%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU685^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : 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 08:25:02 AM UTC 2026
% Result : Theorem 3.31s 0.76s
% Output : CNFRefutation 3.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU685^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n010.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 14:09:03 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.26 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p
% 3.31/0.76 % Version: 3.5.1-ho
% 3.31/0.76 % Preprocessing class: HSLMSLSSLLLCHFA.
% 3.31/0.76 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 3.31/0.76 % Starting ehoh_best5 with 300s (1) cores
% 3.31/0.76 % Starting almost_fo_3_lam with 300s (1) cores
% 3.31/0.76 % Starting new_bool_5 with 300s (1) cores
% 3.31/0.76 % Starting pre_casc_3 with 300s (1) cores
% 3.31/0.76 % Starting ho_unfolding_8 with 300s (1) cores
% 3.31/0.76 % Starting new_ho_10_cnf2 with 300s (1) cores
% 3.31/0.76 % Starting new_bool_3 with 300s (1) cores
% 3.31/0.76 % Starting new_ho_5 with 300s (1) cores
% 3.31/0.76 % new_bool_5 with pid 2912927 completed with status 0
% 3.31/0.76 % Result found by new_bool_5
% 3.31/0.76 % Preprocessing class: HSLMSLSSLLLCHFA.
% 3.31/0.76 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 3.31/0.76 % Starting ehoh_best5 with 300s (1) cores
% 3.31/0.76 % Starting almost_fo_3_lam with 300s (1) cores
% 3.31/0.76 % Starting new_bool_5 with 300s (1) cores
% 3.31/0.76 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 3.31/0.76 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 3.31/0.76 % Search class: HGHSM-FSLM32-MHFMMSBN
% 3.31/0.76 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 3.31/0.76 % Starting SubtermCWHack with 28s (1) cores
% 3.31/0.76 % SubtermCWHack with pid 2912936 completed with status 0
% 3.31/0.76 % Result found by SubtermCWHack
% 3.31/0.76 % Preprocessing class: HSLMSLSSLLLCHFA.
% 3.31/0.76 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 3.31/0.76 % Starting ehoh_best5 with 300s (1) cores
% 3.31/0.76 % Starting almost_fo_3_lam with 300s (1) cores
% 3.31/0.76 % Starting new_bool_5 with 300s (1) cores
% 3.31/0.76 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 3.31/0.76 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 3.31/0.76 % Search class: HGHSM-FSLM32-MHFMMSBN
% 3.31/0.76 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 3.31/0.76 % Starting SubtermCWHack with 28s (1) cores
% 3.31/0.76 % Preprocessing time : 0.006 s
% 3.31/0.76
% 3.31/0.76 % Proof found!
% 3.31/0.76 % SZS status Theorem
% 3.31/0.76 % SZS output start CNFRefutation
% 3.31/0.76 thf(decl_23, type, in: $i > $i > $o).
% 3.31/0.76 thf(decl_24, type, exu: ($i > $o) > $o).
% 3.31/0.76 thf(decl_25, type, setextAx: $o).
% 3.31/0.76 thf(decl_26, type, emptyset: $i).
% 3.31/0.76 thf(decl_27, type, emptysetAx: $o).
% 3.31/0.76 thf(decl_28, type, setadjoin: $i > $i > $i).
% 3.31/0.76 thf(decl_29, type, setadjoinAx: $o).
% 3.31/0.76 thf(decl_30, type, powerset: $i > $i).
% 3.31/0.76 thf(decl_31, type, powersetAx: $o).
% 3.31/0.76 thf(decl_32, type, setunion: $i > $i).
% 3.31/0.76 thf(decl_33, type, setunionAx: $o).
% 3.31/0.76 thf(decl_34, type, omega: $i).
% 3.31/0.76 thf(decl_35, type, omega0Ax: $o).
% 3.31/0.76 thf(decl_36, type, omegaSAx: $o).
% 3.31/0.76 thf(decl_37, type, omegaIndAx: $o).
% 3.31/0.76 thf(decl_38, type, replAx: $o).
% 3.31/0.76 thf(decl_39, type, foundationAx: $o).
% 3.31/0.76 thf(decl_40, type, wellorderingAx: $o).
% 3.31/0.76 thf(decl_41, type, descr: ($i > $o) > $i).
% 3.31/0.76 thf(decl_42, type, descrp: $o).
% 3.31/0.76 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 3.31/0.76 thf(decl_44, type, dsetconstrI: $o).
% 3.31/0.76 thf(decl_45, type, dsetconstrEL: $o).
% 3.31/0.76 thf(decl_46, type, dsetconstrER: $o).
% 3.31/0.76 thf(decl_47, type, exuE1: $o).
% 3.31/0.76 thf(decl_48, type, prop2set: $o > $i).
% 3.31/0.76 thf(decl_49, type, prop2setE: $o).
% 3.31/0.76 thf(decl_50, type, emptysetE: $o).
% 3.31/0.76 thf(decl_51, type, emptysetimpfalse: $o).
% 3.31/0.76 thf(decl_52, type, notinemptyset: $o).
% 3.31/0.76 thf(decl_53, type, exuE3e: $o).
% 3.31/0.76 thf(decl_54, type, setext: $o).
% 3.31/0.76 thf(decl_55, type, emptyI: $o).
% 3.31/0.76 thf(decl_56, type, noeltsimpempty: $o).
% 3.31/0.76 thf(decl_57, type, setbeta: $o).
% 3.31/0.76 thf(decl_58, type, nonempty: $i > $o).
% 3.31/0.76 thf(decl_59, type, nonemptyE1: $o).
% 3.31/0.76 thf(decl_60, type, nonemptyI: $o).
% 3.31/0.76 thf(decl_61, type, nonemptyI1: $o).
% 3.31/0.76 thf(decl_62, type, setadjoinIL: $o).
% 3.31/0.76 thf(decl_63, type, emptyinunitempty: $o).
% 3.31/0.76 thf(decl_64, type, setadjoinIR: $o).
% 3.31/0.76 thf(decl_65, type, setadjoinE: $o).
% 3.31/0.76 thf(decl_66, type, setadjoinOr: $o).
% 3.31/0.76 thf(decl_67, type, setoftrueEq: $o).
% 3.31/0.76 thf(decl_68, type, powersetI: $o).
% 3.31/0.76 thf(decl_69, type, emptyinPowerset: $o).
% 3.31/0.76 thf(decl_70, type, emptyInPowerset: $o).
% 3.31/0.76 thf(decl_71, type, powersetE: $o).
% 3.31/0.76 thf(decl_72, type, setunionI: $o).
% 3.31/0.76 thf(decl_73, type, setunionE: $o).
% 3.31/0.76 thf(decl_74, type, subPowSU: $o).
% 3.31/0.76 thf(decl_75, type, exuE2: $o).
% 3.31/0.76 thf(decl_76, type, nonemptyImpWitness: $o).
% 3.31/0.76 thf(decl_77, type, uniqinunit: $o).
% 3.31/0.76 thf(decl_78, type, notinsingleton: $o).
% 3.31/0.76 thf(decl_79, type, eqinunit: $o).
% 3.31/0.76 thf(decl_80, type, singletonsswitch: $o).
% 3.31/0.76 thf(decl_81, type, upairsetE: $o).
% 3.31/0.76 thf(decl_82, type, upairsetIL: $o).
% 3.31/0.76 thf(decl_83, type, upairsetIR: $o).
% 3.31/0.76 thf(decl_84, type, emptyE1: $o).
% 3.31/0.76 thf(decl_85, type, vacuousDall: $o).
% 3.31/0.76 thf(decl_86, type, quantDeMorgan1: $o).
% 3.31/0.76 thf(decl_87, type, quantDeMorgan2: $o).
% 3.31/0.76 thf(decl_88, type, quantDeMorgan3: $o).
% 3.31/0.76 thf(decl_89, type, quantDeMorgan4: $o).
% 3.31/0.76 thf(decl_90, type, prop2setI: $o).
% 3.31/0.76 thf(decl_92, type, prop2set2propI: $o).
% 3.31/0.76 thf(decl_93, type, notdexE: $o).
% 3.31/0.76 thf(decl_94, type, notdallE: $o).
% 3.31/0.76 thf(decl_95, type, exuI1: $o).
% 3.31/0.76 thf(decl_96, type, exuI3: $o).
% 3.31/0.76 thf(decl_97, type, exuI2: $o).
% 3.31/0.76 thf(decl_98, type, inCongP: $o).
% 3.31/0.76 thf(decl_99, type, in__Cong: $o).
% 3.31/0.76 thf(decl_100, type, exuE3u: $o).
% 3.31/0.76 thf(decl_101, type, exu__Cong: $o).
% 3.31/0.76 thf(decl_102, type, emptyset__Cong: $o).
% 3.31/0.76 thf(decl_103, type, setadjoin__Cong: $o).
% 3.31/0.76 thf(decl_104, type, powerset__Cong: $o).
% 3.31/0.76 thf(decl_105, type, setunion__Cong: $o).
% 3.31/0.76 thf(decl_106, type, omega__Cong: $o).
% 3.31/0.76 thf(decl_107, type, exuEu: $o).
% 3.31/0.76 thf(decl_108, type, descr__Cong: $o).
% 3.31/0.76 thf(decl_109, type, dsetconstr__Cong: $o).
% 3.31/0.76 thf(decl_110, type, subset: $i > $i > $o).
% 3.31/0.76 thf(decl_113, type, subsetI1: $o).
% 3.31/0.76 thf(decl_114, type, eqimpsubset2: $o).
% 3.31/0.76 thf(decl_115, type, eqimpsubset1: $o).
% 3.31/0.76 thf(decl_116, type, subsetI2: $o).
% 3.31/0.76 thf(decl_117, type, emptysetsubset: $o).
% 3.31/0.76 thf(decl_118, type, subsetE: $o).
% 3.31/0.76 thf(decl_119, type, subsetE2: $o).
% 3.31/0.76 thf(decl_120, type, notsubsetI: $o).
% 3.31/0.76 thf(decl_121, type, notequalI1: $o).
% 3.31/0.76 thf(decl_122, type, notequalI2: $o).
% 3.31/0.76 thf(decl_123, type, subsetRefl: $o).
% 3.31/0.76 thf(decl_124, type, subsetTrans: $o).
% 3.31/0.76 thf(decl_125, type, setadjoinSub: $o).
% 3.31/0.76 thf(decl_126, type, setadjoinSub2: $o).
% 3.31/0.76 thf(decl_127, type, subset2powerset: $o).
% 3.31/0.76 thf(decl_128, type, setextsub: $o).
% 3.31/0.76 thf(decl_129, type, subsetemptysetimpeq: $o).
% 3.31/0.76 thf(decl_130, type, powersetI1: $o).
% 3.31/0.76 thf(decl_131, type, powersetE1: $o).
% 3.31/0.76 thf(decl_132, type, inPowerset: $o).
% 3.31/0.76 thf(decl_133, type, powersetsubset: $o).
% 3.31/0.76 thf(decl_134, type, sepInPowerset: $o).
% 3.31/0.76 thf(decl_135, type, sepSubset: $o).
% 3.31/0.76 thf(decl_136, type, binunion: $i > $i > $i).
% 3.31/0.76 thf(decl_137, type, binunionIL: $o).
% 3.31/0.76 thf(decl_138, type, upairset2IR: $o).
% 3.31/0.76 thf(decl_139, type, binunionIR: $o).
% 3.31/0.76 thf(decl_140, type, binunionEcases: $o).
% 3.31/0.76 thf(decl_141, type, binunionE: $o).
% 3.31/0.76 thf(decl_142, type, binunionLsub: $o).
% 3.31/0.76 thf(decl_143, type, binunionRsub: $o).
% 3.31/0.76 thf(decl_144, type, binintersect: $i > $i > $i).
% 3.31/0.76 thf(decl_145, type, binintersectI: $o).
% 3.31/0.76 thf(decl_146, type, binintersectSubset5: $o).
% 3.31/0.76 thf(decl_147, type, binintersectEL: $o).
% 3.31/0.76 thf(decl_148, type, binintersectLsub: $o).
% 3.31/0.76 thf(decl_149, type, binintersectSubset2: $o).
% 3.31/0.76 thf(decl_150, type, binintersectSubset3: $o).
% 3.31/0.76 thf(decl_151, type, binintersectER: $o).
% 3.31/0.76 thf(decl_152, type, disjointsetsI1: $o).
% 3.31/0.76 thf(decl_153, type, binintersectRsub: $o).
% 3.31/0.76 thf(decl_154, type, binintersectSubset4: $o).
% 3.31/0.76 thf(decl_155, type, binintersectSubset1: $o).
% 3.31/0.76 thf(decl_156, type, bs114d: $o).
% 3.31/0.76 thf(decl_158, type, setminus: $i > $i > $i).
% 3.31/0.76 thf(decl_159, type, setminusI: $o).
% 3.31/0.76 thf(decl_160, type, setminusEL: $o).
% 3.31/0.76 thf(decl_161, type, setminusER: $o).
% 3.31/0.76 thf(decl_162, type, setminusSubset2: $o).
% 3.31/0.76 thf(decl_163, type, setminusERneg: $o).
% 3.31/0.76 thf(decl_164, type, setminusELneg: $o).
% 3.31/0.76 thf(decl_165, type, setminusILneg: $o).
% 3.31/0.76 thf(decl_166, type, setminusIRneg: $o).
% 3.31/0.76 thf(decl_167, type, setminusLsub: $o).
% 3.31/0.76 thf(decl_168, type, setminusSubset1: $o).
% 3.31/0.76 thf(decl_169, type, symdiff: $i > $i > $i).
% 3.31/0.76 thf(decl_170, type, symdiffE: $o).
% 3.31/0.76 thf(decl_171, type, symdiffI1: $o).
% 3.31/0.76 thf(decl_172, type, symdiffI2: $o).
% 3.31/0.76 thf(decl_173, type, symdiffIneg1: $o).
% 3.31/0.76 thf(decl_174, type, symdiffIneg2: $o).
% 3.31/0.76 thf(decl_175, type, iskpair: $i > $o).
% 3.31/0.76 thf(decl_176, type, secondinupair: $o).
% 3.31/0.76 thf(decl_177, type, setukpairIL: $o).
% 3.31/0.76 thf(decl_178, type, setukpairIR: $o).
% 3.31/0.76 thf(decl_179, type, kpairiskpair: $o).
% 3.31/0.76 thf(decl_180, type, kpair: $i > $i > $i).
% 3.31/0.76 thf(decl_181, type, kpairp: $o).
% 3.31/0.76 thf(decl_182, type, cartprod: $i > $i > $i).
% 3.31/0.76 thf(decl_183, type, singletonsubset: $o).
% 3.31/0.76 thf(decl_184, type, singletoninpowerset: $o).
% 3.31/0.76 thf(decl_185, type, singletoninpowunion: $o).
% 3.31/0.76 thf(decl_186, type, upairset2E: $o).
% 3.31/0.76 thf(decl_187, type, upairsubunion: $o).
% 3.31/0.76 thf(decl_188, type, upairinpowunion: $o).
% 3.31/0.76 thf(decl_189, type, ubforcartprodlem1: $o).
% 3.31/0.76 thf(decl_190, type, ubforcartprodlem2: $o).
% 3.31/0.76 thf(decl_191, type, ubforcartprodlem3: $o).
% 3.31/0.76 thf(decl_192, type, cartprodpairin: $o).
% 3.31/0.76 thf(decl_193, type, cartprodmempair1: $o).
% 3.31/0.76 thf(decl_194, type, cartprodmempair: $o).
% 3.31/0.76 thf(decl_195, type, setunionE2: $o).
% 3.31/0.76 thf(decl_196, type, setunionsingleton1: $o).
% 3.31/0.76 thf(decl_197, type, setunionsingleton2: $o).
% 3.31/0.76 thf(decl_198, type, setunionsingleton: $o).
% 3.31/0.76 thf(decl_199, type, singleton: $i > $o).
% 3.31/0.76 thf(decl_200, type, singletonprop: $o).
% 3.31/0.76 thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 3.31/0.76 thf(decl_202, type, ex1E1: $o).
% 3.31/0.76 thf(decl_203, type, ex1I: $o).
% 3.31/0.76 thf(decl_204, type, ex1I2: $o).
% 3.31/0.76 thf(decl_205, type, singletonsuniq: $o).
% 3.31/0.76 thf(decl_210, type, setukpairinjL1: $o).
% 3.31/0.76 thf(decl_211, type, kfstsingleton: $o).
% 3.31/0.76 thf(decl_212, type, theprop: $o).
% 3.31/0.76 thf(decl_213, type, kfst: $i > $i).
% 3.31/0.76 thf(decl_214, type, kfstpairEq: $o).
% 3.31/0.76 thf(decl_215, type, cartprodfstin: $o).
% 3.31/0.76 thf(decl_216, type, setukpairinjL2: $o).
% 3.31/0.76 thf(decl_217, type, setukpairinjL: $o).
% 3.31/0.76 thf(decl_218, type, setukpairinjR11: $o).
% 3.31/0.76 thf(decl_219, type, setukpairinjR12: $o).
% 3.31/0.76 thf(decl_220, type, setukpairinjR1: $o).
% 3.31/0.76 thf(decl_221, type, upairequniteq: $o).
% 3.31/0.76 thf(decl_222, type, setukpairinjR2: $o).
% 3.31/0.76 thf(decl_223, type, setukpairinjR: $o).
% 3.31/0.76 thf(decl_224, type, ksndsingleton: $o).
% 3.31/0.76 thf(decl_225, type, ksnd: $i > $i).
% 3.31/0.76 thf(decl_226, type, ksndpairEq: $o).
% 3.31/0.76 thf(decl_227, type, kpairsurjEq: $o).
% 3.31/0.76 thf(decl_228, type, cartprodsndin: $o).
% 3.31/0.76 thf(decl_229, type, cartprodpairmemEL: $o).
% 3.31/0.76 thf(decl_230, type, cartprodpairmemER: $o).
% 3.31/0.76 thf(decl_231, type, cartprodmempaircEq: $o).
% 3.31/0.76 thf(decl_232, type, cartprodfstpairEq: $o).
% 3.31/0.76 thf(decl_233, type, cartprodsndpairEq: $o).
% 3.31/0.76 thf(decl_234, type, cartprodpairsurjEq: $o).
% 3.31/0.76 thf(decl_235, type, breln: $i > $i > $i > $o).
% 3.31/0.76 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 3.31/0.76 thf(decl_237, type, dpsetconstrI: $o).
% 3.31/0.76 thf(decl_238, type, dpsetconstrSub: $o).
% 3.31/0.76 thf(decl_239, type, setOfPairsIsBReln: $o).
% 3.31/0.76 thf(decl_240, type, dpsetconstrERa: $o).
% 3.31/0.76 thf(decl_241, type, dpsetconstrEL1: $o).
% 3.31/0.76 thf(decl_242, type, dpsetconstrEL2: $o).
% 3.31/0.76 thf(decl_243, type, dpsetconstrER: $o).
% 3.31/0.76 thf(decl_244, type, func: $i > $i > $i > $o).
% 3.31/0.76 thf(decl_245, type, funcSet: $i > $i > $i).
% 3.31/0.76 thf(decl_246, type, funcImageSingleton: $o).
% 3.31/0.76 thf(decl_247, type, apProp: $o).
% 3.31/0.76 thf(decl_248, type, ap: $i > $i > $i > $i > $i).
% 3.31/0.76 thf(decl_249, type, app: $o).
% 3.31/0.76 thf(decl_250, type, infuncsetfunc: $o).
% 3.31/0.76 thf(decl_251, type, ap2p: $o).
% 3.31/0.76 thf(decl_252, type, funcinfuncset: $o).
% 3.31/0.76 thf(decl_253, type, lamProp: $o).
% 3.31/0.76 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
% 3.31/0.76 thf(decl_255, type, lamp: $o).
% 3.31/0.76 thf(decl_256, type, lam2p: $o).
% 3.31/0.76 thf(decl_257, type, brelnall1: $o).
% 3.31/0.76 thf(decl_258, type, brelnall2: $o).
% 3.31/0.76 thf(decl_259, type, ex1E2: $o).
% 3.31/0.76 thf(decl_260, type, funcGraphProp1: $o).
% 3.31/0.76 thf(decl_261, type, epred1_0: $o).
% 3.31/0.76 thf(decl_262, type, esk1_2: $i > $i > $i).
% 3.31/0.76 thf(decl_263, type, esk2_2: $i > $i > $i).
% 3.31/0.76 thf(decl_264, type, esk3_2: $i > $i > $i).
% 3.31/0.76 thf(decl_265, type, esk4_1: $i > $i).
% 3.31/0.76 thf(decl_266, type, esk5_2: ($i > $i > $o) > $i > $i).
% 3.31/0.76 thf(decl_267, type, esk6_2: ($i > $i > $o) > $i > $i).
% 3.31/0.76 thf(decl_268, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
% 3.31/0.76 thf(decl_269, type, esk8_1: $i > $i).
% 3.31/0.76 thf(decl_270, type, esk9_1: ($i > $o) > $i).
% 3.31/0.76 thf(decl_271, type, esk10_1: ($i > $o) > $i).
% 3.31/0.76 thf(decl_272, type, esk11_2: $i > $i > $i).
% 3.31/0.76 thf(decl_273, type, esk12_2: $i > $i > $i).
% 3.31/0.76 thf(decl_274, type, esk13_1: $i > $i).
% 3.31/0.76 thf(decl_275, type, esk14_1: $i > $i).
% 3.31/0.76 thf(decl_276, type, esk15_1: $i > $i).
% 3.31/0.76 thf(decl_277, type, esk16_2: $i > $i > $i).
% 3.31/0.76 thf(decl_278, type, esk17_3: $i > $i > $o > $i).
% 3.31/0.76 thf(decl_279, type, esk18_1: ($i > $o) > $i).
% 3.31/0.76 thf(decl_280, type, esk19_1: $i > $i).
% 3.31/0.76 thf(decl_281, type, esk20_2: $i > ($i > $o) > $i).
% 3.31/0.76 thf(decl_282, type, esk21_2: $i > ($i > $o) > $i).
% 3.31/0.76 thf(decl_283, type, esk22_2: $i > ($i > $o) > $i).
% 3.31/0.76 thf(decl_284, type, esk23_2: $i > ($i > $o) > $i).
% 3.31/0.76 thf(decl_285, type, esk24_2: $i > ($i > $o) > $i).
% 3.31/0.76 thf(decl_286, type, esk25_2: $i > ($i > $o) > $i).
% 3.31/0.76 thf(decl_287, type, esk26_2: ($i > $o) > $i > $i).
% 3.31/0.76 thf(decl_288, type, esk27_1: ($i > $o) > $i).
% 3.31/0.76 thf(decl_289, type, esk28_1: ($i > $o) > $i).
% 3.31/0.76 thf(decl_290, type, esk29_2: ($i > $o) > $i > $i).
% 3.31/0.76 thf(decl_291, type, esk30_2: ($i > $o) > ($i > $o) > $i).
% 3.31/0.76 thf(decl_292, type, esk31_2: ($i > $o) > ($i > $o) > $i).
% 3.31/0.76 thf(decl_293, type, esk32_2: ($i > $o) > ($i > $o) > $i).
% 3.31/0.76 thf(decl_294, type, esk33_2: ($i > $o) > ($i > $o) > $i).
% 3.31/0.76 thf(decl_295, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 3.31/0.76 thf(decl_296, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 3.31/0.76 thf(decl_297, type, esk36_2: $i > $i > $i).
% 3.31/0.76 thf(decl_298, type, esk37_2: $i > $i > $i).
% 3.31/0.76 thf(decl_299, type, esk38_2: $i > $i > $i).
% 3.31/0.76 thf(decl_300, type, esk39_3: $i > $i > $i > $i).
% 3.31/0.76 thf(decl_301, type, esk40_3: $i > $i > $i > $i).
% 3.31/0.76 thf(decl_302, type, esk41_2: $i > $i > $i).
% 3.31/0.76 thf(decl_303, type, esk42_2: $i > ($i > $o) > $i).
% 3.31/0.76 thf(decl_304, type, esk43_2: $i > ($i > $o) > $i).
% 3.31/0.76 thf(decl_305, type, esk44_2: $i > ($i > $o) > $i).
% 3.31/0.76 thf(decl_306, type, esk45_3: $i > ($i > $o) > $i > $i).
% 3.31/0.76 thf(decl_307, type, esk46_2: $i > ($i > $o) > $i).
% 3.31/0.76 thf(decl_308, type, esk47_2: $i > ($i > $o) > $i).
% 3.31/0.76 thf(decl_309, type, esk48_3: $i > $i > ($i > $i) > $i).
% 3.31/0.76 thf(decl_310, type, esk49_3: $i > $i > ($i > $i) > $i).
% 3.31/0.76 thf(decl_311, type, esk50_3: $i > $i > ($i > $i) > $i).
% 3.31/0.76 thf(decl_312, type, esk51_4: $i > $i > $i > ($i > $o) > $i).
% 3.31/0.76 thf(decl_313, type, esk52_4: $i > $i > $i > ($i > $o) > $i).
% 3.31/0.76 thf(decl_314, type, esk53_4: $i > $i > $i > ($i > $o) > $i).
% 3.31/0.76 thf(decl_315, type, esk54_4: $i > $i > $i > ($i > $o) > $i).
% 3.31/0.76 thf(decl_316, type, esk55_0: $i).
% 3.31/0.76 thf(decl_317, type, esk56_0: $i).
% 3.31/0.76 thf(decl_318, type, esk57_0: $i).
% 3.31/0.76 thf(decl_319, type, esk58_0: $i).
% 3.31/0.76 thf(funcGraphProp3, 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)=>![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X30 @ X2)) @ X30)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', funcGraphProp3)).
% 3.31/0.76 thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', ex1I)).
% 3.31/0.76 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', ex1E1)).
% 3.31/0.76 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', ex1I2)).
% 3.31/0.76 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', kfstsingleton)).
% 3.31/0.76 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setoftrueEq)).
% 3.31/0.76 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', ksndsingleton)).
% 3.31/0.76 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', dpsetconstrI)).
% 3.31/0.76 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', dpsetconstrSub)).
% 3.31/0.76 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setOfPairsIsBReln)).
% 3.31/0.76 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', dpsetconstrERa)).
% 3.31/0.76 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', dpsetconstrEL1)).
% 3.31/0.76 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', dpsetconstrEL2)).
% 3.31/0.76 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', dpsetconstrER)).
% 3.31/0.76 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X30)))))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', funcImageSingleton)).
% 3.31/0.76 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X30))))) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', apProp)).
% 3.31/0.76 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', exuE2)).
% 3.31/0.76 thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X31 @ X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', lamProp)).
% 3.31/0.76 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X33:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X33 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X33 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', lamp)).
% 3.31/0.76 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X34:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X34 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X34 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', lam2p)).
% 3.31/0.76 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', ex1E2)).
% 3.31/0.76 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', emptyE1)).
% 3.31/0.76 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', exuI1)).
% 3.31/0.76 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', exuI3)).
% 3.31/0.76 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', exu__Cong)).
% 3.31/0.76 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', exuE3u)).
% 3.31/0.76 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', exuI2)).
% 3.31/0.76 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', dsetconstr__Cong)).
% 3.31/0.76 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', descr__Cong)).
% 3.31/0.76 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', exuEu)).
% 3.31/0.76 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', sepSubset)).
% 3.31/0.76 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', sepInPowerset)).
% 3.31/0.76 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', singletonprop)).
% 3.31/0.76 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', nonemptyI)).
% 3.31/0.76 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setbeta)).
% 3.31/0.76 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', exuE3e)).
% 3.31/0.76 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', exuE1)).
% 3.31/0.76 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', dsetconstrER)).
% 3.31/0.76 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', dsetconstrEL)).
% 3.31/0.76 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', dsetconstrI)).
% 3.31/0.76 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', descrp)).
% 3.31/0.76 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', replAx)).
% 3.31/0.76 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', emptyinunitempty)).
% 3.31/0.76 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', singletonsuniq)).
% 3.31/0.76 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setukpairinjL1)).
% 3.31/0.76 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', theprop)).
% 3.31/0.76 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', kfstpairEq)).
% 3.31/0.76 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', cartprodfstin)).
% 3.31/0.76 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setukpairinjL2)).
% 3.31/0.76 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setukpairinjL)).
% 3.31/0.76 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setukpairinjR11)).
% 3.31/0.76 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setukpairinjR12)).
% 3.31/0.76 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setukpairinjR1)).
% 3.31/0.76 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', emptyinPowerset)).
% 3.31/0.76 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', upairequniteq)).
% 3.31/0.76 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', powersetI)).
% 3.31/0.76 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setukpairinjR2)).
% 3.31/0.76 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', nonemptyI1)).
% 3.31/0.76 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setukpairinjR)).
% 3.31/0.76 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setadjoinOr)).
% 3.31/0.76 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', ksndpairEq)).
% 3.31/0.76 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setadjoinE)).
% 3.31/0.76 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', kpairsurjEq)).
% 3.31/0.76 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setadjoinIR)).
% 3.31/0.76 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', cartprodsndin)).
% 3.31/0.76 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', eqinunit)).
% 3.31/0.76 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', quantDeMorgan1)).
% 3.31/0.76 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', cartprodpairmemEL)).
% 3.31/0.76 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', emptyInPowerset)).
% 3.31/0.76 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', cartprodpairmemER)).
% 3.31/0.76 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', cartprodmempaircEq)).
% 3.31/0.76 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', cartprodfstpairEq)).
% 3.31/0.76 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', cartprodsndpairEq)).
% 3.31/0.76 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', cartprodpairsurjEq)).
% 3.31/0.76 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', uniqinunit)).
% 3.31/0.76 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', nonemptyImpWitness)).
% 3.31/0.76 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X30 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', app)).
% 3.31/0.76 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X30)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', infuncsetfunc)).
% 3.31/0.76 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', subPowSU)).
% 3.31/0.76 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X30 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', ap2p)).
% 3.31/0.76 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setunionE)).
% 3.31/0.76 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>(in @ X30 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', funcinfuncset)).
% 3.31/0.76 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setunionI)).
% 3.31/0.76 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', powersetE)).
% 3.31/0.76 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', notinsingleton)).
% 3.31/0.76 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X29:$i]:(((breln @ X4 @ X5 @ X29)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X29)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', brelnall1)).
% 3.31/0.76 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X29:$i]:(((breln @ X4 @ X5 @ X29)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X29)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', brelnall2)).
% 3.31/0.76 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X30 @ X2)) @ X30)))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', funcGraphProp1)).
% 3.31/0.76 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', vacuousDall)).
% 3.31/0.76 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', upairsetIR)).
% 3.31/0.76 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', upairsetIL)).
% 3.31/0.76 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', upairsetE)).
% 3.31/0.76 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', singletonsswitch)).
% 3.31/0.76 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', emptysetsubset)).
% 3.31/0.76 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', subsetI2)).
% 3.31/0.76 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', subsetRefl)).
% 3.31/0.76 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', notdallE)).
% 3.31/0.76 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', notdexE)).
% 3.31/0.76 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', prop2setI)).
% 3.31/0.76 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', quantDeMorgan4)).
% 3.31/0.76 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', quantDeMorgan3)).
% 3.31/0.76 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', quantDeMorgan2)).
% 3.31/0.76 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setadjoinIL)).
% 3.31/0.76 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setadjoin__Cong)).
% 3.31/0.76 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', emptyset__Cong)).
% 3.31/0.76 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', in__Cong)).
% 3.31/0.76 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', inCongP)).
% 3.31/0.76 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', powerset__Cong)).
% 3.31/0.76 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', eqimpsubset2)).
% 3.31/0.76 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', subsetI1)).
% 3.31/0.76 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', omega__Cong)).
% 3.31/0.76 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setunion__Cong)).
% 3.31/0.76 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', eqimpsubset1)).
% 3.31/0.76 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', notequalI2)).
% 3.31/0.76 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', notequalI1)).
% 3.31/0.76 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', notsubsetI)).
% 3.31/0.76 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', subsetE2)).
% 3.31/0.76 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', subsetE)).
% 3.31/0.76 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', powersetI1)).
% 3.31/0.76 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', subsetemptysetimpeq)).
% 3.31/0.76 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setextsub)).
% 3.31/0.76 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', subset2powerset)).
% 3.31/0.76 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setadjoinSub2)).
% 3.31/0.76 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setadjoinSub)).
% 3.31/0.76 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', subsetTrans)).
% 3.31/0.76 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', powersetE1)).
% 3.31/0.76 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', binunionIR)).
% 3.31/0.76 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', upairset2IR)).
% 3.31/0.76 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', binunionIL)).
% 3.31/0.76 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', powersetsubset)).
% 3.31/0.76 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', inPowerset)).
% 3.31/0.76 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', binunionEcases)).
% 3.31/0.76 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', binintersectLsub)).
% 3.31/0.76 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', binintersectEL)).
% 3.31/0.76 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', binintersectSubset5)).
% 3.31/0.76 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', binintersectI)).
% 3.31/0.76 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', binunionRsub)).
% 3.31/0.76 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', binunionLsub)).
% 3.31/0.76 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', binunionE)).
% 3.31/0.76 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', binintersectSubset2)).
% 3.31/0.76 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', bs114d)).
% 3.31/0.76 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', binintersectSubset1)).
% 3.31/0.76 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', binintersectSubset4)).
% 3.31/0.76 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', binintersectRsub)).
% 3.31/0.76 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', disjointsetsI1)).
% 3.31/0.76 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', binintersectER)).
% 3.31/0.76 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', binintersectSubset3)).
% 3.31/0.76 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setminusI)).
% 3.31/0.76 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setminusIRneg)).
% 3.31/0.76 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setminusILneg)).
% 3.31/0.76 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setminusELneg)).
% 3.31/0.76 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setminusERneg)).
% 3.31/0.76 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setminusSubset2)).
% 3.31/0.76 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setminusER)).
% 3.31/0.76 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setminusEL)).
% 3.31/0.76 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setminusLsub)).
% 3.31/0.76 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', secondinupair)).
% 3.31/0.76 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', symdiffIneg2)).
% 3.31/0.76 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', symdiffIneg1)).
% 3.31/0.76 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', symdiffI2)).
% 3.31/0.76 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', symdiffI1)).
% 3.31/0.76 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', symdiffE)).
% 3.31/0.76 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setminusSubset1)).
% 3.31/0.76 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setukpairIL)).
% 3.31/0.76 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', upairset2E)).
% 3.31/0.76 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', singletoninpowunion)).
% 3.31/0.76 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', singletoninpowerset)).
% 3.31/0.76 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', singletonsubset)).
% 3.31/0.76 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', kpairp)).
% 3.31/0.76 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', kpairiskpair)).
% 3.31/0.76 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setukpairIR)).
% 3.31/0.76 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', upairsubunion)).
% 3.31/0.76 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', cartprodmempair)).
% 3.31/0.76 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', cartprodmempair1)).
% 3.31/0.76 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', cartprodpairin)).
% 3.31/0.76 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', ubforcartprodlem3)).
% 3.31/0.76 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', ubforcartprodlem2)).
% 3.31/0.76 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', ubforcartprodlem1)).
% 3.31/0.76 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', upairinpowunion)).
% 3.31/0.76 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setunionsingleton1)).
% 3.31/0.76 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setunionsingleton2)).
% 3.31/0.76 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setunionsingleton)).
% 3.31/0.76 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setunionE2)).
% 3.31/0.76 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', nonemptyE1)).
% 3.31/0.76 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', noeltsimpempty)).
% 3.31/0.76 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', emptyI)).
% 3.31/0.76 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setext)).
% 3.31/0.76 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', notinemptyset)).
% 3.31/0.76 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', emptysetimpfalse)).
% 3.31/0.76 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', emptysetE)).
% 3.31/0.76 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', prop2setE)).
% 3.31/0.76 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', wellorderingAx)).
% 3.31/0.76 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', foundationAx)).
% 3.31/0.76 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', omegaIndAx)).
% 3.31/0.76 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', omegaSAx)).
% 3.31/0.76 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', omega0Ax)).
% 3.31/0.76 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setunionAx)).
% 3.31/0.76 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', powersetAx)).
% 3.31/0.76 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setadjoinAx)).
% 3.31/0.76 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', emptysetAx)).
% 3.31/0.76 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.00drQoKvOk/E---3.1_2912912.p', setextAx)).
% 3.31/0.76 thf(c_0_201, 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)=>![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X30 @ X2)) @ X30))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[funcGraphProp3])).
% 3.31/0.76 thf(c_0_202, plain, ((ex1I)<=>![X4:$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])).
% 3.31/0.76 thf(c_0_203, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 3.31/0.76 thf(c_0_204, plain, ((ex1I2)<=>![X4:$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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 3.31/0.76 thf(c_0_205, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 3.31/0.76 thf(c_0_206, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 3.31/0.76 thf(c_0_207, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 3.31/0.76 thf(c_0_208, 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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 3.31/0.76 thf(c_0_209, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 3.31/0.76 thf(c_0_210, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 3.31/0.76 thf(c_0_211, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 3.31/0.76 thf(c_0_212, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 3.31/0.76 thf(c_0_213, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 3.31/0.76 thf(c_0_214, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 3.31/0.76 thf(c_0_215, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X30)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
% 3.31/0.76 thf(c_0_216, plain, ((apProp)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X30))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
% 3.31/0.76 thf(c_0_217, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 3.31/0.76 thf(c_0_218, plain, ((lamProp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:(((X31 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])).
% 3.31/0.76 thf(c_0_219, plain, ((lamp)<=>![X4:$i, X5:$i, X33:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X33 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X33 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
% 3.31/0.76 thf(c_0_220, plain, ((lam2p)<=>![X4:$i, X5:$i, X34:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X34 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X34 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
% 3.31/0.76 thf(c_0_221, plain, ((ex1E2)<=>![X4:$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])).
% 3.31/0.76 thf(c_0_222, 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])).
% 3.31/0.76 thf(c_0_223, 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])).
% 3.31/0.76 thf(c_0_224, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 3.31/0.76 thf(c_0_225, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 3.31/0.76 thf(c_0_226, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 3.31/0.76 thf(c_0_227, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 3.31/0.76 thf(c_0_228, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 3.31/0.76 thf(c_0_229, plain, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 3.31/0.76 thf(c_0_230, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 3.31/0.76 thf(c_0_231, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 3.31/0.76 thf(c_0_232, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 3.31/0.76 thf(c_0_233, 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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 3.31/0.76 thf(c_0_234, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 3.31/0.76 thf(c_0_235, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 3.31/0.76 thf(c_0_236, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 3.31/0.76 thf(c_0_237, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 3.31/0.76 thf(c_0_238, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 3.31/0.76 thf(c_0_239, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 3.31/0.76 thf(c_0_240, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 3.31/0.76 thf(c_0_241, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 3.31/0.76 thf(c_0_242, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 3.31/0.76 thf(c_0_243, plain, ((epred1_0)<=>![X650:$i]:(?[X651:$i]:((((![X652:$i]:(((in @ X652 @ X651)=>![X653:$i]:(((in @ X653 @ X652)=>(in @ X653 @ X650)))))&![X654:$i, X655:$i]:((((in @ X654 @ X650)&(in @ X655 @ X650))=>(![X656:$i]:(((in @ X656 @ X651)=>((in @ X654 @ X656)<=>(in @ X655 @ X656))))=>((X654)=(X655))))))&![X657:$i, X658:$i]:((((in @ X657 @ X651)&(in @ X658 @ X651))=>(![X659:$i]:(((in @ X659 @ X657)=>(in @ X659 @ X658)))|![X660:$i]:(((in @ X660 @ X658)=>(in @ X660 @ X657)))))))&![X661:$i]:(((![X662:$i]:(((in @ X662 @ X661)=>(in @ X662 @ X650)))&?[X663:$i]:((in @ X663 @ X661)))=>?[X664:$i, X665:$i]:(((((in @ X664 @ X651)&(in @ X665 @ X661))&~(?[X666:$i]:(((in @ X666 @ X664)&(in @ X666 @ X661)))))&![X667:$i]:(((in @ X667 @ X651)=>(![X668:$i]:(((in @ X668 @ X667)=>(in @ X668 @ X664)))|(in @ X665 @ X667)))))))))))), introduced(definition)).
% 3.31/0.76 thf(c_0_244, negated_conjecture, ~((![X623:$i, X624:$i]:((![X625:$i]:(((in @ X625 @ X623)<=>(in @ X625 @ X624)))=>((X623)=(X624))))=>(![X626:$i]:(~(in @ X626 @ emptyset))=>(![X627:$i, X628:$i, X629:$i]:(((in @ X629 @ (setadjoin @ X627 @ X628))<=>(((X629)=(X627))|(in @ X629 @ X628))))=>(![X630:$i, X631:$i]:(((in @ X631 @ (powerset @ X630))<=>![X632:$i]:(((in @ X632 @ X631)=>(in @ X632 @ X630)))))=>(![X633:$i, X634:$i]:(((in @ X634 @ (setunion @ X633))<=>?[X635:$i]:(((in @ X634 @ X635)&(in @ X635 @ X633)))))=>((in @ emptyset @ omega)=>(![X636:$i]:(((in @ X636 @ omega)=>(in @ (setadjoin @ X636 @ X636) @ omega)))=>(![X637:$i]:((((in @ emptyset @ X637)&![X638:$i]:((((in @ X638 @ omega)&(in @ X638 @ X637))=>(in @ (setadjoin @ X638 @ X638) @ X637))))=>![X639:$i]:(((in @ X639 @ omega)=>(in @ X639 @ X637)))))=>(![X640:$i > $i > $o, X641:$i]:((![X642:$i]:(((in @ X642 @ X641)=>(exu @ (X640 @ X642))))=>?[X643:$i]:(![X644:$i]:(((in @ X644 @ X643)<=>?[X645:$i]:(((in @ X645 @ X641)&(X640 @ X645 @ X644))))))))=>(![X646:$i]:((?[X647:$i]:((in @ X647 @ X646))=>?[X648:$i]:(((in @ X648 @ X646)&~(?[X649:$i]:(((in @ X649 @ X648)&(in @ X649 @ X646))))))))=>((epred1_0)=>(![X669:$i > $o]:(((exu @ X669)=>(X669 @ (descr @ (^[Z0:$i]:(X669 @ Z0))))))=>(![X670:$i, X671:$i > $o, X672:$i]:(((in @ X672 @ X670)=>((X671 @ X672)=>(in @ X672 @ (dsetconstr @ X670 @ X671)))))=>(![X673:$i, X674:$i > $o, X675:$i]:(((in @ X675 @ (dsetconstr @ X673 @ X674))=>(in @ X675 @ X673)))=>(![X676:$i, X677:$i > $o, X678:$i]:(((in @ X678 @ (dsetconstr @ X676 @ X677))=>(X677 @ X678)))=>(![X679:$i > $o]:(((exu @ X679)=>?[X680:$i]:(((X679 @ X680)&![X681:$i]:(((X679 @ X681)=>((X680)=(X681))))))))=>(![X682:$o, X683:$i]:(((in @ X683 @ (prop2set @ ((X682))))=>(X682)))=>(![X684:$i]:(((in @ X684 @ emptyset)=>![X685:$o]:((X685))))=>(![X686:$i]:(((in @ X686 @ emptyset)=>~($true)))=>(![X687:$i]:(~(in @ X687 @ emptyset))=>(![X688:$i > $o]:(((exu @ X688)=>?[X689:$i]:((X688 @ X689))))=>(![X690:$i, X691:$i]:((![X692:$i]:(((in @ X692 @ X690)=>(in @ X692 @ X691)))=>(![X693:$i]:(((in @ X693 @ X691)=>(in @ X693 @ X690)))=>((X690)=(X691)))))=>(![X694:$i]:((![X695:$i]:(~(in @ X695 @ X694))=>((X694)=(emptyset))))=>(![X696:$i]:((![X697:$i]:(~(in @ X697 @ X696))=>((X696)=(emptyset))))=>(![X698:$i, X699:$i > $o, X700:$i]:(((in @ X700 @ X698)=>((in @ X700 @ (dsetconstr @ X698 @ X699))<=>(X699 @ X700))))=>(![X701:$i]:(((nonempty @ X701)=>?[X702:$i]:((in @ X702 @ X701))))=>(![X703:$i, X704:$i > $o, X705:$i]:(((in @ X705 @ X703)=>((X704 @ X705)=>(nonempty @ (dsetconstr @ X703 @ X704)))))=>(![X706:$i]:((?[X707:$i]:((in @ X707 @ X706))=>(nonempty @ X706)))=>(![X708:$i, X709:$i]:((in @ X708 @ (setadjoin @ X708 @ X709)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X710:$i, X711:$i, X712:$i]:(((in @ X712 @ X711)=>(in @ X712 @ (setadjoin @ X710 @ X711))))=>(![X713:$i, X714:$i, X715:$i]:(((in @ X715 @ (setadjoin @ X713 @ X714))=>![X716:$o]:(((((X715)=(X713))=>(X716))=>(((in @ X715 @ X714)=>(X716))=>(X716))))))=>(![X717:$i, X718:$i, X719:$i]:(((in @ X719 @ (setadjoin @ X717 @ X718))=>(((X719)=(X717))|(in @ X719 @ X718))))=>(![X720:$i]:(((dsetconstr @ X720 @ (^[Z0:$i]:($true)))=(X720)))=>(![X721:$i, X722:$i]:((![X723:$i]:(((in @ X723 @ X722)=>(in @ X723 @ X721)))=>(in @ X722 @ (powerset @ X721))))=>(![X724:$i]:((in @ emptyset @ (powerset @ X724)))=>(![X725:$i]:((in @ emptyset @ (powerset @ X725)))=>(![X726:$i, X727:$i, X728:$i]:(((in @ X727 @ (powerset @ X726))=>((in @ X728 @ X727)=>(in @ X728 @ X726))))=>(![X729:$i, X730:$i, X731:$i]:(((in @ X730 @ X731)=>((in @ X731 @ X729)=>(in @ X730 @ (setunion @ X729)))))=>(![X732:$i, X733:$i]:(((in @ X733 @ (setunion @ X732))=>![X734:$o]:((![X735:$i]:(((in @ X733 @ X735)=>((in @ X735 @ X732)=>(X734))))=>(X734)))))=>(![X736:$i, X737:$i]:(((in @ X737 @ X736)=>(in @ X737 @ (powerset @ (setunion @ X736)))))=>(![X738:$i > $o]:(((exu @ X738)=>?[X739:$i]:(![X740:$i]:(((X738 @ X740)<=>((X740)=(X739)))))))=>(![X741:$i]:(((nonempty @ X741)=>?[X742:$i]:(((in @ X742 @ X741)&$true))))=>(![X743:$i, X744:$i]:(((in @ X743 @ (setadjoin @ X744 @ emptyset))=>((X743)=(X744))))=>(![X745:$i, X746:$i]:((((X745)!=(X746))=>~(in @ X746 @ (setadjoin @ X745 @ emptyset))))=>(![X747:$i, X748:$i]:((((X747)=(X748))=>(in @ X747 @ (setadjoin @ X748 @ emptyset))))=>(![X749:$i, X750:$i]:(((in @ X749 @ (setadjoin @ X750 @ emptyset))=>(in @ X750 @ (setadjoin @ X749 @ emptyset))))=>(![X751:$i, X752:$i, X753:$i]:(((in @ X753 @ (setadjoin @ X751 @ (setadjoin @ X752 @ emptyset)))=>(((X753)=(X751))|((X753)=(X752)))))=>(![X754:$i, X755:$i]:((in @ X754 @ (setadjoin @ X754 @ (setadjoin @ X755 @ emptyset))))=>(![X756:$i, X757:$i]:((in @ X757 @ (setadjoin @ X756 @ (setadjoin @ X757 @ emptyset))))=>(![X758:$i, X759:$i > $o]:((?[X760:$i]:(((in @ X760 @ X758)&(X759 @ X760)))=>(((dsetconstr @ X758 @ X759)=(emptyset))=>~($true))))=>(![X761:$i > $o, X762:$i]:(((in @ X762 @ emptyset)=>(X761 @ X762)))=>(![X763:$i, X764:$i > $o]:((~(![X765:$i]:(((in @ X765 @ X763)=>(X764 @ X765))))=>?[X766:$i]:(((in @ X766 @ X763)&~((X764 @ X766))))))=>(![X767:$i, X768:$i > $o]:((![X769:$i]:(((in @ X769 @ X767)=>~((X768 @ X769))))=>~(?[X770:$i]:(((in @ X770 @ X767)&(X768 @ X770))))))=>(![X771:$i, X772:$i > $o]:((~(?[X773:$i]:(((in @ X773 @ X771)&(X772 @ X773))))=>![X774:$i]:(((in @ X774 @ X771)=>~((X772 @ X774))))))=>(![X775:$i, X776:$i > $o]:((?[X777:$i]:(((in @ X777 @ X775)&~((X776 @ X777))))=>~(![X778:$i]:(((in @ X778 @ X775)=>(X776 @ X778))))))=>(![X779:$o]:(((X779)=>(in @ emptyset @ (prop2set @ ((X779))))))=>((prop2set2propI)=>(![X780:$i, X781:$i > $o]:((~(?[X782:$i]:(((in @ X782 @ X780)&(X781 @ X782))))=>![X783:$i]:(((in @ X783 @ X780)=>~((X781 @ X783))))))=>(![X784:$i, X785:$i > $o]:((~(![X786:$i]:(((in @ X786 @ X784)=>(X785 @ X786))))=>?[X787:$i]:(((in @ X787 @ X784)&~((X785 @ X787))))))=>(![X788:$i > $o]:((?[X789:$i]:(((X788 @ X789)&![X790:$i]:(((X788 @ X790)=>((X789)=(X790))))))=>(exu @ X788)))=>(![X791:$i > $o]:((?[X792:$i]:((X791 @ 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$o]:((breln @ X1128 @ X1129 @ (dpsetconstr @ X1128 @ X1129 @ X1130)))=>(![X1131:$i, X1132:$i, X1133:$i > $i > $o, X1134:$i]:(((in @ X1134 @ X1131)=>![X1135:$i]:(((in @ X1135 @ X1132)=>((in @ (kpair @ X1134 @ X1135) @ (dpsetconstr @ X1131 @ X1132 @ X1133))=>(X1133 @ X1134 @ X1135))))))=>(![X1136:$i, X1137:$i, X1138:$i > $i > $o, X1139:$i, X1140:$i]:(((in @ (kpair @ X1139 @ X1140) @ (dpsetconstr @ X1136 @ X1137 @ X1138))=>(in @ X1139 @ X1136)))=>(![X1141:$i, X1142:$i, X1143:$i > $i > $o, X1144:$i, X1145:$i]:(((in @ (kpair @ X1144 @ X1145) @ (dpsetconstr @ X1141 @ X1142 @ X1143))=>(in @ X1145 @ X1142)))=>(![X1146:$i, X1147:$i, X1148:$i > $i > $o, X1149:$i, X1150:$i]:(((in @ (kpair @ X1149 @ X1150) @ (dpsetconstr @ X1146 @ X1147 @ X1148))=>(X1148 @ X1149 @ X1150)))=>(![X1151:$i, X1152:$i, X1153:$i]:(((func @ X1151 @ X1152 @ X1153)=>![X1154:$i]:(((in @ X1154 @ X1151)=>(singleton @ (dsetconstr @ X1152 @ (^[Z0:$i]:((in @ (kpair @ X1154 @ Z0) @ X1153)))))))))=>(![X1155:$i, X1156:$i, X1157:$i]:(((func @ X1155 @ X1156 @ X1157)=>![X1158:$i]:(((in @ X1158 @ X1155)=>(in @ (setunion @ (dsetconstr @ X1156 @ (^[Z0:$i]:((in @ (kpair @ X1158 @ Z0) @ X1157))))) @ X1156)))))=>(![X1159:$i, X1160:$i, X1161:$i]:(((func @ X1159 @ X1160 @ X1161)=>![X1162:$i]:(((in @ X1162 @ X1159)=>(in @ (ap @ X1159 @ X1160 @ X1161 @ X1162) @ X1160)))))=>(![X1163:$i, X1164:$i, X1165:$i]:(((in @ X1165 @ (funcSet @ X1163 @ X1164))=>(func @ X1163 @ X1164 @ X1165)))=>(![X1166:$i, X1167:$i, X1168:$i]:(((in @ X1168 @ (funcSet @ X1166 @ X1167))=>![X1169:$i]:(((in @ X1169 @ X1166)=>(in @ (ap @ X1166 @ X1167 @ X1168 @ X1169) @ X1167)))))=>(![X1170:$i, X1171:$i, X1172:$i]:(((func @ X1170 @ X1171 @ X1172)=>(in @ X1172 @ (funcSet @ X1170 @ X1171))))=>(![X1173:$i, X1174:$i, X1175:$i > $i]:((![X1176:$i]:(((in @ X1176 @ X1173)=>(in @ (X1175 @ X1176) @ X1174)))=>(func @ X1173 @ X1174 @ (dpsetconstr @ X1173 @ X1174 @ (^[Z0:$i]:($eq @ (X1175 @ Z0)))))))=>(![X1177:$i, X1178:$i, X1179:$i > $i]:((![X1180:$i]:(((in @ X1180 @ X1177)=>(in @ (X1179 @ X1180) @ X1178)))=>(func @ X1177 @ X1178 @ (lam @ X1177 @ X1178 @ X1179))))=>(![X1181:$i, X1182:$i, X1183:$i > $i]:((![X1184:$i]:(((in @ X1184 @ X1181)=>(in @ (X1183 @ X1184) @ X1182)))=>(in @ (lam @ X1181 @ X1182 @ X1183) @ (funcSet @ X1181 @ X1182))))=>(![X1185:$i, X1186:$i, X1187:$i]:(((breln @ X1185 @ X1186 @ X1187)=>![X1188:$i > $o]:((![X1189:$i]:(((in @ X1189 @ X1185)=>![X1190:$i]:(((in @ X1190 @ X1186)=>((in @ (kpair @ X1189 @ X1190) @ X1187)=>(X1188 @ (kpair @ X1189 @ X1190)))))))=>![X1191:$i]:(((in @ X1191 @ X1187)=>(X1188 @ X1191)))))))=>(![X1192:$i, X1193:$i, X1194:$i]:(((breln @ X1192 @ X1193 @ X1194)=>![X1195:$i > $o]:((![X1196:$i]:(((in @ X1196 @ X1192)=>![X1197:$i]:(((in @ X1197 @ X1193)=>((in @ (kpair @ X1196 @ X1197) @ X1194)=>(X1195 @ (kpair @ X1196 @ X1197)))))))=>![X1198:$i]:(((in @ X1198 @ X1194)=>(X1195 @ X1198)))))))=>(![X1199:$i, X1200:$i > $o]:(((ex1 @ X1199 @ X1200)=>![X1201:$i]:(((in @ X1201 @ X1199)=>![X1202:$i]:(((in @ X1202 @ X1199)=>((X1200 @ X1201)=>((X1200 @ X1202)=>((X1201)=(X1202))))))))))=>(![X1203:$i, X1204:$i, X1205:$i]:(((func @ X1203 @ X1204 @ X1205)=>![X1206:$i]:(((in @ X1206 @ X1203)=>(in @ (kpair @ X1206 @ (ap @ X1203 @ X1204 @ X1205 @ X1206)) @ X1205)))))=>![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X30 @ X2)) @ X30))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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)],[c_0_201, emptyinunitempty]), c_0_202]), c_0_203]), c_0_204]), singletonsuniq]), setukpairinjL1]), c_0_205]), theprop]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), emptyinPowerset]), upairequniteq]), powersetI]), setukpairinjR2]), nonemptyI1]), setukpairinjR]), c_0_206]), c_0_207]), setadjoinOr]), ksndpairEq]), setadjoinE]), kpairsurjEq]), setadjoinIR]), cartprodsndin]), eqinunit]), quantDeMorgan1]), cartprodpairmemEL]), emptyInPowerset]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_208]), c_0_209]), c_0_210]), c_0_211]), c_0_212]), c_0_213]), c_0_214]), c_0_215]), uniqinunit]), c_0_216]), nonemptyImpWitness]), app]), c_0_217]), infuncsetfunc]), subPowSU]), ap2p]), setunionE]), funcinfuncset]), setunionI]), c_0_218]), powersetE]), c_0_219]), notinsingleton]), c_0_220]), brelnall1]), brelnall2]), c_0_221]), funcGraphProp1]), vacuousDall]), c_0_222]), upairsetIR]), upairsetIL]), upairsetE]), singletonsswitch]), emptysetsubset]), subsetI2]), subsetRefl]), c_0_223]), notdallE]), notdexE]), prop2setI]), quantDeMorgan4]), quantDeMorgan3]), quantDeMorgan2]), c_0_224]), setadjoinIL]), setadjoin__Cong]), emptyset__Cong]), c_0_225]), c_0_226]), in__Cong]), inCongP]), c_0_227]), powerset__Cong]), eqimpsubset2]), subsetI1]), c_0_228]), c_0_229]), c_0_230]), omega__Cong]), setunion__Cong]), eqimpsubset1]), notequalI2]), notequalI1]), notsubsetI]), subsetE2]), subsetE]), powersetI1]), subsetemptysetimpeq]), setextsub]), subset2powerset]), setadjoinSub2]), setadjoinSub]), subsetTrans]), powersetE1]), binunionIR]), upairset2IR]), binunionIL]), c_0_231]), c_0_232]), powersetsubset]), inPowerset]), binunionEcases]), binintersectLsub]), binintersectEL]), binintersectSubset5]), binintersectI]), binunionRsub]), binunionLsub]), binunionE]), binintersectSubset2]), bs114d]), binintersectSubset1]), binintersectSubset4]), binintersectRsub]), disjointsetsI1]), binintersectER]), binintersectSubset3]), setminusI]), setminusIRneg]), setminusILneg]), setminusELneg]), setminusERneg]), setminusSubset2]), setminusER]), setminusEL]), setminusLsub]), secondinupair]), symdiffIneg2]), symdiffIneg1]), symdiffI2]), symdiffI1]), symdiffE]), setminusSubset1]), setukpairIL]), upairset2E]), singletoninpowunion]), singletoninpowerset]), singletonsubset]), kpairp]), kpairiskpair]), setukpairIR]), upairsubunion]), cartprodmempair]), cartprodmempair1]), cartprodpairin]), ubforcartprodlem3]), ubforcartprodlem2]), ubforcartprodlem1]), upairinpowunion]), setunionsingleton1]), setunionsingleton2]), setunionsingleton]), c_0_233]), setunionE2]), c_0_234]), nonemptyE1]), c_0_235]), noeltsimpempty]), emptyI]), setext]), c_0_236]), notinemptyset]), emptysetimpfalse]), emptysetE]), prop2setE]), c_0_237]), c_0_238]), c_0_239]), c_0_240]), c_0_241]), wellorderingAx]), foundationAx]), c_0_242]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_243])).
% 3.31/0.77 thf(c_0_245, negated_conjecture, ![X1207:$i, X1208:$i, X1210:$i, X1211:$i, X1212:$i, X1213:$i, X1214:$i, X1215:$i, X1216:$i, X1217:$i, X1218:$i, X1220:$i, X1221:$i, X1223:$i, X1224:$i, X1225:$i, X1226:$i, X1227:$i, X1229:$i, X1230:$i > $i > $o, X1231:$i, X1234:$i, X1236:$i, X1237:$i, X1238:$i, X1239:$i, X1241:$i, X1242:$i > $o, X1243:$i, X1244:$i > $o, X1245:$i, X1246:$i, X1247:$i > $o, X1248:$i, X1249:$i, X1250:$i > $o, X1251:$i, X1252:$i > $o, X1254:$i, X1255:$o, X1256:$i, X1257:$i, X1258:$o, X1259:$i, X1260:$i, X1261:$i > $o, X1263:$i, X1264:$i, X1267:$i, X1269:$i, X1271:$i, X1272:$i > $o, X1273:$i, X1274:$i, X1276:$i, X1277:$i > $o, X1278:$i, X1279:$i, X1280:$i, X1281:$i, X1282:$i, X1283:$i, X1284:$i, X1285:$i, X1286:$i, X1287:$i, X1288:$i, X1289:$o, X1290:$i, X1291:$i, X1292:$i, X1293:$i, X1294:$i, X1295:$i, X1297:$i, X1298:$i, X1299:$i, X1300:$i, X1301:$i, X1302:$i, X1303:$i, X1304:$i, X1305:$i, X1306:$i, X1307:$o, X1309:$i, X1310:$i, X1311:$i > $o, X1313:$i, X1314:$i, X1315:$i, X1317:$i, X1318:$i, X1319:$i, X1320:$i, X1321:$i, X1322:$i, X1323:$i, X1324:$i, X1325:$i, X1326:$i, X1327:$i, X1328:$i, X1329:$i, X1330:$i, X1331:$i, X1332:$i, X1333:$i > $o, X1334:$i, X1335:$i > $o, X1336:$i, X1337:$i, X1338:$i > $o, X1339:$i, X1341:$i, X1342:$i > $o, X1344:$i, X1345:$i, X1346:$i > $o, X1348:$i, X1349:$i, X1350:$i > $o, X1351:$i, X1353:$o, X1354:$i, X1355:$i > $o, X1357:$i, X1358:$i, X1359:$i > $o, X1360:$i, X1362:$i > $o, X1363:$i, X1365:$i > $o, X1366:$i, X1369:$i > $o, X1370:$i, X1372:$i, X1373:$i, X1374:$i, X1375:$i, X1376:$i, X1377:$i, X1378:$i, X1379:$i, X1380:$i > $o, X1381:$i, X1382:$i, X1383:$i > $o, X1384:$i > $o, X1387:$i, X1388:$i, X1389:$i, X1390:$i, X1391:$i, X1392:$i, X1393:$i, X1394:$i, X1395:$i > $o, X1396:$i, X1397:$i, X1398:$i > $o, X1399:$i > $o, X1402:$i, X1403:$i, X1404:$i > $o, X1405:$i > $o, X1408:$i, X1409:$i, X1411:$i, X1412:$i, X1413:$i, X1414:$i, X1415:$i, X1416:$i, X1418:$i, X1419:$i, X1420:$i, X1421:$i, X1422:$i, X1423:$i, X1424:$i, X1425:$i, X1426:$i, X1427:$i, X1428:$i, X1429:$i, X1430:$i, X1431:$i, X1432:$i, X1433:$i, X1434:$i, X1435:$i, X1436:$i, X1437:$i, X1438:$i, X1439:$i, X1440:$i, X1441:$i, X1442:$i, X1443:$i, X1444:$i, X1445:$i, X1446:$i, X1447:$i, X1448:$i, X1449:$i, X1450:$i, X1451:$i, X1452:$i, X1453:$i, X1454:$i, X1455:$i > $o, X1456:$i, X1457:$i > $o, X1458:$i, X1459:$i, X1460:$i, X1461:$i, X1462:$i, X1463:$i, X1464:$i, X1465:$i, X1466:$i, X1467:$i, X1468:$i, X1469:$o, X1470:$i, X1471:$i, X1472:$i, X1473:$i, X1474:$i, X1475:$i, X1476:$i, X1477:$i, X1478:$i, X1479:$i, X1480:$i, X1481:$i, X1482:$i, X1483:$i, X1484:$i, X1485:$i, X1486:$i, X1487:$i, X1488:$i, X1489:$i, X1490:$i, X1491:$i, X1492:$i, X1493:$i, X1494:$i, X1495:$i, X1496:$i, X1498:$i, X1499:$i, X1500:$i, X1501:$i, X1502:$i, X1503:$i, X1504:$i, X1505:$i, X1506:$i, X1507:$i, X1508:$i, X1509:$i, X1510:$i, X1511:$i, X1512:$i, X1513:$i, X1514:$i, X1515:$i, X1516:$i, X1517:$i, X1518:$i, X1519:$i, X1520:$i, X1521:$i, X1522:$i, X1523:$i, X1524:$i, X1525:$i, X1526:$i, X1527:$i, X1528:$i, X1529:$i, X1530:$i, X1531:$i, X1532:$i, X1533:$i, X1534:$i, X1535:$i, X1536:$i, X1537:$o, X1538:$i, X1539:$i, X1540:$i, X1541:$i, X1542:$i, X1543:$i, X1544:$i, X1545:$i, X1546:$i, X1547:$i, X1548:$i, X1549:$i, X1550:$i, X1551:$i, X1552:$i, X1553:$i, X1554:$i, X1555:$i, X1556:$i, X1557:$i, X1558:$i, X1559:$i, X1560:$i, X1561:$i, X1562:$i, X1563:$i, X1564:$i, X1565:$i, X1566:$i, X1567:$i, X1568:$i, X1569:$i, X1570:$i, X1571:$i, X1572:$i, X1573:$i, X1574:$i, X1575:$i, X1576:$i, X1577:$i, X1578:$i, X1579:$i, X1580:$i, X1581:$i, X1582:$i, X1583:$i, X1584:$i, X1585:$i, X1586:$i, X1587:$i, X1588:$i, X1589:$i, X1590:$i, X1591:$i, X1592:$i, X1593:$i, X1594:$i, X1595:$i, X1596:$i, X1599:$i, X1600:$i, X1601:$i, X1602:$i, X1603:$i, X1605:$i, X1606:$i, X1607:$i, X1608:$i, X1609:$i > $o, X1612:$i, X1613:$i, X1614:$i > $o, X1616:$i, X1617:$i > $o, X1618:$i, X1620:$i, X1621:$i > $o, X1624:$i, X1625:$i, X1626:$i, X1627:$i, X1628:$i, X1629:$i, X1630:$i, X1631:$i, X1632:$i, X1633:$i, X1634:$i, X1635:$i, X1636:$i, X1637:$i, X1638:$i, X1639:$i, X1640:$i, X1641:$i, X1642:$i, X1643:$i, X1644:$i, X1645:$i, X1646:$i, X1647:$i, X1648:$i, X1649:$i, X1650:$i, X1651:$i, X1652:$i, X1653:$i, X1654:$i, X1655:$i, X1656:$i, X1657:$i, X1658:$i, X1659:$i, X1660:$i, X1661:$i, X1662:$i, X1663:$i, X1664:$i, X1665:$i, X1666:$i, X1667:$i, X1668:$i, X1669:$i, X1670:$i, X1671:$i, X1672:$i, X1673:$i, X1674:$i, X1675:$i, X1676:$i, X1677:$i, X1678:$i, X1679:$i, X1680:$i, X1681:$i, X1682:$i, X1683:$i, X1684:$i, X1685:$i, X1686:$i, X1687:$i, X1688:$i, X1689:$i, X1690:$i, X1691:$i, X1692:$i, X1693:$i, X1694:$i, X1695:$i, X1696:$i > $i > $o, X1697:$i, X1698:$i, X1699:$i, X1700:$i, X1701:$i > $i > $o, X1702:$i, X1703:$i, X1704:$i > $i > $o, X1705:$i, X1706:$i, X1707:$i > $i > $o, X1708:$i, X1709:$i, X1710:$i, X1711:$i, X1712:$i > $i > $o, X1713:$i, X1714:$i, X1715:$i, X1716:$i, X1717:$i > $i > $o, X1718:$i, X1719:$i, X1720:$i, X1721:$i, X1722:$i > $i > $o, 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(^[Z0:$i]:((in @ (kpair @ X1728 @ Z0) @ X1727)))))))&((~(func @ X1729 @ X1730 @ X1731)|(~(in @ X1732 @ X1729)|(in @ (setunion @ (dsetconstr @ X1730 @ (^[Z0:$i]:((in @ (kpair @ X1732 @ Z0) @ X1731))))) @ X1730)))&((~(func @ X1733 @ X1734 @ X1735)|(~(in @ X1736 @ X1733)|(in @ (ap @ X1733 @ X1734 @ X1735 @ X1736) @ X1734)))&((~(in @ X1739 @ (funcSet @ X1737 @ X1738))|(func @ X1737 @ X1738 @ X1739))&((~(in @ X1742 @ (funcSet @ X1740 @ X1741))|(~(in @ X1743 @ X1740)|(in @ (ap @ X1740 @ X1741 @ X1742 @ X1743) @ X1741)))&((~(func @ X1744 @ X1745 @ X1746)|(in @ X1746 @ (funcSet @ X1744 @ X1745)))&((((in @ (esk48_3 @ X1747 @ X1748 @ X1749) @ X1747)|(func @ X1747 @ X1748 @ (dpsetconstr @ X1747 @ X1748 @ (^[Z0:$i]:($eq @ (X1749 @ Z0))))))&(~(in @ (X1749 @ (esk48_3 @ X1747 @ X1748 @ X1749)) @ X1748)|(func @ X1747 @ X1748 @ (dpsetconstr @ X1747 @ X1748 @ (^[Z0:$i]:($eq @ (X1749 @ Z0)))))))&((((in @ (esk49_3 @ X1751 @ X1752 @ X1753) @ X1751)|(func @ X1751 @ X1752 @ (lam @ X1751 @ X1752 @ X1753)))&(~(in @ (X1753 @ (esk49_3 @ X1751 @ X1752 @ X1753)) @ X1752)|(func @ X1751 @ X1752 @ (lam @ X1751 @ X1752 @ X1753))))&((((in @ (esk50_3 @ X1755 @ X1756 @ X1757) @ X1755)|(in @ (lam @ X1755 @ X1756 @ X1757) @ (funcSet @ X1755 @ X1756)))&(~(in @ (X1757 @ (esk50_3 @ X1755 @ X1756 @ X1757)) @ X1756)|(in @ (lam @ X1755 @ X1756 @ X1757) @ (funcSet @ X1755 @ X1756))))&((((in @ (esk51_4 @ X1759 @ X1760 @ X1761 @ X1762) @ X1759)|(~(in @ X1765 @ X1761)|(X1762 @ X1765))|~(breln @ X1759 @ X1760 @ X1761))&(((in @ (esk52_4 @ X1759 @ X1760 @ X1761 @ X1762) @ X1760)|(~(in @ X1765 @ X1761)|(X1762 @ X1765))|~(breln @ X1759 @ X1760 @ X1761))&(((in @ (kpair @ (esk51_4 @ X1759 @ X1760 @ X1761 @ X1762) @ (esk52_4 @ X1759 @ X1760 @ X1761 @ X1762)) @ X1761)|(~(in @ X1765 @ X1761)|(X1762 @ X1765))|~(breln @ X1759 @ X1760 @ X1761))&(~(X1762 @ (kpair @ (esk51_4 @ X1759 @ X1760 @ X1761 @ X1762) @ (esk52_4 @ X1759 @ X1760 @ X1761 @ X1762)))|(~(in @ X1765 @ X1761)|(X1762 @ X1765))|~(breln @ X1759 @ X1760 @ X1761)))))&((((in @ (esk53_4 @ X1766 @ X1767 @ X1768 @ X1769) @ X1766)|(~(in @ X1772 @ X1768)|(X1769 @ X1772))|~(breln @ X1766 @ X1767 @ X1768))&(((in @ (esk54_4 @ X1766 @ X1767 @ X1768 @ X1769) @ X1767)|(~(in @ X1772 @ X1768)|(X1769 @ X1772))|~(breln @ X1766 @ X1767 @ X1768))&(((in @ (kpair @ (esk53_4 @ X1766 @ X1767 @ X1768 @ X1769) @ (esk54_4 @ X1766 @ X1767 @ X1768 @ X1769)) @ X1768)|(~(in @ X1772 @ X1768)|(X1769 @ X1772))|~(breln @ X1766 @ X1767 @ X1768))&(~(X1769 @ (kpair @ (esk53_4 @ X1766 @ X1767 @ X1768 @ X1769) @ (esk54_4 @ X1766 @ X1767 @ X1768 @ X1769)))|(~(in @ X1772 @ X1768)|(X1769 @ X1772))|~(breln @ X1766 @ X1767 @ X1768)))))&((~(ex1 @ X1773 @ X1774)|(~(in @ X1775 @ X1773)|(~(in @ X1776 @ X1773)|(~(X1774 @ X1775)|(~(X1774 @ X1776)|((X1775)=(X1776)))))))&((~(func @ X1777 @ X1778 @ X1779)|(~(in @ X1780 @ X1777)|(in @ (kpair @ X1780 @ (ap @ X1777 @ X1778 @ X1779 @ X1780)) @ X1779)))&((in @ esk57_0 @ (funcSet @ esk55_0 @ esk56_0))&((in @ esk58_0 @ esk55_0)&~(in @ (kpair @ esk58_0 @ (ap @ esk55_0 @ esk56_0 @ esk57_0 @ esk58_0)) @ esk57_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_244])])])])])])])).
% 3.31/0.77 thf(c_0_246, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((func @ X3 @ X4 @ X2)|~((in @ X2 @ (funcSet @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_245])).
% 3.31/0.77 thf(c_0_247, negated_conjecture, (in @ esk57_0 @ (funcSet @ esk55_0 @ esk56_0)), inference(split_conjunct,[status(thm)],[c_0_245])).
% 3.31/0.77 thf(c_0_248, negated_conjecture, ~((in @ (kpair @ esk58_0 @ (ap @ esk55_0 @ esk56_0 @ esk57_0 @ esk58_0)) @ esk57_0)), inference(split_conjunct,[status(thm)],[c_0_245])).
% 3.31/0.77 thf(c_0_249, negated_conjecture, ![X3:$i, X5:$i, X4:$i, X2:$i]:(((in @ (kpair @ X5 @ (ap @ X2 @ X3 @ X4 @ X5)) @ X4)|~((func @ X2 @ X3 @ X4))|~((in @ X5 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_245])).
% 3.31/0.77 thf(c_0_250, negated_conjecture, (func @ esk55_0 @ esk56_0 @ esk57_0), inference(spm,[status(thm)],[c_0_246, c_0_247])).
% 3.31/0.77 thf(c_0_251, negated_conjecture, (in @ esk58_0 @ esk55_0), inference(split_conjunct,[status(thm)],[c_0_245])).
% 3.31/0.77 thf(c_0_252, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_248, c_0_249]), c_0_250]), c_0_251])]), ['proof']).
% 3.31/0.77 % SZS output end CNFRefutation
% 3.31/0.77 % Parsed axioms : 447
% 3.31/0.77 % Removed by relevancy pruning/SinE : 246
% 3.31/0.77 % Initial clauses : 313
% 3.31/0.77 % Removed in clause preprocessing : 26
% 3.31/0.77 % Initial clauses in saturation : 287
% 3.31/0.77 % Processed clauses : 2266
% 3.31/0.77 % ...of these trivial : 59
% 3.31/0.77 % ...subsumed : 1424
% 3.31/0.77 % ...remaining for further processing : 783
% 3.31/0.77 % Other redundant clauses eliminated : 95
% 3.31/0.77 % Clauses deleted for lack of memory : 0
% 3.31/0.77 % Backward-subsumed : 64
% 3.31/0.77 % Backward-rewritten : 26
% 3.31/0.77 % Generated clauses : 18586
% 3.31/0.77 % ...of the previous two non-redundant : 16214
% 3.31/0.77 % ...aggressively subsumed : 0
% 3.31/0.77 % Contextual simplify-reflections : 0
% 3.31/0.77 % Paramodulations : 18471
% 3.31/0.77 % Factorizations : 14
% 3.31/0.77 % NegExts : 0
% 3.31/0.77 % Equation resolutions : 100
% 3.31/0.77 % Disequality decompositions : 0
% 3.31/0.77 % Total rewrite steps : 2755
% 3.31/0.77 % ...of those cached : 2505
% 3.31/0.77 % Propositional unsat checks : 0
% 3.31/0.77 % Propositional check models : 0
% 3.31/0.77 % Propositional check unsatisfiable : 0
% 3.31/0.77 % Propositional clauses : 0
% 3.31/0.77 % Propositional clauses after purity: 0
% 3.31/0.77 % Propositional unsat core size : 0
% 3.31/0.77 % Propositional preprocessing time : 0.000
% 3.31/0.77 % Propositional encoding time : 0.000
% 3.31/0.77 % Propositional solver time : 0.000
% 3.31/0.77 % Success case prop preproc time : 0.000
% 3.31/0.77 % Success case prop encoding time : 0.000
% 3.31/0.77 % Success case prop solver time : 0.000
% 3.31/0.77 % Current number of processed clauses : 681
% 3.31/0.77 % Positive orientable unit clauses : 139
% 3.31/0.77 % Positive unorientable unit clauses: 0
% 3.31/0.77 % Negative unit clauses : 4
% 3.31/0.77 % Non-unit-clauses : 538
% 3.31/0.77 % Current number of unprocessed clauses: 13653
% 3.31/0.77 % ...number of literals in the above : 44250
% 3.31/0.77 % Current number of archived formulas : 0
% 3.31/0.77 % Current number of archived clauses : 90
% 3.31/0.77 % Clause-clause subsumption calls (NU) : 45545
% 3.31/0.77 % Rec. Clause-clause subsumption calls : 38490
% 3.31/0.77 % Non-unit clause-clause subsumptions : 1358
% 3.31/0.77 % Unit Clause-clause subsumption calls : 665
% 3.31/0.77 % Rewrite failures with RHS unbound : 0
% 3.31/0.77 % BW rewrite match attempts : 149
% 3.31/0.77 % BW rewrite match successes : 13
% 3.31/0.77 % Condensation attempts : 0
% 3.31/0.77 % Condensation successes : 0
% 3.31/0.77 % Termbank termtop insertions : 255162
% 3.31/0.77 % Search garbage collected termcells : 18310
% 3.31/0.77
% 3.31/0.77 % -------------------------------------------------
% 3.31/0.77 % User time : 0.395 s
% 3.31/0.77 % System time : 0.018 s
% 3.31/0.77 % Total time : 0.413 s
% 3.31/0.77 % Maximum resident set size: 7940 pages
% 3.31/0.77
% 3.31/0.77 % -------------------------------------------------
% 3.31/0.77 % User time : 0.408 s
% 3.31/0.77 % System time : 0.024 s
% 3.31/0.77 % Total time : 0.432 s
% 3.31/0.77 % Maximum resident set size: 5376 pages
% 3.31/0.77 % E exiting
%------------------------------------------------------------------------------