%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU673^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 08:27:10 AM UTC 2026
% Result : Theorem 0.68s 0.41s
% Output : CNFRefutation 0.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU673^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.19 % Computer : n004.cluster.edu
% 0.11/0.19 % Model : x86_64 x86_64
% 0.11/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.19 % Memory : 8046.5625MB
% 0.11/0.19 % OS : Linux 6.8.0-71-generic
% 0.11/0.19 % CPULimit : 300
% 0.11/0.19 % WCLimit : 300
% 0.11/0.19 % DateTime : Tue Sep 29 14:07:07 UTC 2026
% 0.11/0.20 % CPUTime :
% 0.11/0.20 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.24 Running higher-order theorem proving
% 0.11/0.27 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p
% 0.68/0.41 % Version: 3.5.1-ho
% 0.68/0.41 % Preprocessing class: HSLMSLSSLLLCHSA.
% 0.68/0.41 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.68/0.41 % Starting ho_unfolding_5 with 1200s (4) cores
% 0.68/0.41 % Starting pre_casc_3 with 300s (1) cores
% 0.68/0.41 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.68/0.41 % Starting full_lambda_10 with 300s (1) cores
% 0.68/0.41 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.68/0.41 % ho_unfolding_5 with pid 1340416 completed with status 0
% 0.68/0.41 % Result found by ho_unfolding_5
% 0.68/0.41 % Preprocessing class: HSLMSLSSLLLCHSA.
% 0.68/0.41 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.68/0.41 % Starting ho_unfolding_5 with 1200s (4) cores
% 0.68/0.41 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.68/0.41 % No SInE strategy applied
% 0.68/0.41 % Search class: HGHSM-FSLM31-MHSMMSBN
% 0.68/0.41 % Scheduled 7 strats onto 4 cores with 1200 seconds (1200 total)
% 0.68/0.41 % Starting SubtermCWHack with 109s (1) cores
% 0.68/0.41 % Starting ho_unfolding_5 with 121s (1) cores
% 0.68/0.41 % Starting pre_casc_3 with 171s (1) cores
% 0.68/0.41 % Starting new_bool_3 with 109s (1) cores
% 0.68/0.41 % new_bool_3 with pid 1340426 completed with status 0
% 0.68/0.41 % Result found by new_bool_3
% 0.68/0.41 % Preprocessing class: HSLMSLSSLLLCHSA.
% 0.68/0.41 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.68/0.41 % Starting ho_unfolding_5 with 1200s (4) cores
% 0.68/0.41 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.68/0.41 % No SInE strategy applied
% 0.68/0.41 % Search class: HGHSM-FSLM31-MHSMMSBN
% 0.68/0.41 % Scheduled 7 strats onto 4 cores with 1200 seconds (1200 total)
% 0.68/0.41 % Starting SubtermCWHack with 109s (1) cores
% 0.68/0.41 % Starting ho_unfolding_5 with 121s (1) cores
% 0.68/0.41 % Starting pre_casc_3 with 171s (1) cores
% 0.68/0.41 % Starting new_bool_3 with 109s (1) cores
% 0.68/0.41 % Preprocessing time : 0.005 s
% 0.68/0.41 % Presaturation interreduction done
% 0.68/0.41
% 0.68/0.41 % Proof found!
% 0.68/0.41 % SZS status Theorem
% 0.68/0.41 % SZS output start CNFRefutation
% 0.68/0.41 thf(decl_23, type, in: $i > $i > $o).
% 0.68/0.41 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.68/0.41 thf(decl_25, type, setextAx: $o).
% 0.68/0.41 thf(decl_26, type, emptyset: $i).
% 0.68/0.41 thf(decl_27, type, emptysetAx: $o).
% 0.68/0.41 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.68/0.41 thf(decl_29, type, setadjoinAx: $o).
% 0.68/0.41 thf(decl_30, type, powerset: $i > $i).
% 0.68/0.41 thf(decl_31, type, powersetAx: $o).
% 0.68/0.41 thf(decl_32, type, setunion: $i > $i).
% 0.68/0.41 thf(decl_33, type, setunionAx: $o).
% 0.68/0.41 thf(decl_34, type, omega: $i).
% 0.68/0.41 thf(decl_35, type, omega0Ax: $o).
% 0.68/0.41 thf(decl_36, type, omegaSAx: $o).
% 0.68/0.41 thf(decl_37, type, omegaIndAx: $o).
% 0.68/0.41 thf(decl_38, type, replAx: $o).
% 0.68/0.41 thf(decl_39, type, foundationAx: $o).
% 0.68/0.41 thf(decl_40, type, wellorderingAx: $o).
% 0.68/0.41 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.68/0.41 thf(decl_42, type, descrp: $o).
% 0.68/0.41 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.68/0.41 thf(decl_44, type, dsetconstrI: $o).
% 0.68/0.41 thf(decl_45, type, dsetconstrEL: $o).
% 0.68/0.41 thf(decl_46, type, dsetconstrER: $o).
% 0.68/0.41 thf(decl_47, type, exuE1: $o).
% 0.68/0.41 thf(decl_48, type, prop2set: $o > $i).
% 0.68/0.41 thf(decl_49, type, prop2setE: $o).
% 0.68/0.41 thf(decl_50, type, emptysetE: $o).
% 0.68/0.41 thf(decl_51, type, emptysetimpfalse: $o).
% 0.68/0.41 thf(decl_52, type, notinemptyset: $o).
% 0.68/0.41 thf(decl_53, type, exuE3e: $o).
% 0.68/0.41 thf(decl_54, type, setext: $o).
% 0.68/0.41 thf(decl_55, type, emptyI: $o).
% 0.68/0.41 thf(decl_56, type, noeltsimpempty: $o).
% 0.68/0.41 thf(decl_57, type, setbeta: $o).
% 0.68/0.41 thf(decl_58, type, nonempty: $i > $o).
% 0.68/0.41 thf(decl_59, type, nonemptyE1: $o).
% 0.68/0.41 thf(decl_60, type, nonemptyI: $o).
% 0.68/0.41 thf(decl_61, type, nonemptyI1: $o).
% 0.68/0.41 thf(decl_62, type, setadjoinIL: $o).
% 0.68/0.41 thf(decl_63, type, emptyinunitempty: $o).
% 0.68/0.41 thf(decl_64, type, setadjoinIR: $o).
% 0.68/0.41 thf(decl_65, type, setadjoinE: $o).
% 0.68/0.41 thf(decl_66, type, setadjoinOr: $o).
% 0.68/0.41 thf(decl_67, type, setoftrueEq: $o).
% 0.68/0.41 thf(decl_68, type, powersetI: $o).
% 0.68/0.41 thf(decl_69, type, emptyinPowerset: $o).
% 0.68/0.41 thf(decl_70, type, emptyInPowerset: $o).
% 0.68/0.41 thf(decl_71, type, powersetE: $o).
% 0.68/0.41 thf(decl_72, type, setunionI: $o).
% 0.68/0.41 thf(decl_73, type, setunionE: $o).
% 0.68/0.41 thf(decl_74, type, subPowSU: $o).
% 0.68/0.41 thf(decl_75, type, exuE2: $o).
% 0.68/0.41 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.68/0.41 thf(decl_77, type, uniqinunit: $o).
% 0.68/0.41 thf(decl_78, type, notinsingleton: $o).
% 0.68/0.41 thf(decl_79, type, eqinunit: $o).
% 0.68/0.41 thf(decl_80, type, singletonsswitch: $o).
% 0.68/0.41 thf(decl_81, type, upairsetE: $o).
% 0.68/0.41 thf(decl_82, type, upairsetIL: $o).
% 0.68/0.41 thf(decl_83, type, upairsetIR: $o).
% 0.68/0.41 thf(decl_84, type, emptyE1: $o).
% 0.68/0.41 thf(decl_85, type, vacuousDall: $o).
% 0.68/0.41 thf(decl_86, type, quantDeMorgan1: $o).
% 0.68/0.41 thf(decl_87, type, quantDeMorgan2: $o).
% 0.68/0.41 thf(decl_88, type, quantDeMorgan3: $o).
% 0.68/0.41 thf(decl_89, type, quantDeMorgan4: $o).
% 0.68/0.41 thf(decl_90, type, prop2setI: $o).
% 0.68/0.41 thf(decl_91, type, set2prop: $i > $o).
% 0.68/0.41 thf(decl_92, type, prop2set2propI: $o).
% 0.68/0.41 thf(decl_93, type, notdexE: $o).
% 0.68/0.41 thf(decl_94, type, notdallE: $o).
% 0.68/0.41 thf(decl_95, type, exuI1: $o).
% 0.68/0.41 thf(decl_96, type, exuI3: $o).
% 0.68/0.41 thf(decl_97, type, exuI2: $o).
% 0.68/0.41 thf(decl_98, type, inCongP: $o).
% 0.68/0.41 thf(decl_99, type, in__Cong: $o).
% 0.68/0.41 thf(decl_100, type, exuE3u: $o).
% 0.68/0.41 thf(decl_101, type, exu__Cong: $o).
% 0.68/0.41 thf(decl_102, type, emptyset__Cong: $o).
% 0.68/0.41 thf(decl_103, type, setadjoin__Cong: $o).
% 0.68/0.41 thf(decl_104, type, powerset__Cong: $o).
% 0.68/0.41 thf(decl_105, type, setunion__Cong: $o).
% 0.68/0.41 thf(decl_106, type, omega__Cong: $o).
% 0.68/0.41 thf(decl_107, type, exuEu: $o).
% 0.68/0.41 thf(decl_108, type, descr__Cong: $o).
% 0.68/0.41 thf(decl_109, type, dsetconstr__Cong: $o).
% 0.68/0.41 thf(decl_110, type, subset: $i > $i > $o).
% 0.68/0.41 thf(decl_113, type, subsetI1: $o).
% 0.68/0.41 thf(decl_114, type, eqimpsubset2: $o).
% 0.68/0.41 thf(decl_115, type, eqimpsubset1: $o).
% 0.68/0.41 thf(decl_116, type, subsetI2: $o).
% 0.68/0.41 thf(decl_117, type, emptysetsubset: $o).
% 0.68/0.41 thf(decl_118, type, subsetE: $o).
% 0.68/0.41 thf(decl_119, type, subsetE2: $o).
% 0.68/0.41 thf(decl_120, type, notsubsetI: $o).
% 0.68/0.41 thf(decl_121, type, notequalI1: $o).
% 0.68/0.41 thf(decl_122, type, notequalI2: $o).
% 0.68/0.41 thf(decl_123, type, subsetRefl: $o).
% 0.68/0.41 thf(decl_124, type, subsetTrans: $o).
% 0.68/0.41 thf(decl_125, type, setadjoinSub: $o).
% 0.68/0.41 thf(decl_126, type, setadjoinSub2: $o).
% 0.68/0.41 thf(decl_127, type, subset2powerset: $o).
% 0.68/0.41 thf(decl_128, type, setextsub: $o).
% 0.68/0.41 thf(decl_129, type, subsetemptysetimpeq: $o).
% 0.68/0.41 thf(decl_130, type, powersetI1: $o).
% 0.68/0.41 thf(decl_131, type, powersetE1: $o).
% 0.68/0.41 thf(decl_132, type, inPowerset: $o).
% 0.68/0.41 thf(decl_133, type, powersetsubset: $o).
% 0.68/0.41 thf(decl_134, type, sepInPowerset: $o).
% 0.68/0.41 thf(decl_135, type, sepSubset: $o).
% 0.68/0.41 thf(decl_136, type, binunion: $i > $i > $i).
% 0.68/0.41 thf(decl_137, type, binunionIL: $o).
% 0.68/0.41 thf(decl_138, type, upairset2IR: $o).
% 0.68/0.41 thf(decl_139, type, binunionIR: $o).
% 0.68/0.41 thf(decl_140, type, binunionEcases: $o).
% 0.68/0.41 thf(decl_141, type, binunionE: $o).
% 0.68/0.41 thf(decl_142, type, binunionLsub: $o).
% 0.68/0.41 thf(decl_143, type, binunionRsub: $o).
% 0.68/0.41 thf(decl_144, type, binintersect: $i > $i > $i).
% 0.68/0.41 thf(decl_145, type, binintersectI: $o).
% 0.68/0.41 thf(decl_146, type, binintersectSubset5: $o).
% 0.68/0.41 thf(decl_147, type, binintersectEL: $o).
% 0.68/0.41 thf(decl_148, type, binintersectLsub: $o).
% 0.68/0.41 thf(decl_149, type, binintersectSubset2: $o).
% 0.68/0.41 thf(decl_150, type, binintersectSubset3: $o).
% 0.68/0.41 thf(decl_151, type, binintersectER: $o).
% 0.68/0.41 thf(decl_152, type, disjointsetsI1: $o).
% 0.68/0.41 thf(decl_153, type, binintersectRsub: $o).
% 0.68/0.41 thf(decl_154, type, binintersectSubset4: $o).
% 0.68/0.41 thf(decl_155, type, binintersectSubset1: $o).
% 0.68/0.41 thf(decl_156, type, bs114d: $o).
% 0.68/0.41 thf(decl_158, type, setminus: $i > $i > $i).
% 0.68/0.41 thf(decl_159, type, setminusI: $o).
% 0.68/0.41 thf(decl_160, type, setminusEL: $o).
% 0.68/0.41 thf(decl_161, type, setminusER: $o).
% 0.68/0.41 thf(decl_162, type, setminusSubset2: $o).
% 0.68/0.41 thf(decl_163, type, setminusERneg: $o).
% 0.68/0.41 thf(decl_164, type, setminusELneg: $o).
% 0.68/0.41 thf(decl_165, type, setminusILneg: $o).
% 0.68/0.41 thf(decl_166, type, setminusIRneg: $o).
% 0.68/0.41 thf(decl_167, type, setminusLsub: $o).
% 0.68/0.41 thf(decl_168, type, setminusSubset1: $o).
% 0.68/0.41 thf(decl_169, type, symdiff: $i > $i > $i).
% 0.68/0.41 thf(decl_170, type, symdiffE: $o).
% 0.68/0.41 thf(decl_171, type, symdiffI1: $o).
% 0.68/0.41 thf(decl_172, type, symdiffI2: $o).
% 0.68/0.41 thf(decl_173, type, symdiffIneg1: $o).
% 0.68/0.41 thf(decl_174, type, symdiffIneg2: $o).
% 0.68/0.41 thf(decl_175, type, iskpair: $i > $o).
% 0.68/0.41 thf(decl_176, type, secondinupair: $o).
% 0.68/0.41 thf(decl_177, type, setukpairIL: $o).
% 0.68/0.41 thf(decl_178, type, setukpairIR: $o).
% 0.68/0.41 thf(decl_179, type, kpairiskpair: $o).
% 0.68/0.41 thf(decl_180, type, kpair: $i > $i > $i).
% 0.68/0.41 thf(decl_181, type, kpairp: $o).
% 0.68/0.41 thf(decl_182, type, cartprod: $i > $i > $i).
% 0.68/0.41 thf(decl_183, type, singletonsubset: $o).
% 0.68/0.41 thf(decl_184, type, singletoninpowerset: $o).
% 0.68/0.41 thf(decl_185, type, singletoninpowunion: $o).
% 0.68/0.41 thf(decl_186, type, upairset2E: $o).
% 0.68/0.41 thf(decl_187, type, upairsubunion: $o).
% 0.68/0.41 thf(decl_188, type, upairinpowunion: $o).
% 0.68/0.41 thf(decl_189, type, ubforcartprodlem1: $o).
% 0.68/0.41 thf(decl_190, type, ubforcartprodlem2: $o).
% 0.68/0.41 thf(decl_191, type, ubforcartprodlem3: $o).
% 0.68/0.41 thf(decl_192, type, cartprodpairin: $o).
% 0.68/0.41 thf(decl_193, type, cartprodmempair1: $o).
% 0.68/0.41 thf(decl_194, type, cartprodmempair: $o).
% 0.68/0.41 thf(decl_195, type, setunionE2: $o).
% 0.68/0.41 thf(decl_196, type, setunionsingleton1: $o).
% 0.68/0.41 thf(decl_197, type, setunionsingleton2: $o).
% 0.68/0.41 thf(decl_198, type, setunionsingleton: $o).
% 0.68/0.41 thf(decl_199, type, singleton: $i > $o).
% 0.68/0.41 thf(decl_200, type, singletonprop: $o).
% 0.68/0.41 thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 0.68/0.41 thf(decl_202, type, ex1E1: $o).
% 0.68/0.41 thf(decl_203, type, ex1I: $o).
% 0.68/0.41 thf(decl_204, type, ex1I2: $o).
% 0.68/0.41 thf(decl_205, type, singletonsuniq: $o).
% 0.68/0.41 thf(decl_210, type, setukpairinjL1: $o).
% 0.68/0.41 thf(decl_211, type, kfstsingleton: $o).
% 0.68/0.41 thf(decl_212, type, theprop: $o).
% 0.68/0.41 thf(decl_213, type, kfst: $i > $i).
% 0.68/0.41 thf(decl_214, type, kfstpairEq: $o).
% 0.68/0.41 thf(decl_215, type, cartprodfstin: $o).
% 0.68/0.41 thf(decl_216, type, setukpairinjL2: $o).
% 0.68/0.41 thf(decl_217, type, setukpairinjL: $o).
% 0.68/0.41 thf(decl_218, type, setukpairinjR11: $o).
% 0.68/0.41 thf(decl_219, type, setukpairinjR12: $o).
% 0.68/0.41 thf(decl_220, type, setukpairinjR1: $o).
% 0.68/0.41 thf(decl_221, type, upairequniteq: $o).
% 0.68/0.41 thf(decl_222, type, setukpairinjR2: $o).
% 0.68/0.41 thf(decl_223, type, setukpairinjR: $o).
% 0.68/0.41 thf(decl_224, type, ksndsingleton: $o).
% 0.68/0.41 thf(decl_225, type, ksnd: $i > $i).
% 0.68/0.41 thf(decl_226, type, ksndpairEq: $o).
% 0.68/0.41 thf(decl_227, type, kpairsurjEq: $o).
% 0.68/0.41 thf(decl_228, type, cartprodsndin: $o).
% 0.68/0.41 thf(decl_229, type, cartprodpairmemEL: $o).
% 0.68/0.41 thf(decl_230, type, cartprodpairmemER: $o).
% 0.68/0.41 thf(decl_231, type, cartprodmempaircEq: $o).
% 0.68/0.41 thf(decl_232, type, cartprodfstpairEq: $o).
% 0.68/0.41 thf(decl_233, type, cartprodsndpairEq: $o).
% 0.68/0.41 thf(decl_234, type, cartprodpairsurjEq: $o).
% 0.68/0.41 thf(decl_235, type, breln: $i > $i > $i > $o).
% 0.68/0.41 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 0.68/0.41 thf(decl_237, type, dpsetconstrI: $o).
% 0.68/0.41 thf(decl_238, type, dpsetconstrSub: $o).
% 0.68/0.41 thf(decl_239, type, setOfPairsIsBReln: $o).
% 0.68/0.41 thf(decl_240, type, dpsetconstrERa: $o).
% 0.68/0.41 thf(decl_241, type, dpsetconstrEL1: $o).
% 0.68/0.41 thf(decl_242, type, dpsetconstrEL2: $o).
% 0.68/0.41 thf(decl_243, type, dpsetconstrER: $o).
% 0.68/0.41 thf(decl_244, type, func: $i > $i > $i > $o).
% 0.68/0.41 thf(decl_246, type, funcImageSingleton: $o).
% 0.68/0.41 thf(decl_247, type, epred1_0: $o).
% 0.68/0.41 thf(decl_248, type, esk1_2: $i > $i > $i).
% 0.68/0.41 thf(decl_249, type, esk2_2: $i > $i > $i).
% 0.68/0.41 thf(decl_250, type, esk3_2: $i > $i > $i).
% 0.68/0.41 thf(decl_251, type, esk4_1: $i > $i).
% 0.68/0.41 thf(decl_252, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.68/0.41 thf(decl_253, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.68/0.41 thf(decl_254, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.68/0.41 thf(decl_255, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.68/0.41 thf(decl_256, type, esk9_1: $i > $i).
% 0.68/0.41 thf(decl_257, type, esk10_2: ($i > $o) > $i > $i).
% 0.68/0.41 thf(decl_258, type, esk11_2: ($i > $o) > $i > $i).
% 0.68/0.41 thf(decl_259, type, esk12_1: ($i > $o) > $i).
% 0.68/0.41 thf(decl_260, type, esk13_2: ($i > $o) > $i > $i).
% 0.68/0.41 thf(decl_261, type, esk14_1: ($i > $o) > $i).
% 0.68/0.41 thf(decl_262, type, esk15_2: $i > $i > $i).
% 0.68/0.41 thf(decl_263, type, esk16_2: $i > $i > $i).
% 0.68/0.41 thf(decl_264, type, esk17_1: $i > $i).
% 0.68/0.41 thf(decl_265, type, esk18_1: $i > $i).
% 0.68/0.41 thf(decl_266, type, esk19_1: $i > $i).
% 0.68/0.41 thf(decl_267, type, esk20_2: $i > $i > $i).
% 0.68/0.41 thf(decl_268, type, esk21_3: $i > $i > $o > $i).
% 0.68/0.41 thf(decl_269, type, esk22_2: ($i > $o) > $i > $i).
% 0.68/0.41 thf(decl_270, type, esk23_1: ($i > $o) > $i).
% 0.68/0.41 thf(decl_271, type, esk24_1: $i > $i).
% 0.68/0.41 thf(decl_272, type, esk25_2: $i > ($i > $o) > $i).
% 0.68/0.41 thf(decl_273, type, esk26_2: $i > ($i > $o) > $i).
% 0.68/0.41 thf(decl_274, type, esk27_2: $i > ($i > $o) > $i).
% 0.68/0.41 thf(decl_275, type, esk28_2: $i > ($i > $o) > $i).
% 0.68/0.41 thf(decl_276, type, esk29_2: $i > ($i > $o) > $i).
% 0.68/0.41 thf(decl_277, type, esk30_2: $i > ($i > $o) > $i).
% 0.68/0.41 thf(decl_278, type, esk31_2: ($i > $o) > $i > $i).
% 0.68/0.41 thf(decl_279, type, esk32_1: ($i > $o) > $i).
% 0.68/0.41 thf(decl_280, type, esk33_1: ($i > $o) > $i).
% 0.68/0.41 thf(decl_281, type, esk34_1: ($i > $o) > $i).
% 0.68/0.41 thf(decl_282, type, esk35_1: ($i > $o) > $i).
% 0.68/0.41 thf(decl_283, type, esk36_2: ($i > $o) > $i > $i).
% 0.68/0.41 thf(decl_284, type, esk37_1: ($i > $o) > $i).
% 0.68/0.41 thf(decl_285, type, esk38_2: ($i > $o) > $i > $i).
% 0.68/0.41 thf(decl_286, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 0.68/0.41 thf(decl_287, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 0.68/0.41 thf(decl_288, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.68/0.41 thf(decl_289, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 0.68/0.41 thf(decl_290, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.68/0.41 thf(decl_291, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 0.68/0.41 thf(decl_292, type, esk45_2: ($i > $o) > $i > $i).
% 0.68/0.41 thf(decl_293, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 0.68/0.41 thf(decl_294, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 0.68/0.41 thf(decl_295, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.68/0.41 thf(decl_296, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.68/0.41 thf(decl_297, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.68/0.41 thf(decl_298, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.68/0.41 thf(decl_299, type, esk52_2: $i > $i > $i).
% 0.68/0.41 thf(decl_300, type, esk53_2: $i > $i > $i).
% 0.68/0.41 thf(decl_301, type, esk54_2: $i > $i > $i).
% 0.68/0.41 thf(decl_302, type, esk55_3: $i > $i > $i > $i).
% 0.68/0.41 thf(decl_303, type, esk56_3: $i > $i > $i > $i).
% 0.68/0.41 thf(decl_304, type, esk57_2: $i > $i > $i).
% 0.68/0.41 thf(decl_305, type, esk58_2: $i > ($i > $o) > $i).
% 0.68/0.41 thf(decl_306, type, esk59_2: $i > ($i > $o) > $i).
% 0.68/0.41 thf(decl_307, type, esk60_2: $i > ($i > $o) > $i).
% 0.68/0.41 thf(decl_308, type, esk61_2: $i > ($i > $o) > $i).
% 0.68/0.41 thf(decl_309, type, esk62_3: $i > ($i > $o) > $i > $i).
% 0.68/0.41 thf(decl_310, type, esk63_3: $i > ($i > $o) > $i > $i).
% 0.68/0.41 thf(decl_311, type, esk64_2: $i > ($i > $o) > $i).
% 0.68/0.41 thf(decl_312, type, esk65_2: $i > ($i > $o) > $i).
% 0.68/0.41 thf(decl_313, type, esk66_2: $i > ($i > $o) > $i).
% 0.68/0.41 thf(decl_314, type, esk67_1: $i > $i).
% 0.68/0.41 thf(decl_315, type, esk68_1: $i > $i).
% 0.68/0.41 thf(decl_316, type, esk69_3: $i > $i > $i > $i).
% 0.68/0.41 thf(decl_317, type, esk70_4: $i > $i > $i > $i > $i).
% 0.68/0.41 thf(decl_318, type, esk71_0: $i).
% 0.68/0.41 thf(decl_319, type, esk72_0: $i).
% 0.68/0.41 thf(decl_320, type, esk73_0: $i).
% 0.68/0.41 thf(decl_321, type, esk74_1: $i > $i).
% 0.68/0.41 thf(decl_322, type, esk75_0: $i).
% 0.68/0.41 thf(decl_328, type, epred2_1: $i > $i > $i > $o).
% 0.68/0.41 thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', ex1)).
% 0.68/0.41 thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:((((in @ X2 @ X4))&(((X4)=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', singleton)).
% 0.68/0.41 thf(func, axiom, ((func)=(^[X4:$i, X5:$i, X29:$i]:((((breln @ X4 @ X5 @ X29))&(![X2:$i]:((((in @ X2 @ X4))=>((ex1 @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', func)).
% 0.68/0.41 thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', breln)).
% 0.68/0.41 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', replAx)).
% 0.68/0.41 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', exu)).
% 0.68/0.41 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', descrp)).
% 0.68/0.41 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', exuE1)).
% 0.68/0.41 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', exuE3e)).
% 0.68/0.41 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', nonempty)).
% 0.68/0.41 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', nonemptyI)).
% 0.68/0.41 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', exuE2)).
% 0.68/0.41 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', exuI1)).
% 0.68/0.41 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', exuI3)).
% 0.68/0.41 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', exuI2)).
% 0.68/0.41 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', exuE3u)).
% 0.68/0.41 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', exu__Cong)).
% 0.68/0.41 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', exuEu)).
% 0.68/0.41 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', descr__Cong)).
% 0.68/0.41 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', singletonprop)).
% 0.68/0.41 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', ex1E1)).
% 0.68/0.41 thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', ex1I)).
% 0.68/0.41 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', ex1I2)).
% 0.68/0.41 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', kfstsingleton)).
% 0.68/0.41 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', ksndsingleton)).
% 0.68/0.41 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setOfPairsIsBReln)).
% 0.68/0.41 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X30)))))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', funcImageSingleton)).
% 0.68/0.41 thf(apProp, 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)=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X30))))) @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', apProp)).
% 0.68/0.41 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', dsetconstrI)).
% 0.68/0.41 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', dsetconstrEL)).
% 0.68/0.41 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', dsetconstrER)).
% 0.68/0.41 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setbeta)).
% 0.68/0.41 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', nonemptyE1)).
% 0.68/0.41 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', nonemptyI1)).
% 0.68/0.41 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setoftrueEq)).
% 0.68/0.41 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', nonemptyImpWitness)).
% 0.68/0.41 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', emptyE1)).
% 0.68/0.41 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', dsetconstr__Cong)).
% 0.68/0.41 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', sepInPowerset)).
% 0.68/0.41 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', sepSubset)).
% 0.68/0.41 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', theprop)).
% 0.68/0.41 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', dpsetconstrI)).
% 0.68/0.41 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', dpsetconstrSub)).
% 0.68/0.41 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', dpsetconstrERa)).
% 0.68/0.41 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', dpsetconstrEL1)).
% 0.68/0.41 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', dpsetconstrEL2)).
% 0.68/0.41 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', dpsetconstrER)).
% 0.68/0.41 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setextAx)).
% 0.68/0.41 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', emptysetAx)).
% 0.68/0.41 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setadjoinAx)).
% 0.68/0.41 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', powersetAx)).
% 0.68/0.41 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setunionAx)).
% 0.68/0.41 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', omega0Ax)).
% 0.68/0.41 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', omegaSAx)).
% 0.68/0.41 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', omegaIndAx)).
% 0.68/0.41 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', foundationAx)).
% 0.68/0.41 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', wellorderingAx)).
% 0.68/0.41 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', prop2setE)).
% 0.68/0.41 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', emptysetE)).
% 0.68/0.41 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', emptysetimpfalse)).
% 0.68/0.41 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', notinemptyset)).
% 0.68/0.41 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setext)).
% 0.68/0.41 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', emptyI)).
% 0.68/0.41 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', noeltsimpempty)).
% 0.68/0.41 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setadjoinIL)).
% 0.68/0.41 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', emptyinunitempty)).
% 0.68/0.41 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setadjoinIR)).
% 0.68/0.41 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setadjoinE)).
% 0.68/0.41 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setadjoinOr)).
% 0.68/0.41 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', powersetI)).
% 0.68/0.41 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', emptyinPowerset)).
% 0.68/0.41 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', emptyInPowerset)).
% 0.68/0.41 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', powersetE)).
% 0.68/0.41 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setunionI)).
% 0.68/0.41 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setunionE)).
% 0.68/0.41 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', subPowSU)).
% 0.68/0.41 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', uniqinunit)).
% 0.68/0.41 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', notinsingleton)).
% 0.68/0.41 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', eqinunit)).
% 0.68/0.41 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', singletonsswitch)).
% 0.68/0.41 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', upairsetE)).
% 0.68/0.41 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', upairsetIL)).
% 0.68/0.41 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', upairsetIR)).
% 0.68/0.41 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', vacuousDall)).
% 0.68/0.41 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', quantDeMorgan1)).
% 0.68/0.41 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', quantDeMorgan2)).
% 0.68/0.41 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', quantDeMorgan3)).
% 0.68/0.41 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', quantDeMorgan4)).
% 0.68/0.41 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', prop2setI)).
% 0.68/0.41 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', prop2set2propI)).
% 0.68/0.41 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', notdexE)).
% 0.68/0.41 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', notdallE)).
% 0.68/0.41 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', inCongP)).
% 0.68/0.41 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', in__Cong)).
% 0.68/0.41 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', emptyset__Cong)).
% 0.68/0.41 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setadjoin__Cong)).
% 0.68/0.41 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', powerset__Cong)).
% 0.68/0.41 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setunion__Cong)).
% 0.68/0.41 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', omega__Cong)).
% 0.68/0.41 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', subsetI1)).
% 0.68/0.41 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', eqimpsubset2)).
% 0.68/0.41 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', eqimpsubset1)).
% 0.68/0.41 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', subsetI2)).
% 0.68/0.41 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', emptysetsubset)).
% 0.68/0.41 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', subsetE)).
% 0.68/0.41 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', subsetE2)).
% 0.68/0.41 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', notsubsetI)).
% 0.68/0.41 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', notequalI1)).
% 0.68/0.41 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', notequalI2)).
% 0.68/0.41 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', subsetRefl)).
% 0.68/0.41 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', subsetTrans)).
% 0.68/0.41 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setadjoinSub)).
% 0.68/0.41 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setadjoinSub2)).
% 0.68/0.41 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', subset2powerset)).
% 0.68/0.41 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setextsub)).
% 0.68/0.41 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', subsetemptysetimpeq)).
% 0.68/0.41 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', powersetI1)).
% 0.68/0.41 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', powersetE1)).
% 0.68/0.41 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', inPowerset)).
% 0.68/0.41 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', powersetsubset)).
% 0.68/0.41 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', binunionIL)).
% 0.68/0.41 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', upairset2IR)).
% 0.68/0.41 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', binunionIR)).
% 0.68/0.41 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', binunionEcases)).
% 0.68/0.41 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', binunionE)).
% 0.68/0.41 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', binunionLsub)).
% 0.68/0.41 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', binunionRsub)).
% 0.68/0.41 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', binintersectI)).
% 0.68/0.41 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', binintersectSubset5)).
% 0.68/0.41 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', binintersectEL)).
% 0.68/0.41 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', binintersectLsub)).
% 0.68/0.41 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', binintersectSubset2)).
% 0.68/0.41 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', binintersectSubset3)).
% 0.68/0.41 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', binintersectER)).
% 0.68/0.41 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', disjointsetsI1)).
% 0.68/0.41 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', binintersectRsub)).
% 0.68/0.41 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', binintersectSubset4)).
% 0.68/0.41 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', binintersectSubset1)).
% 0.68/0.41 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', bs114d)).
% 0.68/0.41 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setminusI)).
% 0.68/0.41 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setminusEL)).
% 0.68/0.41 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setminusER)).
% 0.68/0.41 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setminusSubset2)).
% 0.68/0.41 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setminusERneg)).
% 0.68/0.41 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setminusELneg)).
% 0.68/0.41 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setminusILneg)).
% 0.68/0.41 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setminusIRneg)).
% 0.68/0.41 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setminusLsub)).
% 0.68/0.41 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setminusSubset1)).
% 0.68/0.41 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', symdiffE)).
% 0.68/0.41 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', symdiffI1)).
% 0.68/0.41 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', symdiffI2)).
% 0.68/0.41 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', symdiffIneg1)).
% 0.68/0.41 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', symdiffIneg2)).
% 0.68/0.41 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', secondinupair)).
% 0.68/0.41 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setukpairIL)).
% 0.68/0.41 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setukpairIR)).
% 0.68/0.41 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', kpairiskpair)).
% 0.68/0.41 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', kpairp)).
% 0.68/0.41 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', singletonsubset)).
% 0.68/0.41 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', singletoninpowerset)).
% 0.68/0.41 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', singletoninpowunion)).
% 0.68/0.41 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', upairset2E)).
% 0.68/0.41 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', upairsubunion)).
% 0.68/0.41 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', upairinpowunion)).
% 0.68/0.41 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', ubforcartprodlem1)).
% 0.68/0.41 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', ubforcartprodlem2)).
% 0.68/0.41 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', ubforcartprodlem3)).
% 0.68/0.41 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', cartprodpairin)).
% 0.68/0.41 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', cartprodmempair1)).
% 0.68/0.41 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', cartprodmempair)).
% 0.68/0.41 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setunionE2)).
% 0.68/0.41 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setunionsingleton1)).
% 0.68/0.41 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setunionsingleton2)).
% 0.68/0.41 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setunionsingleton)).
% 0.68/0.41 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', singletonsuniq)).
% 0.68/0.41 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setukpairinjL1)).
% 0.68/0.41 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', kfstpairEq)).
% 0.68/0.41 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', cartprodfstin)).
% 0.68/0.41 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setukpairinjL2)).
% 0.68/0.41 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setukpairinjL)).
% 0.68/0.41 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setukpairinjR11)).
% 0.68/0.41 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setukpairinjR12)).
% 0.68/0.41 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setukpairinjR1)).
% 0.68/0.41 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', upairequniteq)).
% 0.68/0.41 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setukpairinjR2)).
% 0.68/0.41 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', setukpairinjR)).
% 0.68/0.41 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', ksndpairEq)).
% 0.68/0.41 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', kpairsurjEq)).
% 0.68/0.41 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', cartprodsndin)).
% 0.68/0.41 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', cartprodpairmemEL)).
% 0.68/0.41 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', cartprodpairmemER)).
% 0.68/0.41 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', cartprodmempaircEq)).
% 0.68/0.41 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', cartprodfstpairEq)).
% 0.68/0.41 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', cartprodsndpairEq)).
% 0.68/0.41 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.0Fg2QC7S5z/E---3.1_1340402.p', cartprodpairsurjEq)).
% 0.68/0.41 thf(c_0_196, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((?[X597:$i]:((((in @ X597 @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))))&(((dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))=(setadjoin @ X597 @ emptyset))))))))), inference(fof_simplification,[status(thm)],[ex1])).
% 0.68/0.41 thf(c_0_197, plain, ((singleton)=(^[Z0:$i]:(?[X2:$i]:((((in @ X2 @ Z0))&(((Z0)=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[singleton])).
% 0.68/0.41 thf(c_0_198, plain, ((func)=(^[Z0:$i, Z1:$i, Z2:$i]:(((((subset @ Z2 @ (cartprod @ Z0 @ Z1))))&(![X2:$i]:((((in @ X2 @ Z0))=>((?[X604:$i]:((((in @ X604 @ (dsetconstr @ Z1 @ (^[Z3:$i]:(((in @ (kpair @ X2 @ Z3) @ Z2)))))))&(((dsetconstr @ Z1 @ (^[Z3:$i]:(((in @ (kpair @ X2 @ Z3) @ Z2)))))=(setadjoin @ X604 @ emptyset)))))))))))))), inference(fof_simplification,[status(thm)],[func])).
% 0.68/0.41 thf(c_0_199, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((?[X597:$i]:((((in @ X597 @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))))&(((dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))=(setadjoin @ X597 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_196, c_0_197])).
% 0.68/0.41 thf(c_0_200, plain, ((breln)=(^[Z0:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
% 0.68/0.41 thf(c_0_201, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.68/0.41 thf(c_0_202, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.68/0.41 thf(c_0_203, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.68/0.41 thf(c_0_204, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.68/0.41 thf(c_0_205, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.68/0.41 thf(c_0_206, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.68/0.41 thf(c_0_207, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.68/0.41 thf(c_0_208, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.68/0.41 thf(c_0_209, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 0.68/0.41 thf(c_0_210, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.68/0.41 thf(c_0_211, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.68/0.41 thf(c_0_212, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 0.68/0.41 thf(c_0_213, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.68/0.41 thf(c_0_214, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 0.68/0.41 thf(c_0_215, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))=>((exu @ (^[Z0:$i]:((X17 @ Z0))))=>((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 0.68/0.41 thf(c_0_216, plain, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 0.68/0.41 thf(c_0_217, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 0.68/0.41 thf(c_0_218, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])).
% 0.68/0.41 thf(c_0_219, plain, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 0.68/0.41 thf(c_0_220, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 0.68/0.41 thf(c_0_221, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 0.68/0.41 thf(c_0_222, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 0.68/0.41 thf(c_0_223, plain, ((funcImageSingleton)<=>![X4:$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])).
% 0.68/0.41 thf(c_0_224, plain, ((func)=(^[Z0:$i, Z1:$i, Z2:$i]:(((((subset @ Z2 @ (cartprod @ Z0 @ Z1))))&(![X2:$i]:((((in @ X2 @ Z0))=>((?[X604:$i]:((((in @ X604 @ (dsetconstr @ Z1 @ (^[Z3:$i]:(((in @ (kpair @ X2 @ Z3) @ Z2)))))))&(((dsetconstr @ Z1 @ (^[Z3:$i]:(((in @ (kpair @ X2 @ Z3) @ Z2)))))=(setadjoin @ X604 @ emptyset)))))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_198, c_0_199]), c_0_200])).
% 0.68/0.41 thf(c_0_225, 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)=>![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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[apProp])).
% 0.68/0.41 thf(c_0_226, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X568:$i]:(((((X6 @ X2 @ X568)))&(![X569:$i]:(((((X6 @ X2 @ X569)))=>(((X568)=(X569)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_201, c_0_202])).
% 0.68/0.41 thf(c_0_227, plain, ((descrp)=(![X1:$i > $o]:((((?[X570:$i]:(((((X1 @ X570)))&(![X571:$i]:(((((X1 @ X571)))=>(((X570)=(X571))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_203, c_0_202])).
% 0.68/0.41 thf(c_0_228, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.68/0.41 thf(c_0_229, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.68/0.41 thf(c_0_230, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.68/0.41 thf(c_0_231, plain, ((exuE1)=(![X1:$i > $o]:((((?[X572:$i]:(((((X1 @ X572)))&(![X573:$i]:(((((X1 @ X573)))=>(((X572)=(X573))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_204, c_0_202])).
% 0.68/0.41 thf(c_0_232, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X574:$i]:(((((X1 @ X574)))&(![X575:$i]:(((((X1 @ X575)))=>(((X574)=(X575))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_205, c_0_202])).
% 0.68/0.41 thf(c_0_233, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.68/0.41 thf(c_0_234, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_206])).
% 0.68/0.41 thf(c_0_235, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_207, c_0_206])).
% 0.68/0.41 thf(c_0_236, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_206])).
% 0.68/0.41 thf(c_0_237, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.68/0.41 thf(c_0_238, plain, ((exuE2)=(![X1:$i > $o]:((((?[X576:$i]:(((((X1 @ X576)))&(![X577:$i]:(((((X1 @ X577)))=>(((X576)=(X577))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_208, c_0_202])).
% 0.68/0.41 thf(c_0_239, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_206])).
% 0.68/0.41 thf(c_0_240, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
% 0.68/0.41 thf(c_0_241, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X578:$i]:(((((X1 @ X578)))&(![X579:$i]:(((((X1 @ X579)))=>(((X578)=(X579)))))))))))))), inference(apply_def,[status(thm)],[c_0_209, c_0_202])).
% 0.68/0.41 thf(c_0_242, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X580:$i]:(((((X1 @ X580)))&(![X581:$i]:(((((X1 @ X581)))=>(((X580)=(X581)))))))))))))))), inference(apply_def,[status(thm)],[c_0_210, c_0_202])).
% 0.68/0.41 thf(c_0_243, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X582:$i]:(((((X1 @ X582)))&(![X583:$i]:(((((X1 @ X583)))=>(((X582)=(X583)))))))))))))), inference(apply_def,[status(thm)],[c_0_211, c_0_202])).
% 0.68/0.41 thf(c_0_244, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X584:$i]:(((((X1 @ X584)))&(![X585:$i]:(((((X1 @ X585)))=>(((X584)=(X585))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_212, c_0_202])).
% 0.68/0.41 thf(c_0_245, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X586:$i]:(((((X1 @ X586)))&(![X587:$i]:(((((X1 @ X587)))=>(((X586)=(X587))))))))))<=>((?[X588:$i]:(((((X17 @ X588)))&(![X589:$i]:(((((X17 @ X589)))=>(((X588)=(X589)))))))))))))))), inference(apply_def,[status(thm)],[c_0_213, c_0_202])).
% 0.68/0.41 thf(c_0_246, plain, ((exuEu)=(![X1:$i > $o]:((((?[X590:$i]:(((((X1 @ X590)))&(![X591:$i]:(((((X1 @ X591)))=>(((X590)=(X591))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_214, c_0_202])).
% 0.68/0.41 thf(c_0_247, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X592:$i]:(((((X1 @ X592)))&(![X593:$i]:(((((X1 @ X593)))=>(((X592)=(X593))))))))))=>((((?[X594:$i]:(((((X17 @ X594)))&(![X595:$i]:(((((X17 @ X595)))=>(((X594)=(X595))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_215, c_0_202])).
% 0.68/0.41 thf(c_0_248, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 0.68/0.41 thf(c_0_249, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 0.68/0.41 thf(c_0_250, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 0.68/0.41 thf(c_0_251, 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)))))=>((?[X596:$i]:((((in @ X596 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(setadjoin @ X596 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_216, c_0_197])).
% 0.68/0.41 thf(c_0_252, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:((((?[X598:$i]:((((in @ X598 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X598 @ emptyset)))))))=>(?[X2:$i]:((((in @ X2 @ X4))&((X1 @ X2))))))))), inference(apply_def,[status(thm)],[c_0_217, c_0_199])).
% 0.68/0.41 thf(c_0_253, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>(((![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X3))=>(((X3)=(X2))))))))=>((?[X599:$i]:((((in @ X599 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X599 @ emptyset))))))))))))))), inference(apply_def,[status(thm)],[c_0_218, c_0_199])).
% 0.68/0.41 thf(c_0_254, 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)))))=>((?[X600:$i]:((((in @ X600 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X600 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_219, c_0_199])).
% 0.68/0.41 thf(c_0_255, plain, ((kfstsingleton)=(![X18:$i]:((((iskpair @ X18))=>((?[X601:$i]:((((in @ X601 @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))))&(((dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))=(setadjoin @ X601 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_220, c_0_197])).
% 0.68/0.41 thf(c_0_256, axiom, ((theprop)=(![X21:$i]:((((?[X602:$i]:((((in @ X602 @ X21))&(((X21)=(setadjoin @ X602 @ emptyset)))))))=>((in @ (setunion @ X21) @ X21)))))), inference(apply_def,[status(thm)],[theprop, c_0_197])).
% 0.68/0.41 thf(c_0_257, plain, ((ksndsingleton)=(![X18:$i]:((((iskpair @ X18))=>((?[X603:$i]:((((in @ X603 @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))))&(((dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))=(setadjoin @ X603 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_221, c_0_197])).
% 0.68/0.41 thf(c_0_258, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 0.68/0.41 thf(c_0_259, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 0.68/0.41 thf(c_0_260, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_222, c_0_200])).
% 0.68/0.41 thf(c_0_261, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 0.68/0.41 thf(c_0_262, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 0.68/0.41 thf(c_0_263, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 0.68/0.41 thf(c_0_264, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 0.68/0.41 thf(c_0_265, plain, ((funcImageSingleton)=(![X4:$i, X5:$i, X30:$i]:((((((((subset @ X30 @ (cartprod @ X4 @ X5))))&(![X605:$i]:((((in @ X605 @ X4))=>((?[X606:$i]:((((in @ X606 @ (dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X605 @ Z0) @ X30)))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X605 @ Z0) @ X30)))))=(setadjoin @ X606 @ emptyset)))))))))))))=>(![X2:$i]:((((in @ X2 @ X4))=>((?[X607:$i]:((((in @ X607 @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X30))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X30))))=(setadjoin @ X607 @ emptyset)))))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_223, c_0_197]), c_0_224])).
% 0.68/0.41 thf(c_0_266, plain, ((epred1_0)<=>![X639:$i]:(?[X640:$i]:((((![X641:$i]:(((in @ X641 @ X640)=>![X642:$i]:(((in @ X642 @ X641)=>(in @ X642 @ X639)))))&![X643:$i, X644:$i]:((((in @ X643 @ X639)&(in @ X644 @ X639))=>(![X645:$i]:(((in @ X645 @ X640)=>((in @ X643 @ X645)<=>(in @ X644 @ X645))))=>((X643)=(X644))))))&![X646:$i, X647:$i]:((((in @ X646 @ X640)&(in @ X647 @ X640))=>(![X648:$i]:(((in @ X648 @ X646)=>(in @ X648 @ X647)))|![X649:$i]:(((in @ X649 @ X647)=>(in @ X649 @ X646)))))))&![X650:$i]:(((![X651:$i]:(((in @ X651 @ X650)=>(in @ X651 @ X639)))&?[X652:$i]:((in @ X652 @ X650)))=>?[X653:$i, X654:$i]:(((((in @ X653 @ X640)&(in @ X654 @ X650))&~(?[X655:$i]:(((in @ X655 @ X653)&(in @ X655 @ X650)))))&![X656:$i]:(((in @ X656 @ X640)=>(![X657:$i]:(((in @ X657 @ X656)=>(in @ X657 @ X653)))|(in @ X654 @ X656)))))))))))), introduced(definition)).
% 0.68/0.41 thf(c_0_267, negated_conjecture, ~((![X610:$i, X611:$i]:((![X612:$i]:(((in @ X612 @ X610)<=>(in @ X612 @ X611)))=>((X610)=(X611))))=>(![X613:$i]:(~(in @ X613 @ emptyset))=>(![X614:$i, X615:$i, X616:$i]:(((in @ X616 @ (setadjoin @ X614 @ X615))<=>(((X616)=(X614))|(in @ X616 @ X615))))=>(![X617:$i, X618:$i]:(((in @ X618 @ (powerset @ X617))<=>![X619:$i]:(((in @ X619 @ X618)=>(in @ X619 @ X617)))))=>(![X620:$i, X621:$i]:(((in @ X621 @ (setunion @ X620))<=>?[X622:$i]:(((in @ X621 @ X622)&(in @ X622 @ X620)))))=>((in @ emptyset @ omega)=>(![X623:$i]:(((in @ X623 @ omega)=>(in @ (setadjoin @ X623 @ X623) @ omega)))=>(![X624:$i]:((((in @ emptyset @ X624)&![X625:$i]:((((in @ X625 @ omega)&(in @ X625 @ X624))=>(in @ (setadjoin @ X625 @ X625) @ X624))))=>![X626:$i]:(((in @ X626 @ omega)=>(in @ X626 @ X624)))))=>(![X627:$i > $i > $o, X628:$i]:((![X629:$i]:(((in @ X629 @ X628)=>?[X630:$i]:(((X627 @ X629 @ X630)&![X631:$i]:(((X627 @ X629 @ X631)=>((X630)=(X631))))))))=>?[X632:$i]:(![X633:$i]:(((in @ X633 @ X632)<=>?[X634:$i]:(((in @ X634 @ X628)&(X627 @ X634 @ X633))))))))=>(![X635:$i]:((?[X636:$i]:((in @ X636 @ X635))=>?[X637:$i]:(((in @ X637 @ X635)&~(?[X638:$i]:(((in @ X638 @ X637)&(in @ X638 @ X635))))))))=>((epred1_0)=>(![X658:$i > $o]:((?[X659:$i]:(((X658 @ X659)&![X660:$i]:(((X658 @ X660)=>((X659)=(X660))))))=>(X658 @ (descr @ (^[Z0:$i]:(X658 @ Z0))))))=>(![X661:$i, X662:$i > $o, X663:$i]:(((in @ X663 @ X661)=>((X662 @ X663)=>(in @ X663 @ (dsetconstr @ X661 @ X662)))))=>(![X664:$i, X665:$i > $o, X666:$i]:(((in @ X666 @ (dsetconstr @ X664 @ X665))=>(in @ X666 @ X664)))=>(![X667:$i, X668:$i > $o, X669:$i]:(((in @ X669 @ (dsetconstr @ X667 @ X668))=>(X668 @ X669)))=>(![X670:$i > $o]:((?[X671:$i]:(((X670 @ X671)&![X672:$i]:(((X670 @ X672)=>((X671)=(X672))))))=>?[X673:$i]:(((X670 @ X673)&![X674:$i]:(((X670 @ X674)=>((X673)=(X674))))))))=>(![X675:$o, X676:$i]:(((in @ X676 @ (prop2set @ ((X675))))=>(X675)))=>(![X677:$i]:(((in @ X677 @ emptyset)=>![X678:$o]:((X678))))=>(![X679:$i]:(((in @ X679 @ emptyset)=>~($true)))=>(![X680:$i]:(~(in @ X680 @ emptyset))=>(![X681:$i > $o]:((?[X682:$i]:(((X681 @ X682)&![X683:$i]:(((X681 @ X683)=>((X682)=(X683))))))=>?[X684:$i]:((X681 @ X684))))=>(![X685:$i, X686:$i]:((![X687:$i]:(((in @ X687 @ X685)=>(in @ X687 @ X686)))=>(![X688:$i]:(((in @ X688 @ X686)=>(in @ X688 @ X685)))=>((X685)=(X686)))))=>(![X689:$i]:((![X690:$i]:(~(in @ X690 @ X689))=>((X689)=(emptyset))))=>(![X691:$i]:((![X692:$i]:(~(in @ X692 @ X691))=>((X691)=(emptyset))))=>(![X693:$i, X694:$i > $o, X695:$i]:(((in @ X695 @ X693)=>((in @ X695 @ (dsetconstr @ X693 @ X694))<=>(X694 @ X695))))=>(![X696:$i]:((((X696)!=(emptyset))=>?[X697:$i]:((in @ X697 @ X696))))=>(![X698:$i, X699:$i > $o, X700:$i]:(((in @ X700 @ X698)=>((X699 @ X700)=>((dsetconstr @ X698 @ X699)!=(emptyset)))))=>(![X701:$i]:((?[X702:$i]:((in @ X702 @ X701))=>((X701)!=(emptyset))))=>(![X703:$i, X704:$i]:((in @ X703 @ (setadjoin @ X703 @ X704)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X705:$i, X706:$i, X707:$i]:(((in @ X707 @ X706)=>(in @ X707 @ (setadjoin @ X705 @ X706))))=>(![X708:$i, X709:$i, X710:$i]:(((in @ X710 @ (setadjoin @ X708 @ X709))=>![X711:$o]:(((((X710)=(X708))=>(X711))=>(((in @ X710 @ X709)=>(X711))=>(X711))))))=>(![X712:$i, X713:$i, X714:$i]:(((in @ X714 @ (setadjoin @ X712 @ X713))=>(((X714)=(X712))|(in @ X714 @ X713))))=>(![X715:$i]:(((dsetconstr @ X715 @ (^[Z0:$i]:($true)))=(X715)))=>(![X716:$i, X717:$i]:((![X718:$i]:(((in @ X718 @ X717)=>(in @ X718 @ X716)))=>(in @ X717 @ (powerset @ X716))))=>(![X719:$i]:((in @ emptyset @ (powerset @ X719)))=>(![X720:$i]:((in @ emptyset @ (powerset @ X720)))=>(![X721:$i, X722:$i, X723:$i]:(((in @ X722 @ (powerset @ X721))=>((in @ X723 @ X722)=>(in @ X723 @ X721))))=>(![X724:$i, X725:$i, X726:$i]:(((in @ X725 @ X726)=>((in @ X726 @ X724)=>(in @ X725 @ (setunion @ X724)))))=>(![X727:$i, X728:$i]:(((in @ X728 @ (setunion @ X727))=>![X729:$o]:((![X730:$i]:(((in @ X728 @ X730)=>((in @ X730 @ X727)=>(X729))))=>(X729)))))=>(![X731:$i, X732:$i]:(((in @ X732 @ X731)=>(in @ X732 @ (powerset @ (setunion @ X731)))))=>(![X733:$i > $o]:((?[X734:$i]:(((X733 @ X734)&![X735:$i]:(((X733 @ X735)=>((X734)=(X735))))))=>?[X736:$i]:(![X737:$i]:(((X733 @ X737)<=>((X737)=(X736)))))))=>(![X738:$i]:((((X738)!=(emptyset))=>?[X739:$i]:(((in @ X739 @ X738)&$true))))=>(![X740:$i, X741:$i]:(((in @ X740 @ (setadjoin @ X741 @ emptyset))=>((X740)=(X741))))=>(![X742:$i, X743:$i]:((((X742)!=(X743))=>~(in @ X743 @ (setadjoin @ X742 @ emptyset))))=>(![X744:$i, X745:$i]:((((X744)=(X745))=>(in @ X744 @ (setadjoin @ X745 @ emptyset))))=>(![X746:$i, X747:$i]:(((in @ X746 @ (setadjoin @ X747 @ emptyset))=>(in @ X747 @ (setadjoin @ X746 @ emptyset))))=>(![X748:$i, X749:$i, X750:$i]:(((in @ X750 @ (setadjoin @ X748 @ (setadjoin @ X749 @ emptyset)))=>(((X750)=(X748))|((X750)=(X749)))))=>(![X751:$i, X752:$i]:((in @ X751 @ (setadjoin @ X751 @ (setadjoin @ X752 @ emptyset))))=>(![X753:$i, X754:$i]:((in @ X754 @ (setadjoin @ X753 @ (setadjoin @ X754 @ emptyset))))=>(![X755:$i, X756:$i > $o]:((?[X757:$i]:(((in @ X757 @ X755)&(X756 @ X757)))=>(((dsetconstr @ X755 @ X756)=(emptyset))=>~($true))))=>(![X758:$i > $o, X759:$i]:(((in @ X759 @ emptyset)=>(X758 @ X759)))=>(![X760:$i, X761:$i > $o]:((~(![X762:$i]:(((in @ X762 @ X760)=>(X761 @ X762))))=>?[X763:$i]:(((in @ X763 @ X760)&~((X761 @ X763))))))=>(![X764:$i, X765:$i > $o]:((![X766:$i]:(((in @ X766 @ X764)=>~((X765 @ X766))))=>~(?[X767:$i]:(((in @ X767 @ X764)&(X765 @ X767))))))=>(![X768:$i, X769:$i > $o]:((~(?[X770:$i]:(((in @ X770 @ X768)&(X769 @ X770))))=>![X771:$i]:(((in @ X771 @ X768)=>~((X769 @ X771))))))=>(![X772:$i, X773:$i > $o]:((?[X774:$i]:(((in @ X774 @ X772)&~((X773 @ X774))))=>~(![X775:$i]:(((in @ X775 @ X772)=>(X773 @ X775))))))=>(![X776:$o]:(((X776)=>(in @ emptyset @ (prop2set @ ((X776))))))=>(![X777:$o]:(((X777)=>(set2prop @ (prop2set @ ((X777))))))=>(![X778:$i, X779:$i > $o]:((~(?[X780:$i]:(((in @ X780 @ X778)&(X779 @ X780))))=>![X781:$i]:(((in @ X781 @ X778)=>~((X779 @ X781))))))=>(![X782:$i, X783:$i > $o]:((~(![X784:$i]:(((in @ X784 @ X782)=>(X783 @ X784))))=>?[X785:$i]:(((in @ X785 @ X782)&~((X783 @ X785))))))=>(![X786:$i > $o]:((?[X787:$i]:(((X786 @ X787)&![X788:$i]:(((X786 @ X788)=>((X787)=(X788))))))=>?[X789:$i]:(((X786 @ X789)&![X790:$i]:(((X786 @ X790)=>((X789)=(X790))))))))=>(![X791:$i > $o]:((?[X792:$i]:((X791 @ X792))=>(![X793:$i, X794:$i]:(((X791 @ X793)=>((X791 @ X794)=>((X793)=(X794)))))=>?[X795:$i]:(((X791 @ X795)&![X796:$i]:(((X791 @ X796)=>((X795)=(X796)))))))))=>(![X797:$i > $o]:((?[X798:$i]:(![X799:$i]:(((X797 @ X799)<=>((X799)=(X798)))))=>?[X800:$i]:(((X797 @ X800)&![X801:$i]:(((X797 @ X801)=>((X800)=(X801))))))))=>(![X802:$i, X803:$i]:((((X802)=(X803))=>![X804:$i, X805:$i]:((((X804)=(X805))=>((in @ X804 @ X802)=>(in @ X805 @ X803))))))=>(![X806:$i, X807:$i]:((((X806)=(X807))=>![X808:$i, X809:$i]:((((X808)=(X809))=>((in @ X808 @ X806)<=>(in @ X809 @ X807))))))=>(![X810:$i > $o]:((?[X811:$i]:(((X810 @ X811)&![X812:$i]:(((X810 @ X812)=>((X811)=(X812))))))=>![X813:$i, X814:$i]:(((X810 @ X813)=>((X810 @ X814)=>((X813)=(X814)))))))=>(![X815:$i > $o, X816:$i > $o]:((![X817:$i, X818:$i]:((((X817)=(X818))=>((X815 @ X817)<=>(X816 @ X818))))=>(?[X819:$i]:(((X815 @ X819)&![X820:$i]:(((X815 @ X820)=>((X819)=(X820))))))<=>?[X821:$i]:(((X816 @ X821)&![X822:$i]:(((X816 @ X822)=>((X821)=(X822)))))))))=>(((emptyset)=(emptyset))=>(![X823:$i, X824:$i]:((((X823)=(X824))=>![X825:$i, X826:$i]:((((X825)=(X826))=>((setadjoin @ X823 @ X825)=(setadjoin @ X824 @ X826))))))=>(![X827:$i, X828:$i]:((((X827)=(X828))=>((powerset @ X827)=(powerset @ X828))))=>(![X829:$i, X830:$i]:((((X829)=(X830))=>((setunion @ X829)=(setunion @ X830))))=>(((omega)=(omega))=>(![X831:$i > $o]:((?[X832:$i]:(((X831 @ X832)&![X833:$i]:(((X831 @ X833)=>((X832)=(X833))))))=>![X834:$i, X835:$i]:(((X831 @ X834)=>((X831 @ X835)=>((X834)=(X835)))))))=>(![X836:$i > $o, X837:$i > $o]:((![X838:$i, X839:$i]:((((X838)=(X839))=>((X836 @ X838)<=>(X837 @ X839))))=>(?[X840:$i]:(((X836 @ X840)&![X841:$i]:(((X836 @ X841)=>((X840)=(X841))))))=>(?[X842:$i]:(((X837 @ X842)&![X843:$i]:(((X837 @ X843)=>((X842)=(X843))))))=>((descr @ X836)=(descr @ X837))))))=>(![X844:$i, X845:$i]:((((X844)=(X845))=>![X846:$i > $o, X847:$i > $o]:((![X848:$i]:(((in @ X848 @ X844)=>![X849:$i]:(((in @ X849 @ X845)=>(((X848)=(X849))=>((X846 @ X848)<=>(X847 @ X849)))))))=>((dsetconstr @ X844 @ X846)=(dsetconstr @ X845 @ X847))))))=>(![X850:$i, X851:$i]:((![X852:$i]:(((in @ X852 @ X850)=>(in @ X852 @ X851)))=>(subset @ X850 @ X851)))=>(![X853:$i, X854:$i]:((((X853)=(X854))=>(subset @ X854 @ X853)))=>(![X855:$i, X856:$i]:((((X855)=(X856))=>(subset @ X855 @ X856)))=>(![X857:$i, X858:$i]:((![X859:$i]:(((in @ X859 @ X857)=>(in @ X859 @ X858)))=>(subset @ X857 @ X858)))=>(![X860:$i]:((subset @ emptyset @ X860))=>(![X861:$i, X862:$i, X863:$i]:(((subset @ X861 @ X862)=>((in @ X863 @ X861)=>(in @ X863 @ X862))))=>(![X864:$i, X865:$i, X866:$i]:(((subset @ X864 @ X865)=>(~(in @ X866 @ X865)=>~(in @ X866 @ X864))))=>(![X867:$i, X868:$i, X869:$i]:(((in @ X869 @ X867)=>(~(in @ X869 @ X868)=>~(subset @ X867 @ X868))))=>(![X870:$i, X871:$i]:((~(subset @ X870 @ X871)=>((X870)!=(X871))))=>(![X872:$i, X873:$i, X874:$i]:(((in @ X874 @ X872)=>(~(in @ X874 @ X873)=>((X872)!=(X873)))))=>(![X875:$i]:((subset @ X875 @ X875))=>(![X876:$i, X877:$i, X878:$i]:(((subset @ X876 @ X877)=>((subset @ X877 @ X878)=>(subset @ X876 @ X878))))=>(![X879:$i, X880:$i]:((subset @ X880 @ (setadjoin @ X879 @ X880)))=>(![X881:$i, X882:$i, X883:$i]:(((subset @ X881 @ X883)=>(subset @ X881 @ (setadjoin @ X882 @ X883))))=>(![X884:$i, X885:$i]:(((subset @ X884 @ X885)=>(in @ X884 @ (powerset @ X885))))=>(![X886:$i, X887:$i]:(((subset @ X886 @ X887)=>((subset @ X887 @ X886)=>((X886)=(X887)))))=>(![X888:$i]:(((subset @ X888 @ emptyset)=>((X888)=(emptyset))))=>(![X889:$i, X890:$i]:(((subset @ X890 @ X889)=>(in @ X890 @ (powerset @ X889))))=>(![X891:$i, X892:$i]:(((in @ X892 @ (powerset @ X891))=>(subset @ X892 @ X891)))=>(![X893:$i]:((in @ X893 @ (powerset @ X893)))=>(![X894:$i, X895:$i]:(((subset @ X894 @ X895)=>(subset @ (powerset @ X894) @ (powerset @ X895))))=>(![X896:$i, X897:$i > $o]:((in @ (dsetconstr @ X896 @ X897) @ (powerset @ X896)))=>(![X898:$i, X899:$i > $o]:((subset @ (dsetconstr @ X898 @ X899) @ X898))=>(![X900:$i, X901:$i, X902:$i]:(((in @ X902 @ X900)=>(in @ X902 @ (binunion @ X900 @ X901))))=>(![X903:$i, X904:$i]:((in @ X904 @ (setadjoin @ X903 @ (setadjoin @ X904 @ emptyset))))=>(![X905:$i, X906:$i, X907:$i]:(((in @ X907 @ X906)=>(in @ X907 @ (binunion @ X905 @ X906))))=>(![X908:$i, X909:$i, X910:$i, X911:$o]:(((in @ X910 @ (binunion @ X908 @ X909))=>(((in @ X910 @ X908)=>(X911))=>(((in @ X910 @ X909)=>(X911))=>(X911)))))=>(![X912:$i, X913:$i, X914:$i]:(((in @ X914 @ (binunion @ X912 @ X913))=>((in @ X914 @ X912)|(in @ X914 @ X913))))=>(![X915:$i, X916:$i]:((subset @ X915 @ (binunion @ X915 @ X916)))=>(![X917:$i, X918:$i]:((subset @ X918 @ (binunion @ X917 @ X918)))=>(![X919:$i, X920:$i, X921:$i]:(((in @ X921 @ X919)=>((in @ X921 @ X920)=>(in @ X921 @ (binintersect @ X919 @ X920)))))=>(![X922:$i, X923:$i, X924:$i]:(((subset @ X924 @ X922)=>((subset @ X924 @ X923)=>(subset @ X924 @ (binintersect @ X922 @ X923)))))=>(![X925:$i, X926:$i, X927:$i]:(((in @ X927 @ (binintersect @ X925 @ X926))=>(in @ X927 @ X925)))=>(![X928:$i, X929:$i]:((subset @ (binintersect @ X928 @ X929) @ X928))=>(![X930:$i, X931:$i]:(((subset @ X930 @ X931)=>((binintersect @ X930 @ X931)=(X930))))=>(![X932:$i, X933:$i]:((((binintersect @ X932 @ X933)=(X933))=>(subset @ X933 @ X932)))=>(![X934:$i, X935:$i, X936:$i]:(((in @ X936 @ (binintersect @ X934 @ X935))=>(in @ X936 @ X935)))=>(![X937:$i, X938:$i]:((~(?[X939:$i]:(((in @ X939 @ X937)&(in @ X939 @ X938))))=>((binintersect @ X937 @ X938)=(emptyset))))=>(![X940:$i, X941:$i]:((subset @ (binintersect @ X940 @ X941) @ X941))=>(![X942:$i, X943:$i]:(((subset @ X943 @ X942)=>((binintersect @ X942 @ X943)=(X943))))=>(![X944:$i, X945:$i]:((((binintersect @ X944 @ X945)=(X944))=>(subset @ X944 @ X945)))=>(![X946:$i, X947:$i, X948:$i]:(((binintersect @ X946 @ (binunion @ X947 @ X948))=(binunion @ (binintersect @ X946 @ X947) @ (binintersect @ X946 @ X948))))=>(![X949:$i, X950:$i, X951:$i]:(((in @ X951 @ X949)=>(~(in @ X951 @ X950)=>(in @ X951 @ (setminus @ X949 @ X950)))))=>(![X952:$i, X953:$i, X954:$i]:(((in @ X954 @ (setminus @ X952 @ X953))=>(in @ X954 @ X952)))=>(![X955:$i, X956:$i, X957:$i]:(((in @ X957 @ (setminus @ X955 @ X956))=>~(in @ X957 @ X956)))=>(![X958:$i, X959:$i]:(((subset @ X958 @ X959)=>((setminus @ X958 @ X959)=(emptyset))))=>(![X960:$i, X961:$i, X962:$i]:((~(in @ X962 @ (setminus @ X960 @ X961))=>((in @ X962 @ X960)=>(in @ X962 @ X961))))=>(![X963:$i, X964:$i, X965:$i]:((~(in @ X965 @ (setminus @ X963 @ X964))=>(~(in @ X965 @ X964)=>~(in @ X965 @ X963))))=>(![X966:$i, X967:$i, 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setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_226]), foundationAx]), wellorderingAx]), c_0_227]), c_0_228]), c_0_229]), c_0_230]), c_0_231]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_232]), setext]), emptyI]), noeltsimpempty]), c_0_233]), c_0_234]), c_0_235]), c_0_236]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_237]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_238]), c_0_239]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_240]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_241]), c_0_242]), c_0_243]), inCongP]), in__Cong]), c_0_244]), c_0_245]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_246]), c_0_247]), c_0_248]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_249]), c_0_250]), 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_251]), c_0_252]), c_0_253]), c_0_254]), singletonsuniq]), setukpairinjL1]), c_0_255]), c_0_256]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_257]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_258]), c_0_259]), c_0_260]), c_0_261]), c_0_262]), c_0_263]), c_0_264]), c_0_224]), c_0_265])])]), c_0_266])).
% 0.68/0.41 thf(c_0_268, negated_conjecture, ![X1187:$i, X1188:$i, X1190:$i, X1191:$i, X1192:$i, X1193:$i, X1194:$i, X1195:$i, X1196:$i, X1197:$i, X1198:$i, X1200:$i, X1201:$i, X1203:$i, X1204:$i, X1205:$i, X1206:$i, X1207:$i, X1209:$i, X1210:$i > $i > $o, X1211:$i, X1213:$i, X1216:$i, X1218:$i, X1219:$i, X1220:$i, X1221:$i, X1223:$i, X1224:$i > $o, X1225:$i, X1227:$i, X1228:$i > $o, X1229:$i, X1230:$i, X1231:$i > $o, X1232:$i, X1233:$i, X1234:$i > $o, X1235:$i, X1236:$i > $o, X1237:$i, X1240:$i, X1241:$o, X1242:$i, X1243:$i, X1244:$o, X1245:$i, X1246:$i, X1247:$i > $o, X1248:$i, X1251:$i, X1252:$i, X1255:$i, X1257:$i, X1259:$i, X1260:$i > $o, X1261:$i, X1262:$i, X1264:$i, X1265:$i > $o, X1266:$i, X1267:$i, X1268:$i, X1269:$i, X1270:$i, X1271:$i, X1272:$i, X1273:$i, X1274:$i, X1275:$i, X1276:$i, X1277:$o, X1278:$i, X1279:$i, X1280:$i, X1281:$i, X1282:$i, X1283:$i, X1285:$i, X1286:$i, X1287:$i, X1288:$i, X1289:$i, X1290:$i, X1291:$i, X1292:$i, X1293:$i, X1294:$i, X1295:$o, X1297:$i, X1298:$i, X1299:$i > $o, X1300:$i, X1303:$i, X1304:$i, X1305:$i, X1307:$i, X1308:$i, X1309:$i, X1310:$i, X1311:$i, X1312:$i, X1313:$i, X1314:$i, X1315:$i, X1316:$i, X1317:$i, X1318:$i, X1319:$i, X1320:$i, X1321:$i, X1322:$i, X1323:$i > $o, X1324:$i, X1325:$i > $o, X1326:$i, X1327:$i, X1328:$i > $o, X1329:$i, X1331:$i, X1332:$i > $o, X1334:$i, X1335:$i, X1336:$i > $o, X1338:$i, X1339:$i, X1340:$i > $o, X1341:$i, X1343:$o, X1344:$o, X1345:$i, X1346:$i > $o, X1348:$i, X1349:$i, X1350:$i > $o, X1351:$i, X1353:$i > $o, X1354:$i, X1357:$i, X1358:$i > $o, X1359:$i, X1363:$i, X1364:$i > $o, X1365:$i, X1368:$i, X1369:$i, X1370:$i, X1371:$i, X1372:$i, X1373:$i, X1374:$i, X1375:$i, X1376:$i, X1377:$i > $o, X1378:$i, X1380:$i, X1381:$i, X1382:$i > $o, X1383:$i > $o, X1386:$i, X1389:$i, X1390:$i, X1393:$i, X1394:$i, X1395:$i, X1396:$i, X1397:$i, X1398:$i, X1399:$i, X1400:$i, X1401:$i, X1402:$i > $o, X1403:$i, X1405:$i, X1406:$i, X1407:$i > $o, X1408:$i > $o, X1411:$i, X1413:$i, X1415:$i, X1416:$i, X1417:$i > $o, X1418:$i > $o, X1421:$i, X1422:$i, X1424:$i, X1425:$i, X1426:$i, X1427:$i, X1428:$i, X1429:$i, X1431:$i, X1432:$i, X1433:$i, X1434:$i, X1435:$i, X1436:$i, X1437:$i, X1438:$i, X1439:$i, X1440:$i, X1441:$i, X1442:$i, X1443:$i, X1444:$i, X1445:$i, X1446:$i, X1447:$i, X1448:$i, X1449:$i, X1450:$i, X1451:$i, X1452:$i, X1453:$i, X1454:$i, X1455:$i, X1456:$i, X1457:$i, X1458:$i, X1459:$i, X1460:$i, X1461:$i, X1462:$i, X1463:$i, X1464:$i, X1465:$i, X1466:$i, X1467:$i, X1468:$i > $o, X1469:$i, X1470:$i > $o, X1471:$i, X1472:$i, X1473:$i, X1474:$i, X1475:$i, X1476:$i, X1477:$i, X1478:$i, X1479:$i, X1480:$i, X1481:$i, X1482:$o, X1483:$i, X1484:$i, X1485:$i, X1486:$i, X1487:$i, X1488:$i, X1489:$i, X1490:$i, X1491:$i, X1492:$i, X1493:$i, X1494:$i, X1495:$i, X1496:$i, X1497:$i, X1498:$i, X1499:$i, X1500:$i, X1501:$i, X1502:$i, X1503:$i, X1504:$i, X1505:$i, X1506:$i, X1507:$i, X1508:$i, X1509:$i, X1511:$i, X1512:$i, X1513:$i, X1514:$i, X1515:$i, X1516:$i, X1517:$i, X1518:$i, X1519:$i, X1520:$i, X1521:$i, X1522:$i, X1523:$i, X1524:$i, X1525:$i, X1526:$i, X1527:$i, X1528:$i, X1529:$i, X1530:$i, X1531:$i, X1532:$i, X1533:$i, X1534:$i, X1535:$i, X1536:$i, X1537:$i, X1538:$i, X1539:$i, X1540:$i, X1541:$i, X1542:$i, X1543:$i, X1544:$i, X1545:$i, X1546:$i, X1547:$i, X1548:$i, X1549:$i, X1550:$o, X1551:$i, X1552:$i, X1553:$i, X1554:$i, X1555:$i, X1556:$i, X1557:$i, X1558:$i, X1559:$i, X1560:$i, X1561:$i, X1562:$i, X1563:$i, X1564:$i, X1565:$i, X1566:$i, X1567:$i, X1568:$i, X1569:$i, X1570:$i, X1571:$i, X1572:$i, X1573:$i, X1574:$i, X1575:$i, X1576:$i, X1577:$i, X1578:$i, X1579:$i, X1580:$i, X1581:$i, X1582:$i, X1583:$i, X1584:$i, X1585:$i, X1586:$i, X1587:$i, X1588:$i, X1589:$i, X1590:$i, X1591:$i, X1592:$i, X1593:$i, X1594:$i, X1595:$i, X1596:$i, X1597:$i, X1598:$i, X1599:$i, X1600:$i, X1601:$i, X1602:$i, X1603:$i, X1604:$i, X1605:$i, X1606:$i, X1607:$i, X1608:$i, X1609:$i, X1612:$i, X1613:$i, X1614:$i, X1615:$i, X1616:$i, X1618:$i, X1619:$i, X1620:$i, X1621:$i, X1622:$i > $o, X1625:$i, X1627:$i, X1628:$i > $o, X1629:$i, X1631:$i, X1632:$i > $o, X1633:$i, X1636:$i, X1637:$i > $o, X1640:$i, X1642:$i, X1643:$i, X1644:$i, X1645:$i, X1646:$i, X1647:$i, X1649:$i, X1650:$i, X1651:$i, X1652:$i, X1653:$i, X1654:$i, X1655:$i, X1656:$i, X1657:$i, X1658:$i, X1659:$i, X1660:$i, X1661:$i, X1662:$i, X1663:$i, X1664:$i, X1665:$i, X1666:$i, X1667:$i, X1668:$i, X1669:$i, X1670:$i, X1671:$i, X1672:$i, X1673:$i, X1674:$i, X1675:$i, X1676:$i, X1677:$i, X1678:$i, X1679:$i, X1680:$i, X1681:$i, X1682:$i, X1683:$i, X1685:$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, X1704:$i, X1705:$i, X1706:$i, X1707:$i, X1708:$i, X1709:$i, X1710:$i, X1711:$i, X1712:$i, X1713:$i, X1714:$i, X1715:$i, X1716:$i > $i > $o, X1717:$i, X1718:$i, X1719:$i, X1720:$i, X1721:$i > $i > $o, X1722:$i, X1723:$i, X1724:$i > $i > $o, X1725:$i, X1726:$i, X1727:$i > $i > $o, X1728:$i, X1729:$i, X1730:$i, X1731:$i, X1732:$i > $i > $o, X1733:$i, X1734:$i, X1735:$i, X1736:$i, X1737:$i > $i > $o, X1738:$i, X1739:$i, X1740:$i, X1741:$i, X1742:$i > $i > $o, X1743:$i, X1744:$i, X1745:$i, X1746:$i, X1747:$i, X1749:$i, X1750:$i, X1755:$i]:((((~(in @ (esk1_2 @ X1187 @ X1188) @ X1187)|~(in @ (esk1_2 @ X1187 @ X1188) @ X1188)|((X1187)=(X1188)))&((in @ (esk1_2 @ X1187 @ X1188) @ X1187)|(in @ (esk1_2 @ X1187 @ X1188) @ X1188)|((X1187)=(X1188))))&(~(in @ X1190 @ emptyset)&(((~(in @ X1193 @ (setadjoin @ X1191 @ X1192))|(((X1193)=(X1191))|(in @ X1193 @ X1192)))&((((X1193)!=(X1191))|(in @ X1193 @ (setadjoin @ X1191 @ X1192)))&(~(in @ X1193 @ X1192)|(in @ X1193 @ (setadjoin @ X1191 @ X1192)))))&(((~(in @ X1195 @ (powerset @ X1194))|(~(in @ X1196 @ X1195)|(in @ X1196 @ X1194)))&(((in @ (esk2_2 @ X1197 @ X1198) @ X1198)|(in @ X1198 @ (powerset @ X1197)))&(~(in @ (esk2_2 @ X1197 @ X1198) @ X1197)|(in @ X1198 @ (powerset @ X1197)))))&(((((in @ X1201 @ (esk3_2 @ X1200 @ X1201))|~(in @ X1201 @ (setunion @ X1200)))&((in @ (esk3_2 @ X1200 @ X1201) @ X1200)|~(in @ X1201 @ (setunion @ X1200))))&(~(in @ X1204 @ X1205)|~(in @ X1205 @ X1203)|(in @ X1204 @ (setunion @ X1203))))&((in @ emptyset @ omega)&((~(in @ X1206 @ omega)|(in @ (setadjoin @ X1206 @ X1206) @ omega))&(((((in @ (esk4_1 @ X1207) @ omega)|~(in @ emptyset @ X1207)|(~(in @ X1209 @ omega)|(in @ X1209 @ X1207)))&((in @ (esk4_1 @ X1207) @ X1207)|~(in @ emptyset @ X1207)|(~(in @ X1209 @ omega)|(in @ X1209 @ X1207))))&(~(in @ (setadjoin @ (esk4_1 @ X1207) @ (esk4_1 @ X1207)) @ X1207)|~(in @ emptyset @ X1207)|(~(in @ X1209 @ omega)|(in @ X1209 @ X1207))))&((((((in @ (esk8_3 @ X1210 @ X1211 @ X1216) @ X1211)|~(in @ X1216 @ (esk7_2 @ X1210 @ X1211))|(in @ (esk5_2 @ X1210 @ X1211) @ X1211))&((X1210 @ (esk8_3 @ X1210 @ X1211 @ X1216) @ X1216)|~(in @ X1216 @ (esk7_2 @ X1210 @ X1211))|(in @ (esk5_2 @ X1210 @ X1211) @ X1211)))&(~(in @ X1219 @ X1211)|~(X1210 @ X1219 @ X1218)|(in @ X1218 @ (esk7_2 @ X1210 @ X1211))|(in @ (esk5_2 @ X1210 @ X1211) @ X1211)))&(((((in @ (esk8_3 @ X1210 @ X1211 @ X1216) @ X1211)|~(in @ X1216 @ (esk7_2 @ X1210 @ X1211))|((X1210 @ (esk5_2 @ X1210 @ X1211) @ (esk6_3 @ X1210 @ X1211 @ X1213))|~(X1210 @ (esk5_2 @ X1210 @ X1211) @ X1213)))&((X1210 @ (esk8_3 @ X1210 @ X1211 @ X1216) @ X1216)|~(in @ X1216 @ (esk7_2 @ X1210 @ X1211))|((X1210 @ (esk5_2 @ X1210 @ X1211) @ (esk6_3 @ X1210 @ X1211 @ X1213))|~(X1210 @ (esk5_2 @ X1210 @ X1211) @ X1213))))&(~(in @ X1219 @ X1211)|~(X1210 @ X1219 @ X1218)|(in @ X1218 @ (esk7_2 @ X1210 @ X1211))|((X1210 @ (esk5_2 @ X1210 @ X1211) @ (esk6_3 @ X1210 @ X1211 @ X1213))|~(X1210 @ (esk5_2 @ X1210 @ X1211) @ X1213))))&((((in @ (esk8_3 @ X1210 @ X1211 @ X1216) @ X1211)|~(in @ X1216 @ (esk7_2 @ X1210 @ X1211))|(((X1213)!=(esk6_3 @ X1210 @ X1211 @ X1213))|~(X1210 @ (esk5_2 @ X1210 @ X1211) @ X1213)))&((X1210 @ (esk8_3 @ X1210 @ X1211 @ X1216) @ X1216)|~(in @ X1216 @ (esk7_2 @ X1210 @ X1211))|(((X1213)!=(esk6_3 @ X1210 @ X1211 @ 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emptyset))))&((X1628 @ (esk61_2 @ X1627 @ X1628))|(~(in @ X1629 @ (dsetconstr @ X1627 @ X1628))|((dsetconstr @ X1627 @ X1628)!=(setadjoin @ X1629 @ emptyset)))))&(((((in @ (esk63_3 @ X1631 @ X1632 @ X1633) @ (dsetconstr @ X1631 @ X1632))|(in @ (esk62_3 @ X1631 @ X1632 @ X1633) @ X1631)|~(X1632 @ X1633)|~(in @ X1633 @ X1631))&(((dsetconstr @ X1631 @ X1632)=(setadjoin @ (esk63_3 @ X1631 @ X1632 @ X1633) @ emptyset))|(in @ (esk62_3 @ X1631 @ X1632 @ X1633) @ X1631)|~(X1632 @ X1633)|~(in @ X1633 @ X1631)))&((((in @ (esk63_3 @ X1631 @ X1632 @ X1633) @ (dsetconstr @ X1631 @ X1632))|(X1632 @ (esk62_3 @ X1631 @ X1632 @ X1633))|~(X1632 @ X1633)|~(in @ X1633 @ X1631))&(((dsetconstr @ X1631 @ X1632)=(setadjoin @ (esk63_3 @ X1631 @ X1632 @ X1633) @ emptyset))|(X1632 @ (esk62_3 @ X1631 @ X1632 @ X1633))|~(X1632 @ X1633)|~(in @ X1633 @ X1631)))&(((in @ (esk63_3 @ X1631 @ X1632 @ X1633) @ (dsetconstr @ X1631 @ X1632))|((esk62_3 @ X1631 @ X1632 @ X1633)!=(X1633))|~(X1632 @ X1633)|~(in @ X1633 @ X1631))&(((dsetconstr @ X1631 @ X1632)=(setadjoin @ (esk63_3 @ X1631 @ X1632 @ X1633) @ emptyset))|((esk62_3 @ X1631 @ X1632 @ X1633)!=(X1633))|~(X1632 @ X1633)|~(in @ X1633 @ X1631)))))&(((((in @ (esk66_2 @ X1636 @ X1637) @ (dsetconstr @ X1636 @ X1637))|(~(in @ X1640 @ X1636)|~(X1637 @ X1640))|(in @ (esk64_2 @ X1636 @ X1637) @ X1636))&(((dsetconstr @ X1636 @ X1637)=(setadjoin @ (esk66_2 @ X1636 @ X1637) @ emptyset))|(~(in @ X1640 @ X1636)|~(X1637 @ X1640))|(in @ (esk64_2 @ X1636 @ X1637) @ X1636)))&((((in @ (esk66_2 @ X1636 @ X1637) @ (dsetconstr @ X1636 @ X1637))|(~(in @ X1640 @ X1636)|~(X1637 @ X1640))|(in @ (esk65_2 @ X1636 @ X1637) @ X1636))&(((dsetconstr @ X1636 @ X1637)=(setadjoin @ (esk66_2 @ X1636 @ X1637) @ emptyset))|(~(in @ X1640 @ X1636)|~(X1637 @ X1640))|(in @ (esk65_2 @ X1636 @ X1637) @ X1636)))&((((in @ (esk66_2 @ X1636 @ X1637) @ (dsetconstr @ X1636 @ X1637))|(~(in @ X1640 @ X1636)|~(X1637 @ X1640))|(X1637 @ (esk64_2 @ X1636 @ X1637)))&(((dsetconstr @ X1636 @ X1637)=(setadjoin @ (esk66_2 @ X1636 @ X1637) @ emptyset))|(~(in @ X1640 @ X1636)|~(X1637 @ X1640))|(X1637 @ (esk64_2 @ X1636 @ X1637))))&((((in @ (esk66_2 @ X1636 @ X1637) @ (dsetconstr @ X1636 @ X1637))|(~(in @ X1640 @ X1636)|~(X1637 @ X1640))|(X1637 @ (esk65_2 @ X1636 @ X1637)))&(((dsetconstr @ X1636 @ X1637)=(setadjoin @ (esk66_2 @ X1636 @ X1637) @ emptyset))|(~(in @ X1640 @ X1636)|~(X1637 @ X1640))|(X1637 @ (esk65_2 @ X1636 @ X1637))))&(((in @ (esk66_2 @ X1636 @ X1637) @ (dsetconstr @ X1636 @ X1637))|(~(in @ X1640 @ X1636)|~(X1637 @ X1640))|((esk64_2 @ X1636 @ X1637)!=(esk65_2 @ X1636 @ X1637)))&(((dsetconstr @ X1636 @ X1637)=(setadjoin @ (esk66_2 @ X1636 @ X1637) @ emptyset))|(~(in @ X1640 @ X1636)|~(X1637 @ X1640))|((esk64_2 @ X1636 @ X1637)!=(esk65_2 @ X1636 @ X1637))))))))&((((setadjoin @ X1642 @ emptyset)!=(setadjoin @ X1643 @ emptyset))|((X1642)=(X1643)))&((~(in @ (setadjoin @ X1646 @ emptyset) @ (setadjoin @ (setadjoin @ X1644 @ emptyset) @ (setadjoin @ (setadjoin @ X1644 @ (setadjoin @ X1645 @ emptyset)) @ emptyset)))|((X1644)=(X1646)))&((((in @ (esk67_1 @ X1647) @ (dsetconstr @ (setunion @ X1647) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1647)))))|~(iskpair @ X1647))&(((dsetconstr @ (setunion @ X1647) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1647))))=(setadjoin @ (esk67_1 @ X1647) @ emptyset))|~(iskpair @ X1647)))&((~(in @ X1650 @ X1649)|((X1649)!=(setadjoin @ X1650 @ emptyset))|(in @ (setunion @ X1649) @ X1649))&(((kfst @ (kpair @ X1651 @ X1652))=(X1651))&((~(in @ X1655 @ (cartprod @ X1653 @ X1654))|(in @ (kfst @ X1655) @ X1653))&((((setadjoin @ (setadjoin @ X1656 @ emptyset) @ (setadjoin @ (setadjoin @ X1656 @ (setadjoin @ X1657 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1658 @ emptyset) @ (setadjoin @ (setadjoin @ X1658 @ (setadjoin @ X1659 @ emptyset)) @ emptyset)))|((X1656)=(X1658)))&((((kpair @ X1660 @ X1661)!=(kpair @ X1662 @ X1663))|((X1660)=(X1662)))&((((X1664)!=(X1665))|((setadjoin @ X1664 @ (setadjoin @ X1665 @ emptyset))=(setadjoin @ X1664 @ emptyset)))&((((X1666)!=(X1667))|((setadjoin @ (setadjoin @ X1666 @ emptyset) @ (setadjoin @ (setadjoin @ X1666 @ (setadjoin @ X1667 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X1666 @ emptyset) @ emptyset)))&((((setadjoin @ (setadjoin @ X1668 @ emptyset) @ (setadjoin @ (setadjoin @ X1668 @ (setadjoin @ X1669 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1670 @ emptyset) @ (setadjoin @ (setadjoin @ X1670 @ (setadjoin @ X1671 @ emptyset)) @ emptyset)))|(((X1670)!=(X1671))|((X1669)=(X1671))))&((((setadjoin @ X1672 @ (setadjoin @ X1673 @ emptyset))!=(setadjoin @ X1674 @ emptyset))|((X1672)=(X1673)))&((((setadjoin @ (setadjoin @ X1675 @ emptyset) @ (setadjoin @ (setadjoin @ X1675 @ (setadjoin @ X1676 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1677 @ emptyset) @ (setadjoin @ (setadjoin @ X1677 @ (setadjoin @ X1678 @ emptyset)) @ emptyset)))|((X1676)=(X1678)))&((((kpair @ X1679 @ X1680)!=(kpair @ X1681 @ X1682))|((X1680)=(X1682)))&((((in @ (esk68_1 @ X1683) @ (dsetconstr @ (setunion @ X1683) @ (^[Z0:$i]:(((X1683)=(kpair @ (kfst @ X1683) @ Z0))))))|~(iskpair @ X1683))&(((dsetconstr @ (setunion @ X1683) @ (^[Z0:$i]:(((X1683)=(kpair @ (kfst @ X1683) @ Z0)))))=(setadjoin @ (esk68_1 @ X1683) @ emptyset))|~(iskpair @ X1683)))&(((ksnd @ (kpair @ X1685 @ X1686))=(X1686))&((~(iskpair @ X1687)|((kpair @ (kfst @ X1687) @ (ksnd @ X1687))=(X1687)))&((~(in @ X1690 @ (cartprod @ X1688 @ X1689))|(in @ (ksnd @ X1690) @ X1689))&((~(in @ (kpair @ X1693 @ X1694) @ (cartprod @ X1691 @ X1692))|(in @ X1693 @ X1691))&((~(in @ (kpair @ X1697 @ X1698) @ (cartprod @ X1695 @ X1696))|(in @ X1698 @ X1696))&((~(in @ X1701 @ X1699)|(~(in @ X1702 @ X1700)|((kpair @ X1701 @ X1702)=(kpair @ X1701 @ X1702))))&((~(in @ X1705 @ X1703)|(~(in @ X1706 @ X1704)|((kfst @ (kpair @ X1705 @ X1706))=(X1705))))&((~(in @ X1709 @ X1707)|(~(in @ X1710 @ X1708)|((ksnd @ (kpair @ X1709 @ X1710))=(X1710))))&((~(in @ X1713 @ (cartprod @ X1711 @ X1712))|((kpair @ (kfst @ X1713) @ (ksnd @ X1713))=(X1713)))&((~(in @ X1717 @ X1714)|(~(in @ X1718 @ X1715)|(~(X1716 @ X1717 @ X1718)|(in @ (kpair @ X1717 @ X1718) @ (dpsetconstr @ X1714 @ X1715 @ X1716)))))&((subset @ (dpsetconstr @ X1719 @ X1720 @ X1721) @ (cartprod @ X1719 @ X1720))&((subset @ (dpsetconstr @ X1722 @ X1723 @ X1724) @ (cartprod @ X1722 @ X1723))&((~(in @ X1728 @ X1725)|(~(in @ X1729 @ X1726)|(~(in @ (kpair @ X1728 @ X1729) @ (dpsetconstr @ X1725 @ X1726 @ X1727))|(X1727 @ X1728 @ X1729))))&((~(in @ (kpair @ X1733 @ X1734) @ (dpsetconstr @ X1730 @ X1731 @ X1732))|(in @ X1733 @ X1730))&((~(in @ (kpair @ X1738 @ X1739) @ (dpsetconstr @ X1735 @ X1736 @ X1737))|(in @ X1739 @ X1736))&((~(in @ (kpair @ X1743 @ X1744) @ (dpsetconstr @ X1740 @ X1741 @ X1742))|(X1742 @ X1743 @ X1744))&(((((in @ (esk70_4 @ X1745 @ X1746 @ X1747 @ X1750) @ (dsetconstr @ X1746 @ (^[Z0:$i]:((in @ (kpair @ X1750 @ Z0) @ X1747)))))|~(in @ X1750 @ X1745)|((in @ (esk69_3 @ X1745 @ X1746 @ X1747) @ X1745)|~(subset @ X1747 @ (cartprod @ X1745 @ X1746))))&(((dsetconstr @ X1746 @ (^[Z0:$i]:((in @ (kpair @ X1750 @ Z0) @ X1747))))=(setadjoin @ (esk70_4 @ X1745 @ X1746 @ X1747 @ X1750) @ emptyset))|~(in @ X1750 @ X1745)|((in @ (esk69_3 @ X1745 @ X1746 @ X1747) @ X1745)|~(subset @ X1747 @ (cartprod @ X1745 @ X1746)))))&(((in @ (esk70_4 @ X1745 @ X1746 @ X1747 @ X1750) @ (dsetconstr @ X1746 @ (^[Z0:$i]:((in @ (kpair @ X1750 @ Z0) @ X1747)))))|~(in @ X1750 @ X1745)|(~(in @ X1749 @ (dsetconstr @ X1746 @ (^[Z0:$i]:((in @ (kpair @ (esk69_3 @ X1745 @ X1746 @ X1747) @ Z0) @ X1747)))))|((dsetconstr @ X1746 @ (^[Z0:$i]:((in @ (kpair @ (esk69_3 @ X1745 @ X1746 @ X1747) @ Z0) @ X1747))))!=(setadjoin @ X1749 @ emptyset))|~(subset @ X1747 @ (cartprod @ X1745 @ X1746))))&(((dsetconstr @ X1746 @ (^[Z0:$i]:((in @ (kpair @ X1750 @ Z0) @ X1747))))=(setadjoin @ (esk70_4 @ X1745 @ X1746 @ X1747 @ X1750) @ emptyset))|~(in @ X1750 @ X1745)|(~(in @ X1749 @ (dsetconstr @ X1746 @ (^[Z0:$i]:((in @ (kpair @ (esk69_3 @ X1745 @ X1746 @ X1747) @ Z0) @ X1747)))))|((dsetconstr @ X1746 @ (^[Z0:$i]:((in @ (kpair @ (esk69_3 @ X1745 @ X1746 @ X1747) @ Z0) @ X1747))))!=(setadjoin @ X1749 @ emptyset))|~(subset @ X1747 @ (cartprod @ X1745 @ X1746))))))&(((subset @ esk73_0 @ (cartprod @ esk71_0 @ esk72_0))&(((in @ (esk74_1 @ X1755) @ (dsetconstr @ esk72_0 @ (^[Z0:$i]:((in @ (kpair @ X1755 @ Z0) @ esk73_0)))))|~(in @ X1755 @ esk71_0))&(((dsetconstr @ esk72_0 @ (^[Z0:$i]:((in @ (kpair @ X1755 @ Z0) @ esk73_0))))=(setadjoin @ (esk74_1 @ X1755) @ emptyset))|~(in @ X1755 @ esk71_0))))&((in @ esk75_0 @ esk71_0)&~(in @ (setunion @ (dsetconstr @ esk72_0 @ (^[Z0:$i]:((in @ (kpair @ esk75_0 @ Z0) @ esk73_0))))) @ esk72_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_267])])])])])])])).
% 0.68/0.41 thf(c_0_269, plain, ![X1779:$i, X1780:$i, X1777:$i]:(((epred2_1 @ X1777 @ X1780 @ X1779)<=>(in @ (kpair @ X1777 @ X1779) @ X1780))), introduced(definition)).
% 0.68/0.41 thf(c_0_270, negated_conjecture, ![X2:$i]:((((dsetconstr @ esk72_0 @ (epred2_1 @ X2 @ esk73_0))=(setadjoin @ (esk74_1 @ X2) @ emptyset))|~((in @ X2 @ esk71_0)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_268]), c_0_269])).
% 0.68/0.41 thf(c_0_271, negated_conjecture, (in @ esk75_0 @ esk71_0), inference(split_conjunct,[status(thm)],[c_0_268])).
% 0.68/0.41 thf(c_0_272, negated_conjecture, ~((((in @ (setunion @ (dsetconstr @ esk72_0 @ (epred2_1 @ esk75_0 @ esk73_0))) @ esk72_0))=(($true)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_268]), c_0_269])).
% 0.68/0.41 thf(c_0_273, negated_conjecture, ![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2))), inference(split_conjunct,[status(thm)],[c_0_268])).
% 0.68/0.41 thf(c_0_274, negated_conjecture, ((setadjoin @ (esk74_1 @ esk75_0) @ emptyset)=(dsetconstr @ esk72_0 @ (epred2_1 @ esk75_0 @ esk73_0))), inference(spm,[status(thm)],[c_0_270, c_0_271])).
% 0.68/0.41 thf(c_0_275, negated_conjecture, ![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_268])).
% 0.68/0.41 thf(c_0_276, negated_conjecture, ~((in @ (setunion @ (dsetconstr @ esk72_0 @ (epred2_1 @ esk75_0 @ esk73_0))) @ esk72_0)), inference(cn,[status(thm)],[c_0_272])).
% 0.68/0.41 thf(c_0_277, negated_conjecture, ((setunion @ (dsetconstr @ esk72_0 @ (epred2_1 @ esk75_0 @ esk73_0)))=(esk74_1 @ esk75_0)), inference(spm,[status(thm)],[c_0_273, c_0_274])).
% 0.68/0.41 thf(c_0_278, negated_conjecture, ![X3:$i, X2:$i, X1:$i > $o]:(((in @ X2 @ X3)|~((in @ X2 @ (dsetconstr @ X3 @ X1))))), inference(split_conjunct,[status(thm)],[c_0_268])).
% 0.68/0.41 thf(c_0_279, negated_conjecture, (in @ (esk74_1 @ esk75_0) @ (dsetconstr @ esk72_0 @ (epred2_1 @ esk75_0 @ esk73_0))), inference(spm,[status(thm)],[c_0_275, c_0_274])).
% 0.68/0.41 thf(c_0_280, negated_conjecture, ~((in @ (esk74_1 @ esk75_0) @ esk72_0)), inference(rw,[status(thm)],[c_0_276, c_0_277])).
% 0.68/0.41 thf(c_0_281, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_278, c_0_279]), c_0_280]), ['proof']).
% 0.68/0.41 % SZS output end CNFRefutation
% 0.68/0.41 % Parsed axioms : 421
% 0.68/0.41 % Removed by relevancy pruning/SinE : 0
% 0.68/0.41 % Initial clauses : 586
% 0.68/0.41 % Removed in clause preprocessing : 252
% 0.68/0.41 % Initial clauses in saturation : 334
% 0.68/0.41 % Processed clauses : 394
% 0.68/0.41 % ...of these trivial : 9
% 0.68/0.41 % ...subsumed : 29
% 0.68/0.41 % ...remaining for further processing : 356
% 0.68/0.41 % Other redundant clauses eliminated : 20
% 0.68/0.41 % Clauses deleted for lack of memory : 0
% 0.68/0.41 % Backward-subsumed : 0
% 0.68/0.41 % Backward-rewritten : 2
% 0.68/0.41 % Generated clauses : 60
% 0.68/0.41 % ...of the previous two non-redundant : 42
% 0.68/0.41 % ...aggressively subsumed : 0
% 0.68/0.41 % Contextual simplify-reflections : 0
% 0.68/0.41 % Paramodulations : 24
% 0.68/0.41 % Factorizations : 0
% 0.68/0.41 % NegExts : 1
% 0.68/0.41 % Equation resolutions : 20
% 0.68/0.41 % Disequality decompositions : 0
% 0.68/0.41 % Total rewrite steps : 42
% 0.68/0.41 % ...of those cached : 22
% 0.68/0.41 % Propositional unsat checks : 0
% 0.68/0.41 % Propositional check models : 0
% 0.68/0.41 % Propositional check unsatisfiable : 0
% 0.68/0.41 % Propositional clauses : 0
% 0.68/0.41 % Propositional clauses after purity: 0
% 0.68/0.41 % Propositional unsat core size : 0
% 0.68/0.41 % Propositional preprocessing time : 0.000
% 0.68/0.41 % Propositional encoding time : 0.000
% 0.68/0.41 % Propositional solver time : 0.000
% 0.68/0.41 % Success case prop preproc time : 0.000
% 0.68/0.41 % Success case prop encoding time : 0.000
% 0.68/0.41 % Success case prop solver time : 0.000
% 0.68/0.41 % Current number of processed clauses : 48
% 0.68/0.41 % Positive orientable unit clauses : 23
% 0.68/0.41 % Positive unorientable unit clauses: 0
% 0.68/0.41 % Negative unit clauses : 10
% 0.68/0.41 % Non-unit-clauses : 15
% 0.68/0.41 % Current number of unprocessed clauses: 272
% 0.68/0.41 % ...number of literals in the above : 882
% 0.68/0.41 % Current number of archived formulas : 0
% 0.68/0.41 % Current number of archived clauses : 294
% 0.68/0.41 % Clause-clause subsumption calls (NU) : 14917
% 0.68/0.41 % Rec. Clause-clause subsumption calls : 6078
% 0.68/0.41 % Non-unit clause-clause subsumptions : 22
% 0.68/0.41 % Unit Clause-clause subsumption calls : 56
% 0.68/0.41 % Rewrite failures with RHS unbound : 0
% 0.68/0.41 % BW rewrite match attempts : 15
% 0.68/0.41 % BW rewrite match successes : 2
% 0.68/0.41 % Condensation attempts : 0
% 0.68/0.41 % Condensation successes : 0
% 0.68/0.41 % Termbank termtop insertions : 71621
% 0.68/0.41 % Search garbage collected termcells : 19319
% 0.68/0.41
% 0.68/0.41 % -------------------------------------------------
% 0.68/0.41 % User time : 0.078 s
% 0.68/0.41 % System time : 0.011 s
% 0.68/0.41 % Total time : 0.089 s
% 0.68/0.41 % Maximum resident set size: 7908 pages
% 0.68/0.41
% 0.68/0.41 % -------------------------------------------------
% 0.68/0.41 % User time : 0.222 s
% 0.68/0.41 % System time : 0.040 s
% 0.68/0.41 % Total time : 0.261 s
% 0.68/0.41 % Maximum resident set size: 5376 pages
% 0.68/0.41 % E exiting
%------------------------------------------------------------------------------