%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU689^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 08:27:14 AM UTC 2026
% Result : Theorem 1.59s 0.50s
% Output : CNFRefutation 1.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU689^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n007.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 14:07:40 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.28 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p
% 0.87/0.50 % Version: 3.5.1-ho
% 0.87/0.50 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.87/0.50 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.87/0.50 % Starting ehoh_best5 with 300s (1) cores
% 0.87/0.50 % Starting almost_fo_3_lam with 300s (1) cores
% 0.87/0.50 % Starting new_bool_5 with 300s (1) cores
% 0.87/0.50 % Starting pre_casc_3 with 300s (1) cores
% 0.87/0.50 % Starting ho_unfolding_8 with 300s (1) cores
% 0.87/0.50 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.87/0.50 % Starting new_bool_3 with 300s (1) cores
% 0.87/0.50 % Starting new_ho_5 with 300s (1) cores
% 0.87/0.50 % almost_fo_3_lam with pid 3422872 completed with status 0
% 0.87/0.50 % Result found by almost_fo_3_lam
% 0.87/0.50 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.87/0.50 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.87/0.50 % Starting ehoh_best5 with 300s (1) cores
% 0.87/0.50 % Starting almost_fo_3_lam with 300s (1) cores
% 0.87/0.50 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.87/0.50 % No SInE strategy applied
% 0.87/0.50 % Search class: HGHSM-FSLM32-DHFMMSBN
% 0.87/0.50 % partial match(1): HGHSM-FSLM32-MHFMMSBN
% 0.87/0.50 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.87/0.50 % Starting SubtermCWHack with 28s (1) cores
% 1.59/0.50 % SubtermCWHack with pid 3422881 completed with status 0
% 1.59/0.50 % Result found by SubtermCWHack
% 1.59/0.50 % Preprocessing class: HSLMSLSSLLLCHFA.
% 1.59/0.50 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.59/0.50 % Starting ehoh_best5 with 300s (1) cores
% 1.59/0.50 % Starting almost_fo_3_lam with 300s (1) cores
% 1.59/0.50 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.59/0.50 % No SInE strategy applied
% 1.59/0.50 % Search class: HGHSM-FSLM32-DHFMMSBN
% 1.59/0.50 % partial match(1): HGHSM-FSLM32-MHFMMSBN
% 1.59/0.50 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 1.59/0.50 % Starting SubtermCWHack with 28s (1) cores
% 1.59/0.50 % Preprocessing time : 0.004 s
% 1.59/0.50
% 1.59/0.50 % Proof found!
% 1.59/0.50 % SZS status Theorem
% 1.59/0.50 % SZS output start CNFRefutation
% 1.59/0.50 thf(decl_23, type, in: $i > $i > $o).
% 1.59/0.50 thf(decl_24, type, exu: ($i > $o) > $o).
% 1.59/0.50 thf(decl_25, type, setextAx: $o).
% 1.59/0.50 thf(decl_26, type, emptyset: $i).
% 1.59/0.50 thf(decl_27, type, emptysetAx: $o).
% 1.59/0.50 thf(decl_28, type, setadjoin: $i > $i > $i).
% 1.59/0.50 thf(decl_29, type, setadjoinAx: $o).
% 1.59/0.50 thf(decl_30, type, powerset: $i > $i).
% 1.59/0.50 thf(decl_31, type, powersetAx: $o).
% 1.59/0.50 thf(decl_32, type, setunion: $i > $i).
% 1.59/0.50 thf(decl_33, type, setunionAx: $o).
% 1.59/0.50 thf(decl_34, type, omega: $i).
% 1.59/0.50 thf(decl_35, type, omega0Ax: $o).
% 1.59/0.50 thf(decl_36, type, omegaSAx: $o).
% 1.59/0.50 thf(decl_37, type, omegaIndAx: $o).
% 1.59/0.50 thf(decl_38, type, replAx: $o).
% 1.59/0.50 thf(decl_39, type, foundationAx: $o).
% 1.59/0.50 thf(decl_40, type, wellorderingAx: $o).
% 1.59/0.50 thf(decl_41, type, descr: ($i > $o) > $i).
% 1.59/0.50 thf(decl_42, type, descrp: $o).
% 1.59/0.50 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 1.59/0.50 thf(decl_44, type, dsetconstrI: $o).
% 1.59/0.50 thf(decl_45, type, dsetconstrEL: $o).
% 1.59/0.50 thf(decl_46, type, dsetconstrER: $o).
% 1.59/0.50 thf(decl_47, type, exuE1: $o).
% 1.59/0.50 thf(decl_48, type, prop2set: $o > $i).
% 1.59/0.50 thf(decl_49, type, prop2setE: $o).
% 1.59/0.50 thf(decl_50, type, emptysetE: $o).
% 1.59/0.50 thf(decl_51, type, emptysetimpfalse: $o).
% 1.59/0.50 thf(decl_52, type, notinemptyset: $o).
% 1.59/0.50 thf(decl_53, type, exuE3e: $o).
% 1.59/0.50 thf(decl_54, type, setext: $o).
% 1.59/0.50 thf(decl_55, type, emptyI: $o).
% 1.59/0.50 thf(decl_56, type, noeltsimpempty: $o).
% 1.59/0.50 thf(decl_57, type, setbeta: $o).
% 1.59/0.50 thf(decl_58, type, nonempty: $i > $o).
% 1.59/0.50 thf(decl_59, type, nonemptyE1: $o).
% 1.59/0.50 thf(decl_60, type, nonemptyI: $o).
% 1.59/0.50 thf(decl_61, type, nonemptyI1: $o).
% 1.59/0.50 thf(decl_62, type, setadjoinIL: $o).
% 1.59/0.50 thf(decl_63, type, emptyinunitempty: $o).
% 1.59/0.50 thf(decl_64, type, setadjoinIR: $o).
% 1.59/0.50 thf(decl_65, type, setadjoinE: $o).
% 1.59/0.50 thf(decl_66, type, setadjoinOr: $o).
% 1.59/0.50 thf(decl_67, type, setoftrueEq: $o).
% 1.59/0.50 thf(decl_68, type, powersetI: $o).
% 1.59/0.50 thf(decl_69, type, emptyinPowerset: $o).
% 1.59/0.50 thf(decl_70, type, emptyInPowerset: $o).
% 1.59/0.50 thf(decl_71, type, powersetE: $o).
% 1.59/0.50 thf(decl_72, type, setunionI: $o).
% 1.59/0.50 thf(decl_73, type, setunionE: $o).
% 1.59/0.50 thf(decl_74, type, subPowSU: $o).
% 1.59/0.50 thf(decl_75, type, exuE2: $o).
% 1.59/0.50 thf(decl_76, type, nonemptyImpWitness: $o).
% 1.59/0.50 thf(decl_77, type, uniqinunit: $o).
% 1.59/0.50 thf(decl_78, type, notinsingleton: $o).
% 1.59/0.50 thf(decl_79, type, eqinunit: $o).
% 1.59/0.50 thf(decl_80, type, singletonsswitch: $o).
% 1.59/0.50 thf(decl_81, type, upairsetE: $o).
% 1.59/0.50 thf(decl_82, type, upairsetIL: $o).
% 1.59/0.50 thf(decl_83, type, upairsetIR: $o).
% 1.59/0.50 thf(decl_84, type, emptyE1: $o).
% 1.59/0.50 thf(decl_85, type, vacuousDall: $o).
% 1.59/0.50 thf(decl_86, type, quantDeMorgan1: $o).
% 1.59/0.50 thf(decl_87, type, quantDeMorgan2: $o).
% 1.59/0.50 thf(decl_88, type, quantDeMorgan3: $o).
% 1.59/0.50 thf(decl_89, type, quantDeMorgan4: $o).
% 1.59/0.50 thf(decl_90, type, prop2setI: $o).
% 1.59/0.50 thf(decl_91, type, set2prop: $i > $o).
% 1.59/0.50 thf(decl_92, type, prop2set2propI: $o).
% 1.59/0.50 thf(decl_93, type, notdexE: $o).
% 1.59/0.50 thf(decl_94, type, notdallE: $o).
% 1.59/0.50 thf(decl_95, type, exuI1: $o).
% 1.59/0.50 thf(decl_96, type, exuI3: $o).
% 1.59/0.50 thf(decl_97, type, exuI2: $o).
% 1.59/0.50 thf(decl_98, type, inCongP: $o).
% 1.59/0.50 thf(decl_99, type, in__Cong: $o).
% 1.59/0.50 thf(decl_100, type, exuE3u: $o).
% 1.59/0.50 thf(decl_101, type, exu__Cong: $o).
% 1.59/0.50 thf(decl_102, type, emptyset__Cong: $o).
% 1.59/0.50 thf(decl_103, type, setadjoin__Cong: $o).
% 1.59/0.50 thf(decl_104, type, powerset__Cong: $o).
% 1.59/0.50 thf(decl_105, type, setunion__Cong: $o).
% 1.59/0.50 thf(decl_106, type, omega__Cong: $o).
% 1.59/0.50 thf(decl_107, type, exuEu: $o).
% 1.59/0.50 thf(decl_108, type, descr__Cong: $o).
% 1.59/0.50 thf(decl_109, type, dsetconstr__Cong: $o).
% 1.59/0.50 thf(decl_110, type, subset: $i > $i > $o).
% 1.59/0.50 thf(decl_113, type, subsetI1: $o).
% 1.59/0.50 thf(decl_114, type, eqimpsubset2: $o).
% 1.59/0.50 thf(decl_115, type, eqimpsubset1: $o).
% 1.59/0.50 thf(decl_116, type, subsetI2: $o).
% 1.59/0.50 thf(decl_117, type, emptysetsubset: $o).
% 1.59/0.50 thf(decl_118, type, subsetE: $o).
% 1.59/0.50 thf(decl_119, type, subsetE2: $o).
% 1.59/0.50 thf(decl_120, type, notsubsetI: $o).
% 1.59/0.50 thf(decl_121, type, notequalI1: $o).
% 1.59/0.50 thf(decl_122, type, notequalI2: $o).
% 1.59/0.50 thf(decl_123, type, subsetRefl: $o).
% 1.59/0.50 thf(decl_124, type, subsetTrans: $o).
% 1.59/0.50 thf(decl_125, type, setadjoinSub: $o).
% 1.59/0.50 thf(decl_126, type, setadjoinSub2: $o).
% 1.59/0.50 thf(decl_127, type, subset2powerset: $o).
% 1.59/0.50 thf(decl_128, type, setextsub: $o).
% 1.59/0.50 thf(decl_129, type, subsetemptysetimpeq: $o).
% 1.59/0.50 thf(decl_130, type, powersetI1: $o).
% 1.59/0.50 thf(decl_131, type, powersetE1: $o).
% 1.59/0.50 thf(decl_132, type, inPowerset: $o).
% 1.59/0.50 thf(decl_133, type, powersetsubset: $o).
% 1.59/0.50 thf(decl_134, type, sepInPowerset: $o).
% 1.59/0.50 thf(decl_135, type, sepSubset: $o).
% 1.59/0.50 thf(decl_136, type, binunion: $i > $i > $i).
% 1.59/0.50 thf(decl_137, type, binunionIL: $o).
% 1.59/0.50 thf(decl_138, type, upairset2IR: $o).
% 1.59/0.50 thf(decl_139, type, binunionIR: $o).
% 1.59/0.50 thf(decl_140, type, binunionEcases: $o).
% 1.59/0.50 thf(decl_141, type, binunionE: $o).
% 1.59/0.50 thf(decl_142, type, binunionLsub: $o).
% 1.59/0.50 thf(decl_143, type, binunionRsub: $o).
% 1.59/0.50 thf(decl_144, type, binintersect: $i > $i > $i).
% 1.59/0.50 thf(decl_145, type, binintersectI: $o).
% 1.59/0.50 thf(decl_146, type, binintersectSubset5: $o).
% 1.59/0.50 thf(decl_147, type, binintersectEL: $o).
% 1.59/0.50 thf(decl_148, type, binintersectLsub: $o).
% 1.59/0.50 thf(decl_149, type, binintersectSubset2: $o).
% 1.59/0.50 thf(decl_150, type, binintersectSubset3: $o).
% 1.59/0.50 thf(decl_151, type, binintersectER: $o).
% 1.59/0.50 thf(decl_152, type, disjointsetsI1: $o).
% 1.59/0.50 thf(decl_153, type, binintersectRsub: $o).
% 1.59/0.50 thf(decl_154, type, binintersectSubset4: $o).
% 1.59/0.50 thf(decl_155, type, binintersectSubset1: $o).
% 1.59/0.50 thf(decl_156, type, bs114d: $o).
% 1.59/0.50 thf(decl_158, type, setminus: $i > $i > $i).
% 1.59/0.50 thf(decl_159, type, setminusI: $o).
% 1.59/0.50 thf(decl_160, type, setminusEL: $o).
% 1.59/0.50 thf(decl_161, type, setminusER: $o).
% 1.59/0.50 thf(decl_162, type, setminusSubset2: $o).
% 1.59/0.50 thf(decl_163, type, setminusERneg: $o).
% 1.59/0.50 thf(decl_164, type, setminusELneg: $o).
% 1.59/0.50 thf(decl_165, type, setminusILneg: $o).
% 1.59/0.50 thf(decl_166, type, setminusIRneg: $o).
% 1.59/0.50 thf(decl_167, type, setminusLsub: $o).
% 1.59/0.50 thf(decl_168, type, setminusSubset1: $o).
% 1.59/0.50 thf(decl_169, type, symdiff: $i > $i > $i).
% 1.59/0.50 thf(decl_170, type, symdiffE: $o).
% 1.59/0.50 thf(decl_171, type, symdiffI1: $o).
% 1.59/0.50 thf(decl_172, type, symdiffI2: $o).
% 1.59/0.50 thf(decl_173, type, symdiffIneg1: $o).
% 1.59/0.50 thf(decl_174, type, symdiffIneg2: $o).
% 1.59/0.50 thf(decl_175, type, iskpair: $i > $o).
% 1.59/0.50 thf(decl_176, type, secondinupair: $o).
% 1.59/0.50 thf(decl_177, type, setukpairIL: $o).
% 1.59/0.50 thf(decl_178, type, setukpairIR: $o).
% 1.59/0.50 thf(decl_179, type, kpairiskpair: $o).
% 1.59/0.50 thf(decl_180, type, kpair: $i > $i > $i).
% 1.59/0.50 thf(decl_181, type, kpairp: $o).
% 1.59/0.50 thf(decl_182, type, cartprod: $i > $i > $i).
% 1.59/0.50 thf(decl_183, type, singletonsubset: $o).
% 1.59/0.50 thf(decl_184, type, singletoninpowerset: $o).
% 1.59/0.50 thf(decl_185, type, singletoninpowunion: $o).
% 1.59/0.50 thf(decl_186, type, upairset2E: $o).
% 1.59/0.50 thf(decl_187, type, upairsubunion: $o).
% 1.59/0.50 thf(decl_188, type, upairinpowunion: $o).
% 1.59/0.50 thf(decl_189, type, ubforcartprodlem1: $o).
% 1.59/0.50 thf(decl_190, type, ubforcartprodlem2: $o).
% 1.59/0.50 thf(decl_191, type, ubforcartprodlem3: $o).
% 1.59/0.50 thf(decl_192, type, cartprodpairin: $o).
% 1.59/0.50 thf(decl_193, type, cartprodmempair1: $o).
% 1.59/0.50 thf(decl_194, type, cartprodmempair: $o).
% 1.59/0.50 thf(decl_195, type, setunionE2: $o).
% 1.59/0.50 thf(decl_196, type, setunionsingleton1: $o).
% 1.59/0.50 thf(decl_197, type, setunionsingleton2: $o).
% 1.59/0.50 thf(decl_198, type, setunionsingleton: $o).
% 1.59/0.50 thf(decl_199, type, singleton: $i > $o).
% 1.59/0.50 thf(decl_200, type, singletonprop: $o).
% 1.59/0.50 thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 1.59/0.50 thf(decl_202, type, ex1E1: $o).
% 1.59/0.50 thf(decl_203, type, ex1I: $o).
% 1.59/0.50 thf(decl_204, type, ex1I2: $o).
% 1.59/0.50 thf(decl_205, type, singletonsuniq: $o).
% 1.59/0.50 thf(decl_210, type, setukpairinjL1: $o).
% 1.59/0.50 thf(decl_211, type, kfstsingleton: $o).
% 1.59/0.50 thf(decl_212, type, theprop: $o).
% 1.59/0.50 thf(decl_213, type, kfst: $i > $i).
% 1.59/0.50 thf(decl_214, type, kfstpairEq: $o).
% 1.59/0.50 thf(decl_215, type, cartprodfstin: $o).
% 1.59/0.50 thf(decl_216, type, setukpairinjL2: $o).
% 1.59/0.50 thf(decl_217, type, setukpairinjL: $o).
% 1.59/0.50 thf(decl_218, type, setukpairinjR11: $o).
% 1.59/0.50 thf(decl_219, type, setukpairinjR12: $o).
% 1.59/0.50 thf(decl_220, type, setukpairinjR1: $o).
% 1.59/0.50 thf(decl_221, type, upairequniteq: $o).
% 1.59/0.50 thf(decl_222, type, setukpairinjR2: $o).
% 1.59/0.50 thf(decl_223, type, setukpairinjR: $o).
% 1.59/0.50 thf(decl_224, type, ksndsingleton: $o).
% 1.59/0.50 thf(decl_225, type, ksnd: $i > $i).
% 1.59/0.50 thf(decl_226, type, ksndpairEq: $o).
% 1.59/0.50 thf(decl_227, type, kpairsurjEq: $o).
% 1.59/0.50 thf(decl_228, type, cartprodsndin: $o).
% 1.59/0.50 thf(decl_229, type, cartprodpairmemEL: $o).
% 1.59/0.50 thf(decl_230, type, cartprodpairmemER: $o).
% 1.59/0.50 thf(decl_231, type, cartprodmempaircEq: $o).
% 1.59/0.50 thf(decl_232, type, cartprodfstpairEq: $o).
% 1.59/0.50 thf(decl_233, type, cartprodsndpairEq: $o).
% 1.59/0.50 thf(decl_234, type, cartprodpairsurjEq: $o).
% 1.59/0.50 thf(decl_235, type, breln: $i > $i > $i > $o).
% 1.59/0.50 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 1.59/0.50 thf(decl_237, type, dpsetconstrI: $o).
% 1.59/0.50 thf(decl_238, type, dpsetconstrSub: $o).
% 1.59/0.50 thf(decl_239, type, setOfPairsIsBReln: $o).
% 1.59/0.50 thf(decl_240, type, dpsetconstrERa: $o).
% 1.59/0.50 thf(decl_241, type, dpsetconstrEL1: $o).
% 1.59/0.50 thf(decl_242, type, dpsetconstrEL2: $o).
% 1.59/0.50 thf(decl_243, type, dpsetconstrER: $o).
% 1.59/0.50 thf(decl_244, type, func: $i > $i > $i > $o).
% 1.59/0.50 thf(decl_245, type, funcSet: $i > $i > $i).
% 1.59/0.50 thf(decl_246, type, funcImageSingleton: $o).
% 1.59/0.50 thf(decl_247, type, apProp: $o).
% 1.59/0.50 thf(decl_248, type, ap: $i > $i > $i > $i > $i).
% 1.59/0.50 thf(decl_249, type, app: $o).
% 1.59/0.50 thf(decl_250, type, infuncsetfunc: $o).
% 1.59/0.50 thf(decl_251, type, ap2p: $o).
% 1.59/0.50 thf(decl_252, type, funcinfuncset: $o).
% 1.59/0.50 thf(decl_253, type, lamProp: $o).
% 1.59/0.50 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
% 1.59/0.50 thf(decl_255, type, lamp: $o).
% 1.59/0.50 thf(decl_256, type, lam2p: $o).
% 1.59/0.50 thf(decl_257, type, brelnall1: $o).
% 1.59/0.50 thf(decl_258, type, brelnall2: $o).
% 1.59/0.50 thf(decl_259, type, ex1E2: $o).
% 1.59/0.50 thf(decl_260, type, funcGraphProp1: $o).
% 1.59/0.50 thf(decl_261, type, funcGraphProp3: $o).
% 1.59/0.50 thf(decl_262, type, funcGraphProp2: $o).
% 1.59/0.50 thf(decl_263, type, funcextLem: $o).
% 1.59/0.50 thf(decl_264, type, funcGraphProp4: $o).
% 1.59/0.50 thf(decl_265, type, epred1_0: $o).
% 1.59/0.50 thf(decl_266, type, esk1_2: $i > $i > $i).
% 1.59/0.50 thf(decl_267, type, esk2_2: $i > $i > $i).
% 1.59/0.50 thf(decl_268, type, esk3_2: $i > $i > $i).
% 1.59/0.50 thf(decl_269, type, esk4_1: $i > $i).
% 1.59/0.50 thf(decl_270, type, esk5_2: ($i > $i > $o) > $i > $i).
% 1.59/0.50 thf(decl_271, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 1.59/0.50 thf(decl_272, type, esk7_2: ($i > $i > $o) > $i > $i).
% 1.59/0.50 thf(decl_273, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 1.59/0.51 thf(decl_274, type, esk9_1: $i > $i).
% 1.59/0.51 thf(decl_275, type, esk10_2: ($i > $o) > $i > $i).
% 1.59/0.51 thf(decl_276, type, esk11_2: ($i > $o) > $i > $i).
% 1.59/0.51 thf(decl_277, type, esk12_1: ($i > $o) > $i).
% 1.59/0.51 thf(decl_278, type, esk13_2: ($i > $o) > $i > $i).
% 1.59/0.51 thf(decl_279, type, esk14_1: ($i > $o) > $i).
% 1.59/0.51 thf(decl_280, type, esk15_2: $i > $i > $i).
% 1.59/0.51 thf(decl_281, type, esk16_2: $i > $i > $i).
% 1.59/0.51 thf(decl_282, type, esk17_1: $i > $i).
% 1.59/0.51 thf(decl_283, type, esk18_1: $i > $i).
% 1.59/0.51 thf(decl_284, type, esk19_1: $i > $i).
% 1.59/0.51 thf(decl_285, type, esk20_2: $i > $i > $i).
% 1.59/0.51 thf(decl_286, type, esk21_3: $i > $i > $o > $i).
% 1.59/0.51 thf(decl_287, type, esk22_2: ($i > $o) > $i > $i).
% 1.59/0.51 thf(decl_288, type, esk23_1: ($i > $o) > $i).
% 1.59/0.51 thf(decl_289, type, esk24_1: $i > $i).
% 1.59/0.51 thf(decl_290, type, esk25_2: $i > ($i > $o) > $i).
% 1.59/0.51 thf(decl_291, type, esk26_2: $i > ($i > $o) > $i).
% 1.59/0.51 thf(decl_292, type, esk27_2: $i > ($i > $o) > $i).
% 1.59/0.51 thf(decl_293, type, esk28_2: $i > ($i > $o) > $i).
% 1.59/0.51 thf(decl_294, type, esk29_2: $i > ($i > $o) > $i).
% 1.59/0.51 thf(decl_295, type, esk30_2: $i > ($i > $o) > $i).
% 1.59/0.51 thf(decl_296, type, esk31_2: ($i > $o) > $i > $i).
% 1.59/0.51 thf(decl_297, type, esk32_1: ($i > $o) > $i).
% 1.59/0.51 thf(decl_298, type, esk33_1: ($i > $o) > $i).
% 1.59/0.51 thf(decl_299, type, esk34_1: ($i > $o) > $i).
% 1.59/0.51 thf(decl_300, type, esk35_1: ($i > $o) > $i).
% 1.59/0.51 thf(decl_301, type, esk36_2: ($i > $o) > $i > $i).
% 1.59/0.51 thf(decl_302, type, esk37_1: ($i > $o) > $i).
% 1.59/0.51 thf(decl_303, type, esk38_2: ($i > $o) > $i > $i).
% 1.59/0.51 thf(decl_304, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 1.59/0.51 thf(decl_305, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 1.59/0.51 thf(decl_306, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.59/0.51 thf(decl_307, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 1.59/0.51 thf(decl_308, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.59/0.51 thf(decl_309, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 1.59/0.51 thf(decl_310, type, esk45_2: ($i > $o) > $i > $i).
% 1.59/0.51 thf(decl_311, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 1.59/0.51 thf(decl_312, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 1.59/0.51 thf(decl_313, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.59/0.51 thf(decl_314, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.59/0.51 thf(decl_315, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 1.59/0.51 thf(decl_316, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 1.59/0.51 thf(decl_317, type, esk52_2: $i > $i > $i).
% 1.59/0.51 thf(decl_318, type, esk53_2: $i > $i > $i).
% 1.59/0.51 thf(decl_319, type, esk54_2: $i > $i > $i).
% 1.59/0.51 thf(decl_320, type, esk55_3: $i > $i > $i > $i).
% 1.59/0.51 thf(decl_321, type, esk56_3: $i > $i > $i > $i).
% 1.59/0.51 thf(decl_322, type, esk57_2: $i > $i > $i).
% 1.59/0.51 thf(decl_323, type, esk58_2: $i > ($i > $o) > $i).
% 1.59/0.51 thf(decl_324, type, esk59_2: $i > ($i > $o) > $i).
% 1.59/0.51 thf(decl_325, type, esk60_2: $i > ($i > $o) > $i).
% 1.59/0.51 thf(decl_326, type, esk61_2: $i > ($i > $o) > $i).
% 1.59/0.51 thf(decl_327, type, esk62_3: $i > ($i > $o) > $i > $i).
% 1.59/0.51 thf(decl_328, type, esk63_3: $i > ($i > $o) > $i > $i).
% 1.59/0.51 thf(decl_329, type, esk64_2: $i > ($i > $o) > $i).
% 1.59/0.51 thf(decl_330, type, esk65_2: $i > ($i > $o) > $i).
% 1.59/0.51 thf(decl_331, type, esk66_2: $i > ($i > $o) > $i).
% 1.59/0.51 thf(decl_332, type, esk67_1: $i > $i).
% 1.59/0.51 thf(decl_333, type, esk68_1: $i > $i).
% 1.59/0.51 thf(decl_334, type, esk69_3: $i > $i > $i > $i).
% 1.59/0.51 thf(decl_335, type, esk70_4: $i > $i > $i > $i > $i).
% 1.59/0.51 thf(decl_336, type, esk71_3: $i > $i > $i > $i).
% 1.59/0.51 thf(decl_337, type, esk72_3: $i > $i > $i > $i).
% 1.59/0.51 thf(decl_338, type, esk73_4: $i > $i > $i > $i > $i).
% 1.59/0.51 thf(decl_339, type, esk74_3: $i > $i > $i > $i).
% 1.59/0.51 thf(decl_340, type, esk75_3: $i > $i > ($i > $i) > $i).
% 1.59/0.51 thf(decl_341, type, esk76_4: $i > $i > ($i > $i) > $i > $i).
% 1.59/0.51 thf(decl_342, type, esk77_3: $i > $i > ($i > $i) > $i).
% 1.59/0.51 thf(decl_343, type, esk78_4: $i > $i > ($i > $i) > $i > $i).
% 1.59/0.51 thf(decl_344, type, esk79_3: $i > $i > ($i > $i) > $i).
% 1.59/0.51 thf(decl_345, type, esk80_4: $i > $i > $i > ($i > $o) > $i).
% 1.59/0.51 thf(decl_346, type, esk81_4: $i > $i > $i > ($i > $o) > $i).
% 1.59/0.51 thf(decl_347, type, esk82_4: $i > $i > $i > ($i > $o) > $i).
% 1.59/0.51 thf(decl_348, type, esk83_4: $i > $i > $i > ($i > $o) > $i).
% 1.59/0.51 thf(decl_349, type, esk84_3: $i > $i > $i > $i).
% 1.59/0.51 thf(decl_350, type, esk85_3: $i > $i > $i > $i).
% 1.59/0.51 thf(decl_351, type, esk86_3: $i > $i > $i > $i).
% 1.59/0.51 thf(decl_352, type, esk87_4: $i > $i > $i > $i > $i).
% 1.59/0.51 thf(decl_353, type, esk88_4: $i > $i > $i > $i > $i).
% 1.59/0.51 thf(decl_354, type, esk89_0: $i).
% 1.59/0.51 thf(decl_355, type, esk90_0: $i).
% 1.59/0.51 thf(decl_356, type, esk91_0: $i).
% 1.59/0.51 thf(decl_357, type, esk92_0: $i).
% 1.59/0.51 thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', ex1)).
% 1.59/0.51 thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:((((in @ X2 @ X4))&(((X4)=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', singleton)).
% 1.59/0.51 thf(func, axiom, ((func)=(^[X4:$i, X5:$i, X29:$i]:((((breln @ X4 @ X5 @ X29))&(![X2:$i]:((((in @ X2 @ X4))=>((ex1 @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', func)).
% 1.59/0.51 thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', breln)).
% 1.59/0.51 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', replAx)).
% 1.59/0.51 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', exu)).
% 1.59/0.51 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', descrp)).
% 1.59/0.51 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', exuE1)).
% 1.59/0.51 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', exuE3e)).
% 1.59/0.51 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', nonempty)).
% 1.59/0.51 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', nonemptyI)).
% 1.59/0.51 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', exuE2)).
% 1.59/0.51 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', exuI1)).
% 1.59/0.51 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', exuI3)).
% 1.59/0.51 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', exuI2)).
% 1.59/0.51 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', exuE3u)).
% 1.59/0.51 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', exu__Cong)).
% 1.59/0.51 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', exuEu)).
% 1.59/0.51 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', descr__Cong)).
% 1.59/0.51 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', singletonprop)).
% 1.59/0.51 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', ex1E1)).
% 1.59/0.51 thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', ex1I)).
% 1.59/0.51 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', ex1I2)).
% 1.59/0.51 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', kfstsingleton)).
% 1.59/0.51 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', ksndsingleton)).
% 1.59/0.51 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setOfPairsIsBReln)).
% 1.59/0.51 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', funcImageSingleton)).
% 1.59/0.51 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X30))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', apProp)).
% 1.59/0.51 thf(lamProp, axiom, ((lamProp)<=>![X4:$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/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', lamProp)).
% 1.59/0.51 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:$i]:(X33 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', lamp)).
% 1.59/0.51 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', ex1E2)).
% 1.59/0.51 thf(subbreln, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>![X4:$i, X5:$i, X29:$i]:(((breln @ X4 @ X5 @ X29)=>![X36:$i]:(((breln @ X4 @ X5 @ X36)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>(in @ (kpair @ X2 @ X3) @ X36))))))=>(subset @ X29 @ X36))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', subbreln)).
% 1.59/0.51 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', dsetconstrI)).
% 1.59/0.51 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', dsetconstrEL)).
% 1.59/0.51 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', dsetconstrER)).
% 1.59/0.51 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setbeta)).
% 1.59/0.51 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', nonemptyE1)).
% 1.59/0.51 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', nonemptyI1)).
% 1.59/0.51 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setoftrueEq)).
% 1.59/0.51 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', nonemptyImpWitness)).
% 1.59/0.51 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', emptyE1)).
% 1.59/0.51 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', dsetconstr__Cong)).
% 1.59/0.51 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', sepInPowerset)).
% 1.59/0.51 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', sepSubset)).
% 1.59/0.51 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', theprop)).
% 1.59/0.51 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', dpsetconstrI)).
% 1.59/0.51 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', dpsetconstrSub)).
% 1.59/0.51 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', dpsetconstrERa)).
% 1.59/0.51 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', dpsetconstrEL1)).
% 1.59/0.51 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', dpsetconstrEL2)).
% 1.59/0.51 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', dpsetconstrER)).
% 1.59/0.51 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X30 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', app)).
% 1.59/0.51 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X30)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', infuncsetfunc)).
% 1.59/0.51 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>(in @ X30 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', funcinfuncset)).
% 1.59/0.51 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X34:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X34 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X34 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', lam2p)).
% 1.59/0.51 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$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/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', brelnall1)).
% 1.59/0.51 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/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', brelnall2)).
% 1.59/0.51 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/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', funcGraphProp1)).
% 1.59/0.51 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X30)=>((ap @ X4 @ X5 @ X30 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', funcGraphProp2)).
% 1.59/0.51 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X35:$i]:(((func @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X30 @ X2)=(ap @ X4 @ X5 @ X35 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X30)))))))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', funcextLem)).
% 1.59/0.51 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setextAx)).
% 1.59/0.51 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', emptysetAx)).
% 1.59/0.51 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setadjoinAx)).
% 1.59/0.51 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', powersetAx)).
% 1.59/0.51 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setunionAx)).
% 1.59/0.51 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', omega0Ax)).
% 1.59/0.51 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', omegaSAx)).
% 1.59/0.51 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', omegaIndAx)).
% 1.59/0.51 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', foundationAx)).
% 1.59/0.51 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', wellorderingAx)).
% 1.59/0.51 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', prop2setE)).
% 1.59/0.51 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', emptysetE)).
% 1.59/0.51 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', emptysetimpfalse)).
% 1.59/0.51 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', notinemptyset)).
% 1.59/0.51 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setext)).
% 1.59/0.51 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', emptyI)).
% 1.59/0.51 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', noeltsimpempty)).
% 1.59/0.51 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setadjoinIL)).
% 1.59/0.51 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', emptyinunitempty)).
% 1.59/0.51 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setadjoinIR)).
% 1.59/0.51 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setadjoinE)).
% 1.59/0.51 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setadjoinOr)).
% 1.59/0.51 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', powersetI)).
% 1.59/0.51 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', emptyinPowerset)).
% 1.59/0.51 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', emptyInPowerset)).
% 1.59/0.51 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', powersetE)).
% 1.59/0.51 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setunionI)).
% 1.59/0.51 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setunionE)).
% 1.59/0.51 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', subPowSU)).
% 1.59/0.51 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', uniqinunit)).
% 1.59/0.51 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', notinsingleton)).
% 1.59/0.51 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', eqinunit)).
% 1.59/0.51 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', singletonsswitch)).
% 1.59/0.51 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', upairsetE)).
% 1.59/0.51 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', upairsetIL)).
% 1.59/0.51 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', upairsetIR)).
% 1.59/0.51 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', vacuousDall)).
% 1.59/0.51 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', quantDeMorgan1)).
% 1.59/0.51 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', quantDeMorgan2)).
% 1.59/0.51 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', quantDeMorgan3)).
% 1.59/0.51 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', quantDeMorgan4)).
% 1.59/0.51 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', prop2setI)).
% 1.59/0.51 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', prop2set2propI)).
% 1.59/0.51 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', notdexE)).
% 1.59/0.51 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', notdallE)).
% 1.59/0.51 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', inCongP)).
% 1.59/0.51 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', in__Cong)).
% 1.59/0.51 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', emptyset__Cong)).
% 1.59/0.51 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setadjoin__Cong)).
% 1.59/0.51 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', powerset__Cong)).
% 1.59/0.51 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setunion__Cong)).
% 1.59/0.51 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', omega__Cong)).
% 1.59/0.51 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', subsetI1)).
% 1.59/0.51 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', eqimpsubset2)).
% 1.59/0.51 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', eqimpsubset1)).
% 1.59/0.51 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', subsetI2)).
% 1.59/0.51 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', emptysetsubset)).
% 1.59/0.51 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', subsetE)).
% 1.59/0.51 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', subsetE2)).
% 1.59/0.51 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', notsubsetI)).
% 1.59/0.51 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', notequalI1)).
% 1.59/0.51 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', notequalI2)).
% 1.59/0.51 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', subsetRefl)).
% 1.59/0.51 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', subsetTrans)).
% 1.59/0.51 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setadjoinSub)).
% 1.59/0.51 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setadjoinSub2)).
% 1.59/0.51 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', subset2powerset)).
% 1.59/0.51 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setextsub)).
% 1.59/0.51 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', subsetemptysetimpeq)).
% 1.59/0.51 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', powersetI1)).
% 1.59/0.51 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', powersetE1)).
% 1.59/0.51 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', inPowerset)).
% 1.59/0.51 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', powersetsubset)).
% 1.59/0.51 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', binunionIL)).
% 1.59/0.51 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', upairset2IR)).
% 1.59/0.51 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', binunionIR)).
% 1.59/0.51 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', binunionEcases)).
% 1.59/0.51 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', binunionE)).
% 1.59/0.51 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', binunionLsub)).
% 1.59/0.51 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', binunionRsub)).
% 1.59/0.51 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', binintersectI)).
% 1.59/0.51 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', binintersectSubset5)).
% 1.59/0.51 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', binintersectEL)).
% 1.59/0.51 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', binintersectLsub)).
% 1.59/0.51 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', binintersectSubset2)).
% 1.59/0.51 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', binintersectSubset3)).
% 1.59/0.51 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', binintersectER)).
% 1.59/0.51 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', disjointsetsI1)).
% 1.59/0.51 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', binintersectRsub)).
% 1.59/0.51 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', binintersectSubset4)).
% 1.59/0.51 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', binintersectSubset1)).
% 1.59/0.51 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', bs114d)).
% 1.59/0.51 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setminusI)).
% 1.59/0.51 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setminusEL)).
% 1.59/0.51 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setminusER)).
% 1.59/0.51 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setminusSubset2)).
% 1.59/0.51 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setminusERneg)).
% 1.59/0.51 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setminusELneg)).
% 1.59/0.51 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setminusILneg)).
% 1.59/0.51 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setminusIRneg)).
% 1.59/0.51 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setminusLsub)).
% 1.59/0.51 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setminusSubset1)).
% 1.59/0.51 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', symdiffE)).
% 1.59/0.51 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', symdiffI1)).
% 1.59/0.51 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', symdiffI2)).
% 1.59/0.51 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', symdiffIneg1)).
% 1.59/0.51 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', symdiffIneg2)).
% 1.59/0.51 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', secondinupair)).
% 1.59/0.51 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setukpairIL)).
% 1.59/0.51 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setukpairIR)).
% 1.59/0.51 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', kpairiskpair)).
% 1.59/0.51 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', kpairp)).
% 1.59/0.51 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', singletonsubset)).
% 1.59/0.51 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', singletoninpowerset)).
% 1.59/0.51 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', singletoninpowunion)).
% 1.59/0.51 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', upairset2E)).
% 1.59/0.51 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', upairsubunion)).
% 1.59/0.51 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', upairinpowunion)).
% 1.59/0.51 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', ubforcartprodlem1)).
% 1.59/0.51 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', ubforcartprodlem2)).
% 1.59/0.51 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', ubforcartprodlem3)).
% 1.59/0.51 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', cartprodpairin)).
% 1.59/0.51 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', cartprodmempair1)).
% 1.59/0.51 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', cartprodmempair)).
% 1.59/0.51 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setunionE2)).
% 1.59/0.51 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setunionsingleton1)).
% 1.59/0.51 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setunionsingleton2)).
% 1.59/0.51 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setunionsingleton)).
% 1.59/0.51 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', singletonsuniq)).
% 1.59/0.51 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setukpairinjL1)).
% 1.59/0.51 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', kfstpairEq)).
% 1.59/0.51 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', cartprodfstin)).
% 1.59/0.51 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setukpairinjL2)).
% 1.59/0.51 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setukpairinjL)).
% 1.59/0.51 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setukpairinjR11)).
% 1.59/0.51 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setukpairinjR12)).
% 1.59/0.51 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setukpairinjR1)).
% 1.59/0.51 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', upairequniteq)).
% 1.59/0.51 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setukpairinjR2)).
% 1.59/0.51 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', setukpairinjR)).
% 1.59/0.51 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', ksndpairEq)).
% 1.59/0.51 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', kpairsurjEq)).
% 1.59/0.51 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', cartprodsndin)).
% 1.59/0.51 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', cartprodpairmemEL)).
% 1.59/0.51 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', cartprodpairmemER)).
% 1.59/0.51 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', cartprodmempaircEq)).
% 1.59/0.51 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', cartprodfstpairEq)).
% 1.59/0.51 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', cartprodsndpairEq)).
% 1.59/0.51 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', cartprodpairsurjEq)).
% 1.59/0.51 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X30 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', ap2p)).
% 1.59/0.51 thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X30 @ X2)) @ X30)))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', funcGraphProp3)).
% 1.59/0.51 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X30)=>((ap @ X4 @ X5 @ X30 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.512c7d3oOT/E---3.1_3422858.p', funcGraphProp4)).
% 1.59/0.51 thf(c_0_212, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((?[X678:$i]:((((in @ X678 @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))))&(((dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))=(setadjoin @ X678 @ emptyset))))))))), inference(fof_simplification,[status(thm)],[ex1])).
% 1.59/0.51 thf(c_0_213, plain, ((singleton)=(^[Z0:$i]:(?[X2:$i]:((((in @ X2 @ Z0))&(((Z0)=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[singleton])).
% 1.59/0.51 thf(c_0_214, plain, ((func)=(^[Z0:$i, Z1:$i, Z2:$i]:(((((subset @ Z2 @ (cartprod @ Z0 @ Z1))))&(![X2:$i]:((((in @ X2 @ Z0))=>((?[X685:$i]:((((in @ X685 @ (dsetconstr @ Z1 @ (^[Z3:$i]:(((in @ (kpair @ X2 @ Z3) @ Z2)))))))&(((dsetconstr @ Z1 @ (^[Z3:$i]:(((in @ (kpair @ X2 @ Z3) @ Z2)))))=(setadjoin @ X685 @ emptyset)))))))))))))), inference(fof_simplification,[status(thm)],[func])).
% 1.59/0.51 thf(c_0_215, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((?[X678:$i]:((((in @ X678 @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))))&(((dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))=(setadjoin @ X678 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_212, c_0_213])).
% 1.59/0.51 thf(c_0_216, plain, ((breln)=(^[Z0:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
% 1.59/0.51 thf(c_0_217, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 1.59/0.51 thf(c_0_218, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 1.59/0.51 thf(c_0_219, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 1.59/0.51 thf(c_0_220, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 1.59/0.51 thf(c_0_221, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 1.59/0.51 thf(c_0_222, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 1.59/0.51 thf(c_0_223, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 1.59/0.51 thf(c_0_224, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 1.59/0.51 thf(c_0_225, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 1.59/0.51 thf(c_0_226, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 1.59/0.51 thf(c_0_227, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 1.59/0.51 thf(c_0_228, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 1.59/0.51 thf(c_0_229, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 1.59/0.51 thf(c_0_230, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 1.59/0.51 thf(c_0_231, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))=>((exu @ (^[Z0:$i]:((X17 @ Z0))))=>((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 1.59/0.51 thf(c_0_232, plain, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 1.59/0.51 thf(c_0_233, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 1.59/0.51 thf(c_0_234, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])).
% 1.59/0.51 thf(c_0_235, plain, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 1.59/0.51 thf(c_0_236, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 1.59/0.51 thf(c_0_237, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 1.59/0.51 thf(c_0_238, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 1.59/0.51 thf(c_0_239, plain, ((funcImageSingleton)<=>![X4:$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])).
% 1.59/0.51 thf(c_0_240, plain, ((func)=(^[Z0:$i, Z1:$i, Z2:$i]:(((((subset @ Z2 @ (cartprod @ Z0 @ Z1))))&(![X2:$i]:((((in @ X2 @ Z0))=>((?[X685:$i]:((((in @ X685 @ (dsetconstr @ Z1 @ (^[Z3:$i]:(((in @ (kpair @ X2 @ Z3) @ Z2)))))))&(((dsetconstr @ Z1 @ (^[Z3:$i]:(((in @ (kpair @ X2 @ Z3) @ Z2)))))=(setadjoin @ X685 @ emptyset)))))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_214, c_0_215]), c_0_216])).
% 1.59/0.51 thf(c_0_241, plain, ((apProp)<=>![X4:$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])).
% 1.59/0.51 thf(c_0_242, 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])).
% 1.59/0.51 thf(c_0_243, 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:$i]:(X33 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
% 1.59/0.51 thf(c_0_244, plain, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[ex1E2])).
% 1.59/0.51 thf(c_0_245, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>![X4:$i, X5:$i, X29:$i]:(((breln @ X4 @ X5 @ X29)=>![X36:$i]:(((breln @ X4 @ X5 @ X36)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>(in @ (kpair @ X2 @ X3) @ X36))))))=>(subset @ X29 @ X36)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[subbreln])).
% 1.59/0.51 thf(c_0_246, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X649:$i]:(((((X6 @ X2 @ X649)))&(![X650:$i]:(((((X6 @ X2 @ X650)))=>(((X649)=(X650)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_217, c_0_218])).
% 1.59/0.51 thf(c_0_247, plain, ((descrp)=(![X1:$i > $o]:((((?[X651:$i]:(((((X1 @ X651)))&(![X652:$i]:(((((X1 @ X652)))=>(((X651)=(X652))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_219, c_0_218])).
% 1.59/0.51 thf(c_0_248, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 1.59/0.51 thf(c_0_249, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 1.59/0.51 thf(c_0_250, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 1.59/0.51 thf(c_0_251, plain, ((exuE1)=(![X1:$i > $o]:((((?[X653:$i]:(((((X1 @ X653)))&(![X654:$i]:(((((X1 @ X654)))=>(((X653)=(X654))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_220, c_0_218])).
% 1.59/0.51 thf(c_0_252, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X655:$i]:(((((X1 @ X655)))&(![X656:$i]:(((((X1 @ X656)))=>(((X655)=(X656))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_221, c_0_218])).
% 1.59/0.51 thf(c_0_253, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 1.59/0.51 thf(c_0_254, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_222])).
% 1.59/0.51 thf(c_0_255, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_223, c_0_222])).
% 1.59/0.51 thf(c_0_256, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_222])).
% 1.59/0.51 thf(c_0_257, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 1.59/0.51 thf(c_0_258, plain, ((exuE2)=(![X1:$i > $o]:((((?[X657:$i]:(((((X1 @ X657)))&(![X658:$i]:(((((X1 @ X658)))=>(((X657)=(X658))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_224, c_0_218])).
% 1.59/0.51 thf(c_0_259, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_222])).
% 1.59/0.51 thf(c_0_260, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
% 1.59/0.51 thf(c_0_261, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X659:$i]:(((((X1 @ X659)))&(![X660:$i]:(((((X1 @ X660)))=>(((X659)=(X660)))))))))))))), inference(apply_def,[status(thm)],[c_0_225, c_0_218])).
% 1.59/0.51 thf(c_0_262, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X661:$i]:(((((X1 @ X661)))&(![X662:$i]:(((((X1 @ X662)))=>(((X661)=(X662)))))))))))))))), inference(apply_def,[status(thm)],[c_0_226, c_0_218])).
% 1.59/0.51 thf(c_0_263, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X663:$i]:(((((X1 @ X663)))&(![X664:$i]:(((((X1 @ X664)))=>(((X663)=(X664)))))))))))))), inference(apply_def,[status(thm)],[c_0_227, c_0_218])).
% 1.59/0.51 thf(c_0_264, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X665:$i]:(((((X1 @ X665)))&(![X666:$i]:(((((X1 @ X666)))=>(((X665)=(X666))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_228, c_0_218])).
% 1.59/0.51 thf(c_0_265, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X667:$i]:(((((X1 @ X667)))&(![X668:$i]:(((((X1 @ X668)))=>(((X667)=(X668))))))))))<=>((?[X669:$i]:(((((X17 @ X669)))&(![X670:$i]:(((((X17 @ X670)))=>(((X669)=(X670)))))))))))))))), inference(apply_def,[status(thm)],[c_0_229, c_0_218])).
% 1.59/0.51 thf(c_0_266, plain, ((exuEu)=(![X1:$i > $o]:((((?[X671:$i]:(((((X1 @ X671)))&(![X672:$i]:(((((X1 @ X672)))=>(((X671)=(X672))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_230, c_0_218])).
% 1.59/0.51 thf(c_0_267, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X673:$i]:(((((X1 @ X673)))&(![X674:$i]:(((((X1 @ X674)))=>(((X673)=(X674))))))))))=>((((?[X675:$i]:(((((X17 @ X675)))&(![X676:$i]:(((((X17 @ X676)))=>(((X675)=(X676))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_231, c_0_218])).
% 1.59/0.51 thf(c_0_268, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 1.59/0.51 thf(c_0_269, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 1.59/0.51 thf(c_0_270, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 1.59/0.51 thf(c_0_271, 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)))))=>((?[X677:$i]:((((in @ X677 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(setadjoin @ X677 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_232, c_0_213])).
% 1.59/0.51 thf(c_0_272, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:((((?[X679:$i]:((((in @ X679 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X679 @ emptyset)))))))=>(?[X2:$i]:((((in @ X2 @ X4))&((X1 @ X2))))))))), inference(apply_def,[status(thm)],[c_0_233, c_0_215])).
% 1.59/0.51 thf(c_0_273, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>(((![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X3))=>(((X3)=(X2))))))))=>((?[X680:$i]:((((in @ X680 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X680 @ emptyset))))))))))))))), inference(apply_def,[status(thm)],[c_0_234, c_0_215])).
% 1.59/0.51 thf(c_0_274, 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)))))=>((?[X681:$i]:((((in @ X681 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X681 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_235, c_0_215])).
% 1.59/0.51 thf(c_0_275, plain, ((kfstsingleton)=(![X18:$i]:((((iskpair @ X18))=>((?[X682:$i]:((((in @ X682 @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))))&(((dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))=(setadjoin @ X682 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_236, c_0_213])).
% 1.59/0.51 thf(c_0_276, axiom, ((theprop)=(![X21:$i]:((((?[X683:$i]:((((in @ X683 @ X21))&(((X21)=(setadjoin @ X683 @ emptyset)))))))=>((in @ (setunion @ X21) @ X21)))))), inference(apply_def,[status(thm)],[theprop, c_0_213])).
% 1.59/0.51 thf(c_0_277, plain, ((ksndsingleton)=(![X18:$i]:((((iskpair @ X18))=>((?[X684:$i]:((((in @ X684 @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))))&(((dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))=(setadjoin @ X684 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_237, c_0_213])).
% 1.59/0.51 thf(c_0_278, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 1.59/0.51 thf(c_0_279, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 1.59/0.51 thf(c_0_280, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_238, c_0_216])).
% 1.59/0.51 thf(c_0_281, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 1.59/0.51 thf(c_0_282, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 1.59/0.51 thf(c_0_283, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 1.59/0.51 thf(c_0_284, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 1.59/0.51 thf(c_0_285, plain, ((funcImageSingleton)=(![X4:$i, X5:$i, X30:$i]:((((((((subset @ X30 @ (cartprod @ X4 @ X5))))&(![X686:$i]:((((in @ X686 @ X4))=>((?[X687:$i]:((((in @ X687 @ (dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X686 @ Z0) @ X30)))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X686 @ Z0) @ X30)))))=(setadjoin @ X687 @ emptyset)))))))))))))=>(![X2:$i]:((((in @ X2 @ X4))=>((?[X688:$i]:((((in @ X688 @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X30))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X30))))=(setadjoin @ X688 @ emptyset)))))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_239, c_0_213]), c_0_240])).
% 1.59/0.51 thf(c_0_286, plain, ((apProp)=(![X4:$i, X5:$i, X30:$i]:((((((((subset @ X30 @ (cartprod @ X4 @ X5))))&(![X689:$i]:((((in @ X689 @ X4))=>((?[X690:$i]:((((in @ X690 @ (dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X689 @ Z0) @ X30)))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X689 @ Z0) @ X30)))))=(setadjoin @ X690 @ emptyset)))))))))))))=>(![X2:$i]:((((in @ X2 @ X4))=>((in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X30))))) @ X5))))))))), inference(apply_def,[status(thm)],[c_0_241, c_0_240])).
% 1.59/0.51 thf(c_0_287, axiom, ((app)=(![X4:$i, X5:$i, X30:$i]:((((((((subset @ X30 @ (cartprod @ X4 @ X5))))&(![X691:$i]:((((in @ X691 @ X4))=>((?[X692:$i]:((((in @ X692 @ (dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X691 @ Z0) @ X30)))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X691 @ Z0) @ X30)))))=(setadjoin @ X692 @ emptyset)))))))))))))=>(![X2:$i]:((((in @ X2 @ X4))=>((in @ (ap @ X4 @ X5 @ X30 @ X2) @ X5))))))))), inference(apply_def,[status(thm)],[app, c_0_240])).
% 1.59/0.51 thf(c_0_288, axiom, ((infuncsetfunc)=(![X4:$i, X5:$i, X30:$i]:((((in @ X30 @ (funcSet @ X4 @ X5)))=>((((((subset @ X30 @ (cartprod @ X4 @ X5))))&(![X693:$i]:((((in @ X693 @ X4))=>((?[X694:$i]:((((in @ X694 @ (dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X693 @ Z0) @ X30)))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X693 @ Z0) @ X30)))))=(setadjoin @ X694 @ emptyset))))))))))))))))), inference(apply_def,[status(thm)],[infuncsetfunc, c_0_240])).
% 1.59/0.51 thf(c_0_289, axiom, ((funcinfuncset)=(![X4:$i, X5:$i, X30:$i]:((((((((subset @ X30 @ (cartprod @ X4 @ X5))))&(![X695:$i]:((((in @ X695 @ X4))=>((?[X696:$i]:((((in @ X696 @ (dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X695 @ Z0) @ X30)))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X695 @ Z0) @ X30)))))=(setadjoin @ X696 @ emptyset)))))))))))))=>((in @ X30 @ (funcSet @ X4 @ X5))))))), inference(apply_def,[status(thm)],[funcinfuncset, c_0_240])).
% 1.59/0.51 thf(c_0_290, plain, ((lamProp)=(![X4:$i, X5:$i, X31:$i > $i]:(((![X2:$i]:((((in @ X2 @ X4))=>((in @ (X31 @ X2) @ X5)))))=>((((((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:(((X31 @ Z0)=(Z1))))) @ (cartprod @ X4 @ X5))))&(![X697:$i]:((((in @ X697 @ X4))=>((?[X698:$i]:((((in @ X698 @ (dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X697 @ Z0) @ (dpsetconstr @ X4 @ X5 @ (^[Z1:$i, Z2:$i]:(((X31 @ Z1)=(Z2))))))))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X697 @ Z0) @ (dpsetconstr @ X4 @ X5 @ (^[Z1:$i, Z2:$i]:(((X31 @ Z1)=(Z2))))))))))=(setadjoin @ X698 @ emptyset))))))))))))))))), inference(apply_def,[status(thm)],[c_0_242, c_0_240])).
% 1.59/0.51 thf(c_0_291, plain, ((lamp)=(![X4:$i, X5:$i, X33:$i > $i]:(((![X2:$i]:((((in @ X2 @ X4))=>((in @ (X33 @ X2) @ X5)))))=>((((((subset @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X33 @ Z0))) @ (cartprod @ X4 @ X5))))&(![X699:$i]:((((in @ X699 @ X4))=>((?[X700:$i]:((((in @ X700 @ (dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X699 @ Z0) @ (lam @ X4 @ X5 @ (^[Z1:$i]:(X33 @ Z1))))))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X699 @ Z0) @ (lam @ X4 @ X5 @ (^[Z1:$i]:(X33 @ Z1))))))))=(setadjoin @ X700 @ emptyset))))))))))))))))), inference(apply_def,[status(thm)],[c_0_243, c_0_240])).
% 1.59/0.51 thf(c_0_292, plain, ((lam2p)<=>![X4:$i, X5:$i, X34:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X34 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X34 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
% 1.59/0.51 thf(c_0_293, axiom, ((brelnall1)=(![X4:$i, X5:$i, X29:$i]:(((((subset @ X29 @ (cartprod @ X4 @ X5))))=>(![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)))))))))))), inference(apply_def,[status(thm)],[brelnall1, c_0_216])).
% 1.59/0.51 thf(c_0_294, axiom, ((brelnall2)=(![X4:$i, X5:$i, X29:$i]:(((((subset @ X29 @ (cartprod @ X4 @ X5))))=>(![X1:$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)))))))))))), inference(apply_def,[status(thm)],[brelnall2, c_0_216])).
% 1.59/0.51 thf(c_0_295, plain, ((ex1E2)=(![X4:$i, X1:$i > $o]:((((?[X701:$i]:((((in @ X701 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X701 @ emptyset)))))))=>(![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))))))))))), inference(apply_def,[status(thm)],[c_0_244, c_0_215])).
% 1.59/0.51 thf(c_0_296, axiom, ((funcGraphProp1)=(![X4:$i, X5:$i, X30:$i]:((((((((subset @ X30 @ (cartprod @ X4 @ X5))))&(![X702:$i]:((((in @ X702 @ X4))=>((?[X703:$i]:((((in @ X703 @ (dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X702 @ Z0) @ X30)))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X702 @ Z0) @ X30)))))=(setadjoin @ X703 @ emptyset)))))))))))))=>(![X2:$i]:((((in @ X2 @ X4))=>((in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X30 @ X2)) @ X30))))))))), inference(apply_def,[status(thm)],[funcGraphProp1, c_0_240])).
% 1.59/0.51 thf(c_0_297, axiom, ((funcGraphProp2)=(![X4:$i, X5:$i, X30:$i]:((((((((subset @ X30 @ (cartprod @ X4 @ X5))))&(![X704:$i]:((((in @ X704 @ X4))=>((?[X705:$i]:((((in @ X705 @ (dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X704 @ Z0) @ X30)))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X704 @ Z0) @ X30)))))=(setadjoin @ X705 @ emptyset)))))))))))))=>(![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X30))=>(((ap @ X4 @ X5 @ X30 @ X2)=(X3))))))))))))))), inference(apply_def,[status(thm)],[funcGraphProp2, c_0_240])).
% 1.59/0.51 thf(c_0_298, axiom, ((funcextLem)=(![X4:$i, X5:$i, X30:$i]:((((((((subset @ X30 @ (cartprod @ X4 @ X5))))&(![X706:$i]:((((in @ X706 @ X4))=>((?[X707:$i]:((((in @ X707 @ (dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X706 @ Z0) @ X30)))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X706 @ Z0) @ X30)))))=(setadjoin @ X707 @ emptyset)))))))))))))=>(![X35:$i]:((((((((subset @ X35 @ (cartprod @ X4 @ X5))))&(![X708:$i]:((((in @ X708 @ X4))=>((?[X709:$i]:((((in @ X709 @ (dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X708 @ Z0) @ X35)))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X708 @ Z0) @ X35)))))=(setadjoin @ X709 @ emptyset)))))))))))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(((ap @ X4 @ X5 @ X30 @ X2)=(ap @ X4 @ X5 @ X35 @ X2))))))=>(![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X35))=>((in @ (kpair @ X2 @ X3) @ X30))))))))))))))))))), inference(apply_def,[status(thm)],[funcextLem, c_0_240])).
% 1.59/0.51 thf(c_0_299, plain, ((epred1_0)<=>![X739:$i]:(?[X740:$i]:((((![X741:$i]:(((in @ X741 @ X740)=>![X742:$i]:(((in @ X742 @ X741)=>(in @ X742 @ X739)))))&![X743:$i, X744:$i]:((((in @ X743 @ X739)&(in @ X744 @ X739))=>(![X745:$i]:(((in @ X745 @ X740)=>((in @ X743 @ X745)<=>(in @ X744 @ X745))))=>((X743)=(X744))))))&![X746:$i, X747:$i]:((((in @ X746 @ X740)&(in @ X747 @ X740))=>(![X748:$i]:(((in @ X748 @ X746)=>(in @ X748 @ X747)))|![X749:$i]:(((in @ X749 @ X747)=>(in @ X749 @ X746)))))))&![X750:$i]:(((![X751:$i]:(((in @ X751 @ X750)=>(in @ X751 @ X739)))&?[X752:$i]:((in @ X752 @ X750)))=>?[X753:$i, X754:$i]:(((((in @ X753 @ X740)&(in @ X754 @ X750))&~(?[X755:$i]:(((in @ X755 @ X753)&(in @ X755 @ X750)))))&![X756:$i]:(((in @ X756 @ X740)=>(![X757:$i]:(((in @ X757 @ X756)=>(in @ X757 @ X753)))|(in @ X754 @ X756)))))))))))), introduced(definition)).
% 1.59/0.51 thf(c_0_300, negated_conjecture, ~((![X710:$i, X711:$i]:((![X712:$i]:(((in @ X712 @ X710)<=>(in @ X712 @ X711)))=>((X710)=(X711))))=>(![X713:$i]:(~(in @ X713 @ emptyset))=>(![X714:$i, X715:$i, X716:$i]:(((in @ X716 @ (setadjoin @ X714 @ X715))<=>(((X716)=(X714))|(in @ X716 @ X715))))=>(![X717:$i, X718:$i]:(((in @ X718 @ (powerset @ X717))<=>![X719:$i]:(((in @ X719 @ X718)=>(in @ X719 @ X717)))))=>(![X720:$i, X721:$i]:(((in @ X721 @ (setunion @ X720))<=>?[X722:$i]:(((in @ X721 @ X722)&(in @ X722 @ X720)))))=>((in @ emptyset @ omega)=>(![X723:$i]:(((in @ X723 @ omega)=>(in @ (setadjoin @ X723 @ X723) @ omega)))=>(![X724:$i]:((((in @ emptyset @ X724)&![X725:$i]:((((in @ X725 @ omega)&(in @ X725 @ X724))=>(in @ (setadjoin @ X725 @ X725) @ X724))))=>![X726:$i]:(((in @ X726 @ omega)=>(in @ X726 @ X724)))))=>(![X727:$i > $i > $o, X728:$i]:((![X729:$i]:(((in @ X729 @ X728)=>?[X730:$i]:(((X727 @ X729 @ X730)&![X731:$i]:(((X727 @ X729 @ X731)=>((X730)=(X731))))))))=>?[X732:$i]:(![X733:$i]:(((in @ X733 @ X732)<=>?[X734:$i]:(((in @ X734 @ X728)&(X727 @ X734 @ X733))))))))=>(![X735:$i]:((?[X736:$i]:((in @ X736 @ X735))=>?[X737:$i]:(((in @ X737 @ X735)&~(?[X738:$i]:(((in @ X738 @ X737)&(in @ X738 @ X735))))))))=>((epred1_0)=>(![X758:$i > $o]:((?[X759:$i]:(((X758 @ X759)&![X760:$i]:(((X758 @ X760)=>((X759)=(X760))))))=>(X758 @ (descr @ (^[Z0:$i]:(X758 @ Z0))))))=>(![X761:$i, X762:$i > $o, X763:$i]:(((in @ X763 @ X761)=>((X762 @ X763)=>(in @ X763 @ (dsetconstr @ X761 @ X762)))))=>(![X764:$i, X765:$i > $o, X766:$i]:(((in @ X766 @ (dsetconstr @ X764 @ X765))=>(in @ X766 @ X764)))=>(![X767:$i, X768:$i > $o, X769:$i]:(((in @ X769 @ (dsetconstr @ X767 @ X768))=>(X768 @ X769)))=>(![X770:$i > $o]:((?[X771:$i]:(((X770 @ X771)&![X772:$i]:(((X770 @ X772)=>((X771)=(X772))))))=>?[X773:$i]:(((X770 @ X773)&![X774:$i]:(((X770 @ X774)=>((X773)=(X774))))))))=>(![X775:$o, X776:$i]:(((in @ X776 @ (prop2set @ ((X775))))=>(X775)))=>(![X777:$i]:(((in @ X777 @ emptyset)=>![X778:$o]:((X778))))=>(![X779:$i]:(((in @ X779 @ emptyset)=>~($true)))=>(![X780:$i]:(~(in @ X780 @ emptyset))=>(![X781:$i > $o]:((?[X782:$i]:(((X781 @ X782)&![X783:$i]:(((X781 @ X783)=>((X782)=(X783))))))=>?[X784:$i]:((X781 @ X784))))=>(![X785:$i, X786:$i]:((![X787:$i]:(((in @ X787 @ X785)=>(in @ X787 @ X786)))=>(![X788:$i]:(((in @ X788 @ X786)=>(in @ X788 @ X785)))=>((X785)=(X786)))))=>(![X789:$i]:((![X790:$i]:(~(in @ X790 @ X789))=>((X789)=(emptyset))))=>(![X791:$i]:((![X792:$i]:(~(in @ X792 @ X791))=>((X791)=(emptyset))))=>(![X793:$i, X794:$i > $o, X795:$i]:(((in @ X795 @ X793)=>((in @ X795 @ (dsetconstr @ X793 @ X794))<=>(X794 @ X795))))=>(![X796:$i]:((((X796)!=(emptyset))=>?[X797:$i]:((in @ X797 @ X796))))=>(![X798:$i, X799:$i > $o, X800:$i]:(((in @ X800 @ X798)=>((X799 @ X800)=>((dsetconstr @ X798 @ X799)!=(emptyset)))))=>(![X801:$i]:((?[X802:$i]:((in @ X802 @ X801))=>((X801)!=(emptyset))))=>(![X803:$i, X804:$i]:((in @ X803 @ (setadjoin @ X803 @ X804)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X805:$i, X806:$i, X807:$i]:(((in @ X807 @ X806)=>(in @ X807 @ (setadjoin @ X805 @ X806))))=>(![X808:$i, X809:$i, X810:$i]:(((in @ X810 @ (setadjoin @ X808 @ X809))=>![X811:$o]:(((((X810)=(X808))=>(X811))=>(((in @ X810 @ X809)=>(X811))=>(X811))))))=>(![X812:$i, X813:$i, X814:$i]:(((in @ X814 @ (setadjoin @ X812 @ X813))=>(((X814)=(X812))|(in @ X814 @ X813))))=>(![X815:$i]:(((dsetconstr @ X815 @ (^[Z0:$i]:($true)))=(X815)))=>(![X816:$i, X817:$i]:((![X818:$i]:(((in @ X818 @ X817)=>(in @ X818 @ X816)))=>(in @ X817 @ (powerset @ X816))))=>(![X819:$i]:((in @ emptyset @ (powerset @ X819)))=>(![X820:$i]:((in @ emptyset @ (powerset @ X820)))=>(![X821:$i, X822:$i, X823:$i]:(((in @ X822 @ (powerset @ X821))=>((in @ X823 @ X822)=>(in @ X823 @ X821))))=>(![X824:$i, X825:$i, X826:$i]:(((in @ X825 @ X826)=>((in @ X826 @ X824)=>(in @ X825 @ (setunion @ X824)))))=>(![X827:$i, X828:$i]:(((in @ X828 @ (setunion @ X827))=>![X829:$o]:((![X830:$i]:(((in @ X828 @ X830)=>((in @ X830 @ X827)=>(X829))))=>(X829)))))=>(![X831:$i, X832:$i]:(((in @ X832 @ X831)=>(in @ X832 @ (powerset @ (setunion @ X831)))))=>(![X833:$i > $o]:((?[X834:$i]:(((X833 @ X834)&![X835:$i]:(((X833 @ X835)=>((X834)=(X835))))))=>?[X836:$i]:(![X837:$i]:(((X833 @ X837)<=>((X837)=(X836)))))))=>(![X838:$i]:((((X838)!=(emptyset))=>?[X839:$i]:(((in @ X839 @ X838)&$true))))=>(![X840:$i, X841:$i]:(((in @ X840 @ (setadjoin @ X841 @ emptyset))=>((X840)=(X841))))=>(![X842:$i, X843:$i]:((((X842)!=(X843))=>~(in @ X843 @ (setadjoin @ X842 @ emptyset))))=>(![X844:$i, X845:$i]:((((X844)=(X845))=>(in @ X844 @ (setadjoin @ X845 @ emptyset))))=>(![X846:$i, X847:$i]:(((in @ X846 @ (setadjoin @ X847 @ emptyset))=>(in @ X847 @ (setadjoin @ X846 @ emptyset))))=>(![X848:$i, X849:$i, X850:$i]:(((in @ X850 @ (setadjoin @ X848 @ (setadjoin @ X849 @ emptyset)))=>(((X850)=(X848))|((X850)=(X849)))))=>(![X851:$i, X852:$i]:((in @ X851 @ (setadjoin @ X851 @ (setadjoin @ X852 @ emptyset))))=>(![X853:$i, X854:$i]:((in @ X854 @ (setadjoin @ X853 @ (setadjoin @ X854 @ emptyset))))=>(![X855:$i, X856:$i > $o]:((?[X857:$i]:(((in @ X857 @ X855)&(X856 @ X857)))=>(((dsetconstr @ X855 @ X856)=(emptyset))=>~($true))))=>(![X858:$i > $o, X859:$i]:(((in @ X859 @ emptyset)=>(X858 @ X859)))=>(![X860:$i, X861:$i > $o]:((~(![X862:$i]:(((in @ X862 @ X860)=>(X861 @ X862))))=>?[X863:$i]:(((in @ X863 @ X860)&~((X861 @ X863))))))=>(![X864:$i, X865:$i > $o]:((![X866:$i]:(((in @ X866 @ X864)=>~((X865 @ X866))))=>~(?[X867:$i]:(((in @ X867 @ X864)&(X865 @ X867))))))=>(![X868:$i, X869:$i > $o]:((~(?[X870:$i]:(((in @ X870 @ X868)&(X869 @ X870))))=>![X871:$i]:(((in @ X871 @ X868)=>~((X869 @ X871))))))=>(![X872:$i, X873:$i > $o]:((?[X874:$i]:(((in @ X874 @ X872)&~((X873 @ X874))))=>~(![X875:$i]:(((in @ X875 @ X872)=>(X873 @ X875))))))=>(![X876:$o]:(((X876)=>(in @ emptyset @ (prop2set @ ((X876))))))=>(![X877:$o]:(((X877)=>(set2prop @ (prop2set @ ((X877))))))=>(![X878:$i, X879:$i > $o]:((~(?[X880:$i]:(((in @ X880 @ X878)&(X879 @ X880))))=>![X881:$i]:(((in @ X881 @ X878)=>~((X879 @ X881))))))=>(![X882:$i, X883:$i > $o]:((~(![X884:$i]:(((in @ X884 @ X882)=>(X883 @ X884))))=>?[X885:$i]:(((in @ X885 @ X882)&~((X883 @ X885))))))=>(![X886:$i > $o]:((?[X887:$i]:(((X886 @ X887)&![X888:$i]:(((X886 @ X888)=>((X887)=(X888))))))=>?[X889:$i]:(((X886 @ X889)&![X890:$i]:(((X886 @ X890)=>((X889)=(X890))))))))=>(![X891:$i > $o]:((?[X892:$i]:((X891 @ X892))=>(![X893:$i, X894:$i]:(((X891 @ X893)=>((X891 @ X894)=>((X893)=(X894)))))=>?[X895:$i]:(((X891 @ X895)&![X896:$i]:(((X891 @ X896)=>((X895)=(X896)))))))))=>(![X897:$i > $o]:((?[X898:$i]:(![X899:$i]:(((X897 @ X899)<=>((X899)=(X898)))))=>?[X900:$i]:(((X897 @ X900)&![X901:$i]:(((X897 @ X901)=>((X900)=(X901))))))))=>(![X902:$i, X903:$i]:((((X902)=(X903))=>![X904:$i, X905:$i]:((((X904)=(X905))=>((in @ X904 @ X902)=>(in @ X905 @ X903))))))=>(![X906:$i, X907:$i]:((((X906)=(X907))=>![X908:$i, X909:$i]:((((X908)=(X909))=>((in @ X908 @ X906)<=>(in @ X909 @ X907))))))=>(![X910:$i > $o]:((?[X911:$i]:(((X910 @ X911)&![X912:$i]:(((X910 @ X912)=>((X911)=(X912))))))=>![X913:$i, X914:$i]:(((X910 @ X913)=>((X910 @ X914)=>((X913)=(X914)))))))=>(![X915:$i > $o, X916:$i > $o]:((![X917:$i, X918:$i]:((((X917)=(X918))=>((X915 @ X917)<=>(X916 @ X918))))=>(?[X919:$i]:(((X915 @ X919)&![X920:$i]:(((X915 @ X920)=>((X919)=(X920))))))<=>?[X921:$i]:(((X916 @ X921)&![X922:$i]:(((X916 @ X922)=>((X921)=(X922)))))))))=>(((emptyset)=(emptyset))=>(![X923:$i, X924:$i]:((((X923)=(X924))=>![X925:$i, X926:$i]:((((X925)=(X926))=>((setadjoin @ X923 @ X925)=(setadjoin @ X924 @ X926))))))=>(![X927:$i, X928:$i]:((((X927)=(X928))=>((powerset @ X927)=(powerset @ X928))))=>(![X929:$i, X930:$i]:((((X929)=(X930))=>((setunion @ X929)=(setunion @ X930))))=>(((omega)=(omega))=>(![X931:$i > $o]:((?[X932:$i]:(((X931 @ X932)&![X933:$i]:(((X931 @ X933)=>((X932)=(X933))))))=>![X934:$i, X935:$i]:(((X931 @ X934)=>((X931 @ X935)=>((X934)=(X935)))))))=>(![X936:$i > $o, X937:$i > $o]:((![X938:$i, X939:$i]:((((X938)=(X939))=>((X936 @ X938)<=>(X937 @ X939))))=>(?[X940:$i]:(((X936 @ X940)&![X941:$i]:(((X936 @ X941)=>((X940)=(X941))))))=>(?[X942:$i]:(((X937 @ X942)&![X943:$i]:(((X937 @ X943)=>((X942)=(X943))))))=>((descr @ X936)=(descr @ X937))))))=>(![X944:$i, X945:$i]:((((X944)=(X945))=>![X946:$i > $o, X947:$i > $o]:((![X948:$i]:(((in @ X948 @ X944)=>![X949:$i]:(((in @ X949 @ X945)=>(((X948)=(X949))=>((X946 @ X948)<=>(X947 @ X949)))))))=>((dsetconstr @ X944 @ X946)=(dsetconstr @ X945 @ X947))))))=>(![X950:$i, X951:$i]:((![X952:$i]:(((in @ X952 @ X950)=>(in @ X952 @ X951)))=>(subset @ X950 @ X951)))=>(![X953:$i, X954:$i]:((((X953)=(X954))=>(subset @ X954 @ X953)))=>(![X955:$i, X956:$i]:((((X955)=(X956))=>(subset @ X955 @ X956)))=>(![X957:$i, X958:$i]:((![X959:$i]:(((in @ X959 @ X957)=>(in @ X959 @ X958)))=>(subset @ X957 @ X958)))=>(![X960:$i]:((subset @ emptyset @ X960))=>(![X961:$i, X962:$i, X963:$i]:(((subset @ X961 @ X962)=>((in @ X963 @ X961)=>(in @ X963 @ X962))))=>(![X964:$i, X965:$i, X966:$i]:(((subset @ X964 @ X965)=>(~(in @ X966 @ X965)=>~(in @ X966 @ X964))))=>(![X967:$i, X968:$i, X969:$i]:(((in @ X969 @ X967)=>(~(in @ X969 @ X968)=>~(subset @ X967 @ X968))))=>(![X970:$i, X971:$i]:((~(subset @ X970 @ X971)=>((X970)!=(X971))))=>(![X972:$i, X973:$i, X974:$i]:(((in @ X974 @ X972)=>(~(in @ X974 @ X973)=>((X972)!=(X973)))))=>(![X975:$i]:((subset @ X975 @ X975))=>(![X976:$i, X977:$i, X978:$i]:(((subset @ X976 @ X977)=>((subset @ X977 @ X978)=>(subset @ X976 @ X978))))=>(![X979:$i, X980:$i]:((subset @ X980 @ (setadjoin @ X979 @ X980)))=>(![X981:$i, X982:$i, X983:$i]:(((subset @ X981 @ X983)=>(subset @ X981 @ (setadjoin @ X982 @ X983))))=>(![X984:$i, X985:$i]:(((subset @ X984 @ X985)=>(in @ X984 @ (powerset @ X985))))=>(![X986:$i, X987:$i]:(((subset @ X986 @ X987)=>((subset @ X987 @ X986)=>((X986)=(X987)))))=>(![X988:$i]:(((subset @ X988 @ emptyset)=>((X988)=(emptyset))))=>(![X989:$i, X990:$i]:(((subset @ X990 @ X989)=>(in @ X990 @ (powerset @ X989))))=>(![X991:$i, X992:$i]:(((in @ X992 @ (powerset @ X991))=>(subset @ X992 @ X991)))=>(![X993:$i]:((in @ X993 @ (powerset @ X993)))=>(![X994:$i, X995:$i]:(((subset @ X994 @ X995)=>(subset @ (powerset @ X994) @ (powerset @ X995))))=>(![X996:$i, X997:$i > $o]:((in @ (dsetconstr @ X996 @ X997) @ (powerset @ X996)))=>(![X998:$i, X999:$i > $o]:((subset @ (dsetconstr @ X998 @ X999) @ X998))=>(![X1000:$i, X1001:$i, X1002:$i]:(((in @ X1002 @ X1000)=>(in @ X1002 @ (binunion @ X1000 @ X1001))))=>(![X1003:$i, X1004:$i]:((in @ X1004 @ (setadjoin @ X1003 @ (setadjoin @ X1004 @ emptyset))))=>(![X1005:$i, X1006:$i, X1007:$i]:(((in @ X1007 @ X1006)=>(in @ X1007 @ (binunion @ X1005 @ X1006))))=>(![X1008:$i, X1009:$i, X1010:$i, X1011:$o]:(((in @ X1010 @ (binunion @ X1008 @ X1009))=>(((in @ X1010 @ X1008)=>(X1011))=>(((in @ X1010 @ X1009)=>(X1011))=>(X1011)))))=>(![X1012:$i, X1013:$i, X1014:$i]:(((in @ X1014 @ (binunion @ X1012 @ X1013))=>((in @ X1014 @ X1012)|(in @ X1014 @ X1013))))=>(![X1015:$i, X1016:$i]:((subset @ X1015 @ (binunion @ X1015 @ X1016)))=>(![X1017:$i, X1018:$i]:((subset @ X1018 @ (binunion @ X1017 @ X1018)))=>(![X1019:$i, X1020:$i, X1021:$i]:(((in @ X1021 @ X1019)=>((in @ X1021 @ X1020)=>(in @ X1021 @ (binintersect @ X1019 @ X1020)))))=>(![X1022:$i, X1023:$i, X1024:$i]:(((subset @ X1024 @ X1022)=>((subset @ X1024 @ X1023)=>(subset @ X1024 @ (binintersect @ X1022 @ X1023)))))=>(![X1025:$i, X1026:$i, X1027:$i]:(((in @ X1027 @ (binintersect @ X1025 @ X1026))=>(in @ X1027 @ X1025)))=>(![X1028:$i, X1029:$i]:((subset @ (binintersect @ X1028 @ X1029) @ X1028))=>(![X1030:$i, X1031:$i]:(((subset @ X1030 @ X1031)=>((binintersect @ X1030 @ X1031)=(X1030))))=>(![X1032:$i, X1033:$i]:((((binintersect @ X1032 @ X1033)=(X1033))=>(subset @ X1033 @ X1032)))=>(![X1034:$i, X1035:$i, X1036:$i]:(((in @ X1036 @ (binintersect @ X1034 @ X1035))=>(in @ X1036 @ X1035)))=>(![X1037:$i, X1038:$i]:((~(?[X1039:$i]:(((in @ X1039 @ X1037)&(in @ X1039 @ 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X1350 @ X1351)) @ X1350)))))=>(![X1352:$i, X1353:$i, X1354:$i]:((((subset @ X1354 @ (cartprod @ X1352 @ X1353))&![X1355:$i]:(((in @ X1355 @ X1352)=>?[X1356:$i]:(((in @ X1356 @ (dsetconstr @ X1353 @ (^[Z0:$i]:((in @ (kpair @ X1355 @ Z0) @ X1354)))))&((dsetconstr @ X1353 @ (^[Z0:$i]:((in @ (kpair @ X1355 @ Z0) @ X1354))))=(setadjoin @ X1356 @ emptyset)))))))=>![X1357:$i]:(((in @ X1357 @ X1352)=>![X1358:$i]:(((in @ X1358 @ X1353)=>((in @ (kpair @ X1357 @ X1358) @ X1354)=>((ap @ X1352 @ X1353 @ X1354 @ X1357)=(X1358)))))))))=>(![X1359:$i, X1360:$i, X1361:$i]:((((subset @ X1361 @ (cartprod @ X1359 @ X1360))&![X1362:$i]:(((in @ X1362 @ X1359)=>?[X1363:$i]:(((in @ X1363 @ (dsetconstr @ X1360 @ (^[Z0:$i]:((in @ (kpair @ X1362 @ Z0) @ X1361)))))&((dsetconstr @ X1360 @ (^[Z0:$i]:((in @ (kpair @ X1362 @ Z0) @ X1361))))=(setadjoin @ X1363 @ emptyset)))))))=>![X1364:$i]:((((subset @ X1364 @ (cartprod @ X1359 @ X1360))&![X1365:$i]:(((in @ X1365 @ X1359)=>?[X1366:$i]:(((in @ X1366 @ (dsetconstr @ X1360 @ (^[Z0:$i]:((in @ (kpair @ X1365 @ Z0) @ X1364)))))&((dsetconstr @ X1360 @ (^[Z0:$i]:((in @ (kpair @ X1365 @ Z0) @ X1364))))=(setadjoin @ X1366 @ emptyset)))))))=>(![X1367:$i]:(((in @ X1367 @ X1359)=>((ap @ X1359 @ X1360 @ X1361 @ X1367)=(ap @ X1359 @ X1360 @ X1364 @ X1367))))=>![X1368:$i]:(((in @ X1368 @ X1359)=>![X1369:$i]:(((in @ X1369 @ X1360)=>((in @ (kpair @ X1368 @ X1369) @ X1364)=>(in @ (kpair @ X1368 @ X1369) @ X1361)))))))))))=>(![X1370:$i, X1371:$i, X1372:$i]:(((in @ X1372 @ (funcSet @ X1370 @ X1371))=>![X1373:$i]:(((in @ X1373 @ X1370)=>![X1374:$i]:(((in @ X1374 @ X1371)=>((in @ (kpair @ X1373 @ X1374) @ X1372)=>((ap @ X1370 @ X1371 @ X1372 @ X1373)=(X1374)))))))))=>![X4:$i, X5:$i, X29:$i]:(((subset @ X29 @ (cartprod @ X4 @ X5))=>![X36:$i]:(((subset @ X36 @ (cartprod @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>(in @ (kpair @ X2 @ X3) @ X36))))))=>(subset @ X29 @ X36)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_245, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_246]), foundationAx]), wellorderingAx]), c_0_247]), c_0_248]), c_0_249]), c_0_250]), c_0_251]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_252]), setext]), emptyI]), noeltsimpempty]), c_0_253]), c_0_254]), c_0_255]), c_0_256]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_257]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_258]), c_0_259]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_260]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_261]), c_0_262]), c_0_263]), inCongP]), in__Cong]), c_0_264]), c_0_265]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_266]), c_0_267]), c_0_268]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_269]), c_0_270]), 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]), c_0_271]), c_0_272]), c_0_273]), c_0_274]), singletonsuniq]), setukpairinjL1]), c_0_275]), c_0_276]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_277]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_216]), c_0_278]), c_0_279]), c_0_280]), c_0_281]), c_0_282]), c_0_283]), c_0_284]), c_0_285]), c_0_286]), c_0_287]), c_0_288]), ap2p]), c_0_289]), c_0_290]), c_0_291]), c_0_292]), c_0_293]), c_0_294]), c_0_295]), c_0_296]), funcGraphProp3]), c_0_297]), c_0_298]), funcGraphProp4])])]), c_0_299])).
% 1.59/0.51 thf(c_0_301, negated_conjecture, ![X1381:$i, X1382:$i, X1384:$i, X1385:$i, X1386:$i, X1387:$i, X1388:$i, X1389:$i, X1390:$i, X1391:$i, X1392:$i, X1394:$i, X1395:$i, X1397:$i, X1398:$i, X1399:$i, X1400:$i, X1401:$i, X1403:$i, X1404:$i > $i > $o, X1405:$i, X1407:$i, X1410:$i, X1412:$i, X1413:$i, X1414:$i, X1415:$i, X1417:$i, X1418:$i > $o, X1419:$i, X1421:$i, X1422:$i > $o, X1423:$i, X1424:$i, X1425:$i > $o, X1426:$i, X1427:$i, X1428:$i > $o, X1429:$i, X1430:$i > $o, X1431:$i, X1434:$i, X1435:$o, X1436:$i, X1437:$i, X1438:$o, X1439:$i, X1440:$i, X1441:$i > $o, X1442:$i, X1445:$i, X1446:$i, X1449:$i, X1451:$i, X1453:$i, X1454:$i > $o, X1455:$i, X1456:$i, X1458:$i, X1459:$i > $o, X1460:$i, X1461:$i, X1462:$i, X1463:$i, X1464:$i, X1465:$i, X1466:$i, X1467:$i, X1468:$i, X1469:$i, X1470:$i, X1471:$o, X1472:$i, X1473:$i, X1474:$i, X1475:$i, X1476:$i, X1477:$i, X1479:$i, X1480:$i, X1481:$i, X1482:$i, X1483:$i, X1484:$i, X1485:$i, X1486:$i, X1487:$i, X1488:$i, X1489:$o, X1491:$i, X1492:$i, X1493:$i > $o, X1494:$i, X1497:$i, X1498:$i, X1499:$i, X1501:$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 > $o, X1518:$i, X1519:$i > $o, X1520:$i, X1521:$i, X1522:$i > $o, X1523:$i, X1525:$i, X1526:$i > $o, X1528:$i, X1529:$i, X1530:$i > $o, X1532:$i, X1533:$i, X1534:$i > $o, X1535:$i, X1537:$o, X1538:$o, X1539:$i, X1540:$i > $o, X1542:$i, X1543:$i, X1544:$i > $o, X1545:$i, X1547:$i > $o, X1548:$i, X1551:$i, X1552:$i > $o, X1553:$i, X1557:$i, X1558:$i > $o, X1559:$i, X1562:$i, X1563:$i, X1564:$i, X1565:$i, X1566:$i, X1567:$i, X1568:$i, X1569:$i, X1570:$i, X1571:$i > $o, X1572:$i, X1574:$i, X1575:$i, X1576:$i > $o, X1577:$i > $o, X1580:$i, X1583:$i, X1584:$i, X1587:$i, X1588:$i, X1589:$i, X1590:$i, X1591:$i, X1592:$i, X1593:$i, X1594:$i, X1595:$i, X1596:$i > $o, X1597:$i, X1599:$i, X1600:$i, X1601:$i > $o, X1602:$i > $o, X1605:$i, X1607:$i, X1609:$i, X1610:$i, X1611:$i > $o, X1612:$i > $o, X1615:$i, X1616:$i, X1618:$i, X1619:$i, X1620:$i, X1621:$i, X1622:$i, X1623:$i, X1625:$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 > $o, X1663:$i, X1664:$i > $o, X1665:$i, X1666:$i, X1667:$i, X1668:$i, X1669:$i, X1670:$i, X1671:$i, X1672:$i, X1673:$i, X1674:$i, X1675:$i, X1676:$o, X1677:$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:$i, X1697:$i, X1698:$i, X1699:$i, X1700:$i, X1701:$i, X1702:$i, X1703:$i, X1705:$i, X1706:$i, X1707:$i, X1708:$i, X1709:$i, X1710:$i, X1711:$i, X1712:$i, X1713:$i, X1714:$i, X1715:$i, X1716:$i, X1717:$i, X1718:$i, X1719:$i, X1720:$i, X1721:$i, X1722:$i, X1723:$i, X1724:$i, X1725:$i, X1726:$i, X1727:$i, X1728:$i, X1729:$i, X1730:$i, X1731:$i, X1732:$i, X1733:$i, X1734:$i, X1735:$i, X1736:$i, X1737:$i, X1738:$i, X1739:$i, X1740:$i, X1741:$i, X1742:$i, X1743:$i, X1744:$o, X1745:$i, X1746:$i, X1747:$i, X1748:$i, X1749:$i, X1750:$i, X1751:$i, X1752:$i, X1753:$i, X1754:$i, X1755:$i, X1756:$i, X1757:$i, X1758:$i, X1759:$i, X1760:$i, X1761:$i, X1762:$i, X1763:$i, X1764:$i, X1765:$i, X1766:$i, X1767:$i, X1768:$i, X1769:$i, X1770:$i, X1771:$i, X1772:$i, X1773:$i, X1774:$i, X1775:$i, X1776:$i, X1777:$i, X1778:$i, X1779:$i, X1780:$i, X1781:$i, X1782:$i, X1783:$i, X1784:$i, X1785:$i, X1786:$i, X1787:$i, X1788:$i, X1789:$i, X1790:$i, X1791:$i, X1792:$i, X1793:$i, X1794:$i, X1795:$i, X1796:$i, X1797:$i, X1798:$i, X1799:$i, X1800:$i, X1801:$i, X1802:$i, X1803:$i, X1806:$i, X1807:$i, X1808:$i, X1809:$i, X1810:$i, X1812:$i, X1813:$i, X1814:$i, X1815:$i, X1816:$i > $o, X1819:$i, X1821:$i, X1822:$i > $o, X1823:$i, X1825:$i, X1826:$i > $o, X1827:$i, X1830:$i, X1831:$i > $o, X1834:$i, X1836:$i, X1837:$i, X1838:$i, X1839:$i, X1840:$i, X1841:$i, X1843:$i, X1844:$i, X1845:$i, X1846:$i, X1847:$i, X1848:$i, X1849:$i, X1850:$i, X1851:$i, X1852:$i, X1853:$i, X1854:$i, X1855:$i, X1856:$i, X1857:$i, X1858:$i, X1859:$i, X1860:$i, X1861:$i, X1862:$i, X1863:$i, X1864:$i, X1865:$i, X1866:$i, X1867:$i, X1868:$i, X1869:$i, X1870:$i, X1871:$i, X1872:$i, X1873:$i, X1874:$i, X1875:$i, X1876:$i, X1877:$i, X1879:$i, X1880:$i, X1881:$i, X1882:$i, X1883:$i, X1884:$i, X1885:$i, X1886:$i, X1887:$i, X1888:$i, X1889:$i, X1890:$i, X1891:$i, X1892:$i, X1893:$i, X1894:$i, X1895:$i, X1896:$i, X1897:$i, X1898:$i, X1899:$i, X1900:$i, X1901:$i, X1902:$i, X1903:$i, X1904:$i, X1905:$i, X1906:$i, X1907:$i, X1908:$i, X1909:$i, X1910:$i > $i > $o, X1911:$i, X1912:$i, X1913:$i, X1914:$i, X1915:$i > $i > $o, X1916:$i, X1917:$i, X1918:$i > $i > $o, X1919:$i, X1920:$i, X1921:$i > $i > $o, X1922:$i, X1923:$i, X1924:$i, X1925:$i, X1926:$i > $i > $o, X1927:$i, X1928:$i, X1929:$i, X1930:$i, X1931:$i > $i > $o, X1932:$i, X1933:$i, X1934:$i, X1935:$i, X1936:$i > $i > $o, X1937:$i, X1938:$i, X1939:$i, X1940:$i, X1941:$i, X1943:$i, X1944:$i, X1946:$i, X1947:$i, X1948:$i, X1950:$i, X1951:$i, X1952:$i, X1953:$i, X1954:$i, X1956:$i, X1957:$i, X1958:$i, X1959:$i, X1960:$i, X1961:$i, X1963:$i, X1964:$i, X1965:$i, X1966:$i, X1967:$i, X1968:$i, X1969:$i, X1971:$i, X1972:$i, X1973:$i, X1974:$i > $i, X1976:$i, X1978:$i, X1979:$i, X1980:$i > $i, X1982:$i, X1984:$i, X1985:$i, X1986:$i > $i, X1988:$i, X1989:$i, X1990:$i, X1991:$i > $o, X1994:$i, X1995:$i, X1996:$i, X1997:$i, X1998:$i > $o, X2001:$i, X2002:$i, X2003:$i > $o, X2004:$i, X2005:$i, X2006:$i, X2007:$i, X2008:$i, X2009:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2015:$i, X2016:$i, X2017:$i, X2018:$i, X2019:$i, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2025:$i, X2026:$i, X2028:$i, X2029:$i, X2031:$i, X2033:$i, X2034:$i, X2035:$i, 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X1954)))))|((dsetconstr @ X1953 @ (^[Z0:$i]:((in @ (kpair @ (esk72_3 @ X1952 @ X1953 @ X1954) @ Z0) @ X1954))))!=(setadjoin @ X1956 @ emptyset))|~(subset @ X1954 @ (cartprod @ X1952 @ X1953))|(~(in @ X1957 @ X1952)|(in @ (ap @ X1952 @ X1953 @ X1954 @ X1957) @ X1953))))&((((subset @ X1960 @ (cartprod @ X1958 @ X1959))|~(in @ X1960 @ (funcSet @ X1958 @ X1959)))&(((in @ (esk73_4 @ X1958 @ X1959 @ X1960 @ X1961) @ (dsetconstr @ X1959 @ (^[Z0:$i]:((in @ (kpair @ X1961 @ Z0) @ X1960)))))|~(in @ X1961 @ X1958)|~(in @ X1960 @ (funcSet @ X1958 @ X1959)))&(((dsetconstr @ X1959 @ (^[Z0:$i]:((in @ (kpair @ X1961 @ Z0) @ X1960))))=(setadjoin @ (esk73_4 @ X1958 @ X1959 @ X1960 @ X1961) @ emptyset))|~(in @ X1961 @ X1958)|~(in @ X1960 @ (funcSet @ X1958 @ X1959)))))&((~(in @ X1965 @ (funcSet @ X1963 @ X1964))|(~(in @ X1966 @ X1963)|(in @ (ap @ X1963 @ X1964 @ X1965 @ X1966) @ X1964)))&((((in @ (esk74_3 @ X1967 @ X1968 @ X1969) @ X1967)|~(subset @ X1969 @ (cartprod @ X1967 @ X1968))|(in @ X1969 @ (funcSet @ X1967 @ X1968)))&(~(in @ X1971 @ (dsetconstr @ X1968 @ (^[Z0:$i]:((in @ (kpair @ (esk74_3 @ X1967 @ X1968 @ X1969) @ Z0) @ X1969)))))|((dsetconstr @ X1968 @ (^[Z0:$i]:((in @ (kpair @ (esk74_3 @ X1967 @ X1968 @ X1969) @ Z0) @ X1969))))!=(setadjoin @ X1971 @ emptyset))|~(subset @ X1969 @ (cartprod @ X1967 @ X1968))|(in @ X1969 @ (funcSet @ X1967 @ X1968))))&(((((subset @ (dpsetconstr @ X1972 @ X1973 @ (^[Z0:$i]:($eq @ (X1974 @ Z0)))) @ (cartprod @ X1972 @ X1973))|(in @ (esk75_3 @ X1972 @ X1973 @ X1974) @ X1972))&(((in @ (esk76_4 @ X1972 @ X1973 @ X1974 @ X1976) @ (dsetconstr @ X1973 @ (^[Z0:$i]:((in @ (kpair @ X1976 @ Z0) @ (dpsetconstr @ X1972 @ X1973 @ (^[Z1:$i]:($eq @ (X1974 @ Z1)))))))))|~(in @ X1976 @ X1972)|(in @ (esk75_3 @ X1972 @ X1973 @ X1974) @ X1972))&(((dsetconstr @ X1973 @ (^[Z0:$i]:((in @ (kpair @ X1976 @ Z0) @ (dpsetconstr @ X1972 @ X1973 @ (^[Z1:$i]:($eq @ (X1974 @ Z1))))))))=(setadjoin @ (esk76_4 @ X1972 @ X1973 @ X1974 @ X1976) @ emptyset))|~(in @ X1976 @ X1972)|(in @ (esk75_3 @ X1972 @ X1973 @ X1974) @ X1972))))&(((subset @ (dpsetconstr @ X1972 @ X1973 @ (^[Z0:$i]:($eq @ (X1974 @ Z0)))) @ (cartprod @ X1972 @ X1973))|~(in @ (X1974 @ (esk75_3 @ X1972 @ X1973 @ X1974)) @ X1973))&(((in @ (esk76_4 @ X1972 @ X1973 @ X1974 @ X1976) @ (dsetconstr @ X1973 @ (^[Z0:$i]:((in @ (kpair @ X1976 @ Z0) @ (dpsetconstr @ X1972 @ X1973 @ (^[Z1:$i]:($eq @ (X1974 @ Z1)))))))))|~(in @ X1976 @ X1972)|~(in @ (X1974 @ (esk75_3 @ X1972 @ X1973 @ X1974)) @ X1973))&(((dsetconstr @ X1973 @ (^[Z0:$i]:((in @ (kpair @ X1976 @ Z0) @ (dpsetconstr @ X1972 @ X1973 @ (^[Z1:$i]:($eq @ (X1974 @ Z1))))))))=(setadjoin @ (esk76_4 @ X1972 @ X1973 @ X1974 @ X1976) @ emptyset))|~(in @ X1976 @ X1972)|~(in @ (X1974 @ (esk75_3 @ X1972 @ X1973 @ X1974)) @ X1973)))))&(((((subset @ (lam @ X1978 @ X1979 @ X1980) @ (cartprod @ X1978 @ X1979))|(in @ (esk77_3 @ X1978 @ X1979 @ X1980) @ X1978))&(((in @ (esk78_4 @ X1978 @ X1979 @ X1980 @ X1982) @ (dsetconstr @ X1979 @ (^[Z0:$i]:((in @ (kpair @ X1982 @ Z0) @ (lam @ X1978 @ X1979 @ X1980))))))|~(in @ X1982 @ X1978)|(in @ (esk77_3 @ X1978 @ X1979 @ X1980) @ X1978))&(((dsetconstr @ X1979 @ (^[Z0:$i]:((in @ (kpair @ X1982 @ Z0) @ (lam @ X1978 @ X1979 @ X1980)))))=(setadjoin @ (esk78_4 @ X1978 @ X1979 @ X1980 @ X1982) @ emptyset))|~(in @ X1982 @ X1978)|(in @ (esk77_3 @ X1978 @ X1979 @ X1980) @ X1978))))&(((subset @ (lam @ X1978 @ X1979 @ X1980) @ (cartprod @ X1978 @ X1979))|~(in @ (X1980 @ (esk77_3 @ X1978 @ X1979 @ X1980)) @ X1979))&(((in @ (esk78_4 @ X1978 @ X1979 @ X1980 @ X1982) @ (dsetconstr @ X1979 @ (^[Z0:$i]:((in @ (kpair @ X1982 @ Z0) @ (lam @ X1978 @ X1979 @ X1980))))))|~(in @ X1982 @ X1978)|~(in @ (X1980 @ (esk77_3 @ X1978 @ X1979 @ X1980)) @ X1979))&(((dsetconstr @ X1979 @ (^[Z0:$i]:((in @ (kpair @ X1982 @ Z0) @ (lam @ X1978 @ X1979 @ X1980)))))=(setadjoin @ (esk78_4 @ X1978 @ X1979 @ X1980 @ X1982) @ emptyset))|~(in @ X1982 @ X1978)|~(in @ (X1980 @ (esk77_3 @ X1978 @ X1979 @ X1980)) @ X1979)))))&((((in @ (esk79_3 @ X1984 @ X1985 @ X1986) @ X1984)|(in @ (lam @ X1984 @ X1985 @ X1986) @ (funcSet @ X1984 @ X1985)))&(~(in @ (X1986 @ (esk79_3 @ X1984 @ X1985 @ X1986)) @ X1985)|(in @ (lam @ X1984 @ X1985 @ X1986) @ (funcSet @ X1984 @ X1985))))&((((in @ (esk80_4 @ X1988 @ X1989 @ X1990 @ X1991) @ X1988)|(~(in @ X1994 @ X1990)|(X1991 @ X1994))|~(subset @ X1990 @ (cartprod @ X1988 @ X1989)))&(((in @ (esk81_4 @ X1988 @ X1989 @ X1990 @ X1991) @ X1989)|(~(in @ X1994 @ X1990)|(X1991 @ X1994))|~(subset @ X1990 @ (cartprod @ X1988 @ X1989)))&(((in @ (kpair @ (esk80_4 @ X1988 @ X1989 @ X1990 @ X1991) @ (esk81_4 @ X1988 @ X1989 @ X1990 @ X1991)) @ X1990)|(~(in @ X1994 @ X1990)|(X1991 @ X1994))|~(subset @ X1990 @ (cartprod @ X1988 @ X1989)))&(~(X1991 @ (kpair @ (esk80_4 @ X1988 @ X1989 @ X1990 @ X1991) @ (esk81_4 @ X1988 @ X1989 @ X1990 @ X1991)))|(~(in @ X1994 @ X1990)|(X1991 @ X1994))|~(subset @ X1990 @ (cartprod @ X1988 @ X1989))))))&((((in @ (esk82_4 @ X1995 @ X1996 @ X1997 @ X1998) @ X1995)|(~(in @ X2001 @ X1997)|(X1998 @ X2001))|~(subset @ X1997 @ (cartprod @ X1995 @ X1996)))&(((in @ (esk83_4 @ X1995 @ X1996 @ X1997 @ X1998) @ X1996)|(~(in @ X2001 @ X1997)|(X1998 @ X2001))|~(subset @ X1997 @ (cartprod @ X1995 @ X1996)))&(((in @ (kpair @ (esk82_4 @ X1995 @ X1996 @ X1997 @ X1998) @ (esk83_4 @ X1995 @ X1996 @ X1997 @ X1998)) @ X1997)|(~(in @ X2001 @ X1997)|(X1998 @ X2001))|~(subset @ X1997 @ (cartprod @ X1995 @ X1996)))&(~(X1998 @ (kpair @ (esk82_4 @ X1995 @ X1996 @ X1997 @ X1998) @ (esk83_4 @ X1995 @ X1996 @ X1997 @ X1998)))|(~(in @ X2001 @ X1997)|(X1998 @ X2001))|~(subset @ X1997 @ (cartprod @ X1995 @ X1996))))))&((~(in @ X2004 @ (dsetconstr @ X2002 @ X2003))|((dsetconstr @ X2002 @ X2003)!=(setadjoin @ X2004 @ emptyset))|(~(in @ X2005 @ X2002)|(~(in @ X2006 @ X2002)|(~(X2003 @ X2005)|(~(X2003 @ X2006)|((X2005)=(X2006)))))))&((((in @ (esk84_3 @ X2007 @ X2008 @ X2009) @ X2007)|~(subset @ X2009 @ (cartprod @ X2007 @ X2008))|(~(in @ X2012 @ X2007)|(in @ (kpair @ X2012 @ (ap @ X2007 @ X2008 @ X2009 @ X2012)) @ X2009)))&(~(in @ X2011 @ (dsetconstr @ X2008 @ (^[Z0:$i]:((in @ (kpair @ (esk84_3 @ X2007 @ X2008 @ X2009) @ Z0) @ X2009)))))|((dsetconstr @ X2008 @ (^[Z0:$i]:((in @ (kpair @ (esk84_3 @ X2007 @ X2008 @ X2009) @ Z0) @ X2009))))!=(setadjoin @ X2011 @ emptyset))|~(subset @ X2009 @ (cartprod @ X2007 @ X2008))|(~(in @ X2012 @ X2007)|(in @ (kpair @ X2012 @ (ap @ X2007 @ X2008 @ X2009 @ X2012)) @ X2009))))&((~(in @ X2015 @ (funcSet @ X2013 @ X2014))|(~(in @ X2016 @ X2013)|(in @ (kpair @ X2016 @ (ap @ X2013 @ X2014 @ X2015 @ X2016)) @ X2015)))&((((in @ (esk85_3 @ X2017 @ X2018 @ X2019) @ X2017)|~(subset @ X2019 @ (cartprod @ X2017 @ X2018))|(~(in @ X2022 @ X2017)|(~(in @ X2023 @ X2018)|(~(in @ (kpair @ X2022 @ X2023) @ X2019)|((ap @ X2017 @ X2018 @ X2019 @ X2022)=(X2023))))))&(~(in @ X2021 @ (dsetconstr @ X2018 @ (^[Z0:$i]:((in @ (kpair @ (esk85_3 @ X2017 @ X2018 @ X2019) @ Z0) @ X2019)))))|((dsetconstr @ X2018 @ (^[Z0:$i]:((in @ (kpair @ (esk85_3 @ X2017 @ X2018 @ X2019) @ Z0) @ X2019))))!=(setadjoin @ X2021 @ emptyset))|~(subset @ X2019 @ (cartprod @ X2017 @ X2018))|(~(in @ X2022 @ X2017)|(~(in @ X2023 @ X2018)|(~(in @ (kpair @ X2022 @ X2023) @ X2019)|((ap @ X2017 @ X2018 @ X2019 @ X2022)=(X2023)))))))&((((((in @ (esk88_4 @ X2024 @ X2025 @ X2026 @ X2029) @ X2024)|(~(in @ X2033 @ X2024)|(~(in @ X2034 @ X2025)|(~(in @ (kpair @ X2033 @ X2034) @ X2029)|(in @ (kpair @ X2033 @ X2034) @ X2026))))|((in @ (esk87_4 @ X2024 @ X2025 @ X2026 @ X2029) @ X2024)|~(subset @ X2029 @ (cartprod @ X2024 @ X2025)))|((in @ (esk86_3 @ X2024 @ X2025 @ X2026) @ X2024)|~(subset @ X2026 @ (cartprod @ X2024 @ X2025))))&(((ap @ X2024 @ X2025 @ X2026 @ (esk88_4 @ X2024 @ X2025 @ X2026 @ X2029))!=(ap @ X2024 @ X2025 @ X2029 @ (esk88_4 @ X2024 @ X2025 @ X2026 @ X2029)))|(~(in @ X2033 @ X2024)|(~(in @ X2034 @ X2025)|(~(in @ (kpair @ X2033 @ X2034) @ X2029)|(in @ (kpair @ X2033 @ X2034) @ X2026))))|((in @ (esk87_4 @ X2024 @ X2025 @ X2026 @ X2029) @ X2024)|~(subset @ X2029 @ (cartprod @ X2024 @ X2025)))|((in @ (esk86_3 @ X2024 @ X2025 @ X2026) @ X2024)|~(subset @ X2026 @ (cartprod @ X2024 @ X2025)))))&(((in @ (esk88_4 @ X2024 @ X2025 @ X2026 @ X2029) @ X2024)|(~(in @ X2033 @ X2024)|(~(in @ X2034 @ X2025)|(~(in @ (kpair @ X2033 @ X2034) @ X2029)|(in @ (kpair @ X2033 @ X2034) @ X2026))))|(~(in @ X2031 @ (dsetconstr @ X2025 @ (^[Z0:$i]:((in @ (kpair @ (esk87_4 @ X2024 @ X2025 @ X2026 @ X2029) @ Z0) @ X2029)))))|((dsetconstr @ X2025 @ (^[Z0:$i]:((in @ (kpair @ (esk87_4 @ X2024 @ X2025 @ X2026 @ X2029) @ Z0) @ X2029))))!=(setadjoin @ X2031 @ emptyset))|~(subset @ X2029 @ (cartprod @ X2024 @ X2025)))|((in @ (esk86_3 @ X2024 @ X2025 @ X2026) @ X2024)|~(subset @ X2026 @ (cartprod @ X2024 @ X2025))))&(((ap @ X2024 @ X2025 @ X2026 @ (esk88_4 @ X2024 @ X2025 @ X2026 @ X2029))!=(ap @ X2024 @ X2025 @ X2029 @ (esk88_4 @ X2024 @ X2025 @ X2026 @ X2029)))|(~(in @ X2033 @ X2024)|(~(in @ X2034 @ X2025)|(~(in @ (kpair @ X2033 @ X2034) @ X2029)|(in @ (kpair @ X2033 @ X2034) @ X2026))))|(~(in @ X2031 @ (dsetconstr @ X2025 @ (^[Z0:$i]:((in @ (kpair @ (esk87_4 @ X2024 @ X2025 @ X2026 @ X2029) @ Z0) @ X2029)))))|((dsetconstr @ X2025 @ (^[Z0:$i]:((in @ (kpair @ (esk87_4 @ X2024 @ X2025 @ X2026 @ X2029) @ Z0) @ X2029))))!=(setadjoin @ X2031 @ emptyset))|~(subset @ X2029 @ (cartprod @ X2024 @ X2025)))|((in @ (esk86_3 @ X2024 @ X2025 @ X2026) @ X2024)|~(subset @ X2026 @ (cartprod @ X2024 @ X2025))))))&((((in @ (esk88_4 @ X2024 @ X2025 @ X2026 @ X2029) @ X2024)|(~(in @ X2033 @ X2024)|(~(in @ X2034 @ X2025)|(~(in @ (kpair @ X2033 @ X2034) @ X2029)|(in @ (kpair @ X2033 @ X2034) @ X2026))))|((in @ (esk87_4 @ X2024 @ X2025 @ X2026 @ X2029) @ X2024)|~(subset @ X2029 @ (cartprod @ X2024 @ X2025)))|(~(in @ X2028 @ (dsetconstr @ X2025 @ (^[Z0:$i]:((in @ (kpair @ (esk86_3 @ X2024 @ X2025 @ X2026) @ Z0) @ X2026)))))|((dsetconstr @ X2025 @ (^[Z0:$i]:((in @ (kpair @ (esk86_3 @ X2024 @ X2025 @ X2026) @ Z0) @ X2026))))!=(setadjoin @ X2028 @ emptyset))|~(subset @ X2026 @ (cartprod @ X2024 @ X2025))))&(((ap @ X2024 @ X2025 @ X2026 @ (esk88_4 @ X2024 @ X2025 @ X2026 @ X2029))!=(ap @ X2024 @ X2025 @ X2029 @ (esk88_4 @ X2024 @ X2025 @ X2026 @ X2029)))|(~(in @ X2033 @ X2024)|(~(in @ X2034 @ X2025)|(~(in @ (kpair @ X2033 @ X2034) @ X2029)|(in @ (kpair @ X2033 @ X2034) @ X2026))))|((in @ (esk87_4 @ X2024 @ X2025 @ X2026 @ X2029) @ X2024)|~(subset @ X2029 @ (cartprod @ X2024 @ X2025)))|(~(in @ X2028 @ (dsetconstr @ X2025 @ (^[Z0:$i]:((in @ (kpair @ (esk86_3 @ X2024 @ X2025 @ X2026) @ Z0) @ X2026)))))|((dsetconstr @ X2025 @ (^[Z0:$i]:((in @ (kpair @ (esk86_3 @ X2024 @ X2025 @ X2026) @ Z0) @ X2026))))!=(setadjoin @ X2028 @ emptyset))|~(subset @ X2026 @ (cartprod @ X2024 @ X2025)))))&(((in @ (esk88_4 @ X2024 @ X2025 @ X2026 @ X2029) @ X2024)|(~(in @ X2033 @ X2024)|(~(in @ X2034 @ X2025)|(~(in @ (kpair @ X2033 @ X2034) @ X2029)|(in @ (kpair @ X2033 @ X2034) @ X2026))))|(~(in @ X2031 @ (dsetconstr @ X2025 @ (^[Z0:$i]:((in @ (kpair @ (esk87_4 @ X2024 @ X2025 @ X2026 @ X2029) @ Z0) @ X2029)))))|((dsetconstr @ X2025 @ (^[Z0:$i]:((in @ (kpair @ (esk87_4 @ X2024 @ X2025 @ X2026 @ X2029) @ Z0) @ X2029))))!=(setadjoin @ X2031 @ emptyset))|~(subset @ X2029 @ (cartprod @ X2024 @ X2025)))|(~(in @ X2028 @ (dsetconstr @ X2025 @ (^[Z0:$i]:((in @ (kpair @ (esk86_3 @ X2024 @ X2025 @ X2026) @ Z0) @ X2026)))))|((dsetconstr @ X2025 @ (^[Z0:$i]:((in @ (kpair @ (esk86_3 @ X2024 @ X2025 @ X2026) @ Z0) @ X2026))))!=(setadjoin @ X2028 @ emptyset))|~(subset @ X2026 @ (cartprod @ X2024 @ X2025))))&(((ap @ X2024 @ X2025 @ X2026 @ (esk88_4 @ X2024 @ X2025 @ X2026 @ X2029))!=(ap @ X2024 @ X2025 @ X2029 @ (esk88_4 @ X2024 @ X2025 @ X2026 @ X2029)))|(~(in @ X2033 @ X2024)|(~(in @ X2034 @ X2025)|(~(in @ (kpair @ X2033 @ X2034) @ X2029)|(in @ (kpair @ X2033 @ X2034) @ X2026))))|(~(in @ X2031 @ (dsetconstr @ X2025 @ (^[Z0:$i]:((in @ (kpair @ (esk87_4 @ X2024 @ X2025 @ X2026 @ X2029) @ Z0) @ X2029)))))|((dsetconstr @ X2025 @ (^[Z0:$i]:((in @ (kpair @ (esk87_4 @ X2024 @ X2025 @ X2026 @ X2029) @ Z0) @ X2029))))!=(setadjoin @ X2031 @ emptyset))|~(subset @ X2029 @ (cartprod @ X2024 @ X2025)))|(~(in @ X2028 @ (dsetconstr @ X2025 @ (^[Z0:$i]:((in @ (kpair @ (esk86_3 @ X2024 @ X2025 @ X2026) @ Z0) @ X2026)))))|((dsetconstr @ X2025 @ (^[Z0:$i]:((in @ (kpair @ (esk86_3 @ X2024 @ X2025 @ X2026) @ Z0) @ X2026))))!=(setadjoin @ X2028 @ emptyset))|~(subset @ X2026 @ (cartprod @ X2024 @ X2025)))))))&((~(in @ X2037 @ (funcSet @ X2035 @ X2036))|(~(in @ X2038 @ X2035)|(~(in @ X2039 @ X2036)|(~(in @ (kpair @ X2038 @ X2039) @ X2037)|((ap @ X2035 @ X2036 @ X2037 @ X2038)=(X2039))))))&((subset @ esk91_0 @ (cartprod @ esk89_0 @ esk90_0))&((subset @ esk92_0 @ (cartprod @ esk89_0 @ esk90_0))&((~(in @ X2044 @ esk89_0)|(~(in @ X2045 @ esk90_0)|(~(in @ (kpair @ X2044 @ X2045) @ esk91_0)|(in @ (kpair @ X2044 @ X2045) @ esk92_0))))&~(subset @ esk91_0 @ esk92_0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_300])])])])])])])).
% 1.59/0.51 thf(c_0_302, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:(((in @ X4 @ X3)|~((subset @ X2 @ X3))|~((in @ X4 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_301])).
% 1.59/0.51 thf(c_0_303, negated_conjecture, (subset @ esk91_0 @ (cartprod @ esk89_0 @ esk90_0)), inference(split_conjunct,[status(thm)],[c_0_301])).
% 1.59/0.51 thf(c_0_304, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ (kfst @ X2) @ X3)|~((in @ X2 @ (cartprod @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_301])).
% 1.59/0.51 thf(c_0_305, negated_conjecture, ![X2:$i]:(((in @ X2 @ (cartprod @ esk89_0 @ esk90_0))|~((in @ X2 @ esk91_0)))), inference(spm,[status(thm)],[c_0_302, c_0_303])).
% 1.59/0.51 thf(c_0_306, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ (ksnd @ X2) @ X4)|~((in @ X2 @ (cartprod @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_301])).
% 1.59/0.51 thf(c_0_307, negated_conjecture, ![X2:$i]:(((in @ (kfst @ X2) @ esk89_0)|~((in @ X2 @ esk91_0)))), inference(spm,[status(thm)],[c_0_304, c_0_305])).
% 1.59/0.51 thf(c_0_308, negated_conjecture, ![X3:$i, X2:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2))), inference(split_conjunct,[status(thm)],[c_0_301])).
% 1.59/0.51 thf(c_0_309, negated_conjecture, ![X2:$i]:(((in @ (ksnd @ X2) @ esk90_0)|~((in @ X2 @ esk91_0)))), inference(spm,[status(thm)],[c_0_306, c_0_305])).
% 1.59/0.51 thf(c_0_310, negated_conjecture, ![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3))), inference(split_conjunct,[status(thm)],[c_0_301])).
% 1.59/0.51 thf(c_0_311, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ esk92_0)|~((in @ X2 @ esk89_0))|~((in @ X3 @ esk90_0))|~((in @ (kpair @ X2 @ X3) @ esk91_0)))), inference(split_conjunct,[status(thm)],[c_0_301])).
% 1.59/0.51 thf(c_0_312, negated_conjecture, ![X2:$i, X3:$i]:(((in @ X2 @ esk89_0)|~((in @ (kpair @ X2 @ X3) @ esk91_0)))), inference(spm,[status(thm)],[c_0_307, c_0_308])).
% 1.59/0.51 thf(c_0_313, negated_conjecture, ![X3:$i, X2:$i]:(((in @ X2 @ esk90_0)|~((in @ (kpair @ X3 @ X2) @ esk91_0)))), inference(spm,[status(thm)],[c_0_309, c_0_310])).
% 1.59/0.51 thf(c_0_314, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((iskpair @ X2)|~((in @ X2 @ (cartprod @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_301])).
% 1.59/0.51 thf(c_0_315, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ esk92_0)|~((in @ (kpair @ X2 @ X3) @ esk91_0)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_311, c_0_312]), c_0_313])).
% 1.59/0.51 thf(c_0_316, negated_conjecture, ![X2:$i]:((((kpair @ (kfst @ X2) @ (ksnd @ X2))=(X2))|~((iskpair @ X2)))), inference(split_conjunct,[status(thm)],[c_0_301])).
% 1.59/0.51 thf(c_0_317, negated_conjecture, ![X2:$i]:(((iskpair @ X2)|~((in @ X2 @ esk91_0)))), inference(spm,[status(thm)],[c_0_314, c_0_305])).
% 1.59/0.51 thf(c_0_318, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ X3)|~((in @ (esk53_2 @ X2 @ X3) @ X3)))), inference(split_conjunct,[status(thm)],[c_0_301])).
% 1.59/0.51 thf(c_0_319, negated_conjecture, ![X2:$i]:(((in @ X2 @ esk92_0)|~((in @ X2 @ esk91_0)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_315, c_0_316]), c_0_317])).
% 1.59/0.51 thf(c_0_320, negated_conjecture, ![X2:$i]:(((subset @ X2 @ esk92_0)|~((in @ (esk53_2 @ X2 @ esk92_0) @ esk91_0)))), inference(spm,[status(thm)],[c_0_318, c_0_319])).
% 1.59/0.51 thf(c_0_321, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (esk53_2 @ X2 @ X3) @ X2)|(subset @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_301])).
% 1.59/0.51 thf(c_0_322, negated_conjecture, ~((subset @ esk91_0 @ esk92_0)), inference(split_conjunct,[status(thm)],[c_0_301])).
% 1.59/0.51 thf(c_0_323, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_320, c_0_321]), c_0_322]), ['proof']).
% 1.59/0.51 % SZS output end CNFRefutation
% 1.59/0.51 % Parsed axioms : 455
% 1.59/0.51 % Removed by relevancy pruning/SinE : 0
% 1.59/0.51 % Initial clauses : 637
% 1.59/0.51 % Removed in clause preprocessing : 267
% 1.59/0.51 % Initial clauses in saturation : 370
% 1.59/0.51 % Processed clauses : 1241
% 1.59/0.51 % ...of these trivial : 14
% 1.59/0.51 % ...subsumed : 740
% 1.59/0.51 % ...remaining for further processing : 487
% 1.59/0.51 % Other redundant clauses eliminated : 29
% 1.59/0.51 % Clauses deleted for lack of memory : 0
% 1.59/0.51 % Backward-subsumed : 1
% 1.59/0.51 % Backward-rewritten : 4
% 1.59/0.51 % Generated clauses : 12946
% 1.59/0.51 % ...of the previous two non-redundant : 10383
% 1.59/0.51 % ...aggressively subsumed : 0
% 1.59/0.51 % Contextual simplify-reflections : 3
% 1.59/0.51 % Paramodulations : 12912
% 1.59/0.51 % Factorizations : 2
% 1.59/0.51 % NegExts : 0
% 1.59/0.51 % Equation resolutions : 32
% 1.59/0.51 % Disequality decompositions : 0
% 1.59/0.51 % Total rewrite steps : 6159
% 1.59/0.51 % ...of those cached : 5991
% 1.59/0.51 % Propositional unsat checks : 0
% 1.59/0.51 % Propositional check models : 0
% 1.59/0.51 % Propositional check unsatisfiable : 0
% 1.59/0.51 % Propositional clauses : 0
% 1.59/0.51 % Propositional clauses after purity: 0
% 1.59/0.51 % Propositional unsat core size : 0
% 1.59/0.51 % Propositional preprocessing time : 0.000
% 1.59/0.51 % Propositional encoding time : 0.000
% 1.59/0.51 % Propositional solver time : 0.000
% 1.59/0.51 % Success case prop preproc time : 0.000
% 1.59/0.51 % Success case prop encoding time : 0.000
% 1.59/0.51 % Success case prop solver time : 0.000
% 1.59/0.51 % Current number of processed clauses : 472
% 1.59/0.51 % Positive orientable unit clauses : 192
% 1.59/0.51 % Positive unorientable unit clauses: 0
% 1.59/0.51 % Negative unit clauses : 4
% 1.59/0.51 % Non-unit-clauses : 276
% 1.59/0.51 % Current number of unprocessed clauses: 9496
% 1.59/0.51 % ...number of literals in the above : 29790
% 1.59/0.51 % Current number of archived formulas : 0
% 1.59/0.51 % Current number of archived clauses : 5
% 1.59/0.51 % Clause-clause subsumption calls (NU) : 18877
% 1.59/0.51 % Rec. Clause-clause subsumption calls : 12545
% 1.59/0.51 % Non-unit clause-clause subsumptions : 704
% 1.59/0.51 % Unit Clause-clause subsumption calls : 871
% 1.59/0.51 % Rewrite failures with RHS unbound : 0
% 1.59/0.51 % BW rewrite match attempts : 943
% 1.59/0.51 % BW rewrite match successes : 3
% 1.59/0.51 % Condensation attempts : 0
% 1.59/0.51 % Condensation successes : 0
% 1.59/0.51 % Termbank termtop insertions : 238947
% 1.59/0.51 % Search garbage collected termcells : 22094
% 1.59/0.51
% 1.59/0.51 % -------------------------------------------------
% 1.59/0.51 % User time : 0.163 s
% 1.59/0.51 % System time : 0.019 s
% 1.59/0.51 % Total time : 0.182 s
% 1.59/0.51 % Maximum resident set size: 8464 pages
% 1.59/0.51
% 1.59/0.51 % -------------------------------------------------
% 1.59/0.51 % User time : 0.177 s
% 1.59/0.51 % System time : 0.025 s
% 1.59/0.51 % Total time : 0.202 s
% 1.59/0.51 % Maximum resident set size: 5376 pages
% 1.59/0.51 % E exiting
%------------------------------------------------------------------------------