%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU745^1 : 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 : n010.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 08:25:27 AM UTC 2026
% Result : Theorem 0.75s 0.50s
% Output : CNFRefutation 1.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU745^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.18 % Computer : n010.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Tue Sep 29 14:20:33 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.23 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.RcafZaxWN3/E---3.1_2929893.p
% 0.75/0.50 % Version: 3.5.1-ho
% 0.75/0.50 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.75/0.50 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.75/0.50 % Starting ehoh_best5 with 300s (1) cores
% 0.75/0.50 % Starting almost_fo_3_lam with 300s (1) cores
% 0.75/0.50 % Starting new_bool_5 with 300s (1) cores
% 0.75/0.50 % Starting pre_casc_3 with 300s (1) cores
% 0.75/0.50 % Starting ho_unfolding_8 with 300s (1) cores
% 0.75/0.50 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.75/0.50 % Starting new_bool_3 with 300s (1) cores
% 0.75/0.50 % Starting new_ho_5 with 300s (1) cores
% 0.75/0.50 % pre_casc_3 with pid 2929944 completed with status 9
% 0.75/0.50 % new_bool_5 with pid 2929943 completed with status 0
% 0.75/0.50 % Result found by new_bool_5
% 0.75/0.50 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.75/0.50 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.75/0.50 % Starting ehoh_best5 with 300s (1) cores
% 0.75/0.50 % Starting almost_fo_3_lam with 300s (1) cores
% 0.75/0.50 % Starting new_bool_5 with 300s (1) cores
% 0.75/0.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 0.75/0.50 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 0.75/0.50 % Search class: HGHSM-FSLM32-MHFMMSBN
% 0.75/0.50 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.75/0.50 % Starting SubtermCWHack with 28s (1) cores
% 0.75/0.50 % SubtermCWHack with pid 2929975 completed with status 0
% 0.75/0.50 % Result found by SubtermCWHack
% 0.75/0.50 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.75/0.50 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.75/0.50 % Starting ehoh_best5 with 300s (1) cores
% 0.75/0.50 % Starting almost_fo_3_lam with 300s (1) cores
% 0.75/0.50 % Starting new_bool_5 with 300s (1) cores
% 0.75/0.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 0.75/0.50 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 0.75/0.50 % Search class: HGHSM-FSLM32-MHFMMSBN
% 0.75/0.50 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.75/0.50 % Starting SubtermCWHack with 28s (1) cores
% 0.75/0.50 % Preprocessing time : 0.007 s
% 0.75/0.50
% 0.75/0.50 % Proof found!
% 0.75/0.50 % SZS status Theorem
% 0.75/0.50 % SZS output start CNFRefutation
% 0.75/0.50 thf(decl_23, type, in: $i > $i > $o).
% 0.75/0.50 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.75/0.50 thf(decl_25, type, setextAx: $o).
% 0.75/0.50 thf(decl_26, type, emptyset: $i).
% 0.75/0.50 thf(decl_27, type, emptysetAx: $o).
% 0.75/0.50 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.75/0.50 thf(decl_29, type, setadjoinAx: $o).
% 0.75/0.50 thf(decl_30, type, powerset: $i > $i).
% 0.75/0.50 thf(decl_31, type, powersetAx: $o).
% 0.75/0.50 thf(decl_32, type, setunion: $i > $i).
% 0.75/0.50 thf(decl_33, type, setunionAx: $o).
% 0.75/0.50 thf(decl_34, type, omega: $i).
% 0.75/0.50 thf(decl_35, type, omega0Ax: $o).
% 0.75/0.50 thf(decl_36, type, omegaSAx: $o).
% 0.75/0.50 thf(decl_37, type, omegaIndAx: $o).
% 0.75/0.50 thf(decl_38, type, replAx: $o).
% 0.75/0.50 thf(decl_39, type, foundationAx: $o).
% 0.75/0.50 thf(decl_40, type, wellorderingAx: $o).
% 0.75/0.50 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.75/0.50 thf(decl_42, type, descrp: $o).
% 0.75/0.50 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.75/0.50 thf(decl_44, type, dsetconstrI: $o).
% 0.75/0.50 thf(decl_45, type, dsetconstrEL: $o).
% 0.75/0.50 thf(decl_46, type, dsetconstrER: $o).
% 0.75/0.50 thf(decl_47, type, exuE1: $o).
% 0.75/0.50 thf(decl_48, type, prop2set: $o > $i).
% 0.75/0.50 thf(decl_49, type, prop2setE: $o).
% 0.75/0.50 thf(decl_50, type, emptysetE: $o).
% 0.75/0.50 thf(decl_51, type, emptysetimpfalse: $o).
% 0.75/0.50 thf(decl_52, type, notinemptyset: $o).
% 0.75/0.50 thf(decl_53, type, exuE3e: $o).
% 0.75/0.50 thf(decl_54, type, setext: $o).
% 0.75/0.50 thf(decl_55, type, emptyI: $o).
% 0.75/0.50 thf(decl_56, type, noeltsimpempty: $o).
% 0.75/0.50 thf(decl_57, type, setbeta: $o).
% 0.75/0.50 thf(decl_58, type, nonempty: $i > $o).
% 0.75/0.50 thf(decl_59, type, nonemptyE1: $o).
% 0.75/0.50 thf(decl_60, type, nonemptyI: $o).
% 0.75/0.50 thf(decl_61, type, nonemptyI1: $o).
% 0.75/0.50 thf(decl_62, type, setadjoinIL: $o).
% 0.75/0.50 thf(decl_63, type, emptyinunitempty: $o).
% 0.75/0.50 thf(decl_64, type, setadjoinIR: $o).
% 0.75/0.50 thf(decl_65, type, setadjoinE: $o).
% 0.75/0.50 thf(decl_66, type, setadjoinOr: $o).
% 0.75/0.50 thf(decl_67, type, setoftrueEq: $o).
% 0.75/0.50 thf(decl_68, type, powersetI: $o).
% 0.75/0.50 thf(decl_69, type, emptyinPowerset: $o).
% 0.75/0.50 thf(decl_70, type, emptyInPowerset: $o).
% 0.75/0.50 thf(decl_71, type, powersetE: $o).
% 0.75/0.50 thf(decl_72, type, setunionI: $o).
% 0.75/0.50 thf(decl_73, type, setunionE: $o).
% 0.75/0.50 thf(decl_74, type, subPowSU: $o).
% 0.75/0.50 thf(decl_75, type, exuE2: $o).
% 0.75/0.50 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.75/0.50 thf(decl_77, type, uniqinunit: $o).
% 0.75/0.50 thf(decl_78, type, notinsingleton: $o).
% 0.75/0.50 thf(decl_79, type, eqinunit: $o).
% 0.75/0.50 thf(decl_80, type, singletonsswitch: $o).
% 0.75/0.50 thf(decl_81, type, upairsetE: $o).
% 0.75/0.50 thf(decl_82, type, upairsetIL: $o).
% 0.75/0.50 thf(decl_83, type, upairsetIR: $o).
% 0.75/0.50 thf(decl_84, type, emptyE1: $o).
% 0.75/0.50 thf(decl_85, type, vacuousDall: $o).
% 0.75/0.50 thf(decl_86, type, quantDeMorgan1: $o).
% 0.75/0.50 thf(decl_87, type, quantDeMorgan2: $o).
% 0.75/0.50 thf(decl_88, type, quantDeMorgan3: $o).
% 0.75/0.50 thf(decl_89, type, quantDeMorgan4: $o).
% 0.75/0.50 thf(decl_90, type, prop2setI: $o).
% 0.75/0.50 thf(decl_92, type, prop2set2propI: $o).
% 0.75/0.50 thf(decl_93, type, notdexE: $o).
% 0.75/0.50 thf(decl_94, type, notdallE: $o).
% 0.75/0.50 thf(decl_95, type, exuI1: $o).
% 0.75/0.50 thf(decl_96, type, exuI3: $o).
% 0.75/0.50 thf(decl_97, type, exuI2: $o).
% 0.75/0.50 thf(decl_98, type, inCongP: $o).
% 0.75/0.50 thf(decl_99, type, in__Cong: $o).
% 0.75/0.50 thf(decl_100, type, exuE3u: $o).
% 0.75/0.50 thf(decl_101, type, exu__Cong: $o).
% 0.75/0.50 thf(decl_102, type, emptyset__Cong: $o).
% 0.75/0.50 thf(decl_103, type, setadjoin__Cong: $o).
% 0.75/0.50 thf(decl_104, type, powerset__Cong: $o).
% 0.75/0.50 thf(decl_105, type, setunion__Cong: $o).
% 0.75/0.50 thf(decl_106, type, omega__Cong: $o).
% 0.75/0.50 thf(decl_107, type, exuEu: $o).
% 0.75/0.50 thf(decl_108, type, descr__Cong: $o).
% 0.75/0.50 thf(decl_109, type, dsetconstr__Cong: $o).
% 0.75/0.50 thf(decl_110, type, subset: $i > $i > $o).
% 0.75/0.50 thf(decl_113, type, subsetI1: $o).
% 0.75/0.50 thf(decl_114, type, eqimpsubset2: $o).
% 0.75/0.50 thf(decl_115, type, eqimpsubset1: $o).
% 0.75/0.50 thf(decl_116, type, subsetI2: $o).
% 0.75/0.50 thf(decl_117, type, emptysetsubset: $o).
% 0.75/0.50 thf(decl_118, type, subsetE: $o).
% 0.75/0.50 thf(decl_119, type, subsetE2: $o).
% 0.75/0.50 thf(decl_120, type, notsubsetI: $o).
% 0.75/0.50 thf(decl_121, type, notequalI1: $o).
% 0.75/0.50 thf(decl_122, type, notequalI2: $o).
% 0.75/0.50 thf(decl_123, type, subsetRefl: $o).
% 0.75/0.50 thf(decl_124, type, subsetTrans: $o).
% 0.75/0.50 thf(decl_125, type, setadjoinSub: $o).
% 0.75/0.50 thf(decl_126, type, setadjoinSub2: $o).
% 0.75/0.50 thf(decl_127, type, subset2powerset: $o).
% 0.75/0.50 thf(decl_128, type, setextsub: $o).
% 0.75/0.50 thf(decl_129, type, subsetemptysetimpeq: $o).
% 0.75/0.50 thf(decl_130, type, powersetI1: $o).
% 0.75/0.50 thf(decl_131, type, powersetE1: $o).
% 0.75/0.50 thf(decl_132, type, inPowerset: $o).
% 0.75/0.50 thf(decl_133, type, powersetsubset: $o).
% 0.75/0.50 thf(decl_134, type, sepInPowerset: $o).
% 0.75/0.50 thf(decl_135, type, sepSubset: $o).
% 0.75/0.50 thf(decl_136, type, binunion: $i > $i > $i).
% 0.75/0.50 thf(decl_137, type, binunionIL: $o).
% 0.75/0.50 thf(decl_138, type, upairset2IR: $o).
% 0.75/0.50 thf(decl_139, type, binunionIR: $o).
% 0.75/0.50 thf(decl_140, type, binunionEcases: $o).
% 0.75/0.50 thf(decl_141, type, binunionE: $o).
% 0.75/0.50 thf(decl_142, type, binunionLsub: $o).
% 0.75/0.50 thf(decl_143, type, binunionRsub: $o).
% 0.75/0.50 thf(decl_144, type, binintersect: $i > $i > $i).
% 0.75/0.50 thf(decl_145, type, binintersectI: $o).
% 0.75/0.50 thf(decl_146, type, binintersectSubset5: $o).
% 0.75/0.50 thf(decl_147, type, binintersectEL: $o).
% 0.75/0.50 thf(decl_148, type, binintersectLsub: $o).
% 0.75/0.50 thf(decl_149, type, binintersectSubset2: $o).
% 0.75/0.50 thf(decl_150, type, binintersectSubset3: $o).
% 0.75/0.50 thf(decl_151, type, binintersectER: $o).
% 0.75/0.50 thf(decl_152, type, disjointsetsI1: $o).
% 0.75/0.50 thf(decl_153, type, binintersectRsub: $o).
% 0.75/0.50 thf(decl_154, type, binintersectSubset4: $o).
% 0.75/0.50 thf(decl_155, type, binintersectSubset1: $o).
% 0.75/0.50 thf(decl_156, type, bs114d: $o).
% 0.75/0.50 thf(decl_158, type, setminus: $i > $i > $i).
% 0.75/0.50 thf(decl_159, type, setminusI: $o).
% 0.75/0.50 thf(decl_160, type, setminusEL: $o).
% 0.75/0.50 thf(decl_161, type, setminusER: $o).
% 0.75/0.50 thf(decl_162, type, setminusSubset2: $o).
% 0.75/0.50 thf(decl_163, type, setminusERneg: $o).
% 0.75/0.50 thf(decl_164, type, setminusELneg: $o).
% 0.75/0.50 thf(decl_165, type, setminusILneg: $o).
% 0.75/0.50 thf(decl_166, type, setminusIRneg: $o).
% 0.75/0.50 thf(decl_167, type, setminusLsub: $o).
% 0.75/0.50 thf(decl_168, type, setminusSubset1: $o).
% 0.75/0.50 thf(decl_169, type, symdiff: $i > $i > $i).
% 0.75/0.50 thf(decl_170, type, symdiffE: $o).
% 0.75/0.50 thf(decl_171, type, symdiffI1: $o).
% 0.75/0.50 thf(decl_172, type, symdiffI2: $o).
% 0.75/0.50 thf(decl_173, type, symdiffIneg1: $o).
% 0.75/0.50 thf(decl_174, type, symdiffIneg2: $o).
% 0.75/0.50 thf(decl_175, type, iskpair: $i > $o).
% 0.75/0.50 thf(decl_176, type, secondinupair: $o).
% 0.75/0.50 thf(decl_177, type, setukpairIL: $o).
% 0.75/0.50 thf(decl_178, type, setukpairIR: $o).
% 0.75/0.50 thf(decl_179, type, kpairiskpair: $o).
% 0.75/0.50 thf(decl_180, type, kpair: $i > $i > $i).
% 0.75/0.50 thf(decl_181, type, kpairp: $o).
% 0.75/0.50 thf(decl_182, type, cartprod: $i > $i > $i).
% 0.75/0.50 thf(decl_183, type, singletonsubset: $o).
% 0.75/0.50 thf(decl_184, type, singletoninpowerset: $o).
% 0.75/0.50 thf(decl_185, type, singletoninpowunion: $o).
% 0.75/0.50 thf(decl_186, type, upairset2E: $o).
% 0.75/0.50 thf(decl_187, type, upairsubunion: $o).
% 0.75/0.50 thf(decl_188, type, upairinpowunion: $o).
% 0.75/0.50 thf(decl_189, type, ubforcartprodlem1: $o).
% 0.75/0.50 thf(decl_190, type, ubforcartprodlem2: $o).
% 0.75/0.50 thf(decl_191, type, ubforcartprodlem3: $o).
% 0.75/0.50 thf(decl_192, type, cartprodpairin: $o).
% 0.75/0.50 thf(decl_193, type, cartprodmempair1: $o).
% 0.75/0.50 thf(decl_194, type, cartprodmempair: $o).
% 0.75/0.50 thf(decl_195, type, setunionE2: $o).
% 0.75/0.50 thf(decl_196, type, setunionsingleton1: $o).
% 0.75/0.50 thf(decl_197, type, setunionsingleton2: $o).
% 0.75/0.50 thf(decl_198, type, setunionsingleton: $o).
% 0.75/0.50 thf(decl_199, type, singleton: $i > $o).
% 0.75/0.50 thf(decl_200, type, singletonprop: $o).
% 0.75/0.50 thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 0.75/0.50 thf(decl_202, type, ex1E1: $o).
% 0.75/0.50 thf(decl_203, type, ex1I: $o).
% 0.75/0.50 thf(decl_204, type, ex1I2: $o).
% 0.75/0.50 thf(decl_205, type, singletonsuniq: $o).
% 0.75/0.50 thf(decl_210, type, setukpairinjL1: $o).
% 0.75/0.50 thf(decl_211, type, kfstsingleton: $o).
% 0.75/0.50 thf(decl_212, type, theprop: $o).
% 0.75/0.50 thf(decl_213, type, kfst: $i > $i).
% 0.75/0.50 thf(decl_214, type, kfstpairEq: $o).
% 0.75/0.50 thf(decl_215, type, cartprodfstin: $o).
% 0.75/0.50 thf(decl_216, type, setukpairinjL2: $o).
% 0.75/0.50 thf(decl_217, type, setukpairinjL: $o).
% 0.75/0.50 thf(decl_218, type, setukpairinjR11: $o).
% 0.75/0.50 thf(decl_219, type, setukpairinjR12: $o).
% 0.75/0.50 thf(decl_220, type, setukpairinjR1: $o).
% 0.75/0.50 thf(decl_221, type, upairequniteq: $o).
% 0.75/0.50 thf(decl_222, type, setukpairinjR2: $o).
% 0.75/0.50 thf(decl_223, type, setukpairinjR: $o).
% 0.75/0.50 thf(decl_224, type, ksndsingleton: $o).
% 0.75/0.50 thf(decl_225, type, ksnd: $i > $i).
% 0.75/0.50 thf(decl_226, type, ksndpairEq: $o).
% 0.75/0.50 thf(decl_227, type, kpairsurjEq: $o).
% 0.75/0.50 thf(decl_228, type, cartprodsndin: $o).
% 0.75/0.50 thf(decl_229, type, cartprodpairmemEL: $o).
% 0.75/0.50 thf(decl_230, type, cartprodpairmemER: $o).
% 0.75/0.50 thf(decl_231, type, cartprodmempaircEq: $o).
% 0.75/0.50 thf(decl_232, type, cartprodfstpairEq: $o).
% 0.75/0.50 thf(decl_233, type, cartprodsndpairEq: $o).
% 0.75/0.50 thf(decl_234, type, cartprodpairsurjEq: $o).
% 0.75/0.50 thf(decl_235, type, breln: $i > $i > $i > $o).
% 0.75/0.50 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 0.75/0.50 thf(decl_237, type, dpsetconstrI: $o).
% 0.75/0.50 thf(decl_238, type, dpsetconstrSub: $o).
% 0.75/0.50 thf(decl_239, type, setOfPairsIsBReln: $o).
% 0.75/0.50 thf(decl_240, type, dpsetconstrERa: $o).
% 0.75/0.50 thf(decl_241, type, dpsetconstrEL1: $o).
% 0.75/0.50 thf(decl_242, type, dpsetconstrEL2: $o).
% 0.75/0.50 thf(decl_243, type, dpsetconstrER: $o).
% 0.75/0.50 thf(decl_244, type, func: $i > $i > $i > $o).
% 0.75/0.50 thf(decl_245, type, funcSet: $i > $i > $i).
% 0.75/0.50 thf(decl_246, type, funcImageSingleton: $o).
% 0.75/0.50 thf(decl_247, type, apProp: $o).
% 0.75/0.50 thf(decl_248, type, ap: $i > $i > $i > $i > $i).
% 0.75/0.50 thf(decl_249, type, app: $o).
% 0.75/0.50 thf(decl_250, type, infuncsetfunc: $o).
% 0.75/0.50 thf(decl_251, type, ap2p: $o).
% 0.75/0.50 thf(decl_252, type, funcinfuncset: $o).
% 0.75/0.50 thf(decl_253, type, lamProp: $o).
% 0.75/0.50 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
% 0.75/0.50 thf(decl_255, type, lamp: $o).
% 0.75/0.50 thf(decl_256, type, lam2p: $o).
% 0.75/0.50 thf(decl_257, type, brelnall1: $o).
% 0.75/0.50 thf(decl_258, type, brelnall2: $o).
% 0.75/0.50 thf(decl_259, type, ex1E2: $o).
% 0.75/0.50 thf(decl_260, type, funcGraphProp1: $o).
% 0.75/0.50 thf(decl_261, type, funcGraphProp3: $o).
% 0.75/0.50 thf(decl_262, type, funcGraphProp2: $o).
% 0.75/0.50 thf(decl_263, type, funcextLem: $o).
% 0.75/0.50 thf(decl_264, type, funcGraphProp4: $o).
% 0.75/0.50 thf(decl_265, type, subbreln: $o).
% 0.75/0.50 thf(decl_266, type, eqbreln: $o).
% 0.75/0.50 thf(decl_267, type, funcext: $o).
% 0.75/0.50 thf(decl_268, type, funcext2: $o).
% 0.75/0.50 thf(decl_269, type, ap2apEq1: $o).
% 0.75/0.50 thf(decl_270, type, ap2apEq2: $o).
% 0.75/0.50 thf(decl_271, type, beta1: $o).
% 0.75/0.50 thf(decl_272, type, eta1: $o).
% 0.75/0.50 thf(decl_273, type, lam2lamEq: $o).
% 0.75/0.50 thf(decl_274, type, beta2: $o).
% 0.75/0.50 thf(decl_275, type, eta2: $o).
% 0.75/0.50 thf(decl_276, type, iffalseProp1: $o).
% 0.75/0.50 thf(decl_277, type, iffalseProp2: $o).
% 0.75/0.50 thf(decl_278, type, iftrueProp1: $o).
% 0.75/0.50 thf(decl_279, type, iftrueProp2: $o).
% 0.75/0.50 thf(decl_280, type, ifSingleton: $o).
% 0.75/0.50 thf(decl_281, type, if: $i > $o > $i > $i > $i).
% 0.75/0.50 thf(decl_282, type, ifp: $o).
% 0.75/0.50 thf(decl_283, type, theeq: $o).
% 0.75/0.50 thf(decl_284, type, iftrue: $o).
% 0.75/0.50 thf(decl_285, type, iffalse: $o).
% 0.75/0.50 thf(decl_286, type, iftrueorfalse: $o).
% 0.75/0.50 thf(decl_287, type, binintersectT_lem: $o).
% 0.75/0.50 thf(decl_288, type, binunionT_lem: $o).
% 0.75/0.50 thf(decl_289, type, powersetT_lem: $o).
% 0.75/0.50 thf(decl_290, type, setminusT_lem: $o).
% 0.75/0.50 thf(decl_291, type, complementT_lem: $o).
% 0.75/0.50 thf(decl_292, type, setextT: $o).
% 0.75/0.50 thf(decl_293, type, subsetTI: $o).
% 0.75/0.50 thf(decl_294, type, powersetTI1: $o).
% 0.75/0.50 thf(decl_295, type, powersetTE1: $o).
% 0.75/0.50 thf(decl_296, type, complementTI1: $o).
% 0.75/0.50 thf(decl_297, type, complementTE1: $o).
% 0.75/0.50 thf(decl_298, type, binintersectTELcontra: $o).
% 0.75/0.50 thf(decl_299, type, binintersectTERcontra: $o).
% 0.75/0.50 thf(decl_300, type, contrasubsetT: $o).
% 0.75/0.50 thf(decl_301, type, contrasubsetT1: $o).
% 0.75/0.50 thf(decl_302, type, contrasubsetT2: $o).
% 0.75/0.50 thf(decl_303, type, contrasubsetT3: $o).
% 0.75/0.50 thf(decl_304, type, doubleComplementI1: $o).
% 0.75/0.50 thf(decl_305, type, doubleComplementE1: $o).
% 0.75/0.50 thf(decl_306, type, doubleComplementSub1: $o).
% 0.75/0.50 thf(decl_307, type, doubleComplementSub2: $o).
% 0.75/0.50 thf(decl_308, type, doubleComplementEq: $o).
% 0.75/0.50 thf(decl_309, type, complementTnotintersectT: $o).
% 0.75/0.50 thf(decl_310, type, complementImpComplementIntersect: $o).
% 0.75/0.50 thf(decl_311, type, complementSubsetComplementIntersect: $o).
% 0.75/0.50 thf(decl_312, type, complementInPowersetComplementIntersect: $o).
% 0.75/0.50 thf(decl_313, type, contraSubsetComplement: $o).
% 0.75/0.50 thf(decl_314, type, complementTcontraSubset: $o).
% 0.75/0.50 thf(decl_315, type, binunionTILcontra: $o).
% 0.75/0.50 thf(decl_316, type, binunionTIRcontra: $o).
% 0.75/0.50 thf(decl_317, type, inIntersectImpInUnion: $o).
% 0.75/0.50 thf(decl_318, type, inIntersectImpInUnion2: $o).
% 0.75/0.50 thf(decl_319, type, inIntersectImpInIntersectUnions: $o).
% 0.75/0.50 thf(decl_320, type, intersectInPowersetIntersectUnions: $o).
% 0.75/0.50 thf(decl_321, type, inComplementUnionImpNotIn1: $o).
% 0.75/0.50 thf(decl_322, type, epred1_0: $o).
% 0.75/0.50 thf(decl_323, type, esk1_2: $i > $i > $i).
% 0.75/0.50 thf(decl_324, type, esk2_2: $i > $i > $i).
% 0.75/0.50 thf(decl_325, type, esk3_2: $i > $i > $i).
% 0.75/0.50 thf(decl_326, type, esk4_1: $i > $i).
% 0.75/0.50 thf(decl_327, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.75/0.50 thf(decl_328, type, esk6_2: ($i > $i > $o) > $i > $i).
% 0.75/0.50 thf(decl_329, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
% 0.75/0.50 thf(decl_330, type, esk8_1: $i > $i).
% 0.75/0.50 thf(decl_331, type, esk9_1: ($i > $o) > $i).
% 0.75/0.50 thf(decl_332, type, esk10_1: ($i > $o) > $i).
% 0.75/0.50 thf(decl_333, type, esk11_2: $i > $i > $i).
% 0.75/0.50 thf(decl_334, type, esk12_2: $i > $i > $i).
% 0.75/0.50 thf(decl_335, type, esk13_1: $i > $i).
% 0.75/0.50 thf(decl_336, type, esk14_1: $i > $i).
% 0.75/0.50 thf(decl_337, type, esk15_1: $i > $i).
% 0.75/0.50 thf(decl_338, type, esk16_2: $i > $i > $i).
% 0.75/0.50 thf(decl_339, type, esk17_3: $i > $i > $o > $i).
% 0.75/0.50 thf(decl_340, type, esk18_1: ($i > $o) > $i).
% 0.75/0.50 thf(decl_341, type, esk19_1: $i > $i).
% 0.75/0.50 thf(decl_342, type, esk20_2: $i > ($i > $o) > $i).
% 0.75/0.50 thf(decl_343, type, esk21_2: $i > ($i > $o) > $i).
% 0.75/0.50 thf(decl_344, type, esk22_2: $i > ($i > $o) > $i).
% 0.75/0.50 thf(decl_345, type, esk23_2: $i > ($i > $o) > $i).
% 0.75/0.50 thf(decl_346, type, esk24_2: $i > ($i > $o) > $i).
% 0.75/0.50 thf(decl_347, type, esk25_2: $i > ($i > $o) > $i).
% 0.75/0.50 thf(decl_348, type, esk26_2: ($i > $o) > $i > $i).
% 0.75/0.50 thf(decl_349, type, esk27_1: ($i > $o) > $i).
% 0.75/0.50 thf(decl_350, type, esk28_1: ($i > $o) > $i).
% 0.75/0.50 thf(decl_351, type, esk29_2: ($i > $o) > $i > $i).
% 0.75/0.50 thf(decl_352, type, esk30_2: ($i > $o) > ($i > $o) > $i).
% 0.75/0.50 thf(decl_353, type, esk31_2: ($i > $o) > ($i > $o) > $i).
% 0.75/0.50 thf(decl_354, type, esk32_2: ($i > $o) > ($i > $o) > $i).
% 0.75/0.50 thf(decl_355, type, esk33_2: ($i > $o) > ($i > $o) > $i).
% 0.75/0.50 thf(decl_356, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.75/0.50 thf(decl_357, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.75/0.50 thf(decl_358, type, esk36_2: $i > $i > $i).
% 0.75/0.50 thf(decl_359, type, esk37_2: $i > $i > $i).
% 0.75/0.50 thf(decl_360, type, esk38_2: $i > $i > $i).
% 0.75/0.50 thf(decl_361, type, esk39_3: $i > $i > $i > $i).
% 0.75/0.50 thf(decl_362, type, esk40_3: $i > $i > $i > $i).
% 0.75/0.50 thf(decl_363, type, esk41_2: $i > $i > $i).
% 0.75/0.50 thf(decl_364, type, esk42_2: $i > ($i > $o) > $i).
% 0.75/0.50 thf(decl_365, type, esk43_2: $i > ($i > $o) > $i).
% 0.75/0.50 thf(decl_366, type, esk44_2: $i > ($i > $o) > $i).
% 0.75/0.50 thf(decl_367, type, esk45_3: $i > ($i > $o) > $i > $i).
% 0.75/0.50 thf(decl_368, type, esk46_2: $i > ($i > $o) > $i).
% 0.75/0.50 thf(decl_369, type, esk47_2: $i > ($i > $o) > $i).
% 0.75/0.50 thf(decl_370, type, esk48_3: $i > $i > ($i > $i) > $i).
% 0.75/0.50 thf(decl_371, type, esk49_3: $i > $i > ($i > $i) > $i).
% 0.75/0.50 thf(decl_372, type, esk50_3: $i > $i > ($i > $i) > $i).
% 0.75/0.50 thf(decl_373, type, esk51_4: $i > $i > $i > ($i > $o) > $i).
% 0.75/0.50 thf(decl_374, type, esk52_4: $i > $i > $i > ($i > $o) > $i).
% 0.75/0.50 thf(decl_375, type, esk53_4: $i > $i > $i > ($i > $o) > $i).
% 0.75/0.50 thf(decl_376, type, esk54_4: $i > $i > $i > ($i > $o) > $i).
% 0.75/0.50 thf(decl_377, type, esk55_4: $i > $i > $i > $i > $i).
% 0.75/0.50 thf(decl_378, type, esk56_4: $i > $i > $i > $i > $i).
% 0.75/0.50 thf(decl_379, type, esk57_4: $i > $i > $i > $i > $i).
% 0.75/0.50 thf(decl_380, type, esk58_4: $i > $i > $i > $i > $i).
% 0.75/0.50 thf(decl_381, type, esk59_4: $i > $i > $i > $i > $i).
% 0.75/0.50 thf(decl_382, type, esk60_4: $i > $i > $i > $i > $i).
% 0.75/0.50 thf(decl_383, type, esk61_4: $i > $i > $i > $i > $i).
% 0.75/0.50 thf(decl_384, type, esk62_4: $i > $i > $i > $i > $i).
% 0.75/0.50 thf(decl_385, type, esk63_4: $i > $i > $i > $i > $i).
% 0.75/0.50 thf(decl_386, type, esk64_3: $i > $i > ($i > $i) > $i).
% 0.75/0.50 thf(decl_387, type, esk65_3: $i > $i > ($i > $i) > $i).
% 0.75/0.50 thf(decl_388, type, esk66_3: $i > $i > ($i > $i) > $i).
% 0.75/0.50 thf(decl_389, type, esk67_3: $i > $i > $i > $i).
% 0.75/0.50 thf(decl_390, type, esk68_3: $i > $i > $i > $i).
% 0.75/0.50 thf(decl_391, type, esk69_3: $i > $i > $i > $i).
% 0.75/0.50 thf(decl_392, type, esk70_3: $i > $i > $i > $i).
% 0.75/0.50 thf(decl_393, type, esk71_0: $i).
% 0.75/0.50 thf(decl_394, type, esk72_0: $i).
% 0.75/0.50 thf(decl_395, type, esk73_0: $i).
% 0.75/0.50 thf(decl_396, type, esk74_0: $i).
% 0.75/0.50 thf(inComplementUnionImpInComplement1, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>((subbreln)=>((eqbreln)=>((funcext)=>((funcext2)=>((ap2apEq1)=>((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>((beta2)=>((eta2)=>((iffalseProp1)=>((iffalseProp2)=>((iftrueProp1)=>((iftrueProp2)=>((ifSingleton)=>((ifp)=>((theeq)=>((iftrue)=>((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>((setminusT_lem)=>((complementT_lem)=>((setextT)=>((subsetTI)=>((powersetTI1)=>((powersetTE1)=>((complementTI1)=>((complementTE1)=>((binintersectTELcontra)=>((binintersectTERcontra)=>((contrasubsetT)=>((contrasubsetT1)=>((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>((doubleComplementE1)=>((doubleComplementSub1)=>((doubleComplementSub2)=>((doubleComplementEq)=>((complementTnotintersectT)=>((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>((complementInPowersetComplementIntersect)=>((contraSubsetComplement)=>((complementTcontraSubset)=>((binunionTILcontra)=>((binunionTIRcontra)=>((inIntersectImpInUnion)=>((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>((inComplementUnionImpNotIn1)=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', inComplementUnionImpInComplement1)).
% 0.75/0.50 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', exu__Cong)).
% 0.75/0.50 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$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.RcafZaxWN3/E---3.1_2929893.p', iffalseProp2)).
% 0.75/0.50 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X39))&(((X14)=(X2)))))|(((~((X39)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', iffalseProp1)).
% 0.75/0.50 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$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.RcafZaxWN3/E---3.1_2929893.p', iftrueProp1)).
% 0.75/0.50 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X42))&(((X14)=(X2)))))|(((~((X42)))&(((X14)=(X3)))))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', iftrueProp2)).
% 0.75/0.50 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$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.RcafZaxWN3/E---3.1_2929893.p', ifSingleton)).
% 0.75/0.50 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.RcafZaxWN3/E---3.1_2929893.p', exuE3u)).
% 0.75/0.50 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.RcafZaxWN3/E---3.1_2929893.p', exuI2)).
% 0.75/0.50 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', exuI3)).
% 0.75/0.50 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', exuI1)).
% 0.75/0.50 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', dsetconstr__Cong)).
% 0.75/0.50 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', descr__Cong)).
% 0.75/0.50 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', exuEu)).
% 0.75/0.50 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', sepSubset)).
% 0.75/0.50 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', sepInPowerset)).
% 0.75/0.50 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', ex1E1)).
% 0.75/0.50 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', singletonprop)).
% 0.75/0.50 thf(ex1I, axiom, ((ex1I)<=>![X4:$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.RcafZaxWN3/E---3.1_2929893.p', ex1I)).
% 0.75/0.50 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.RcafZaxWN3/E---3.1_2929893.p', kfstsingleton)).
% 0.75/0.50 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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', ex1I2)).
% 0.75/0.50 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', ksndsingleton)).
% 0.75/0.50 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', dpsetconstrEL2)).
% 0.75/0.50 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', dpsetconstrEL1)).
% 0.75/0.50 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', dpsetconstrERa)).
% 0.75/0.50 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', setOfPairsIsBReln)).
% 0.75/0.50 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', dpsetconstrSub)).
% 0.75/0.50 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', dpsetconstrI)).
% 0.75/0.50 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', dpsetconstrER)).
% 0.75/0.50 thf(lamProp, axiom, ((lamProp)<=>![X4:$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.RcafZaxWN3/E---3.1_2929893.p', lamProp)).
% 0.75/0.50 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', apProp)).
% 0.75/0.50 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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.RcafZaxWN3/E---3.1_2929893.p', funcImageSingleton)).
% 0.75/0.50 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:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', lamp)).
% 0.75/0.50 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$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.RcafZaxWN3/E---3.1_2929893.p', ex1E2)).
% 0.75/0.50 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:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', lam2p)).
% 0.75/0.50 thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', eta1)).
% 0.75/0.50 thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$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.RcafZaxWN3/E---3.1_2929893.p', lam2lamEq)).
% 0.75/0.50 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.RcafZaxWN3/E---3.1_2929893.p', beta2)).
% 0.75/0.50 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.RcafZaxWN3/E---3.1_2929893.p', eta2)).
% 0.75/0.50 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.RcafZaxWN3/E---3.1_2929893.p', beta1)).
% 0.75/0.50 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.RcafZaxWN3/E---3.1_2929893.p', emptyE1)).
% 0.75/0.50 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.RcafZaxWN3/E---3.1_2929893.p', exuE2)).
% 0.75/0.50 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', setoftrueEq)).
% 0.75/0.50 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', nonemptyI)).
% 0.75/0.50 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', setbeta)).
% 0.75/0.50 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', exuE3e)).
% 0.75/0.50 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', exuE1)).
% 0.75/0.50 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', dsetconstrER)).
% 0.75/0.50 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', dsetconstrEL)).
% 0.75/0.50 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', dsetconstrI)).
% 0.75/0.50 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', descrp)).
% 0.75/0.50 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', replAx)).
% 0.75/0.50 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', notdexE)).
% 0.75/0.50 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', prop2setI)).
% 0.75/0.50 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.RcafZaxWN3/E---3.1_2929893.p', ifp)).
% 0.75/0.50 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', quantDeMorgan4)).
% 0.75/0.50 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', theeq)).
% 0.75/0.50 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', notdallE)).
% 0.75/0.50 thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', iftrue)).
% 0.75/0.50 thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', iffalse)).
% 0.75/0.50 thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', iftrueorfalse)).
% 0.75/0.50 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$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.RcafZaxWN3/E---3.1_2929893.p', binintersectT_lem)).
% 0.75/0.50 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', binunionT_lem)).
% 0.75/0.50 thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', powersetT_lem)).
% 0.75/0.50 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$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.RcafZaxWN3/E---3.1_2929893.p', setminusT_lem)).
% 0.75/0.50 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.RcafZaxWN3/E---3.1_2929893.p', complementT_lem)).
% 0.75/0.50 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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', setextT)).
% 0.75/0.50 thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', subsetTI)).
% 0.75/0.50 thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', powersetTI1)).
% 0.75/0.50 thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', powersetTE1)).
% 0.75/0.50 thf(complementTI1, axiom, ((complementTI1)<=>![X4:$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.RcafZaxWN3/E---3.1_2929893.p', complementTI1)).
% 0.75/0.50 thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', complementTE1)).
% 0.75/0.50 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', notsubsetI)).
% 0.75/0.50 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', subsetE2)).
% 0.75/0.50 thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', binintersectTELcontra)).
% 0.75/0.50 thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', binintersectTERcontra)).
% 0.75/0.50 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', in__Cong)).
% 0.75/0.50 thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', contrasubsetT)).
% 0.75/0.50 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', inCongP)).
% 0.75/0.50 thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', contrasubsetT1)).
% 0.75/0.50 thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$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.RcafZaxWN3/E---3.1_2929893.p', contrasubsetT2)).
% 0.75/0.50 thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', contrasubsetT3)).
% 0.75/0.50 thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$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.RcafZaxWN3/E---3.1_2929893.p', doubleComplementI1)).
% 0.75/0.50 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', emptyset__Cong)).
% 0.75/0.50 thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', doubleComplementE1)).
% 0.75/0.50 thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', doubleComplementSub1)).
% 0.75/0.50 thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', doubleComplementSub2)).
% 0.75/0.50 thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', doubleComplementEq)).
% 0.75/0.50 thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', complementTnotintersectT)).
% 0.75/0.50 thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', complementImpComplementIntersect)).
% 0.75/0.50 thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$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.RcafZaxWN3/E---3.1_2929893.p', complementSubsetComplementIntersect)).
% 0.75/0.50 thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', complementInPowersetComplementIntersect)).
% 0.75/0.50 thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', contraSubsetComplement)).
% 0.75/0.50 thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$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.RcafZaxWN3/E---3.1_2929893.p', complementTcontraSubset)).
% 0.75/0.50 thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', binunionTILcontra)).
% 0.75/0.50 thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', binunionTIRcontra)).
% 0.75/0.50 thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', inIntersectImpInUnion)).
% 0.75/0.50 thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', inIntersectImpInUnion2)).
% 0.75/0.50 thf(inIntersectImpInIntersectUnions, axiom, ((inIntersectImpInIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', inIntersectImpInIntersectUnions)).
% 0.75/0.50 thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', intersectInPowersetIntersectUnions)).
% 0.75/0.50 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', omega__Cong)).
% 0.75/0.50 thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', inComplementUnionImpNotIn1)).
% 0.75/0.50 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', setunion__Cong)).
% 0.75/0.50 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', powerset__Cong)).
% 0.75/0.50 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', setadjoin__Cong)).
% 0.75/0.50 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', subsetI1)).
% 0.75/0.50 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', binintersectSubset4)).
% 0.75/0.50 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', binintersectRsub)).
% 0.75/0.50 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', disjointsetsI1)).
% 0.75/0.50 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', binintersectER)).
% 0.75/0.50 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', binintersectSubset3)).
% 0.75/0.50 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', subsetE)).
% 0.75/0.50 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', emptysetsubset)).
% 0.75/0.50 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', subsetI2)).
% 0.75/0.50 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', eqimpsubset1)).
% 0.75/0.50 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', eqimpsubset2)).
% 0.75/0.50 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', notequalI1)).
% 0.75/0.50 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', setextsub)).
% 0.75/0.50 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', subset2powerset)).
% 0.75/0.50 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', setadjoinSub2)).
% 0.75/0.50 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', setadjoinSub)).
% 0.75/0.50 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', subsetTrans)).
% 0.75/0.50 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', subsetRefl)).
% 0.75/0.50 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', notequalI2)).
% 0.75/0.50 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', subsetemptysetimpeq)).
% 0.75/0.50 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', binunionIL)).
% 0.75/0.50 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', powersetsubset)).
% 0.75/0.50 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', inPowerset)).
% 0.75/0.50 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', powersetE1)).
% 0.75/0.50 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', powersetI1)).
% 0.75/0.50 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', upairset2IR)).
% 0.75/0.50 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', binintersectSubset5)).
% 0.75/0.50 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', binintersectI)).
% 0.75/0.50 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', binunionRsub)).
% 0.75/0.50 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', binunionLsub)).
% 0.75/0.50 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', binunionE)).
% 0.75/0.50 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', binunionEcases)).
% 0.75/0.50 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', binunionIR)).
% 0.75/0.50 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', binintersectEL)).
% 0.75/0.50 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$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.RcafZaxWN3/E---3.1_2929893.p', funcGraphProp4)).
% 0.75/0.50 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', binintersectSubset2)).
% 0.75/0.50 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', binintersectLsub)).
% 0.75/0.50 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', binintersectSubset1)).
% 0.75/0.50 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', setminusELneg)).
% 0.75/0.50 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', setminusERneg)).
% 0.75/0.50 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', setminusSubset2)).
% 0.75/0.50 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', setminusER)).
% 0.75/0.50 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', setminusEL)).
% 0.75/0.50 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', setminusI)).
% 0.75/0.50 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', bs114d)).
% 0.75/0.50 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', setminusILneg)).
% 0.75/0.50 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', symdiffIneg1)).
% 0.75/0.50 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', symdiffI2)).
% 0.75/0.50 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', symdiffI1)).
% 0.75/0.50 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.RcafZaxWN3/E---3.1_2929893.p', symdiffE)).
% 0.75/0.50 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', setminusSubset1)).
% 0.75/0.50 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', setminusLsub)).
% 0.75/0.50 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', setminusIRneg)).
% 0.75/0.50 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', symdiffIneg2)).
% 0.75/0.50 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', singletoninpowerset)).
% 0.75/0.50 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', singletonsubset)).
% 0.75/0.50 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', kpairp)).
% 0.75/0.50 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.RcafZaxWN3/E---3.1_2929893.p', kpairiskpair)).
% 0.75/0.50 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.RcafZaxWN3/E---3.1_2929893.p', setukpairIR)).
% 0.75/0.50 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.RcafZaxWN3/E---3.1_2929893.p', setukpairIL)).
% 0.75/0.50 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', secondinupair)).
% 0.75/0.50 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', singletoninpowunion)).
% 0.75/0.50 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', cartprodpairin)).
% 0.75/0.50 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', ubforcartprodlem3)).
% 0.75/0.50 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', ubforcartprodlem2)).
% 0.75/0.50 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', ubforcartprodlem1)).
% 0.75/0.50 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', upairinpowunion)).
% 0.75/0.50 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', upairsubunion)).
% 0.75/0.50 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', upairset2E)).
% 0.75/0.50 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', cartprodmempair1)).
% 0.75/0.50 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', setunionsingleton)).
% 0.75/0.50 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', setunionsingleton2)).
% 0.75/0.50 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', setunionsingleton1)).
% 0.75/0.50 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', setunionE2)).
% 0.75/0.50 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', cartprodmempair)).
% 0.75/0.50 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', cartprodfstin)).
% 0.75/0.50 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', kfstpairEq)).
% 0.75/0.50 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', theprop)).
% 0.75/0.50 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', setukpairinjL1)).
% 0.75/0.50 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', singletonsuniq)).
% 0.75/0.50 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', setukpairinjL2)).
% 0.75/0.50 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', setukpairinjR)).
% 0.75/0.50 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', setukpairinjR2)).
% 0.75/0.50 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', upairequniteq)).
% 0.75/0.50 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.RcafZaxWN3/E---3.1_2929893.p', setukpairinjR1)).
% 0.75/0.50 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.RcafZaxWN3/E---3.1_2929893.p', setukpairinjR12)).
% 0.75/0.50 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', setukpairinjR11)).
% 0.75/0.50 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.RcafZaxWN3/E---3.1_2929893.p', setukpairinjL)).
% 0.75/0.50 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.RcafZaxWN3/E---3.1_2929893.p', cartprodfstpairEq)).
% 0.75/0.50 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.RcafZaxWN3/E---3.1_2929893.p', cartprodmempaircEq)).
% 0.75/0.50 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.RcafZaxWN3/E---3.1_2929893.p', cartprodpairmemER)).
% 0.75/0.50 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.RcafZaxWN3/E---3.1_2929893.p', cartprodpairmemEL)).
% 0.75/0.50 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', cartprodsndin)).
% 0.75/0.50 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', kpairsurjEq)).
% 0.75/0.50 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', ksndpairEq)).
% 0.75/0.50 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.RcafZaxWN3/E---3.1_2929893.p', cartprodsndpairEq)).
% 0.75/0.50 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', cartprodpairsurjEq)).
% 0.75/0.50 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', funcinfuncset)).
% 0.75/0.50 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.RcafZaxWN3/E---3.1_2929893.p', ap2p)).
% 0.75/0.50 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', infuncsetfunc)).
% 0.75/0.50 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', app)).
% 0.75/0.50 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$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.RcafZaxWN3/E---3.1_2929893.p', funcGraphProp2)).
% 0.75/0.50 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.RcafZaxWN3/E---3.1_2929893.p', funcGraphProp3)).
% 0.75/0.50 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.RcafZaxWN3/E---3.1_2929893.p', funcGraphProp1)).
% 0.75/0.50 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.RcafZaxWN3/E---3.1_2929893.p', brelnall2)).
% 0.75/0.50 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.RcafZaxWN3/E---3.1_2929893.p', brelnall1)).
% 0.75/0.50 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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', funcextLem)).
% 0.75/0.50 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', ap2apEq2)).
% 0.75/0.50 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', ap2apEq1)).
% 0.75/0.50 thf(funcext2, axiom, ((funcext2)<=>![X4:$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.RcafZaxWN3/E---3.1_2929893.p', funcext2)).
% 0.75/0.50 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', funcext)).
% 0.75/0.50 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', eqbreln)).
% 0.75/0.50 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', subbreln)).
% 0.75/0.50 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', quantDeMorgan3)).
% 0.75/0.50 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', quantDeMorgan2)).
% 0.75/0.50 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', quantDeMorgan1)).
% 0.75/0.50 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', vacuousDall)).
% 0.75/0.50 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', upairsetIR)).
% 0.75/0.50 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', upairsetIL)).
% 0.75/0.50 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', upairsetE)).
% 0.75/0.50 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', singletonsswitch)).
% 0.75/0.50 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', eqinunit)).
% 0.75/0.50 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', notinsingleton)).
% 0.75/0.50 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', uniqinunit)).
% 0.75/0.50 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', nonemptyImpWitness)).
% 0.75/0.50 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', subPowSU)).
% 0.75/0.50 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.RcafZaxWN3/E---3.1_2929893.p', setunionE)).
% 0.75/0.50 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', setunionI)).
% 0.75/0.50 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', powersetE)).
% 0.75/0.50 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', emptyInPowerset)).
% 0.75/0.50 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', emptyinPowerset)).
% 0.75/0.50 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', powersetI)).
% 0.75/0.50 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', setadjoinOr)).
% 0.75/0.50 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.RcafZaxWN3/E---3.1_2929893.p', setadjoinE)).
% 0.75/0.50 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', setadjoinIR)).
% 0.75/0.50 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', emptyinunitempty)).
% 0.75/0.50 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', setadjoinIL)).
% 0.75/0.50 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', nonemptyI1)).
% 0.75/0.50 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', nonemptyE1)).
% 0.75/0.50 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', noeltsimpempty)).
% 0.75/0.50 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', emptyI)).
% 0.75/0.50 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', setext)).
% 0.75/0.50 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', notinemptyset)).
% 0.75/0.50 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', emptysetimpfalse)).
% 0.75/0.50 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', emptysetE)).
% 0.75/0.50 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', prop2setE)).
% 0.75/0.50 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', wellorderingAx)).
% 0.75/0.50 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', foundationAx)).
% 0.75/0.50 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.RcafZaxWN3/E---3.1_2929893.p', omegaIndAx)).
% 0.75/0.50 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', omegaSAx)).
% 0.75/0.50 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', omega0Ax)).
% 0.75/0.50 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', setunionAx)).
% 0.75/0.50 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', powersetAx)).
% 0.75/0.50 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', setadjoinAx)).
% 0.75/0.50 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', emptysetAx)).
% 0.75/0.50 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.RcafZaxWN3/E---3.1_2929893.p', setextAx)).
% 0.75/0.50 thf(c_0_261, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>((subbreln)=>((eqbreln)=>((funcext)=>((funcext2)=>((ap2apEq1)=>((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>((beta2)=>((eta2)=>((iffalseProp1)=>((iffalseProp2)=>((iftrueProp1)=>((iftrueProp2)=>((ifSingleton)=>((ifp)=>((theeq)=>((iftrue)=>((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>((setminusT_lem)=>((complementT_lem)=>((setextT)=>((subsetTI)=>((powersetTI1)=>((powersetTE1)=>((complementTI1)=>((complementTE1)=>((binintersectTELcontra)=>((binintersectTERcontra)=>((contrasubsetT)=>((contrasubsetT1)=>((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>((doubleComplementE1)=>((doubleComplementSub1)=>((doubleComplementSub2)=>((doubleComplementEq)=>((complementTnotintersectT)=>((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>((complementInPowersetComplementIntersect)=>((contraSubsetComplement)=>((complementTcontraSubset)=>((binunionTILcontra)=>((binunionTIRcontra)=>((inIntersectImpInUnion)=>((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>((inComplementUnionImpNotIn1)=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[inComplementUnionImpInComplement1])).
% 0.75/0.50 thf(c_0_262, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.75/0.50 thf(c_0_263, plain, ((iffalseProp2)<=>![X4:$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])).
% 0.75/0.50 thf(c_0_264, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X39))&(((Z0)=(X2)))))|(((~((X39)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
% 0.75/0.50 thf(c_0_265, plain, ((iftrueProp1)<=>![X4:$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])).
% 0.75/0.50 thf(c_0_266, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X42))&(((Z0)=(X2)))))|(((~((X42)))&(((Z0)=(X3)))))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])).
% 0.75/0.50 thf(c_0_267, plain, ((ifSingleton)<=>![X4:$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])).
% 0.75/0.50 thf(c_0_268, 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])).
% 0.75/0.50 thf(c_0_269, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.75/0.50 thf(c_0_270, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.75/0.50 thf(c_0_271, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 0.75/0.50 thf(c_0_272, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 0.75/0.50 thf(c_0_273, plain, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 0.75/0.50 thf(c_0_274, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 0.75/0.50 thf(c_0_275, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 0.75/0.50 thf(c_0_276, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 0.75/0.50 thf(c_0_277, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 0.75/0.50 thf(c_0_278, plain, ((singletonprop)<=>![X4:$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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 0.75/0.50 thf(c_0_279, plain, ((ex1I)<=>![X4:$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])).
% 0.75/0.50 thf(c_0_280, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 0.75/0.50 thf(c_0_281, 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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 0.75/0.50 thf(c_0_282, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 0.75/0.50 thf(c_0_283, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 0.75/0.50 thf(c_0_284, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 0.75/0.50 thf(c_0_285, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 0.75/0.50 thf(c_0_286, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 0.75/0.50 thf(c_0_287, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 0.75/0.50 thf(c_0_288, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 0.75/0.50 thf(c_0_289, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 0.75/0.50 thf(c_0_290, plain, ((lamProp)<=>![X4:$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])).
% 0.75/0.50 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:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
% 0.75/0.50 thf(c_0_292, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
% 0.75/0.50 thf(c_0_293, 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:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
% 0.75/0.50 thf(c_0_294, plain, ((ex1E2)<=>![X4:$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])).
% 0.75/0.50 thf(c_0_295, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
% 0.75/0.50 thf(c_0_296, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])).
% 0.75/0.50 thf(c_0_297, plain, ((lam2lamEq)<=>![X4:$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])).
% 0.75/0.50 thf(c_0_298, 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])).
% 0.75/0.50 thf(c_0_299, 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])).
% 0.75/0.50 thf(c_0_300, plain, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X36 @ Z0))) @ X2)=(X36 @ X2))))))), inference(fof_simplification,[status(thm)],[beta1])).
% 1.61/0.50 thf(c_0_301, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
% 1.61/0.50 thf(c_0_302, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 1.61/0.50 thf(c_0_303, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 1.61/0.50 thf(c_0_304, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 1.61/0.50 thf(c_0_305, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 1.61/0.50 thf(c_0_306, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 1.61/0.50 thf(c_0_307, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 1.61/0.50 thf(c_0_308, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 1.61/0.50 thf(c_0_309, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 1.61/0.50 thf(c_0_310, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 1.61/0.50 thf(c_0_311, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 1.61/0.50 thf(c_0_312, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 1.61/0.50 thf(c_0_313, plain, ((epred1_0)<=>![X898:$i]:(?[X899:$i]:((((![X900:$i]:(((in @ X900 @ X899)=>![X901:$i]:(((in @ X901 @ X900)=>(in @ X901 @ X898)))))&![X902:$i, X903:$i]:((((in @ X902 @ X898)&(in @ X903 @ X898))=>(![X904:$i]:(((in @ X904 @ X899)=>((in @ X902 @ X904)<=>(in @ X903 @ X904))))=>((X902)=(X903))))))&![X905:$i, X906:$i]:((((in @ X905 @ X899)&(in @ X906 @ X899))=>(![X907:$i]:(((in @ X907 @ X905)=>(in @ X907 @ X906)))|![X908:$i]:(((in @ X908 @ X906)=>(in @ X908 @ X905)))))))&![X909:$i]:(((![X910:$i]:(((in @ X910 @ X909)=>(in @ X910 @ X898)))&?[X911:$i]:((in @ X911 @ X909)))=>?[X912:$i, X913:$i]:(((((in @ X912 @ X899)&(in @ X913 @ X909))&~(?[X914:$i]:(((in @ X914 @ X912)&(in @ X914 @ X909)))))&![X915:$i]:(((in @ X915 @ X899)=>(![X916:$i]:(((in @ X916 @ X915)=>(in @ X916 @ X912)))|(in @ X913 @ X915)))))))))))), introduced(definition)).
% 1.61/0.50 thf(c_0_314, negated_conjecture, ~((![X871:$i, X872:$i]:((![X873:$i]:(((in @ X873 @ X871)<=>(in @ X873 @ X872)))=>((X871)=(X872))))=>(![X874:$i]:(~(in @ X874 @ emptyset))=>(![X875:$i, X876:$i, X877:$i]:(((in @ X877 @ (setadjoin @ X875 @ X876))<=>(((X877)=(X875))|(in @ X877 @ X876))))=>(![X878:$i, X879:$i]:(((in @ X879 @ (powerset @ X878))<=>![X880:$i]:(((in @ X880 @ X879)=>(in @ X880 @ X878)))))=>(![X881:$i, X882:$i]:(((in @ X882 @ (setunion @ X881))<=>?[X883:$i]:(((in @ X882 @ X883)&(in @ X883 @ X881)))))=>((in @ emptyset @ omega)=>(![X884:$i]:(((in @ X884 @ omega)=>(in @ (setadjoin @ X884 @ X884) @ omega)))=>(![X885:$i]:((((in @ emptyset @ X885)&![X886:$i]:((((in @ X886 @ omega)&(in @ X886 @ X885))=>(in @ (setadjoin @ X886 @ X886) @ X885))))=>![X887:$i]:(((in @ X887 @ omega)=>(in @ X887 @ X885)))))=>(![X888:$i > $i > $o, X889:$i]:((![X890:$i]:(((in @ X890 @ X889)=>(exu @ (X888 @ X890))))=>?[X891:$i]:(![X892:$i]:(((in @ X892 @ X891)<=>?[X893:$i]:(((in @ X893 @ X889)&(X888 @ X893 @ X892))))))))=>(![X894:$i]:((?[X895:$i]:((in @ X895 @ X894))=>?[X896:$i]:(((in @ X896 @ X894)&~(?[X897:$i]:(((in @ X897 @ X896)&(in @ X897 @ X894))))))))=>((epred1_0)=>(![X917:$i > $o]:(((exu @ X917)=>(X917 @ (descr @ (^[Z0:$i]:(X917 @ Z0))))))=>(![X918:$i, X919:$i > $o, X920:$i]:(((in @ X920 @ X918)=>((X919 @ X920)=>(in @ X920 @ (dsetconstr @ X918 @ X919)))))=>(![X921:$i, X922:$i > $o, X923:$i]:(((in @ X923 @ (dsetconstr @ X921 @ X922))=>(in @ X923 @ X921)))=>(![X924:$i, X925:$i > $o, X926:$i]:(((in @ X926 @ (dsetconstr @ X924 @ X925))=>(X925 @ X926)))=>(![X927:$i > $o]:(((exu @ X927)=>?[X928:$i]:(((X927 @ X928)&![X929:$i]:(((X927 @ X929)=>((X928)=(X929))))))))=>(![X930:$o, X931:$i]:(((in @ X931 @ (prop2set @ ((X930))))=>(X930)))=>(![X932:$i]:(((in @ X932 @ emptyset)=>![X933:$o]:((X933))))=>(![X934:$i]:(((in @ X934 @ emptyset)=>~($true)))=>(![X935:$i]:(~(in @ X935 @ emptyset))=>(![X936:$i > $o]:(((exu @ X936)=>?[X937:$i]:((X936 @ X937))))=>(![X938:$i, X939:$i]:((![X940:$i]:(((in @ X940 @ X938)=>(in @ X940 @ X939)))=>(![X941:$i]:(((in @ X941 @ X939)=>(in @ X941 @ X938)))=>((X938)=(X939)))))=>(![X942:$i]:((![X943:$i]:(~(in @ X943 @ X942))=>((X942)=(emptyset))))=>(![X944:$i]:((![X945:$i]:(~(in @ X945 @ X944))=>((X944)=(emptyset))))=>(![X946:$i, X947:$i > $o, X948:$i]:(((in @ X948 @ X946)=>((in @ X948 @ (dsetconstr @ X946 @ X947))<=>(X947 @ X948))))=>(![X949:$i]:(((nonempty @ X949)=>?[X950:$i]:((in @ X950 @ X949))))=>(![X951:$i, X952:$i > $o, X953:$i]:(((in @ X953 @ X951)=>((X952 @ X953)=>(nonempty @ (dsetconstr @ X951 @ X952)))))=>(![X954:$i]:((?[X955:$i]:((in @ X955 @ X954))=>(nonempty @ X954)))=>(![X956:$i, X957:$i]:((in @ X956 @ (setadjoin @ X956 @ X957)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X958:$i, X959:$i, X960:$i]:(((in @ X960 @ X959)=>(in @ X960 @ (setadjoin @ X958 @ X959))))=>(![X961:$i, X962:$i, X963:$i]:(((in @ X963 @ (setadjoin @ X961 @ X962))=>![X964:$o]:(((((X963)=(X961))=>(X964))=>(((in @ X963 @ X962)=>(X964))=>(X964))))))=>(![X965:$i, X966:$i, X967:$i]:(((in @ X967 @ (setadjoin @ X965 @ X966))=>(((X967)=(X965))|(in @ X967 @ X966))))=>(![X968:$i]:(((dsetconstr @ X968 @ (^[Z0:$i]:($true)))=(X968)))=>(![X969:$i, X970:$i]:((![X971:$i]:(((in @ X971 @ X970)=>(in @ X971 @ X969)))=>(in @ X970 @ (powerset @ X969))))=>(![X972:$i]:((in @ emptyset @ (powerset @ X972)))=>(![X973:$i]:((in @ emptyset @ (powerset @ X973)))=>(![X974:$i, X975:$i, X976:$i]:(((in @ X975 @ (powerset @ X974))=>((in @ X976 @ X975)=>(in @ X976 @ X974))))=>(![X977:$i, X978:$i, X979:$i]:(((in @ X978 @ X979)=>((in @ X979 @ X977)=>(in @ X978 @ (setunion @ X977)))))=>(![X980:$i, X981:$i]:(((in @ X981 @ (setunion @ X980))=>![X982:$o]:((![X983:$i]:(((in @ X981 @ X983)=>((in @ X983 @ X980)=>(X982))))=>(X982)))))=>(![X984:$i, X985:$i]:(((in @ X985 @ X984)=>(in @ X985 @ (powerset @ (setunion @ X984)))))=>(![X986:$i > $o]:(((exu @ X986)=>?[X987:$i]:(![X988:$i]:(((X986 @ X988)<=>((X988)=(X987)))))))=>(![X989:$i]:(((nonempty @ X989)=>?[X990:$i]:(((in @ X990 @ X989)&$true))))=>(![X991:$i, X992:$i]:(((in @ X991 @ (setadjoin @ X992 @ emptyset))=>((X991)=(X992))))=>(![X993:$i, X994:$i]:((((X993)!=(X994))=>~(in @ X994 @ (setadjoin @ X993 @ emptyset))))=>(![X995:$i, X996:$i]:((((X995)=(X996))=>(in @ X995 @ (setadjoin @ X996 @ emptyset))))=>(![X997:$i, X998:$i]:(((in @ X997 @ (setadjoin @ X998 @ emptyset))=>(in @ X998 @ (setadjoin @ X997 @ emptyset))))=>(![X999:$i, X1000:$i, X1001:$i]:(((in @ X1001 @ (setadjoin @ X999 @ (setadjoin @ X1000 @ emptyset)))=>(((X1001)=(X999))|((X1001)=(X1000)))))=>(![X1002:$i, X1003:$i]:((in @ X1002 @ (setadjoin @ X1002 @ (setadjoin @ X1003 @ emptyset))))=>(![X1004:$i, X1005:$i]:((in @ X1005 @ (setadjoin @ X1004 @ (setadjoin @ X1005 @ emptyset))))=>(![X1006:$i, X1007:$i > $o]:((?[X1008:$i]:(((in @ X1008 @ X1006)&(X1007 @ X1008)))=>(((dsetconstr @ X1006 @ X1007)=(emptyset))=>~($true))))=>(![X1009:$i > $o, X1010:$i]:(((in @ X1010 @ emptyset)=>(X1009 @ X1010)))=>(![X1011:$i, X1012:$i > $o]:((~(![X1013:$i]:(((in @ X1013 @ X1011)=>(X1012 @ X1013))))=>?[X1014:$i]:(((in @ X1014 @ X1011)&~((X1012 @ X1014))))))=>(![X1015:$i, X1016:$i > $o]:((![X1017:$i]:(((in @ X1017 @ X1015)=>~((X1016 @ X1017))))=>~(?[X1018:$i]:(((in @ X1018 @ X1015)&(X1016 @ X1018))))))=>(![X1019:$i, X1020:$i > $o]:((~(?[X1021:$i]:(((in @ X1021 @ X1019)&(X1020 @ X1021))))=>![X1022:$i]:(((in @ X1022 @ X1019)=>~((X1020 @ X1022))))))=>(![X1023:$i, X1024:$i > $o]:((?[X1025:$i]:(((in @ X1025 @ X1023)&~((X1024 @ X1025))))=>~(![X1026:$i]:(((in @ X1026 @ X1023)=>(X1024 @ X1026))))))=>(![X1027:$o]:(((X1027)=>(in @ emptyset @ (prop2set @ ((X1027))))))=>((prop2set2propI)=>(![X1028:$i, X1029:$i > $o]:((~(?[X1030:$i]:(((in @ X1030 @ X1028)&(X1029 @ X1030))))=>![X1031:$i]:(((in @ X1031 @ X1028)=>~((X1029 @ X1031))))))=>(![X1032:$i, X1033:$i > $o]:((~(![X1034:$i]:(((in @ X1034 @ X1032)=>(X1033 @ X1034))))=>?[X1035:$i]:(((in @ X1035 @ X1032)&~((X1033 @ X1035))))))=>(![X1036:$i > $o]:((?[X1037:$i]:(((X1036 @ X1037)&![X1038:$i]:(((X1036 @ X1038)=>((X1037)=(X1038))))))=>(exu @ X1036)))=>(![X1039:$i > $o]:((?[X1040:$i]:((X1039 @ X1040))=>(![X1041:$i, X1042:$i]:(((X1039 @ X1041)=>((X1039 @ X1042)=>((X1041)=(X1042)))))=>(exu @ X1039))))=>(![X1043:$i > $o]:((?[X1044:$i]:(![X1045:$i]:(((X1043 @ X1045)<=>((X1045)=(X1044)))))=>(exu @ X1043)))=>(![X1046:$i, X1047:$i]:((((X1046)=(X1047))=>![X1048:$i, X1049:$i]:((((X1048)=(X1049))=>((in @ X1048 @ X1046)=>(in @ X1049 @ X1047))))))=>(![X1050:$i, X1051:$i]:((((X1050)=(X1051))=>![X1052:$i, X1053:$i]:((((X1052)=(X1053))=>((in @ X1052 @ X1050)<=>(in @ X1053 @ X1051))))))=>(![X1054:$i > $o]:(((exu @ X1054)=>![X1055:$i, X1056:$i]:(((X1054 @ X1055)=>((X1054 @ X1056)=>((X1055)=(X1056)))))))=>(![X1057:$i > $o, X1058:$i > $o]:((![X1059:$i, X1060:$i]:((((X1059)=(X1060))=>((X1057 @ X1059)<=>(X1058 @ X1060))))=>((exu @ X1057)<=>(exu @ X1058))))=>(((emptyset)=(emptyset))=>(![X1061:$i, X1062:$i]:((((X1061)=(X1062))=>![X1063:$i, X1064:$i]:((((X1063)=(X1064))=>((setadjoin @ X1061 @ X1063)=(setadjoin @ X1062 @ X1064))))))=>(![X1065:$i, X1066:$i]:((((X1065)=(X1066))=>((powerset @ X1065)=(powerset @ X1066))))=>(![X1067:$i, X1068:$i]:((((X1067)=(X1068))=>((setunion @ X1067)=(setunion @ X1068))))=>(((omega)=(omega))=>(![X1069:$i > $o]:(((exu @ X1069)=>![X1070:$i, X1071:$i]:(((X1069 @ X1070)=>((X1069 @ X1071)=>((X1070)=(X1071)))))))=>(![X1072:$i > $o, X1073:$i > $o]:((![X1074:$i, X1075:$i]:((((X1074)=(X1075))=>((X1072 @ X1074)<=>(X1073 @ X1075))))=>((exu @ X1072)=>((exu @ X1073)=>((descr @ X1072)=(descr @ X1073))))))=>(![X1076:$i, X1077:$i]:((((X1076)=(X1077))=>![X1078:$i > $o, X1079:$i > $o]:((![X1080:$i]:(((in @ X1080 @ X1076)=>![X1081:$i]:(((in @ X1081 @ X1077)=>(((X1080)=(X1081))=>((X1078 @ X1080)<=>(X1079 @ X1081)))))))=>((dsetconstr @ X1076 @ X1078)=(dsetconstr @ X1077 @ X1079))))))=>(![X1082:$i, X1083:$i]:((![X1084:$i]:(((in @ X1084 @ X1082)=>(in @ X1084 @ X1083)))=>(subset @ X1082 @ X1083)))=>(![X1085:$i, X1086:$i]:((((X1085)=(X1086))=>(subset @ X1086 @ X1085)))=>(![X1087:$i, X1088:$i]:((((X1087)=(X1088))=>(subset @ X1087 @ X1088)))=>(![X1089:$i, X1090:$i]:((![X1091:$i]:(((in @ X1091 @ X1089)=>(in @ X1091 @ X1090)))=>(subset @ X1089 @ X1090)))=>(![X1092:$i]:((subset @ emptyset @ X1092))=>(![X1093:$i, X1094:$i, X1095:$i]:(((subset @ X1093 @ X1094)=>((in @ X1095 @ X1093)=>(in @ X1095 @ X1094))))=>(![X1096:$i, X1097:$i, X1098:$i]:(((subset @ X1096 @ X1097)=>(~(in @ X1098 @ X1097)=>~(in @ X1098 @ X1096))))=>(![X1099:$i, X1100:$i, X1101:$i]:(((in @ X1101 @ X1099)=>(~(in @ X1101 @ X1100)=>~(subset @ X1099 @ X1100))))=>(![X1102:$i, X1103:$i]:((~(subset @ X1102 @ X1103)=>((X1102)!=(X1103))))=>(![X1104:$i, X1105:$i, X1106:$i]:(((in @ X1106 @ X1104)=>(~(in @ X1106 @ X1105)=>((X1104)!=(X1105)))))=>(![X1107:$i]:((subset @ X1107 @ X1107))=>(![X1108:$i, X1109:$i, X1110:$i]:(((subset @ X1108 @ X1109)=>((subset @ X1109 @ X1110)=>(subset @ X1108 @ X1110))))=>(![X1111:$i, X1112:$i]:((subset @ X1112 @ 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inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_261, c_0_262]), c_0_263]), c_0_264]), c_0_265]), c_0_266]), notdexE]), c_0_267]), prop2setI]), ifp]), quantDeMorgan4]), theeq]), notdallE]), iftrue]), iffalse]), iftrueorfalse]), binintersectT_lem]), binunionT_lem]), powersetT_lem]), setminusT_lem]), complementT_lem]), setextT]), subsetTI]), powersetTI1]), powersetTE1]), complementTI1]), complementTE1]), notsubsetI]), subsetE2]), binintersectTELcontra]), c_0_268]), binintersectTERcontra]), in__Cong]), contrasubsetT]), inCongP]), contrasubsetT1]), c_0_269]), contrasubsetT2]), c_0_270]), contrasubsetT3]), c_0_271]), doubleComplementI1]), emptyset__Cong]), doubleComplementE1]), doubleComplementSub1]), doubleComplementSub2]), doubleComplementEq]), complementTnotintersectT]), complementImpComplementIntersect]), complementSubsetComplementIntersect]), complementInPowersetComplementIntersect]), contraSubsetComplement]), complementTcontraSubset]), binunionTILcontra]), binunionTIRcontra]), inIntersectImpInUnion]), c_0_272]), inIntersectImpInUnion2]), c_0_273]), inIntersectImpInIntersectUnions]), c_0_274]), intersectInPowersetIntersectUnions]), omega__Cong]), inComplementUnionImpNotIn1]), setunion__Cong]), powerset__Cong]), setadjoin__Cong]), subsetI1]), binintersectSubset4]), binintersectRsub]), disjointsetsI1]), binintersectER]), binintersectSubset3]), subsetE]), emptysetsubset]), subsetI2]), eqimpsubset1]), eqimpsubset2]), notequalI1]), setextsub]), subset2powerset]), setadjoinSub2]), setadjoinSub]), subsetTrans]), subsetRefl]), notequalI2]), subsetemptysetimpeq]), binunionIL]), c_0_275]), c_0_276]), powersetsubset]), inPowerset]), powersetE1]), powersetI1]), upairset2IR]), binintersectSubset5]), binintersectI]), binunionRsub]), binunionLsub]), binunionE]), binunionEcases]), binunionIR]), binintersectEL]), funcGraphProp4]), binintersectSubset2]), binintersectLsub]), binintersectSubset1]), setminusELneg]), setminusERneg]), setminusSubset2]), setminusER]), setminusEL]), setminusI]), bs114d]), setminusILneg]), symdiffIneg1]), symdiffI2]), symdiffI1]), symdiffE]), setminusSubset1]), setminusLsub]), setminusIRneg]), symdiffIneg2]), singletoninpowerset]), singletonsubset]), kpairp]), kpairiskpair]), setukpairIR]), setukpairIL]), secondinupair]), singletoninpowunion]), cartprodpairin]), ubforcartprodlem3]), ubforcartprodlem2]), ubforcartprodlem1]), upairinpowunion]), upairsubunion]), upairset2E]), cartprodmempair1]), c_0_277]), c_0_278]), setunionsingleton]), setunionsingleton2]), setunionsingleton1]), setunionE2]), cartprodmempair]), c_0_279]), cartprodfstin]), kfstpairEq]), theprop]), c_0_280]), setukpairinjL1]), singletonsuniq]), c_0_281]), setukpairinjL2]), setukpairinjR]), setukpairinjR2]), upairequniteq]), setukpairinjR1]), setukpairinjR12]), setukpairinjR11]), setukpairinjL]), c_0_282]), cartprodfstpairEq]), cartprodmempaircEq]), cartprodpairmemER]), cartprodpairmemEL]), cartprodsndin]), kpairsurjEq]), ksndpairEq]), cartprodsndpairEq]), c_0_283]), c_0_284]), c_0_285]), c_0_286]), c_0_287]), c_0_288]), cartprodpairsurjEq]), c_0_289]), c_0_290]), funcinfuncset]), ap2p]), infuncsetfunc]), app]), c_0_291]), c_0_292]), c_0_293]), funcGraphProp2]), funcGraphProp3]), funcGraphProp1]), c_0_294]), brelnall2]), brelnall1]), c_0_295]), funcextLem]), ap2apEq2]), ap2apEq1]), funcext2]), funcext]), eqbreln]), subbreln]), c_0_296]), c_0_297]), c_0_298]), c_0_299]), c_0_300]), quantDeMorgan3]), quantDeMorgan2]), quantDeMorgan1]), vacuousDall]), c_0_301]), upairsetIR]), upairsetIL]), upairsetE]), singletonsswitch]), eqinunit]), notinsingleton]), uniqinunit]), nonemptyImpWitness]), c_0_302]), subPowSU]), setunionE]), setunionI]), powersetE]), emptyInPowerset]), emptyinPowerset]), powersetI]), c_0_303]), setadjoinOr]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), nonemptyI1]), c_0_304]), nonemptyE1]), c_0_305]), noeltsimpempty]), emptyI]), setext]), c_0_306]), notinemptyset]), emptysetimpfalse]), emptysetE]), prop2setE]), c_0_307]), c_0_308]), c_0_309]), c_0_310]), c_0_311]), wellorderingAx]), foundationAx]), c_0_312]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_313])).
% 1.61/0.50 thf(c_0_315, negated_conjecture, ![X1688:$i, X1689:$i, X1691:$i, X1692:$i, X1693:$i, X1694:$i, X1695:$i, X1696:$i, X1697:$i, X1698:$i, X1699:$i, X1701:$i, X1702:$i, X1704:$i, X1705:$i, X1706:$i, X1707:$i, X1708:$i, X1710:$i, X1711:$i > $i > $o, X1712:$i, X1715:$i, X1717:$i, X1718:$i, X1719:$i, X1720:$i, X1722:$i, X1723:$i > $o, X1724:$i, X1725:$i > $o, X1726:$i, X1727:$i, X1728:$i > $o, X1729:$i, X1730:$i, X1731:$i > $o, X1732:$i, X1733:$i > $o, X1735:$i, X1736:$o, X1737:$i, X1738:$i, X1739:$o, X1740:$i, X1741:$i, X1742:$i > $o, X1744:$i, X1745:$i, X1748:$i, X1750:$i, X1752:$i, X1753:$i > $o, X1754:$i, X1755:$i, X1757:$i, X1758:$i > $o, X1759:$i, X1760:$i, X1761:$i, X1762:$i, X1763:$i, X1764:$i, X1765:$i, X1766:$i, X1767:$i, X1768:$i, X1769:$i, X1770:$o, X1771:$i, X1772:$i, X1773:$i, X1774:$i, X1775:$i, X1776:$i, X1778:$i, X1779:$i, X1780:$i, X1781:$i, X1782:$i, X1783:$i, X1784:$i, X1785:$i, X1786:$i, X1787:$i, X1788:$o, X1790:$i, X1791:$i, X1792:$i > $o, X1794:$i, X1795:$i, X1796:$i, X1798:$i, X1799:$i, X1800:$i, X1801:$i, X1802:$i, X1803:$i, X1804:$i, X1805:$i, X1806:$i, X1807:$i, X1808:$i, X1809:$i, X1810:$i, X1811:$i, X1812:$i, X1813:$i, X1814:$i > $o, X1815:$i, X1816:$i > $o, X1817:$i, X1818:$i, X1819:$i > $o, X1820:$i, X1822:$i, X1823:$i > $o, X1825:$i, X1826:$i, X1827:$i > $o, X1829:$i, X1830:$i, X1831:$i > $o, X1832:$i, X1834:$o, X1835:$i, X1836:$i > $o, X1838:$i, X1839:$i, X1840:$i > $o, X1841:$i, X1843:$i > $o, X1844:$i, X1846:$i > $o, X1847:$i, X1850:$i > $o, X1851:$i, X1853:$i, X1854:$i, X1855:$i, X1856:$i, X1857:$i, X1858:$i, X1859:$i, X1860:$i, X1861:$i > $o, X1862:$i, X1863:$i, X1864:$i > $o, X1865:$i > $o, X1868:$i, X1869:$i, X1870:$i, X1871:$i, X1872:$i, X1873:$i, X1874:$i, X1875:$i, X1876:$i > $o, X1877:$i, X1878:$i, X1879:$i > $o, X1880:$i > $o, X1883:$i, X1884:$i, X1885:$i > $o, X1886:$i > $o, X1889:$i, X1890:$i, X1892:$i, X1893:$i, X1894:$i, X1895:$i, X1896:$i, X1897:$i, X1899:$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:$i, X1915:$i, X1916:$i, X1917:$i, X1918:$i, X1919:$i, X1920:$i, X1921:$i, X1922:$i, X1923:$i, X1924:$i, X1925:$i, X1926:$i, X1927:$i, X1928:$i, X1929:$i, X1930:$i, X1931:$i, X1932:$i, X1933:$i, X1934:$i, X1935:$i, X1936:$i > $o, X1937:$i, X1938:$i > $o, X1939:$i, X1940:$i, X1941:$i, X1942:$i, X1943:$i, X1944:$i, X1945:$i, X1946:$i, X1947:$i, X1948:$i, X1949:$i, X1950:$o, X1951:$i, X1952:$i, X1953:$i, X1954:$i, X1955:$i, X1956:$i, X1957:$i, X1958:$i, X1959:$i, X1960:$i, X1961:$i, X1962:$i, X1963:$i, X1964:$i, X1965:$i, X1966:$i, X1967:$i, X1968:$i, X1969:$i, X1970:$i, X1971:$i, X1972:$i, X1973:$i, X1974:$i, X1975:$i, X1976:$i, X1977:$i, 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, X2015:$i, X2016:$i, X2017:$i, X2018:$o, X2019:$i, X2020:$i, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2025:$i, X2026:$i, X2027:$i, X2028:$i, X2029:$i, X2030:$i, X2031:$i, X2032:$i, X2033:$i, X2034:$i, X2035:$i, X2036:$i, X2037:$i, X2038:$i, X2039:$i, X2040:$i, X2041:$i, X2042:$i, X2043:$i, X2044:$i, X2045:$i, X2046:$i, X2047:$i, X2048:$i, X2049:$i, X2050:$i, X2051:$i, X2052:$i, X2053:$i, X2054:$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:$i, X2080:$i, X2081:$i, X2082:$i, X2083:$i, X2084:$i, X2086:$i, X2087:$i, X2088:$i, X2089:$i, X2090:$i > $o, X2093:$i, X2094:$i, X2095:$i > $o, X2097:$i, X2098:$i > $o, X2099:$i, X2101:$i, X2102:$i > $o, X2105:$i, X2106:$i, X2107:$i, X2108:$i, X2109:$i, X2110:$i, 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X2393) @ X2391)|(subset @ X2392 @ X2393)|~(in @ X2393 @ (powerset @ X2391))|~(in @ X2392 @ (powerset @ X2391)))&(((in @ (esk69_3 @ X2391 @ X2392 @ X2393) @ X2392)|(subset @ X2392 @ X2393)|~(in @ X2393 @ (powerset @ X2391))|~(in @ X2392 @ (powerset @ X2391)))&(~(in @ (esk69_3 @ X2391 @ X2392 @ X2393) @ X2393)|(subset @ X2392 @ X2393)|~(in @ X2393 @ (powerset @ X2391))|~(in @ X2392 @ (powerset @ X2391)))))&((((in @ (esk70_3 @ X2395 @ X2396 @ X2397) @ X2395)|(in @ X2396 @ (powerset @ X2397))|~(in @ X2397 @ (powerset @ X2395))|~(in @ X2396 @ (powerset @ X2395)))&(((in @ (esk70_3 @ X2395 @ X2396 @ X2397) @ X2396)|(in @ X2396 @ (powerset @ X2397))|~(in @ X2397 @ (powerset @ X2395))|~(in @ X2396 @ (powerset @ X2395)))&(~(in @ (esk70_3 @ X2395 @ X2396 @ X2397) @ X2397)|(in @ X2396 @ (powerset @ X2397))|~(in @ X2397 @ (powerset @ X2395))|~(in @ X2396 @ (powerset @ X2395)))))&((~(in @ X2400 @ (powerset @ X2399))|(~(in @ X2401 @ (powerset @ X2399))|(~(in @ X2402 @ X2399)|(~(in @ X2400 @ (powerset @ X2401))|(~(in @ X2402 @ X2400)|(in @ X2402 @ X2401))))))&((~(in @ X2404 @ (powerset @ X2403))|(~(in @ X2405 @ X2403)|(~(in @ X2405 @ X2404)|~(in @ X2405 @ (setminus @ X2403 @ X2404)))))&((~(in @ X2407 @ (powerset @ X2406))|(~(in @ X2408 @ X2406)|((in @ X2408 @ (setminus @ X2406 @ X2407))|(in @ X2408 @ X2407))))&((~(in @ X2410 @ (powerset @ X2409))|(~(in @ X2411 @ (powerset @ X2409))|(~(in @ X2412 @ X2409)|((in @ X2412 @ X2410)|~(in @ X2412 @ (binintersect @ X2410 @ X2411))))))&((~(in @ X2414 @ (powerset @ X2413))|(~(in @ X2415 @ (powerset @ X2413))|(~(in @ X2416 @ X2413)|((in @ X2416 @ X2415)|~(in @ X2416 @ (binintersect @ X2414 @ X2415))))))&((~(in @ X2418 @ (powerset @ X2417))|(~(in @ X2419 @ (powerset @ X2417))|(~(in @ X2420 @ X2417)|(~(subset @ X2418 @ (setminus @ X2417 @ X2419))|(~(in @ X2420 @ X2419)|~(in @ X2420 @ X2418))))))&((~(in @ X2422 @ (powerset @ X2421))|(~(in @ X2423 @ (powerset @ X2421))|(~(in @ X2424 @ X2421)|(~(subset @ X2422 @ X2423)|((in @ X2424 @ X2423)|~(in @ X2424 @ X2422))))))&((~(in @ X2426 @ (powerset @ X2425))|(~(in @ X2427 @ (powerset @ X2425))|(~(subset @ X2426 @ X2427)|(subset @ (setminus @ X2425 @ X2427) @ (setminus @ X2425 @ X2426)))))&((~(in @ X2429 @ (powerset @ X2428))|(~(in @ X2430 @ (powerset @ X2428))|(~(subset @ (setminus @ X2428 @ X2430) @ (setminus @ X2428 @ X2429))|(subset @ X2429 @ X2430))))&((~(in @ X2432 @ (powerset @ X2431))|(~(in @ X2433 @ X2431)|(~(in @ X2433 @ X2432)|(in @ X2433 @ (setminus @ X2431 @ (setminus @ X2431 @ X2432))))))&((~(in @ X2435 @ (powerset @ X2434))|(~(in @ X2436 @ X2434)|(~(in @ X2436 @ (setminus @ X2434 @ (setminus @ X2434 @ X2435)))|(in @ X2436 @ X2435))))&((~(in @ X2438 @ (powerset @ X2437))|(subset @ X2438 @ (setminus @ X2437 @ (setminus @ X2437 @ X2438))))&((~(in @ X2440 @ (powerset @ X2439))|(subset @ (setminus @ X2439 @ (setminus @ X2439 @ X2440)) @ X2440))&((~(in @ X2442 @ (powerset @ X2441))|((X2442)=(setminus @ X2441 @ (setminus @ X2441 @ X2442))))&((~(in @ X2444 @ (powerset @ X2443))|(~(in @ X2445 @ (powerset @ X2443))|(~(in @ X2446 @ X2443)|(~(in @ X2446 @ (setminus @ X2443 @ X2444))|~(in @ X2446 @ (binintersect @ X2444 @ X2445))))))&((~(in @ X2448 @ (powerset @ X2447))|(~(in @ X2449 @ (powerset @ X2447))|(~(in @ X2450 @ X2447)|(~(in @ X2450 @ (setminus @ X2447 @ X2448))|(in @ X2450 @ (setminus @ X2447 @ (binintersect @ X2448 @ X2449)))))))&((~(in @ X2452 @ (powerset @ X2451))|(~(in @ X2453 @ (powerset @ X2451))|(subset @ (setminus @ X2451 @ X2452) @ (setminus @ X2451 @ (binintersect @ X2452 @ X2453)))))&((~(in @ X2455 @ (powerset @ X2454))|(~(in @ X2456 @ (powerset @ X2454))|(in @ (setminus @ X2454 @ X2455) @ (powerset @ (setminus @ X2454 @ (binintersect @ X2455 @ X2456))))))&((~(in @ X2458 @ (powerset @ X2457))|(~(in @ X2459 @ (powerset @ X2457))|(~(subset @ X2458 @ (setminus @ X2457 @ X2459))|(~(in @ X2460 @ X2457)|(~(in @ X2460 @ X2459)|(in @ X2460 @ (setminus @ X2457 @ X2458)))))))&((~(in @ X2462 @ (powerset @ X2461))|(~(in @ X2463 @ (powerset @ X2461))|(~(subset @ X2462 @ (setminus @ X2461 @ X2463))|(subset @ X2463 @ (setminus @ X2461 @ X2462)))))&((~(in @ X2465 @ (powerset @ X2464))|(~(in @ X2466 @ (powerset @ X2464))|(~(in @ X2467 @ X2464)|((in @ X2467 @ (binunion @ X2465 @ X2466))|~(in @ X2467 @ X2465)))))&((~(in @ X2469 @ (powerset @ X2468))|(~(in @ X2470 @ (powerset @ X2468))|(~(in @ X2471 @ X2468)|((in @ X2471 @ (binunion @ X2469 @ X2470))|~(in @ X2471 @ X2470)))))&((~(in @ X2473 @ (powerset @ X2472))|(~(in @ X2474 @ (powerset @ X2472))|(~(in @ X2475 @ (powerset @ X2472))|(~(in @ X2476 @ X2472)|(~(in @ X2476 @ (binintersect @ X2473 @ X2474))|(in @ X2476 @ (binunion @ X2473 @ X2475)))))))&((~(in @ X2478 @ (powerset @ X2477))|(~(in @ X2479 @ (powerset @ X2477))|(~(in @ X2480 @ (powerset @ X2477))|(~(in @ X2481 @ X2477)|(~(in @ X2481 @ (binintersect @ X2478 @ X2479))|(in @ X2481 @ (binunion @ X2479 @ X2480)))))))&((~(in @ X2483 @ (powerset @ X2482))|(~(in @ X2484 @ (powerset @ X2482))|(~(in @ X2485 @ (powerset @ X2482))|(~(in @ X2486 @ X2482)|(~(in @ X2486 @ (binintersect @ X2483 @ X2484))|(in @ X2486 @ (binintersect @ (binunion @ X2483 @ X2485) @ (binunion @ X2484 @ X2485))))))))&((~(in @ X2488 @ (powerset @ X2487))|(~(in @ X2489 @ (powerset @ X2487))|(~(in @ X2490 @ (powerset @ X2487))|(in @ (binintersect @ X2488 @ X2489) @ (powerset @ (binintersect @ (binunion @ X2488 @ X2490) @ (binunion @ X2489 @ X2490)))))))&((~(in @ X2492 @ (powerset @ X2491))|(~(in @ X2493 @ (powerset @ X2491))|(~(in @ X2494 @ X2491)|(~(in @ X2494 @ (setminus @ X2491 @ (binunion @ X2492 @ X2493)))|~(in @ X2494 @ X2492)))))&((in @ esk72_0 @ (powerset @ esk71_0))&((in @ esk73_0 @ (powerset @ esk71_0))&((in @ esk74_0 @ esk71_0)&((in @ esk74_0 @ (setminus @ esk71_0 @ (binunion @ esk72_0 @ esk73_0)))&~(in @ esk74_0 @ (setminus @ esk71_0 @ 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_314])])])])])])])).
% 1.61/0.50 thf(c_0_316, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:((~((in @ X2 @ (setminus @ X3 @ X4)))|~((in @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_315])).
% 1.61/0.50 thf(c_0_317, negated_conjecture, (in @ esk74_0 @ (setminus @ esk71_0 @ (binunion @ esk72_0 @ esk73_0))), inference(split_conjunct,[status(thm)],[c_0_315])).
% 1.61/0.50 thf(c_0_318, negated_conjecture, ~((in @ esk74_0 @ (binunion @ esk72_0 @ esk73_0))), inference(spm,[status(thm)],[c_0_316, c_0_317])).
% 1.61/0.50 thf(c_0_319, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (binunion @ X3 @ X4))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_315])).
% 1.61/0.50 thf(c_0_320, negated_conjecture, ~((in @ esk74_0 @ (setminus @ esk71_0 @ esk72_0))), inference(split_conjunct,[status(thm)],[c_0_315])).
% 1.61/0.50 thf(c_0_321, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (setminus @ X3 @ X4))|(in @ X2 @ X4)|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_315])).
% 1.61/0.50 thf(c_0_322, negated_conjecture, (in @ esk74_0 @ esk71_0), inference(split_conjunct,[status(thm)],[c_0_315])).
% 1.61/0.50 thf(c_0_323, negated_conjecture, ~((in @ esk74_0 @ esk72_0)), inference(spm,[status(thm)],[c_0_318, c_0_319])).
% 1.61/0.50 thf(c_0_324, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_320, c_0_321]), c_0_322])]), c_0_323]), ['proof']).
% 1.61/0.50 % SZS output end CNFRefutation
% 1.61/0.50 % Parsed axioms : 565
% 1.61/0.50 % Removed by relevancy pruning/SinE : 304
% 1.61/0.50 % Initial clauses : 423
% 1.61/0.50 % Removed in clause preprocessing : 34
% 1.61/0.50 % Initial clauses in saturation : 389
% 1.61/0.50 % Processed clauses : 704
% 1.61/0.50 % ...of these trivial : 48
% 1.61/0.50 % ...subsumed : 310
% 1.61/0.50 % ...remaining for further processing : 346
% 1.61/0.50 % Other redundant clauses eliminated : 29
% 1.61/0.50 % Clauses deleted for lack of memory : 0
% 1.61/0.50 % Backward-subsumed : 1
% 1.61/0.50 % Backward-rewritten : 13
% 1.61/0.50 % Generated clauses : 2669
% 1.61/0.50 % ...of the previous two non-redundant : 2287
% 1.61/0.50 % ...aggressively subsumed : 0
% 1.61/0.50 % Contextual simplify-reflections : 0
% 1.61/0.50 % Paramodulations : 2636
% 1.61/0.50 % Factorizations : 0
% 1.61/0.50 % NegExts : 0
% 1.61/0.50 % Equation resolutions : 32
% 1.61/0.50 % Disequality decompositions : 0
% 1.61/0.50 % Total rewrite steps : 412
% 1.61/0.50 % ...of those cached : 318
% 1.61/0.50 % Propositional unsat checks : 0
% 1.61/0.50 % Propositional check models : 0
% 1.61/0.50 % Propositional check unsatisfiable : 0
% 1.61/0.50 % Propositional clauses : 0
% 1.61/0.50 % Propositional clauses after purity: 0
% 1.61/0.50 % Propositional unsat core size : 0
% 1.61/0.50 % Propositional preprocessing time : 0.000
% 1.61/0.50 % Propositional encoding time : 0.000
% 1.61/0.50 % Propositional solver time : 0.000
% 1.61/0.50 % Success case prop preproc time : 0.000
% 1.61/0.50 % Success case prop encoding time : 0.000
% 1.61/0.50 % Success case prop solver time : 0.000
% 1.61/0.50 % Current number of processed clauses : 322
% 1.61/0.50 % Positive orientable unit clauses : 75
% 1.61/0.50 % Positive unorientable unit clauses: 0
% 1.61/0.50 % Negative unit clauses : 10
% 1.61/0.50 % Non-unit-clauses : 237
% 1.61/0.50 % Current number of unprocessed clauses: 1905
% 1.61/0.50 % ...number of literals in the above : 5203
% 1.61/0.50 % Current number of archived formulas : 0
% 1.61/0.50 % Current number of archived clauses : 14
% 1.61/0.50 % Clause-clause subsumption calls (NU) : 10113
% 1.61/0.50 % Rec. Clause-clause subsumption calls : 8435
% 1.61/0.50 % Non-unit clause-clause subsumptions : 273
% 1.61/0.50 % Unit Clause-clause subsumption calls : 797
% 1.61/0.50 % Rewrite failures with RHS unbound : 0
% 1.61/0.50 % BW rewrite match attempts : 24
% 1.61/0.50 % BW rewrite match successes : 9
% 1.61/0.50 % Condensation attempts : 0
% 1.61/0.50 % Condensation successes : 0
% 1.61/0.50 % Termbank termtop insertions : 91939
% 1.61/0.50 % Search garbage collected termcells : 26169
% 1.61/0.50
% 1.61/0.50 % -------------------------------------------------
% 1.61/0.50 % User time : 0.145 s
% 1.61/0.50 % System time : 0.016 s
% 1.61/0.50 % Total time : 0.161 s
% 1.61/0.50 % Maximum resident set size: 9900 pages
% 1.61/0.50
% 1.61/0.50 % -------------------------------------------------
% 1.61/0.50 % User time : 0.268 s
% 1.61/0.50 % System time : 0.064 s
% 1.61/0.50 % Total time : 0.332 s
% 1.61/0.50 % Maximum resident set size: 5632 pages
% 1.61/0.50 % E exiting
%------------------------------------------------------------------------------