 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.HvOPs3palg/E---3.1_2731752.p', complementT_lem)).
% 0.75/0.43 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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setextT)).
% 0.75/0.43 thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', subsetTI)).
% 0.75/0.43 thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', powersetTI1)).
% 0.75/0.43 thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', powersetTE1)).
% 0.75/0.43 thf(complementTI1, axiom, ((complementTI1)<=>![X4:$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.HvOPs3palg/E---3.1_2731752.p', complementTI1)).
% 0.75/0.43 thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', complementTE1)).
% 0.75/0.43 thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', binintersectTELcontra)).
% 0.75/0.43 thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', binintersectTERcontra)).
% 0.75/0.43 thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', contrasubsetT)).
% 0.75/0.43 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', emptyset__Cong)).
% 0.75/0.43 thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', contrasubsetT1)).
% 0.75/0.43 thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$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.HvOPs3palg/E---3.1_2731752.p', contrasubsetT2)).
% 0.75/0.43 thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', contrasubsetT3)).
% 0.75/0.43 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', in__Cong)).
% 0.75/0.43 thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$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.HvOPs3palg/E---3.1_2731752.p', doubleComplementI1)).
% 0.75/0.43 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.HvOPs3palg/E---3.1_2731752.p', inCongP)).
% 0.75/0.43 thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', doubleComplementE1)).
% 0.75/0.43 thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', doubleComplementSub1)).
% 0.75/0.43 thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', doubleComplementSub2)).
% 0.75/0.43 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setadjoin__Cong)).
% 0.75/0.43 thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', doubleComplementEq)).
% 0.75/0.43 thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', complementTnotintersectT)).
% 0.75/0.43 thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', complementImpComplementIntersect)).
% 0.75/0.43 thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$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.HvOPs3palg/E---3.1_2731752.p', complementSubsetComplementIntersect)).
% 0.75/0.43 thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', complementInPowersetComplementIntersect)).
% 0.75/0.43 thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', contraSubsetComplement)).
% 0.75/0.43 thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$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.HvOPs3palg/E---3.1_2731752.p', complementTcontraSubset)).
% 0.75/0.43 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', subsetI1)).
% 0.75/0.43 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', omega__Cong)).
% 0.75/0.43 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setunion__Cong)).
% 0.75/0.43 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', powerset__Cong)).
% 0.75/0.43 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', eqimpsubset2)).
% 0.75/0.43 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', notequalI1)).
% 0.75/0.43 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', notsubsetI)).
% 0.75/0.43 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', subsetE2)).
% 0.75/0.43 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', subsetE)).
% 0.75/0.43 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', emptysetsubset)).
% 0.75/0.43 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', subsetI2)).
% 0.75/0.43 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', eqimpsubset1)).
% 0.75/0.43 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', notequalI2)).
% 0.75/0.43 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', subsetemptysetimpeq)).
% 0.75/0.43 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setextsub)).
% 0.75/0.43 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', subset2powerset)).
% 0.75/0.43 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setadjoinSub2)).
% 0.75/0.43 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setadjoinSub)).
% 0.75/0.43 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', subsetTrans)).
% 0.75/0.43 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', subsetRefl)).
% 0.75/0.43 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', powersetI1)).
% 0.75/0.43 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', upairset2IR)).
% 0.75/0.43 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', binunionIL)).
% 0.75/0.43 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', powersetsubset)).
% 0.75/0.43 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', inPowerset)).
% 0.75/0.43 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', powersetE1)).
% 0.75/0.43 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', binunionIR)).
% 0.75/0.43 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', binintersectEL)).
% 0.75/0.43 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', binintersectSubset5)).
% 0.75/0.43 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', binintersectI)).
% 0.75/0.43 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', binunionRsub)).
% 0.75/0.43 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', binunionLsub)).
% 0.75/0.43 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', binunionE)).
% 0.75/0.43 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.HvOPs3palg/E---3.1_2731752.p', binunionEcases)).
% 0.75/0.43 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', binintersectLsub)).
% 0.75/0.43 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', binintersectSubset1)).
% 0.75/0.43 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', binintersectSubset4)).
% 0.75/0.43 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', binintersectRsub)).
% 0.75/0.43 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', disjointsetsI1)).
% 0.75/0.43 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', binintersectER)).
% 0.75/0.43 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', binintersectSubset3)).
% 0.75/0.43 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', binintersectSubset2)).
% 0.75/0.43 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', bs114d)).
% 0.75/0.43 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setminusILneg)).
% 0.75/0.43 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setminusELneg)).
% 0.75/0.43 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setminusERneg)).
% 0.75/0.43 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setminusSubset2)).
% 0.75/0.43 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setminusER)).
% 0.75/0.43 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setminusEL)).
% 0.75/0.43 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setminusI)).
% 0.75/0.43 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setminusIRneg)).
% 0.75/0.43 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', symdiffIneg2)).
% 0.75/0.43 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', symdiffIneg1)).
% 0.75/0.43 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', symdiffI2)).
% 0.75/0.43 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', symdiffI1)).
% 0.75/0.43 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.HvOPs3palg/E---3.1_2731752.p', symdiffE)).
% 0.75/0.43 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setminusSubset1)).
% 0.75/0.43 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setminusLsub)).
% 0.75/0.43 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', secondinupair)).
% 0.75/0.43 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', singletoninpowunion)).
% 0.75/0.43 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', singletoninpowerset)).
% 0.75/0.43 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', singletonsubset)).
% 0.75/0.43 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', kpairp)).
% 0.75/0.43 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', kpairiskpair)).
% 0.75/0.43 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setukpairIR)).
% 0.75/0.43 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setukpairIL)).
% 0.75/0.43 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', upairset2E)).
% 0.75/0.43 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', cartprodmempair1)).
% 0.75/0.43 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', cartprodpairin)).
% 0.75/0.43 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', ubforcartprodlem3)).
% 0.75/0.43 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', ubforcartprodlem2)).
% 0.75/0.43 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', ubforcartprodlem1)).
% 0.75/0.43 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', upairinpowunion)).
% 0.75/0.43 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', upairsubunion)).
% 0.75/0.43 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', cartprodmempair)).
% 0.75/0.43 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setunionsingleton)).
% 0.75/0.43 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setunionsingleton2)).
% 0.75/0.43 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setunionsingleton1)).
% 0.75/0.43 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setunionE2)).
% 0.75/0.43 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.HvOPs3palg/E---3.1_2731752.p', setukpairinjL2)).
% 0.75/0.43 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', cartprodfstin)).
% 0.75/0.43 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', kfstpairEq)).
% 0.75/0.43 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', theprop)).
% 0.75/0.43 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setukpairinjL1)).
% 0.75/0.43 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', singletonsuniq)).
% 0.75/0.43 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setukpairinjL)).
% 0.75/0.43 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setukpairinjR)).
% 0.75/0.43 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setukpairinjR2)).
% 0.75/0.43 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', upairequniteq)).
% 0.75/0.43 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.HvOPs3palg/E---3.1_2731752.p', setukpairinjR1)).
% 0.75/0.43 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.HvOPs3palg/E---3.1_2731752.p', setukpairinjR12)).
% 0.75/0.43 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setukpairinjR11)).
% 0.75/0.43 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', ksndpairEq)).
% 0.75/0.43 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.HvOPs3palg/E---3.1_2731752.p', cartprodsndpairEq)).
% 0.75/0.43 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.HvOPs3palg/E---3.1_2731752.p', cartprodfstpairEq)).
% 0.75/0.43 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.HvOPs3palg/E---3.1_2731752.p', cartprodmempaircEq)).
% 0.75/0.43 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.HvOPs3palg/E---3.1_2731752.p', cartprodpairmemER)).
% 0.75/0.43 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.HvOPs3palg/E---3.1_2731752.p', cartprodpairmemEL)).
% 0.75/0.43 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', cartprodsndin)).
% 0.75/0.43 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', kpairsurjEq)).
% 0.75/0.43 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', cartprodpairsurjEq)).
% 0.75/0.43 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', funcinfuncset)).
% 0.75/0.43 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.HvOPs3palg/E---3.1_2731752.p', ap2p)).
% 0.75/0.43 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', infuncsetfunc)).
% 0.75/0.43 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', app)).
% 0.75/0.43 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$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.HvOPs3palg/E---3.1_2731752.p', funcextLem)).
% 0.75/0.43 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', funcGraphProp2)).
% 0.75/0.43 thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', funcGraphProp3)).
% 0.75/0.43 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', funcGraphProp1)).
% 0.75/0.43 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$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.HvOPs3palg/E---3.1_2731752.p', brelnall2)).
% 0.75/0.43 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.HvOPs3palg/E---3.1_2731752.p', brelnall1)).
% 0.75/0.43 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.HvOPs3palg/E---3.1_2731752.p', subbreln)).
% 0.75/0.43 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.HvOPs3palg/E---3.1_2731752.p', eqbreln)).
% 0.75/0.43 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', funcext)).
% 0.75/0.43 thf(funcext2, axiom, ((funcext2)<=>![X4:$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.HvOPs3palg/E---3.1_2731752.p', funcext2)).
% 0.75/0.43 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', funcGraphProp4)).
% 0.75/0.43 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', upairsetIR)).
% 0.75/0.43 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', upairsetIL)).
% 0.75/0.43 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', upairsetE)).
% 0.75/0.43 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', singletonsswitch)).
% 0.75/0.43 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', eqinunit)).
% 0.75/0.43 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', notinsingleton)).
% 0.75/0.43 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', uniqinunit)).
% 0.75/0.43 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', nonemptyImpWitness)).
% 0.75/0.43 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', subPowSU)).
% 0.75/0.43 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setunionE)).
% 0.75/0.43 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setunionI)).
% 0.75/0.43 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', powersetE)).
% 0.75/0.43 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', emptyInPowerset)).
% 0.75/0.43 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', emptyinPowerset)).
% 0.75/0.43 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', powersetI)).
% 0.75/0.43 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setadjoinOr)).
% 0.75/0.43 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setadjoinE)).
% 0.75/0.43 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setadjoinIR)).
% 0.75/0.43 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', emptyinunitempty)).
% 0.75/0.43 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setadjoinIL)).
% 0.75/0.43 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', nonemptyI1)).
% 0.75/0.43 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', nonemptyE1)).
% 0.75/0.43 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', noeltsimpempty)).
% 0.75/0.43 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', emptyI)).
% 0.75/0.43 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.HvOPs3palg/E---3.1_2731752.p', setext)).
% 0.75/0.43 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', notinemptyset)).
% 0.75/0.43 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', emptysetimpfalse)).
% 0.75/0.43 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', emptysetE)).
% 0.75/0.43 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', prop2setE)).
% 0.75/0.43 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.HvOPs3palg/E---3.1_2731752.p', wellorderingAx)).
% 0.75/0.43 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.HvOPs3palg/E---3.1_2731752.p', foundationAx)).
% 0.75/0.43 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', omegaIndAx)).
% 0.75/0.43 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', omegaSAx)).
% 0.75/0.43 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', omega0Ax)).
% 0.75/0.43 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setunionAx)).
% 0.75/0.43 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', powersetAx)).
% 0.75/0.43 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setadjoinAx)).
% 0.75/0.43 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', emptysetAx)).
% 0.75/0.43 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.HvOPs3palg/E---3.1_2731752.p', setextAx)).
% 0.75/0.43 thf(c_0_254, 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)=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[binunionTILcontra])).
% 0.75/0.43 thf(c_0_255, plain, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X36 @ Z0))) @ X2)=(X36 @ X2))))))), inference(fof_simplification,[status(thm)],[beta1])).
% 0.75/0.43 thf(c_0_256, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])).
% 0.75/0.43 thf(c_0_257, plain, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[Z0:$i]:(X37 @ Z0)))=(lam @ X4 @ X5 @ (^[Z0:$i]:(X37 @ Z0))))))), inference(fof_simplification,[status(thm)],[lam2lamEq])).
% 0.75/0.43 thf(c_0_258, plain, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X38 @ Z0))) @ X2)=(X38 @ X2))))))), inference(fof_simplification,[status(thm)],[beta2])).
% 0.75/0.43 thf(c_0_259, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])).
% 0.75/0.43 thf(c_0_260, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X39))&(((Z0)=(X2)))))|(((~((X39)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
% 0.75/0.43 thf(c_0_261, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X40))&(((Z0)=(X2)))))|(((~((X40)))&(((Z0)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])).
% 0.75/0.43 thf(c_0_262, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X41))&(((Z0)=(X2)))))|(((~((X41)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
% 0.75/0.43 thf(c_0_263, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X42))&(((Z0)=(X2)))))|(((~((X42)))&(((Z0)=(X3)))))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])).
% 0.75/0.43 thf(c_0_264, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X43))&(((Z0)=(X2)))))|(((~((X43)))&(((Z0)=(X3))))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
% 0.75/0.43 thf(c_0_265, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 0.75/0.43 thf(c_0_266, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.75/0.43 thf(c_0_267, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 0.75/0.43 thf(c_0_268, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.75/0.43 thf(c_0_269, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.75/0.43 thf(c_0_270, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 0.75/0.43 thf(c_0_271, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))=>((exu @ (^[Z0:$i]:((X17 @ Z0))))=>((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 0.75/0.43 thf(c_0_272, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 0.75/0.43 thf(c_0_273, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 0.75/0.43 thf(c_0_274, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 0.75/0.43 thf(c_0_275, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])).
% 0.75/0.43 thf(c_0_276, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 0.75/0.43 thf(c_0_277, plain, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 0.75/0.43 thf(c_0_278, plain, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 0.75/0.43 thf(c_0_279, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 0.75/0.43 thf(c_0_280, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 0.75/0.43 thf(c_0_281, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 0.75/0.43 thf(c_0_282, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 0.75/0.43 thf(c_0_283, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 0.75/0.43 thf(c_0_284, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 0.75/0.43 thf(c_0_285, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 0.75/0.43 thf(c_0_286, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 0.75/0.43 thf(c_0_287, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 0.75/0.43 thf(c_0_288, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
% 0.75/0.43 thf(c_0_289, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
% 0.75/0.43 thf(c_0_290, plain, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:(((X30 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])).
% 0.75/0.43 thf(c_0_291, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
% 0.75/0.43 thf(c_0_292, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
% 0.75/0.43 thf(c_0_293, plain, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[ex1E2])).
% 0.75/0.43 thf(c_0_294, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
% 0.75/0.43 thf(c_0_295, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.75/0.43 thf(c_0_296, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.75/0.43 thf(c_0_297, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.75/0.43 thf(c_0_298, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.75/0.43 thf(c_0_299, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.75/0.43 thf(c_0_300, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.75/0.43 thf(c_0_301, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.75/0.43 thf(c_0_302, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.75/0.43 thf(c_0_303, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.75/0.43 thf(c_0_304, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.75/0.43 thf(c_0_305, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.75/0.43 thf(c_0_306, plain, ((epred1_0)<=>![X866:$i]:(?[X867:$i]:((((![X868:$i]:(((in @ X868 @ X867)=>![X869:$i]:(((in @ X869 @ X868)=>(in @ X869 @ X866)))))&![X870:$i, X871:$i]:((((in @ X870 @ X866)&(in @ X871 @ X866))=>(![X872:$i]:(((in @ X872 @ X867)=>((in @ X870 @ X872)<=>(in @ X871 @ X872))))=>((X870)=(X871))))))&![X873:$i, X874:$i]:((((in @ X873 @ X867)&(in @ X874 @ X867))=>(![X875:$i]:(((in @ X875 @ X873)=>(in @ X875 @ X874)))|![X876:$i]:(((in @ X876 @ X874)=>(in @ X876 @ X873)))))))&![X877:$i]:(((![X878:$i]:(((in @ X878 @ X877)=>(in @ X878 @ X866)))&?[X879:$i]:((in @ X879 @ X877)))=>?[X880:$i, X881:$i]:(((((in @ X880 @ X867)&(in @ X881 @ X877))&~(?[X882:$i]:(((in @ X882 @ X880)&(in @ X882 @ X877)))))&![X883:$i]:(((in @ X883 @ X867)=>(![X884:$i]:(((in @ X884 @ X883)=>(in @ X884 @ X880)))|(in @ X881 @ X883)))))))))))), introduced(definition)).
% 0.75/0.43 thf(c_0_307, negated_conjecture, ~((![X839:$i, X840:$i]:((![X841:$i]:(((in @ X841 @ X839)<=>(in @ X841 @ X840)))=>((X839)=(X840))))=>(![X842:$i]:(~(in @ X842 @ emptyset))=>(![X843:$i, X844:$i, X845:$i]:(((in @ X845 @ (setadjoin @ X843 @ X844))<=>(((X845)=(X843))|(in @ X845 @ X844))))=>(![X846:$i, X847:$i]:(((in @ X847 @ (powerset @ X846))<=>![X848:$i]:(((in @ X848 @ X847)=>(in @ X848 @ X846)))))=>(![X849:$i, X850:$i]:(((in @ X850 @ (setunion @ X849))<=>?[X851:$i]:(((in @ X850 @ X851)&(in @ X851 @ X849)))))=>((in @ emptyset @ omega)=>(![X852:$i]:(((in @ X852 @ omega)=>(in @ (setadjoin @ X852 @ X852) @ omega)))=>(![X853:$i]:((((in @ emptyset @ X853)&![X854:$i]:((((in @ X854 @ omega)&(in @ X854 @ X853))=>(in @ (setadjoin @ X854 @ X854) @ X853))))=>![X855:$i]:(((in @ X855 @ omega)=>(in @ X855 @ X853)))))=>(![X856:$i > $i > $o, X857:$i]:((![X858:$i]:(((in @ X858 @ X857)=>(exu @ (X856 @ X858))))=>?[X859:$i]:(![X860:$i]:(((in @ X860 @ X859)<=>?[X861:$i]:(((in @ X861 @ X857)&(X856 @ X861 @ X860))))))))=>(![X862:$i]:((?[X863:$i]:((in @ X863 @ X862))=>?[X864:$i]:(((in @ X864 @ X862)&~(?[X865:$i]:(((in @ X865 @ X864)&(in @ X865 @ X862))))))))=>((epred1_0)=>(![X885:$i > $o]:(((exu @ X885)=>(X885 @ (descr @ (^[Z0:$i]:(X885 @ Z0))))))=>(![X886:$i, X887:$i > $o, X888:$i]:(((in @ X888 @ X886)=>((X887 @ X888)=>(in @ X888 @ (dsetconstr @ X886 @ X887)))))=>(![X889:$i, X890:$i > $o, X891:$i]:(((in @ X891 @ (dsetconstr @ X889 @ X890))=>(in @ X891 @ X889)))=>(![X892:$i, X893:$i > $o, X894:$i]:(((in @ X894 @ (dsetconstr @ X892 @ X893))=>(X893 @ X894)))=>(![X895:$i > $o]:(((exu @ X895)=>?[X896:$i]:(((X895 @ X896)&![X897:$i]:(((X895 @ X897)=>((X896)=(X897))))))))=>(![X898:$o, X899:$i]:(((in @ X899 @ (prop2set @ ((X898))))=>(X898)))=>(![X900:$i]:(((in @ X900 @ emptyset)=>![X901:$o]:((X901))))=>(![X902:$i]:(((in @ X902 @ emptyset)=>~($true)))=>(![X903:$i]:(~(in @ X903 @ emptyset))=>(![X904:$i > $o]:(((exu @ X904)=>?[X905:$i]:((X904 @ X905))))=>(![X906:$i, X907:$i]:((![X908:$i]:(((in @ X908 @ X906)=>(in @ X908 @ X907)))=>(![X909:$i]:(((in @ X909 @ X907)=>(in @ X909 @ X906)))=>((X906)=(X907)))))=>(![X910:$i]:((![X911:$i]:(~(in @ X911 @ X910))=>((X910)=(emptyset))))=>(![X912:$i]:((![X913:$i]:(~(in @ X913 @ X912))=>((X912)=(emptyset))))=>(![X914:$i, X915:$i > $o, X916:$i]:(((in @ X916 @ X914)=>((in @ X916 @ (dsetconstr @ X914 @ X915))<=>(X915 @ X916))))=>(![X917:$i]:(((nonempty @ X917)=>?[X918:$i]:((in @ X918 @ X917))))=>(![X919:$i, X920:$i > $o, X921:$i]:(((in @ X921 @ X919)=>((X920 @ X921)=>(nonempty @ (dsetconstr @ X919 @ X920)))))=>(![X922:$i]:((?[X923:$i]:((in @ X923 @ X922))=>(nonempty @ X922)))=>(![X924:$i, X925:$i]:((in @ X924 @ (setadjoin @ X924 @ X925)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X926:$i, X927:$i, X928:$i]:(((in @ X928 @ X927)=>(in @ X928 @ (setadjoin @ X926 @ X927))))=>(![X929:$i, X930:$i, X931:$i]:(((in @ X931 @ (setadjoin @ X929 @ X930))=>![X932:$o]:(((((X931)=(X929))=>(X932))=>(((in @ X931 @ X930)=>(X932))=>(X932))))))=>(![X933:$i, X934:$i, X935:$i]:(((in @ X935 @ (setadjoin @ X933 @ X934))=>(((X935)=(X933))|(in @ X935 @ X934))))=>(![X936:$i]:(((dsetconstr @ X936 @ (^[Z0:$i]:($true)))=(X936)))=>(![X937:$i, X938:$i]:((![X939:$i]:(((in @ X939 @ X938)=>(in @ X939 @ X937)))=>(in @ X938 @ (powerset @ X937))))=>(![X940:$i]:((in @ emptyset @ (powerset @ X940)))=>(![X941:$i]:((in @ emptyset @ (powerset @ X941)))=>(![X942:$i, X943:$i, X944:$i]:(((in @ X943 @ (powerset @ X942))=>((in @ X944 @ X943)=>(in @ X944 @ X942))))=>(![X945:$i, X946:$i, X947:$i]:(((in @ X946 @ X947)=>((in @ X947 @ X945)=>(in @ X946 @ (setunion @ X945)))))=>(![X948:$i, X949:$i]:(((in @ X949 @ (setunion @ X948))=>![X950:$o]:((![X951:$i]:(((in @ X949 @ X951)=>((in @ X951 @ X948)=>(X950))))=>(X950)))))=>(![X952:$i, X953:$i]:(((in @ X953 @ X952)=>(in @ X953 @ (powerset @ (setunion @ X952)))))=>(![X954:$i > $o]:(((exu @ X954)=>?[X955:$i]:(![X956:$i]:(((X954 @ X956)<=>((X956)=(X955)))))))=>(![X957:$i]:(((nonempty @ X957)=>?[X958:$i]:(((in @ X958 @ X957)&$true))))=>(![X959:$i, X960:$i]:(((in @ X959 @ (setadjoin @ X960 @ emptyset))=>((X959)=(X960))))=>(![X961:$i, X962:$i]:((((X961)!=(X962))=>~(in @ X962 @ (setadjoin @ X961 @ emptyset))))=>(![X963:$i, X964:$i]:((((X963)=(X964))=>(in @ X963 @ (setadjoin @ X964 @ emptyset))))=>(![X965:$i, X966:$i]:(((in @ X965 @ (setadjoin @ X966 @ emptyset))=>(in @ X966 @ (setadjoin @ X965 @ emptyset))))=>(![X967:$i, X968:$i, X969:$i]:(((in @ X969 @ (setadjoin @ X967 @ (setadjoin @ X968 @ emptyset)))=>(((X969)=(X967))|((X969)=(X968)))))=>(![X970:$i, X971:$i]:((in @ X970 @ (setadjoin @ X970 @ (setadjoin @ X971 @ emptyset))))=>(![X972:$i, X973:$i]:((in @ X973 @ (setadjoin @ X972 @ (setadjoin @ X973 @ emptyset))))=>(![X974:$i, X975:$i > $o]:((?[X976:$i]:(((in @ X976 @ X974)&(X975 @ X976)))=>(((dsetconstr @ X974 @ X975)=(emptyset))=>~($true))))=>(![X977:$i > $o, X978:$i]:(((in @ X978 @ emptyset)=>(X977 @ X978)))=>(![X979:$i, X980:$i > $o]:((~(![X981:$i]:(((in @ X981 @ X979)=>(X980 @ X981))))=>?[X982:$i]:(((in @ X982 @ X979)&~((X980 @ X982))))))=>(![X983:$i, X984:$i > $o]:((![X985:$i]:(((in @ X985 @ X983)=>~((X984 @ X985))))=>~(?[X986:$i]:(((in @ X986 @ X983)&(X984 @ X986))))))=>(![X987:$i, X988:$i > $o]:((~(?[X989:$i]:(((in @ X989 @ X987)&(X988 @ X989))))=>![X990:$i]:(((in @ X990 @ X987)=>~((X988 @ X990))))))=>(![X991:$i, X992:$i > $o]:((?[X993:$i]:(((in @ X993 @ X991)&~((X992 @ X993))))=>~(![X994:$i]:(((in @ X994 @ X991)=>(X992 @ X994))))))=>(![X995:$o]:(((X995)=>(in @ emptyset @ (prop2set @ ((X995))))))=>((prop2set2propI)=>(![X996:$i, X997:$i > $o]:((~(?[X998:$i]:(((in @ X998 @ X996)&(X997 @ X998))))=>![X999:$i]:(((in @ X999 @ X996)=>~((X997 @ X999))))))=>(![X1000:$i, X1001:$i > $o]:((~(![X1002:$i]:(((in @ X1002 @ X1000)=>(X1001 @ X1002))))=>?[X1003:$i]:(((in @ X1003 @ X1000)&~((X1001 @ X1003))))))=>(![X1004:$i > $o]:((?[X1005:$i]:(((X1004 @ X1005)&![X1006:$i]:(((X1004 @ X1006)=>((X1005)=(X1006))))))=>(exu @ X1004)))=>(![X1007:$i > $o]:((?[X1008:$i]:((X1007 @ X1008))=>(![X1009:$i, X1010:$i]:(((X1007 @ X1009)=>((X1007 @ X1010)=>((X1009)=(X1010)))))=>(exu @ X1007))))=>(![X1011:$i > $o]:((?[X1012:$i]:(![X1013:$i]:(((X1011 @ X1013)<=>((X1013)=(X1012)))))=>(exu @ X1011)))=>(![X1014:$i, X1015:$i]:((((X1014)=(X1015))=>![X1016:$i, X1017:$i]:((((X1016)=(X1017))=>((in @ X1016 @ X1014)=>(in @ X1017 @ X1015))))))=>(![X1018:$i, X1019:$i]:((((X1018)=(X1019))=>![X1020:$i, X1021:$i]:((((X1020)=(X1021))=>((in @ X1020 @ X1018)<=>(in @ X1021 @ X1019))))))=>(![X1022:$i > $o]:(((exu @ X1022)=>![X1023:$i, X1024:$i]:(((X1022 @ X1023)=>((X1022 @ X1024)=>((X1023)=(X1024)))))))=>(![X1025:$i > $o, X1026:$i > $o]:((![X1027:$i, X1028:$i]:((((X1027)=(X1028))=>((X1025 @ X1027)<=>(X1026 @ X1028))))=>((exu @ X1025)<=>(exu @ X1026))))=>(((emptyset)=(emptyset))=>(![X1029:$i, X1030:$i]:((((X1029)=(X1030))=>![X1031:$i, X1032:$i]:((((X1031)=(X1032))=>((setadjoin @ X1029 @ X1031)=(setadjoin @ X1030 @ X1032))))))=>(![X1033:$i, X1034:$i]:((((X1033)=(X1034))=>((powerset @ X1033)=(powerset @ X1034))))=>(![X1035:$i, X1036:$i]:((((X1035)=(X1036))=>((setunion @ X1035)=(setunion @ X1036))))=>(((omega)=(omega))=>(![X1037:$i > $o]:(((exu @ X1037)=>![X1038:$i, X1039:$i]:(((X1037 @ X1038)=>((X1037 @ X1039)=>((X1038)=(X1039)))))))=>(![X1040:$i > $o, X1041:$i > $o]:((![X1042:$i, X1043:$i]:((((X1042)=(X1043))=>((X1040 @ X1042)<=>(X1041 @ X1043))))=>((exu @ X1040)=>((exu @ X1041)=>((descr @ X1040)=(descr @ X1041))))))=>(![X1044:$i, X1045:$i]:((((X1044)=(X1045))=>![X1046:$i > $o, X1047:$i > $o]:((![X1048:$i]:(((in @ X1048 @ X1044)=>![X1049:$i]:(((in @ X1049 @ X1045)=>(((X1048)=(X1049))=>((X1046 @ X1048)<=>(X1047 @ X1049)))))))=>((dsetconstr @ X1044 @ X1046)=(dsetconstr @ X1045 @ X1047))))))=>(![X1050:$i, X1051:$i]:((![X1052:$i]:(((in @ X1052 @ X1050)=>(in @ X1052 @ X1051)))=>(subset @ X1050 @ X1051)))=>(![X1053:$i, X1054:$i]:((((X1053)=(X1054))=>(subset @ X1054 @ X1053)))=>(![X1055:$i, X1056:$i]:((((X1055)=(X1056))=>(subset @ X1055 @ X1056)))=>(![X1057:$i, X1058:$i]:((![X1059:$i]:(((in @ X1059 @ X1057)=>(in @ X1059 @ X1058)))=>(subset @ X1057 @ X1058)))=>(![X1060:$i]:((subset @ emptyset @ X1060))=>(![X1061:$i, X1062:$i, X1063:$i]:(((subset @ X1061 @ X1062)=>((in @ X1063 @ X1061)=>(in @ X1063 @ X1062))))=>(![X1064:$i, X1065:$i, X1066:$i]:(((subset @ X1064 @ X1065)=>(~(in @ X1066 @ X1065)=>~(in @ X1066 @ X1064))))=>(![X1067:$i, X1068:$i, X1069:$i]:(((in @ X1069 @ X1067)=>(~(in @ X1069 @ X1068)=>~(subset @ X1067 @ X1068))))=>(![X1070:$i, X1071:$i]:((~(subset @ X1070 @ X1071)=>((X1070)!=(X1071))))=>(![X1072:$i, X1073:$i, X1074:$i]:(((in @ X1074 @ X1072)=>(~(in @ X1074 @ X1073)=>((X1072)!=(X1073)))))=>(![X1075:$i]:((subset @ X1075 @ X1075))=>(![X1076:$i, X1077:$i, X1078:$i]:(((subset @ X1076 @ X1077)=>((subset @ X1077 @ X1078)=>(subset @ X1076 @ X1078))))=>(![X1079:$i, X1080:$i]:((subset @ X1080 @ (setadjoin @ X1079 @ X1080)))=>(![X1081:$i, X1082:$i, X1083:$i]:(((subset @ X1081 @ X1083)=>(subset @ X1081 @ (setadjoin @ X1082 @ X1083))))=>(![X1084:$i, X1085:$i]:(((subset @ X1084 @ X1085)=>(in @ X1084 @ (powerset @ X1085))))=>(![X1086:$i, X1087:$i]:(((subset @ X1086 @ X1087)=>((subset @ X1087 @ X1086)=>((X1086)=(X1087)))))=>(![X1088:$i]:(((subset @ X1088 @ emptyset)=>((X1088)=(emptyset))))=>(![X1089:$i, X1090:$i]:(((subset @ X1090 @ X1089)=>(in @ X1090 @ (powerset @ X1089))))=>(![X1091:$i, X1092:$i]:(((in @ X1092 @ (powerset @ X1091))=>(subset @ X1092 @ X1091)))=>(![X1093:$i]:((in @ X1093 @ (powerset @ X1093)))=>(![X1094:$i, X1095:$i]:(((subset @ X1094 @ X1095)=>(subset @ (powerset @ X1094) @ (powerset @ X1095))))=>(![X1096:$i, X1097:$i > $o]:((in @ (dsetconstr @ X1096 @ X1097) @ (powerset @ X1096)))=>(![X1098:$i, X1099:$i > $o]:((subset @ (dsetconstr @ X1098 @ X1099) @ X1098))=>(![X1100:$i, X1101:$i, X1102:$i]:(((in @ X1102 @ X1100)=>(in @ X1102 @ (binunion @ X1100 @ X1101))))=>(![X1103:$i, X1104:$i]:((in @ X1104 @ (setadjoin @ X1103 @ (setadjoin @ X1104 @ emptyset))))=>(![X1105:$i, X1106:$i, X1107:$i]:(((in @ X1107 @ X1106)=>(in @ X1107 @ (binunion @ X1105 @ X1106))))=>(![X1108:$i, X1109:$i, X1110:$i, X1111:$o]:(((in @ X1110 @ (binunion @ X1108 @ X1109))=>(((in @ X1110 @ X1108)=>(X1111))=>(((in @ X1110 @ X1109)=>(X1111))=>(X1111)))))=>(![X1112:$i, X1113:$i, X1114:$i]:(((in @ X1114 @ (binunion @ X1112 @ X1113))=>((in @ X1114 @ X1112)|(in @ X1114 @ X1113))))=>(![X1115:$i, X1116:$i]:((subset @ X1115 @ (binunion @ X1115 @ X1116)))=>(![X1117:$i, X1118:$i]:((subset @ X1118 @ (binunion @ X1117 @ X1118)))=>(![X1119:$i, X1120:$i, X1121:$i]:(((in @ X1121 @ X1119)=>((in @ X1121 @ X1120)=>(in @ X1121 @ (binintersect @ X1119 @ X1120)))))=>(![X1122:$i, X1123:$i, X1124:$i]:(((subset @ X1124 @ X1122)=>((subset @ X1124 @ X1123)=>(subset @ X1124 @ (binintersect @ X1122 @ X1123)))))=>(![X1125:$i, X1126:$i, X1127:$i]:(((in @ X1127 @ (binintersect @ X1125 @ X1126))=>(in @ X1127 @ X1125)))=>(![X1128:$i, X1129:$i]:((subset @ (binintersect @ X1128 @ X1129) @ X1128))=>(![X1130:$i, X1131:$i]:(((subset @ X1130 @ X1131)=>((binintersect @ X1130 @ X1131)=(X1130))))=>(![X1132:$i, X1133:$i]:((((binintersect @ X1132 @ X1133)=(X1133))=>(subset @ X1133 @ X1132)))=>(![X1134:$i, X1135:$i, X1136:$i]:(((in @ X1136 @ (binintersect @ X1134 @ X1135))=>(in @ X1136 @ X1135)))=>(![X1137:$i, X1138:$i]:((~(?[X1139:$i]:(((in @ X1139 @ X1137)&(in @ X1139 @ X1138))))=>((binintersect @ X1137 @ X1138)=(emptyset))))=>(![X1140:$i, X1141:$i]:((subset @ (binintersect @ X1140 @ X1141) @ X1141))=>(![X1142:$i, X1143:$i]:(((subset @ X1143 @ X1142)=>((binintersect @ X1142 @ X1143)=(X1143))))=>(![X1144:$i, X1145:$i]:((((binintersect @ X1144 @ X1145)=(X1144))=>(subset @ X1144 @ X1145)))=>(![X1146:$i, X1147:$i, X1148:$i]:(((binintersect @ X1146 @ (binunion @ X1147 @ X1148))=(binunion @ (binintersect @ X1146 @ X1147) @ (binintersect @ X1146 @ X1148))))=>(![X1149:$i, X1150:$i, X1151:$i]:(((in @ X1151 @ X1149)=>(~(in @ X1151 @ X1150)=>(in @ X1151 @ (setminus @ X1149 @ X1150)))))=>(![X1152:$i, X1153:$i, X1154:$i]:(((in @ X1154 @ (setminus @ X1152 @ X1153))=>(in @ X1154 @ X1152)))=>(![X1155:$i, X1156:$i, X1157:$i]:(((in @ X1157 @ (setminus @ X1155 @ X1156))=>~(in @ X1157 @ X1156)))=>(![X1158:$i, X1159:$i]:(((subset @ X1158 @ X1159)=>((setminus @ X1158 @ X1159)=(emptyset))))=>(![X1160:$i, X1161:$i, X1162:$i]:((~(in @ X1162 @ (setminus @ X1160 @ X1161))=>((in @ X1162 @ X1160)=>(in @ X1162 @ X1161))))=>(![X1163:$i, X1164:$i, X1165:$i]:((~(in @ X1165 @ (setminus @ X1163 @ X1164))=>(~(in @ X1165 @ X1164)=>~(in @ X1165 @ X1163))))=>(![X1166:$i, X1167:$i, X1168:$i]:((~(in @ X1168 @ X1166)=>~(in @ X1168 @ (setminus @ X1166 @ X1167))))=>(![X1169:$i, X1170:$i, X1171:$i]:(((in @ X1171 @ X1170)=>~(in @ X1171 @ (setminus @ X1169 @ X1170))))=>(![X1172:$i, X1173:$i]:((subset @ (setminus @ X1172 @ X1173) @ X1172))=>(![X1174:$i, X1175:$i]:((((setminus @ X1174 @ X1175)=(emptyset))=>(subset @ X1174 @ X1175)))=>(![X1176:$i, X1177:$i, X1178:$i]:(((in @ X1178 @ (symdiff @ X1176 @ X1177))=>![X1179:$o]:((((in 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X1622))=>((subset @ X1623 @ (setminus @ X1622 @ X1624))=>(subset @ X1624 @ (setminus @ X1622 @ X1623)))))))=>![X4:$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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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)],[c_0_254, ap2apEq2]), ap2apEq1]), c_0_255]), c_0_256]), c_0_257]), c_0_258]), c_0_259]), c_0_260]), c_0_261]), c_0_262]), notdallE]), c_0_263]), notdexE]), c_0_264]), prop2setI]), ifp]), quantDeMorgan4]), theeq]), quantDeMorgan3]), iftrue]), quantDeMorgan2]), iffalse]), vacuousDall]), iftrueorfalse]), quantDeMorgan1]), binintersectT_lem]), c_0_265]), binunionT_lem]), powersetT_lem]), setminusT_lem]), complementT_lem]), setextT]), subsetTI]), powersetTI1]), powersetTE1]), complementTI1]), complementTE1]), binintersectTELcontra]), binintersectTERcontra]), contrasubsetT]), emptyset__Cong]), contrasubsetT1]), c_0_266]), contrasubsetT2]), c_0_267]), contrasubsetT3]), in__Cong]), doubleComplementI1]), inCongP]), doubleComplementE1]), c_0_268]), doubleComplementSub1]), c_0_269]), doubleComplementSub2]), setadjoin__Cong]), doubleComplementEq]), complementTnotintersectT]), complementImpComplementIntersect]), complementSubsetComplementIntersect]), complementInPowersetComplementIntersect]), contraSubsetComplement]), complementTcontraSubset]), subsetI1]), c_0_270]), c_0_271]), c_0_272]), omega__Cong]), setunion__Cong]), powerset__Cong]), eqimpsubset2]), notequalI1]), notsubsetI]), subsetE2]), subsetE]), emptysetsubset]), subsetI2]), eqimpsubset1]), notequalI2]), subsetemptysetimpeq]), setextsub]), subset2powerset]), setadjoinSub2]), setadjoinSub]), subsetTrans]), subsetRefl]), powersetI1]), upairset2IR]), binunionIL]), c_0_273]), c_0_274]), powersetsubset]), inPowerset]), powersetE1]), binunionIR]), binintersectEL]), binintersectSubset5]), binintersectI]), binunionRsub]), binunionLsub]), binunionE]), binunionEcases]), binintersectLsub]), binintersectSubset1]), binintersectSubset4]), binintersectRsub]), disjointsetsI1]), binintersectER]), binintersectSubset3]), binintersectSubset2]), bs114d]), setminusILneg]), setminusELneg]), setminusERneg]), setminusSubset2]), setminusER]), setminusEL]), setminusI]), setminusIRneg]), symdiffIneg2]), symdiffIneg1]), symdiffI2]), symdiffI1]), symdiffE]), setminusSubset1]), setminusLsub]), secondinupair]), singletoninpowunion]), singletoninpowerset]), singletonsubset]), kpairp]), kpairiskpair]), setukpairIR]), setukpairIL]), upairset2E]), cartprodmempair1]), cartprodpairin]), ubforcartprodlem3]), ubforcartprodlem2]), ubforcartprodlem1]), upairinpowunion]), upairsubunion]), cartprodmempair]), c_0_275]), c_0_276]), c_0_277]), setunionsingleton]), setunionsingleton2]), setunionsingleton1]), setunionE2]), c_0_278]), setukpairinjL2]), cartprodfstin]), kfstpairEq]), theprop]), c_0_279]), setukpairinjL1]), singletonsuniq]), setukpairinjL]), c_0_280]), setukpairinjR]), setukpairinjR2]), upairequniteq]), setukpairinjR1]), setukpairinjR12]), setukpairinjR11]), ksndpairEq]), cartprodsndpairEq]), cartprodfstpairEq]), cartprodmempaircEq]), cartprodpairmemER]), cartprodpairmemEL]), cartprodsndin]), kpairsurjEq]), cartprodpairsurjEq]), c_0_281]), c_0_282]), c_0_283]), c_0_284]), c_0_285]), c_0_286]), c_0_287]), c_0_288]), c_0_289]), c_0_290]), funcinfuncset]), ap2p]), infuncsetfunc]), app]), c_0_291]), c_0_292]), funcextLem]), funcGraphProp2]), funcGraphProp3]), funcGraphProp1]), c_0_293]), brelnall2]), brelnall1]), subbreln]), eqbreln]), funcext]), funcext2]), funcGraphProp4]), c_0_294]), upairsetIR]), upairsetIL]), upairsetE]), singletonsswitch]), eqinunit]), notinsingleton]), uniqinunit]), nonemptyImpWitness]), c_0_295]), subPowSU]), setunionE]), setunionI]), powersetE]), emptyInPowerset]), emptyinPowerset]), powersetI]), c_0_296]), setadjoinOr]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), nonemptyI1]), c_0_297]), nonemptyE1]), c_0_298]), noeltsimpempty]), emptyI]), setext]), c_0_299]), notinemptyset]), emptysetimpfalse]), emptysetE]), prop2setE]), c_0_300]), c_0_301]), c_0_302]), c_0_303]), c_0_304]), wellorderingAx]), foundationAx]), c_0_305]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_306])).
% 0.75/0.43 thf(c_0_308, negated_conjecture, ![X1625:$i, X1626:$i, X1628:$i, X1629:$i, X1630:$i, X1631:$i, X1632:$i, X1633:$i, X1634:$i, X1635:$i, X1636:$i, X1638:$i, X1639:$i, X1641:$i, X1642:$i, X1643:$i, X1644:$i, X1645:$i, X1647:$i, X1648:$i > $i > $o, X1649:$i, X1652:$i, X1654:$i, X1655:$i, X1656:$i, X1657:$i, X1659:$i, X1660:$i > $o, X1661:$i, X1662:$i > $o, X1663:$i, X1664:$i, X1665:$i > $o, X1666:$i, X1667:$i, X1668:$i > $o, X1669:$i, X1670:$i > $o, X1672:$i, X1673:$o, X1674:$i, X1675:$i, X1676:$o, X1677:$i, X1678:$i, X1679:$i > $o, X1681:$i, X1682:$i, X1685:$i, X1687:$i, X1689:$i, X1690:$i > $o, X1691:$i, X1692:$i, X1694:$i, X1695:$i > $o, X1696:$i, X1697:$i, X1698:$i, X1699:$i, X1700:$i, X1701:$i, X1702:$i, X1703:$i, X1704:$i, X1705:$i, X1706:$i, X1707:$o, X1708:$i, X1709:$i, X1710:$i, X1711:$i, X1712:$i, X1713:$i, X1715:$i, X1716:$i, X1717:$i, X1718:$i, X1719:$i, X1720:$i, X1721:$i, X1722:$i, X1723:$i, X1724:$i, X1725:$o, X1727:$i, X1728:$i, X1729:$i > $o, X1731:$i, X1732:$i, X1733:$i, X1735:$i, X1736:$i, X1737:$i, X1738:$i, X1739:$i, X1740:$i, X1741:$i, X1742:$i, X1743:$i, X1744:$i, X1745:$i, X1746:$i, X1747:$i, X1748:$i, X1749:$i, X1750:$i, X1751:$i > $o, X1752:$i, X1753:$i > $o, X1754:$i, X1755:$i, X1756:$i > $o, X1757:$i, X1759:$i, X1760:$i > $o, X1762:$i, X1763:$i, X1764:$i > $o, X1766:$i, X1767:$i, X1768:$i > $o, X1769:$i, X1771:$o, X1772:$i, X1773:$i > $o, X1775:$i, X1776:$i, X1777:$i > $o, X1778:$i, X1780:$i > $o, X1781:$i, X1783:$i > $o, X1784:$i, X1787:$i > $o, X1788:$i, X1790:$i, X1791:$i, X1792:$i, X1793:$i, X1794:$i, X1795:$i, X1796:$i, X1797:$i, X1798:$i > $o, X1799:$i, X1800:$i, X1801:$i > $o, X1802:$i > $o, X1805:$i, X1806:$i, X1807:$i, X1808:$i, X1809:$i, X1810:$i, X1811:$i, X1812:$i, X1813:$i > $o, X1814:$i, X1815:$i, X1816:$i > $o, X1817:$i > $o, X1820:$i, X1821:$i, X1822:$i > $o, X1823:$i > $o, X1826:$i, X1827:$i, X1829:$i, X1830:$i, X1831:$i, X1832:$i, X1833:$i, X1834:$i, X1836:$i, X1837:$i, X1838:$i, X1839:$i, X1840:$i, X1841:$i, X1842:$i, X1843:$i, X1844:$i, X1845:$i, X1846:$i, X1847:$i, X1848:$i, X1849:$i, X1850:$i, X1851:$i, X1852:$i, X1853:$i, X1854:$i, X1855:$i, X1856:$i, X1857:$i, X1858:$i, X1859:$i, X1860:$i, X1861:$i, X1862:$i, X1863:$i, X1864:$i, X1865:$i, X1866:$i, X1867:$i, X1868:$i, X1869:$i, X1870:$i, X1871:$i, X1872:$i, X1873:$i > $o, X1874:$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:$i, X1894:$i, X1895:$i, X1896:$i, X1897:$i, X1898:$i, X1899:$i, X1900:$i, X1901:$i, X1902:$i, X1903:$i, X1904:$i, X1905:$i, X1906:$i, X1907:$i, X1908:$i, X1909:$i, X1910:$i, X1911:$i, X1912:$i, X1913:$i, X1914:$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, X1932:$i, X1933:$i, X1934:$i, X1935:$i, X1936:$i, X1937:$i, X1938:$i, X1939:$i, X1940:$i, X1941:$i, X1942:$i, X1943:$i, X1944:$i, X1945:$i, X1946:$i, X1947:$i, X1948:$i, X1949:$i, X1950:$i, X1951:$i, X1952:$i, X1953:$i, X1954:$i, X1955:$o, X1956:$i, X1957:$i, X1958:$i, X1959:$i, X1960:$i, X1961:$i, X1962:$i, X1963:$i, X1964:$i, X1965:$i, X1966:$i, X1967:$i, X1968:$i, X1969:$i, X1970:$i, X1971:$i, X1972:$i, X1973:$i, X1974:$i, X1975:$i, X1976:$i, X1977:$i, X1978:$i, X1979:$i, X1980:$i, X1981:$i, X1982:$i, X1983:$i, X1984:$i, X1985:$i, X1986:$i, X1987:$i, X1988:$i, X1989:$i, X1990:$i, X1991:$i, X1992:$i, X1993:$i, X1994:$i, X1995:$i, X1996:$i, X1997:$i, X1998:$i, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$i, X2004:$i, X2005:$i, X2006:$i, X2007:$i, X2008:$i, X2009:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$i, X2021:$i, X2023:$i, X2024:$i, X2025:$i, X2026:$i, X2027:$i > $o, X2030:$i, X2031:$i, X2032:$i > $o, X2034:$i, X2035:$i > $o, X2036:$i, X2038:$i, X2039:$i > $o, X2042:$i, X2043:$i, X2044:$i, X2045:$i, X2046:$i, X2047:$i, X2048:$i, X2049:$i, X2050:$i, X2051:$i, X2052:$i, X2053:$i, X2054:$i, X2055:$i, X2056:$i, X2057:$i, X2058:$i, X2059:$i, X2060:$i, X2061:$i, X2062:$i, X2063:$i, X2064:$i, X2065:$i, X2066:$i, X2067:$i, X2068:$i, X2069:$i, X2070:$i, X2071:$i, X2072:$i, X2073:$i, X2074:$i, X2075:$i, X2076:$i, X2077:$i, X2078:$i, X2079:$i, X2080:$i, X2081:$i, X2082:$i, X2083:$i, X2084:$i, X2085:$i, X2086:$i, X2087:$i, X2088:$i, X2089:$i, X2090:$i, X2091:$i, X2092:$i, X2093:$i, X2094:$i, X2095:$i, X2096:$i, X2097:$i, X2098:$i, X2099:$i, X2100:$i, X2101:$i, X2102:$i, X2103:$i, X2104:$i, X2105:$i, X2106:$i, X2107:$i, X2108:$i, X2109:$i, X2110:$i, X2111:$i, X2112:$i, X2113:$i, X2114:$i > $i > $o, X2115:$i, X2116:$i, X2117:$i, X2118:$i, X2119:$i > $i > $o, X2120:$i, X2121:$i, X2122:$i > $i > $o, X2123:$i, X2124:$i, X2125:$i > $i > $o, X2126:$i, X2127:$i, X2128:$i, X2129:$i, X2130:$i > $i > $o, X2131:$i, X2132:$i, X2133:$i, X2134:$i, X2135:$i > $i > $o, X2136:$i, X2137:$i, X2138:$i, X2139:$i, X2140:$i > $i > $o, X2141:$i, X2142:$i, X2143:$i, X2144:$i, X2145:$i, X2146:$i, X2147:$i, X2148:$i, X2149:$i, X2150:$i, X2151:$i, X2152:$i, X2153:$i, X2154:$i, X2155:$i, X2156:$i, X2157:$i, X2158:$i, X2159:$i, X2160:$i, X2161:$i, X2162:$i, X2163:$i, X2164:$i, X2165:$i, X2166:$i, X2167:$i > $i, X2169:$i, X2170:$i, X2171:$i > $i, X2173:$i, X2174:$i, X2175:$i > $i, X2177:$i, X2178:$i, X2179:$i, X2180:$i > $o, X2183:$i, X2184:$i, X2185:$i, X2186:$i, X2187:$i > $o, X2190:$i, X2191:$i, X2192:$i > $o, X2193:$i, X2194:$i, X2195:$i, X2196:$i, X2197:$i, X2198:$i, X2199:$i, X2200:$i, X2201:$i, X2202:$i, X2203:$i, X2204:$i, X2205:$i, X2206:$i, X2207:$i, X2208:$i, X2209:$i, X2210:$i, X2211:$i, X2213:$i, X2214:$i, X2215:$i, X2216:$i, X2217:$i, X2218:$i, X2219:$i, X2220:$i, X2221:$i, X2222:$i, X2223:$i, X2226:$i, X2227:$i, X2228:$i, X2229:$i, X2234:$i, X2235:$i, X2236:$i, X2237:$i, X2239:$i, X2240:$i, X2241:$i, X2242:$i, X2244:$i, X2245:$i, X2246:$i, X2247:$i, X2248:$i, X2249:$i, X2250:$i, X2251:$i, X2252:$i, X2253:$i, X2254:$i > $i, X2256:$i, X2257:$i, X2258:$i, X2259:$i, X2260:$i, X2261:$i, X2262:$i > $i, X2264:$i, X2265:$i, X2266:$i > $i, X2268:$i, X2269:$i, X2270:$i, X2271:$i, X2272:$i, X2273:$o, X2274:$i, X2275:$i, X2276:$i, X2277:$o, X2278:$i, X2279:$i, X2280:$i, X2281:$o, X2282:$i, X2283:$i, X2284:$i, X2285:$o, X2286:$i, X2287:$i, X2288:$i, X2289:$o, X2290:$i, X2291:$i, X2292:$i, X2293:$o, X2294:$i, X2295:$i, X2296:$i, X2297:$i, X2298:$i, X2299:$o, X2300:$i, X2301:$i, X2302:$i, X2303:$o, X2304:$i, X2305:$i, X2306:$i, X2307:$o, X2308:$i, X2309:$i, X2310:$i, X2311:$i, X2312:$i, X2313:$i, X2314:$i, X2315:$i, X2316:$i, X2317:$i, X2318:$i, X2319:$i, X2320:$i, X2321:$i, X2322:$i, X2323:$i, X2324:$i, X2325:$i, X2328:$i, X2329:$i, X2330:$i, X2332:$i, X2333:$i, X2334:$i, X2336:$i, X2337:$i, X2338:$i, X2339:$i, X2340:$i, X2341:$i, X2342:$i, X2343:$i, X2344:$i, X2345:$i, X2346:$i, X2347:$i, X2348:$i, X2349:$i, X2350:$i, X2351:$i, X2352:$i, X2353:$i, X2354:$i, X2355:$i, X2356:$i, X2357:$i, X2358:$i, 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(powerset @ X2328)))&(~(in @ (esk69_3 @ X2328 @ X2329 @ X2330) @ X2330)|(subset @ X2329 @ X2330)|~(in @ X2330 @ (powerset @ X2328))|~(in @ X2329 @ (powerset @ X2328)))))&((((in @ (esk70_3 @ X2332 @ X2333 @ X2334) @ X2332)|(in @ X2333 @ (powerset @ X2334))|~(in @ X2334 @ (powerset @ X2332))|~(in @ X2333 @ (powerset @ X2332)))&(((in @ (esk70_3 @ X2332 @ X2333 @ X2334) @ X2333)|(in @ X2333 @ (powerset @ X2334))|~(in @ X2334 @ (powerset @ X2332))|~(in @ X2333 @ (powerset @ X2332)))&(~(in @ (esk70_3 @ X2332 @ X2333 @ X2334) @ X2334)|(in @ X2333 @ (powerset @ X2334))|~(in @ X2334 @ (powerset @ X2332))|~(in @ X2333 @ (powerset @ X2332)))))&((~(in @ X2337 @ (powerset @ X2336))|(~(in @ X2338 @ (powerset @ X2336))|(~(in @ X2339 @ X2336)|(~(in @ X2337 @ (powerset @ X2338))|(~(in @ X2339 @ X2337)|(in @ X2339 @ X2338))))))&((~(in @ X2341 @ (powerset @ X2340))|(~(in @ X2342 @ X2340)|(~(in @ X2342 @ X2341)|~(in @ X2342 @ (setminus @ X2340 @ X2341)))))&((~(in @ X2344 @ (powerset @ X2343))|(~(in @ X2345 @ X2343)|((in @ X2345 @ (setminus @ X2343 @ X2344))|(in @ X2345 @ X2344))))&((~(in @ X2347 @ (powerset @ X2346))|(~(in @ X2348 @ (powerset @ X2346))|(~(in @ X2349 @ X2346)|((in @ X2349 @ X2347)|~(in @ X2349 @ (binintersect @ X2347 @ X2348))))))&((~(in @ X2351 @ (powerset @ X2350))|(~(in @ X2352 @ (powerset @ X2350))|(~(in @ X2353 @ X2350)|((in @ X2353 @ X2352)|~(in @ X2353 @ (binintersect @ X2351 @ X2352))))))&((~(in @ X2355 @ (powerset @ X2354))|(~(in @ X2356 @ (powerset @ X2354))|(~(in @ X2357 @ X2354)|(~(subset @ X2355 @ (setminus @ X2354 @ X2356))|(~(in @ X2357 @ X2356)|~(in @ X2357 @ X2355))))))&((~(in @ X2359 @ (powerset @ X2358))|(~(in @ X2360 @ (powerset @ X2358))|(~(in @ X2361 @ X2358)|(~(subset @ X2359 @ X2360)|((in @ X2361 @ X2360)|~(in @ X2361 @ X2359))))))&((~(in @ X2363 @ (powerset @ X2362))|(~(in @ X2364 @ (powerset @ X2362))|(~(subset @ X2363 @ X2364)|(subset @ (setminus @ X2362 @ X2364) @ (setminus @ X2362 @ X2363)))))&((~(in @ X2366 @ (powerset @ X2365))|(~(in @ X2367 @ (powerset @ X2365))|(~(subset @ (setminus @ X2365 @ X2367) @ (setminus @ X2365 @ X2366))|(subset @ X2366 @ X2367))))&((~(in @ X2369 @ (powerset @ X2368))|(~(in @ X2370 @ X2368)|(~(in @ X2370 @ X2369)|(in @ X2370 @ (setminus @ X2368 @ (setminus @ X2368 @ X2369))))))&((~(in @ X2372 @ (powerset @ X2371))|(~(in @ X2373 @ X2371)|(~(in @ X2373 @ (setminus @ X2371 @ (setminus @ X2371 @ X2372)))|(in @ X2373 @ X2372))))&((~(in @ X2375 @ (powerset @ X2374))|(subset @ X2375 @ (setminus @ X2374 @ (setminus @ X2374 @ X2375))))&((~(in @ X2377 @ (powerset @ X2376))|(subset @ (setminus @ X2376 @ (setminus @ X2376 @ X2377)) @ X2377))&((~(in @ X2379 @ (powerset @ X2378))|((X2379)=(setminus @ X2378 @ (setminus @ X2378 @ X2379))))&((~(in @ X2381 @ (powerset @ X2380))|(~(in @ X2382 @ (powerset @ X2380))|(~(in @ X2383 @ X2380)|(~(in @ X2383 @ (setminus @ X2380 @ X2381))|~(in @ X2383 @ (binintersect @ X2381 @ X2382))))))&((~(in @ X2385 @ (powerset @ X2384))|(~(in @ X2386 @ (powerset @ X2384))|(~(in @ X2387 @ X2384)|(~(in @ X2387 @ (setminus @ X2384 @ X2385))|(in @ X2387 @ (setminus @ X2384 @ (binintersect @ X2385 @ X2386)))))))&((~(in @ X2389 @ (powerset @ X2388))|(~(in @ X2390 @ (powerset @ X2388))|(subset @ (setminus @ X2388 @ X2389) @ (setminus @ X2388 @ (binintersect @ X2389 @ X2390)))))&((~(in @ X2392 @ (powerset @ X2391))|(~(in @ X2393 @ (powerset @ X2391))|(in @ (setminus @ X2391 @ X2392) @ (powerset @ (setminus @ X2391 @ (binintersect @ X2392 @ X2393))))))&((~(in @ X2395 @ (powerset @ X2394))|(~(in @ X2396 @ (powerset @ X2394))|(~(subset @ X2395 @ (setminus @ X2394 @ X2396))|(~(in @ X2397 @ X2394)|(~(in @ X2397 @ X2396)|(in @ X2397 @ (setminus @ X2394 @ X2395)))))))&((~(in @ X2399 @ (powerset @ X2398))|(~(in @ X2400 @ (powerset @ X2398))|(~(subset @ X2399 @ (setminus @ X2398 @ X2400))|(subset @ X2400 @ (setminus @ X2398 @ X2399)))))&((in @ esk72_0 @ (powerset @ esk71_0))&((in @ esk73_0 @ (powerset @ esk71_0))&((in @ esk74_0 @ esk71_0)&(~(in @ esk74_0 @ (binunion @ esk72_0 @ esk73_0))&(in @ esk74_0 @ esk72_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_307])])])])])])])).
% 0.75/0.43 thf(c_0_309, negated_conjecture, ~((in @ esk74_0 @ (binunion @ esk72_0 @ esk73_0))), inference(split_conjunct,[status(thm)],[c_0_308])).
% 0.75/0.43 thf(c_0_310, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (binunion @ X3 @ X4))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_308])).
% 0.75/0.43 thf(c_0_311, negated_conjecture, (in @ esk74_0 @ esk72_0), inference(split_conjunct,[status(thm)],[c_0_308])).
% 0.75/0.43 thf(c_0_312, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_309, c_0_310]), c_0_311])]), ['proof']).
% 0.75/0.43 % SZS output end CNFRefutation
% 0.75/0.43 % Parsed axioms : 551
% 0.75/0.43 % Removed by relevancy pruning/SinE : 297
% 0.75/0.43 % Initial clauses : 416
% 0.75/0.43 % Removed in clause preprocessing : 34
% 0.75/0.43 % Initial clauses in saturation : 382
% 0.75/0.43 % Processed clauses : 410
% 0.75/0.43 % ...of these trivial : 31
% 0.75/0.43 % ...subsumed : 163
% 0.75/0.43 % ...remaining for further processing : 216
% 0.75/0.43 % Other redundant clauses eliminated : 24
% 0.75/0.43 % Clauses deleted for lack of memory : 0
% 0.75/0.43 % Backward-subsumed : 1
% 0.75/0.43 % Backward-rewritten : 6
% 0.75/0.43 % Generated clauses : 1092
% 0.75/0.43 % ...of the previous two non-redundant : 888
% 0.75/0.43 % ...aggressively subsumed : 0
% 0.75/0.43 % Contextual simplify-reflections : 0
% 0.75/0.43 % Paramodulations : 1064
% 0.75/0.43 % Factorizations : 0
% 0.75/0.43 % NegExts : 0
% 0.75/0.43 % Equation resolutions : 27
% 0.75/0.43 % Disequality decompositions : 0
% 0.75/0.43 % Total rewrite steps : 209
% 0.75/0.43 % ...of those cached : 143
% 0.75/0.43 % Propositional unsat checks : 0
% 0.75/0.43 % Propositional check models : 0
% 0.75/0.43 % Propositional check unsatisfiable : 0
% 0.75/0.43 % Propositional clauses : 0
% 0.75/0.43 % Propositional clauses after purity: 0
% 0.75/0.43 % Propositional unsat core size : 0
% 0.75/0.43 % Propositional preprocessing time : 0.000
% 0.75/0.43 % Propositional encoding time : 0.000
% 0.75/0.43 % Propositional solver time : 0.000
% 0.75/0.43 % Success case prop preproc time : 0.000
% 0.75/0.43 % Success case prop encoding time : 0.000
% 0.75/0.43 % Success case prop solver time : 0.000
% 0.75/0.43 % Current number of processed clauses : 201
% 0.75/0.43 % Positive orientable unit clauses : 66
% 0.75/0.43 % Positive unorientable unit clauses: 0
% 0.75/0.43 % Negative unit clauses : 4
% 0.75/0.43 % Non-unit-clauses : 131
% 0.75/0.43 % Current number of unprocessed clauses: 813
% 0.75/0.43 % ...number of literals in the above : 2219
% 0.75/0.43 % Current number of archived formulas : 0
% 0.75/0.43 % Current number of archived clauses : 7
% 0.75/0.43 % Clause-clause subsumption calls (NU) : 3710
% 0.75/0.43 % Rec. Clause-clause subsumption calls : 3239
% 0.75/0.43 % Non-unit clause-clause subsumptions : 154
% 0.75/0.43 % Unit Clause-clause subsumption calls : 191
% 0.75/0.43 % Rewrite failures with RHS unbound : 0
% 0.75/0.43 % BW rewrite match attempts : 14
% 0.75/0.43 % BW rewrite match successes : 6
% 0.75/0.43 % Condensation attempts : 0
% 0.75/0.43 % Condensation successes : 0
% 0.75/0.43 % Termbank termtop insertions : 73313
% 0.75/0.43 % Search garbage collected termcells : 25160
% 0.75/0.43
% 0.75/0.43 % -------------------------------------------------
% 0.75/0.43 % User time : 0.088 s
% 0.75/0.43 % System time : 0.011 s
% 0.75/0.43 % Total time : 0.099 s
% 0.75/0.43 % Maximum resident set size: 10132 pages
% 0.75/0.43
% 0.75/0.43 % -------------------------------------------------
% 0.75/0.43 % User time : 0.104 s
% 0.75/0.43 % System time : 0.017 s
% 0.75/0.43 % Total time : 0.121 s
% 0.75/0.43 % Maximum resident set size: 5376 pages
% 0.75/0.43 % E exiting
%------------------------------------------------------------------------------