0.03/0.13	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.13	% Command    : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 240 THM
0.14/0.34	% Computer : n009.cluster.edu
0.14/0.34	% Model    : x86_64 x86_64
0.14/0.34	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.14/0.34	% Memory   : 8042.1875MB
0.14/0.34	% OS       : Linux 3.10.0-693.el7.x86_64
0.14/0.34	% CPULimit   : 1920
0.14/0.34	% WCLimit    : 240
0.14/0.34	% DateTime   : Wed Jul 30 06:12:04 EDT 2025
0.14/0.34	% CPUTime    : 
0.22/0.49	Running higher-order theorem proving
0.22/0.52	Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=240 /export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p
118.52/15.57	# Version: 3.0.0-ho
118.52/15.57	# Preprocessing class: HSLMSLSSLLLCHFA.
118.52/15.57	# Scheduled 8 strats onto 8 cores with 240 seconds (1920 total)
118.52/15.57	# Starting ehoh_best5 with 240s (1) cores
118.52/15.57	# Starting almost_fo_3_lam with 240s (1) cores
118.52/15.57	# Starting new_bool_5 with 240s (1) cores
118.52/15.57	# Starting pre_casc_3 with 240s (1) cores
118.52/15.57	# Starting ho_unfolding_8 with 240s (1) cores
118.52/15.57	# Starting new_ho_10_cnf2 with 240s (1) cores
118.52/15.57	# Starting new_bool_3 with 240s (1) cores
118.52/15.57	# Starting new_ho_5 with 240s (1) cores
118.52/15.57	# new_bool_5 with pid 25870 completed with status 0
118.52/15.57	# Result found by new_bool_5
118.52/15.57	# Preprocessing class: HSLMSLSSLLLCHFA.
118.52/15.57	# Scheduled 8 strats onto 8 cores with 240 seconds (1920 total)
118.52/15.57	# Starting ehoh_best5 with 240s (1) cores
118.52/15.57	# Starting almost_fo_3_lam with 240s (1) cores
118.52/15.57	# Starting new_bool_5 with 240s (1) cores
118.52/15.57	# SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
118.52/15.57	# Search class: HGHSM-FSLM31-MHFMMSBN
118.52/15.57	# Scheduled 6 strats onto 1 cores with 240 seconds (240 total)
118.52/15.57	# Starting new_ho_10_cnf2 with 130s (1) cores
118.52/15.57	# new_ho_10_cnf2 with pid 25876 completed with status 0
118.52/15.57	# Result found by new_ho_10_cnf2
118.52/15.57	# Preprocessing class: HSLMSLSSLLLCHFA.
118.52/15.57	# Scheduled 8 strats onto 8 cores with 240 seconds (1920 total)
118.52/15.57	# Starting ehoh_best5 with 240s (1) cores
118.52/15.57	# Starting almost_fo_3_lam with 240s (1) cores
118.52/15.57	# Starting new_bool_5 with 240s (1) cores
118.52/15.57	# SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
118.52/15.57	# Search class: HGHSM-FSLM31-MHFMMSBN
118.52/15.57	# Scheduled 6 strats onto 1 cores with 240 seconds (240 total)
118.52/15.57	# Starting new_ho_10_cnf2 with 130s (1) cores
118.52/15.57	# Preprocessing time       : 0.005 s
118.52/15.57	# Presaturation interreduction done
118.52/15.57	
118.52/15.57	# Proof found!
118.52/15.57	# SZS status Theorem
118.52/15.57	# SZS output start CNFRefutation
118.52/15.57	thf(decl_23, type, in: $i > $i > $o).
118.52/15.57	thf(decl_24, type, exu: ($i > $o) > $o).
118.52/15.57	thf(decl_25, type, setextAx: $o).
118.52/15.57	thf(decl_26, type, emptyset: $i).
118.52/15.57	thf(decl_27, type, emptysetAx: $o).
118.52/15.57	thf(decl_28, type, setadjoin: $i > $i > $i).
118.52/15.57	thf(decl_29, type, setadjoinAx: $o).
118.52/15.57	thf(decl_30, type, powerset: $i > $i).
118.52/15.57	thf(decl_31, type, powersetAx: $o).
118.52/15.57	thf(decl_32, type, setunion: $i > $i).
118.52/15.57	thf(decl_33, type, setunionAx: $o).
118.52/15.57	thf(decl_34, type, omega: $i).
118.52/15.57	thf(decl_35, type, omega0Ax: $o).
118.52/15.57	thf(decl_36, type, omegaSAx: $o).
118.52/15.57	thf(decl_37, type, omegaIndAx: $o).
118.52/15.57	thf(decl_38, type, replAx: $o).
118.52/15.57	thf(decl_39, type, foundationAx: $o).
118.52/15.57	thf(decl_40, type, wellorderingAx: $o).
118.52/15.57	thf(decl_41, type, descr: ($i > $o) > $i).
118.52/15.57	thf(decl_42, type, descrp: $o).
118.52/15.57	thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
118.52/15.57	thf(decl_44, type, dsetconstrI: $o).
118.52/15.57	thf(decl_45, type, dsetconstrEL: $o).
118.52/15.57	thf(decl_46, type, dsetconstrER: $o).
118.52/15.57	thf(decl_47, type, exuE1: $o).
118.52/15.57	thf(decl_48, type, prop2set: $o > $i).
118.52/15.57	thf(decl_49, type, prop2setE: $o).
118.52/15.57	thf(decl_50, type, emptysetE: $o).
118.52/15.57	thf(decl_51, type, emptysetimpfalse: $o).
118.52/15.57	thf(decl_52, type, notinemptyset: $o).
118.52/15.57	thf(decl_53, type, exuE3e: $o).
118.52/15.57	thf(decl_54, type, setext: $o).
118.52/15.57	thf(decl_55, type, emptyI: $o).
118.52/15.57	thf(decl_56, type, noeltsimpempty: $o).
118.52/15.57	thf(decl_57, type, setbeta: $o).
118.52/15.57	thf(decl_58, type, nonempty: $i > $o).
118.52/15.57	thf(decl_59, type, nonemptyE1: $o).
118.52/15.57	thf(decl_60, type, nonemptyI: $o).
118.52/15.57	thf(decl_61, type, nonemptyI1: $o).
118.52/15.57	thf(decl_62, type, setadjoinIL: $o).
118.52/15.57	thf(decl_63, type, emptyinunitempty: $o).
118.52/15.57	thf(decl_64, type, setadjoinIR: $o).
118.52/15.57	thf(decl_65, type, setadjoinE: $o).
118.52/15.57	thf(decl_66, type, setadjoinOr: $o).
118.52/15.57	thf(decl_67, type, setoftrueEq: $o).
118.52/15.57	thf(decl_68, type, powersetI: $o).
118.52/15.57	thf(decl_69, type, emptyinPowerset: $o).
118.52/15.57	thf(decl_70, type, emptyInPowerset: $o).
118.52/15.57	thf(decl_71, type, powersetE: $o).
118.52/15.57	thf(decl_72, type, setunionI: $o).
118.52/15.57	thf(decl_73, type, setunionE: $o).
118.52/15.57	thf(decl_74, type, subPowSU: $o).
118.52/15.57	thf(decl_75, type, exuE2: $o).
118.52/15.57	thf(decl_76, type, nonemptyImpWitness: $o).
118.52/15.57	thf(decl_77, type, uniqinunit: $o).
118.52/15.57	thf(decl_78, type, notinsingleton: $o).
118.52/15.57	thf(decl_79, type, eqinunit: $o).
118.52/15.57	thf(decl_80, type, singletonsswitch: $o).
118.52/15.57	thf(decl_81, type, upairsetE: $o).
118.52/15.57	thf(decl_82, type, upairsetIL: $o).
118.52/15.57	thf(decl_83, type, upairsetIR: $o).
118.52/15.57	thf(decl_84, type, emptyE1: $o).
118.52/15.57	thf(decl_85, type, vacuousDall: $o).
118.52/15.57	thf(decl_86, type, quantDeMorgan1: $o).
118.52/15.57	thf(decl_87, type, quantDeMorgan2: $o).
118.52/15.57	thf(decl_88, type, quantDeMorgan3: $o).
118.52/15.57	thf(decl_89, type, quantDeMorgan4: $o).
118.52/15.57	thf(decl_90, type, prop2setI: $o).
118.52/15.57	thf(decl_92, type, prop2set2propI: $o).
118.52/15.57	thf(decl_93, type, notdexE: $o).
118.52/15.57	thf(decl_94, type, notdallE: $o).
118.52/15.57	thf(decl_95, type, exuI1: $o).
118.52/15.57	thf(decl_96, type, exuI3: $o).
118.52/15.57	thf(decl_97, type, exuI2: $o).
118.52/15.57	thf(decl_98, type, inCongP: $o).
118.52/15.57	thf(decl_99, type, in__Cong: $o).
118.52/15.57	thf(decl_100, type, exuE3u: $o).
118.52/15.57	thf(decl_101, type, exu__Cong: $o).
118.52/15.57	thf(decl_102, type, emptyset__Cong: $o).
118.52/15.57	thf(decl_103, type, setadjoin__Cong: $o).
118.52/15.57	thf(decl_104, type, powerset__Cong: $o).
118.52/15.57	thf(decl_105, type, setunion__Cong: $o).
118.52/15.57	thf(decl_106, type, omega__Cong: $o).
118.52/15.57	thf(decl_107, type, exuEu: $o).
118.52/15.57	thf(decl_108, type, descr__Cong: $o).
118.52/15.57	thf(decl_109, type, dsetconstr__Cong: $o).
118.52/15.57	thf(decl_110, type, subset: $i > $i > $o).
118.52/15.57	thf(decl_113, type, subsetI1: $o).
118.52/15.57	thf(decl_114, type, eqimpsubset2: $o).
118.52/15.57	thf(decl_115, type, eqimpsubset1: $o).
118.52/15.57	thf(decl_116, type, subsetI2: $o).
118.52/15.57	thf(decl_117, type, emptysetsubset: $o).
118.52/15.57	thf(decl_118, type, subsetE: $o).
118.52/15.57	thf(decl_119, type, subsetE2: $o).
118.52/15.57	thf(decl_120, type, notsubsetI: $o).
118.52/15.57	thf(decl_121, type, notequalI1: $o).
118.52/15.57	thf(decl_122, type, notequalI2: $o).
118.52/15.57	thf(decl_123, type, subsetRefl: $o).
118.52/15.57	thf(decl_124, type, subsetTrans: $o).
118.52/15.57	thf(decl_125, type, setadjoinSub: $o).
118.52/15.57	thf(decl_126, type, setadjoinSub2: $o).
118.52/15.57	thf(decl_127, type, subset2powerset: $o).
118.52/15.57	thf(decl_128, type, setextsub: $o).
118.52/15.57	thf(decl_129, type, subsetemptysetimpeq: $o).
118.52/15.57	thf(decl_130, type, powersetI1: $o).
118.52/15.57	thf(decl_131, type, powersetE1: $o).
118.52/15.57	thf(decl_132, type, inPowerset: $o).
118.52/15.57	thf(decl_133, type, powersetsubset: $o).
118.52/15.57	thf(decl_134, type, sepInPowerset: $o).
118.52/15.57	thf(decl_135, type, sepSubset: $o).
118.52/15.57	thf(decl_136, type, binunion: $i > $i > $i).
118.52/15.57	thf(decl_137, type, binunionIL: $o).
118.52/15.57	thf(decl_138, type, upairset2IR: $o).
118.52/15.57	thf(decl_139, type, binunionIR: $o).
118.52/15.57	thf(decl_140, type, binunionEcases: $o).
118.52/15.57	thf(decl_141, type, binunionE: $o).
118.52/15.57	thf(decl_142, type, binunionLsub: $o).
118.52/15.57	thf(decl_143, type, binunionRsub: $o).
118.52/15.57	thf(decl_144, type, binintersect: $i > $i > $i).
118.52/15.57	thf(decl_145, type, binintersectI: $o).
118.52/15.57	thf(decl_146, type, binintersectSubset5: $o).
118.52/15.57	thf(decl_147, type, binintersectEL: $o).
118.52/15.57	thf(decl_148, type, binintersectLsub: $o).
118.52/15.57	thf(decl_149, type, binintersectSubset2: $o).
118.52/15.57	thf(decl_150, type, binintersectSubset3: $o).
118.52/15.57	thf(decl_151, type, binintersectER: $o).
118.52/15.57	thf(decl_152, type, disjointsetsI1: $o).
118.52/15.57	thf(decl_153, type, binintersectRsub: $o).
118.52/15.57	thf(decl_154, type, binintersectSubset4: $o).
118.52/15.57	thf(decl_155, type, binintersectSubset1: $o).
118.52/15.57	thf(decl_156, type, bs114d: $o).
118.52/15.57	thf(decl_158, type, setminus: $i > $i > $i).
118.52/15.57	thf(decl_159, type, setminusI: $o).
118.52/15.57	thf(decl_160, type, setminusEL: $o).
118.52/15.57	thf(decl_161, type, setminusER: $o).
118.52/15.57	thf(decl_162, type, setminusSubset2: $o).
118.52/15.57	thf(decl_163, type, setminusERneg: $o).
118.52/15.57	thf(decl_164, type, setminusELneg: $o).
118.52/15.57	thf(decl_165, type, setminusILneg: $o).
118.52/15.57	thf(decl_166, type, setminusIRneg: $o).
118.52/15.57	thf(decl_167, type, setminusLsub: $o).
118.52/15.57	thf(decl_168, type, setminusSubset1: $o).
118.52/15.57	thf(decl_169, type, symdiff: $i > $i > $i).
118.52/15.57	thf(decl_170, type, symdiffE: $o).
118.52/15.57	thf(decl_171, type, symdiffI1: $o).
118.52/15.57	thf(decl_172, type, symdiffI2: $o).
118.52/15.57	thf(decl_173, type, symdiffIneg1: $o).
118.52/15.57	thf(decl_174, type, symdiffIneg2: $o).
118.52/15.57	thf(decl_175, type, iskpair: $i > $o).
118.52/15.57	thf(decl_176, type, secondinupair: $o).
118.52/15.57	thf(decl_177, type, setukpairIL: $o).
118.52/15.57	thf(decl_178, type, setukpairIR: $o).
118.52/15.57	thf(decl_179, type, kpairiskpair: $o).
118.52/15.57	thf(decl_180, type, kpair: $i > $i > $i).
118.52/15.57	thf(decl_181, type, kpairp: $o).
118.52/15.57	thf(decl_182, type, cartprod: $i > $i > $i).
118.52/15.57	thf(decl_183, type, singletonsubset: $o).
118.52/15.57	thf(decl_184, type, singletoninpowerset: $o).
118.52/15.57	thf(decl_185, type, singletoninpowunion: $o).
118.52/15.57	thf(decl_186, type, upairset2E: $o).
118.52/15.57	thf(decl_187, type, upairsubunion: $o).
118.52/15.57	thf(decl_188, type, upairinpowunion: $o).
118.52/15.57	thf(decl_189, type, ubforcartprodlem1: $o).
118.52/15.57	thf(decl_190, type, ubforcartprodlem2: $o).
118.52/15.57	thf(decl_191, type, ubforcartprodlem3: $o).
118.52/15.57	thf(decl_192, type, epred1_0: $o).
118.52/15.57	thf(decl_193, type, esk1_2: $i > $i > $i).
118.52/15.57	thf(decl_194, type, esk2_2: $i > $i > $i).
118.52/15.57	thf(decl_195, type, esk3_2: $i > $i > $i).
118.52/15.57	thf(decl_196, type, esk4_1: $i > $i).
118.52/15.57	thf(decl_197, type, esk5_2: ($i > $i > $o) > $i > $i).
118.52/15.57	thf(decl_198, type, esk6_2: ($i > $i > $o) > $i > $i).
118.52/15.57	thf(decl_199, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
118.52/15.57	thf(decl_200, type, esk8_1: $i > $i).
118.52/15.57	thf(decl_201, type, esk9_1: ($i > $o) > $i).
118.52/15.57	thf(decl_202, type, esk10_1: ($i > $o) > $i).
118.52/15.57	thf(decl_203, type, esk11_2: $i > $i > $i).
118.52/15.57	thf(decl_204, type, esk12_2: $i > $i > $i).
118.52/15.57	thf(decl_205, type, esk13_1: $i > $i).
118.52/15.57	thf(decl_206, type, esk14_1: $i > $i).
118.52/15.57	thf(decl_207, type, esk15_1: $i > $i).
118.52/15.57	thf(decl_208, type, esk16_2: $i > $i > $i).
118.52/15.57	thf(decl_209, type, esk17_3: $i > $i > $o > $i).
118.52/15.57	thf(decl_210, type, esk18_1: ($i > $o) > $i).
118.52/15.57	thf(decl_211, type, esk19_1: $i > $i).
118.52/15.57	thf(decl_212, type, esk20_2: $i > ($i > $o) > $i).
118.52/15.57	thf(decl_213, type, esk21_2: $i > ($i > $o) > $i).
118.52/15.57	thf(decl_214, type, esk22_2: $i > ($i > $o) > $i).
118.52/15.57	thf(decl_215, type, esk23_2: $i > ($i > $o) > $i).
118.52/15.57	thf(decl_216, type, esk24_2: $i > ($i > $o) > $i).
118.52/15.57	thf(decl_217, type, esk25_2: $i > ($i > $o) > $i).
118.52/15.57	thf(decl_218, type, esk26_2: ($i > $o) > $i > $i).
118.52/15.57	thf(decl_219, type, esk27_1: ($i > $o) > $i).
118.52/15.57	thf(decl_220, type, esk28_1: ($i > $o) > $i).
118.52/15.57	thf(decl_221, type, esk29_2: ($i > $o) > $i > $i).
118.52/15.57	thf(decl_222, type, esk30_2: ($i > $o) > ($i > $o) > $i).
118.52/15.57	thf(decl_223, type, esk31_2: ($i > $o) > ($i > $o) > $i).
118.52/15.57	thf(decl_224, type, esk32_2: ($i > $o) > ($i > $o) > $i).
118.52/15.57	thf(decl_225, type, esk33_2: ($i > $o) > ($i > $o) > $i).
118.52/15.57	thf(decl_226, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i).
118.52/15.57	thf(decl_227, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i).
118.52/15.57	thf(decl_228, type, esk36_2: $i > $i > $i).
118.52/15.57	thf(decl_229, type, esk37_2: $i > $i > $i).
118.52/15.57	thf(decl_230, type, esk38_2: $i > $i > $i).
118.52/15.57	thf(decl_231, type, esk39_0: $i).
118.52/15.57	thf(decl_232, type, esk40_0: $i).
118.52/15.57	thf(decl_233, type, esk41_0: $i).
118.52/15.57	thf(decl_234, type, esk42_0: $i).
118.52/15.57	thf(decl_241, type, epred3_2: $i > $i > $i > $o).
118.52/15.57	thf(decl_242, type, esk48_3: $i > $i > $i > $i).
118.52/15.57	thf(decl_243, type, esk49_3: $i > $i > $i > $i).
118.52/15.57	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', setoftrueEq)).
118.52/15.57	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', nonemptyI)).
118.52/15.57	thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', exuE3u)).
118.52/15.57	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', exuE1)).
118.52/15.57	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', dsetconstrER)).
118.52/15.57	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', dsetconstrEL)).
118.52/15.57	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', dsetconstrI)).
118.52/15.57	thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', replAx)).
118.52/15.57	thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', exu__Cong)).
118.52/15.57	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', sepSubset)).
118.52/15.57	thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', descr__Cong)).
118.52/15.57	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', sepInPowerset)).
118.52/15.57	thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', dsetconstr__Cong)).
118.52/15.57	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', exuEu)).
118.52/15.57	thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', exuI1)).
118.52/15.57	thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', exuI2)).
118.52/15.57	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', exuI3)).
118.52/15.57	thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', emptyE1)).
118.52/15.57	thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', exuE2)).
118.52/15.57	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', setbeta)).
118.52/15.57	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', exuE3e)).
118.52/15.57	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', descrp)).
118.52/15.57	thf(cartprodpairin, conjecture, (((((((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>(((foundationAx)=>((wellorderingAx)=>((descrp)=>((((((prop2setE)=>((((notinemptyset)=>((exuE3e)=>((setext)=>(((noeltsimpempty)=>((setbeta)=>(((((setadjoinIL)=>((((setadjoinE)=>((((powersetI)=>(((emptyInPowerset)=>((powersetE)=>((setunionI)=>((((exuE2)=>(((uniqinunit)=>((((singletonsswitch)=>((upairsetE)=>((((emptyE1)=>((vacuousDall)=>(((quantDeMorgan2)=>((quantDeMorgan3)=>((((prop2set2propI)=>((notdexE)=>((((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((((powerset__Cong)=>(((((descr__Cong)=>(((subsetI1)=>((eqimpsubset2)=>(((subsetI2)=>((emptysetsubset)=>(((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>(((subset2powerset)=>((((((inPowerset)=>((((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((((((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>(((binintersectSubset3)=>(((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>(((setminusI)=>((setminusEL)=>((setminusER)=>(((setminusERneg)=>(((setminusILneg)=>((setminusIRneg)=>(((((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>(((secondinupair)=>(((setukpairIR)=>(((kpairp)=>((((((upairsubunion)=>(((((ubforcartprodlem3)=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))<=(in @ X3 @ X5))))))<=(ubforcartprodlem2))<=(ubforcartprodlem1))<=(upairinpowunion)))<=(upairset2E))<=(singletoninpowunion))<=(singletoninpowerset))<=(singletonsubset)))<=(kpairiskpair)))<=(setukpairIL)))<=(symdiffIneg2)))))<=(symdiffE))<=(setminusSubset1))<=(setminusLsub))))<=(setminusELneg)))<=(setminusSubset2)))))<=(bs114d))))))<=(binintersectER)))<=(binintersectSubset2))))))<=(binunionRsub))<=(binunionLsub))<=(binunionE))<=(binunionEcases))))))<=(sepInPowerset))<=(powersetsubset)))<=(powersetE1))<=(powersetI1))<=(subsetemptysetimpeq))<=(setextsub)))<=(setadjoinSub2)))))))))<=(subsetE))))<=(eqimpsubset1))))<=(dsetconstr__Cong)))<=(exuEu))<=(omega__Cong))<=(setunion__Cong)))<=(setadjoin__Cong))<=(emptyset__Cong))))))))<=(exuI1))<=(notdallE))))<=(prop2setI))<=(quantDeMorgan4))))<=(quantDeMorgan1))))<=(upairsetIR))<=(upairsetIL))))<=(eqinunit))<=(notinsingleton)))<=(nonemptyImpWitness)))<=(subPowSU))<=(setunionE)))))<=(emptyinPowerset)))<=(setoftrueEq))<=(setadjoinOr)))<=(setadjoinIR))<=(emptyinunitempty)))<=(nonemptyI1))<=(nonemptyI))<=(nonemptyE1))))<=(emptyI)))))<=(emptysetimpfalse))<=(emptysetE)))<=(exuE1))<=(dsetconstrER))<=(dsetconstrEL))<=(dsetconstrI)))))<=(replAx)))))<=(setunionAx))<=(powersetAx))<=(setadjoinAx))<=(emptysetAx))<=(setextAx)), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', cartprodpairin)).
118.52/15.57	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', setextAx)).
118.52/15.57	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', upairsetIL)).
118.52/15.57	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', eqinunit)).
118.52/15.57	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', notinsingleton)).
118.52/15.57	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', subsetI1)).
118.52/15.57	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', nonemptyImpWitness)).
118.52/15.57	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', subPowSU)).
118.52/15.57	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', eqimpsubset2)).
118.52/15.57	thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', setunionE)).
118.52/15.57	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', emptyinPowerset)).
118.52/15.57	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', subsetI2)).
118.52/15.57	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', setadjoinOr)).
118.52/15.57	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', setadjoinIR)).
118.52/15.57	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', emptysetsubset)).
118.52/15.57	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', emptyinunitempty)).
118.52/15.57	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', nonemptyI1)).
118.52/15.57	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', subsetE2)).
118.52/15.57	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', nonemptyE1)).
118.52/15.57	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', emptyI)).
118.52/15.57	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', emptysetimpfalse)).
118.52/15.57	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', notsubsetI)).
118.52/15.57	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', emptysetE)).
118.52/15.57	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', notequalI1)).
118.52/15.57	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', disjointsetsI1)).
118.52/15.57	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', notequalI2)).
118.52/15.57	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', setunionAx)).
118.52/15.57	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', powersetAx)).
118.52/15.57	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', setadjoinAx)).
118.52/15.57	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', subsetRefl)).
118.52/15.57	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', emptysetAx)).
118.52/15.57	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', subsetTrans)).
118.52/15.57	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', setadjoinSub)).
118.52/15.57	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', subset2powerset)).
118.52/15.57	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', inPowerset)).
118.52/15.57	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', binunionIL)).
118.52/15.57	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', upairset2IR)).
118.52/15.57	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', powerset__Cong)).
118.52/15.57	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', binunionIR)).
118.52/15.57	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', binintersectI)).
118.52/15.57	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', binintersectSubset5)).
118.52/15.57	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', binintersectEL)).
118.52/15.57	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', binintersectLsub)).
118.52/15.57	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', binintersectSubset3)).
118.52/15.57	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', setminusSubset2)).
118.52/15.57	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', bs114d)).
118.52/15.57	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', binintersectER)).
118.52/15.57	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', binintersectSubset2)).
118.52/15.57	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', binunionRsub)).
118.52/15.57	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', binintersectRsub)).
118.52/15.57	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', binintersectSubset4)).
118.52/15.57	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', binintersectSubset1)).
118.52/15.57	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', setminusI)).
118.52/15.57	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', setminusEL)).
118.52/15.57	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', setminusER)).
118.52/15.57	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', setminusERneg)).
118.52/15.57	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', setminusILneg)).
118.52/15.57	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', setminusIRneg)).
118.52/15.57	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', symdiffI1)).
118.52/15.57	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', symdiffI2)).
118.52/15.57	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', symdiffIneg1)).
118.52/15.57	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', secondinupair)).
118.52/15.57	thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', setukpairIR)).
118.52/15.57	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', kpairp)).
118.52/15.57	thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', upairsubunion)).
118.52/15.57	thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', ubforcartprodlem3)).
118.52/15.57	thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', ubforcartprodlem2)).
118.52/15.57	thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', ubforcartprodlem1)).
118.52/15.57	thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', upairinpowunion)).
118.52/15.57	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', upairset2E)).
118.52/15.57	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', singletoninpowunion)).
118.52/15.57	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', singletoninpowerset)).
118.52/15.57	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', singletonsubset)).
118.52/15.57	thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', kpairiskpair)).
118.52/15.57	thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', setukpairIL)).
118.52/15.57	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', symdiffIneg2)).
118.52/15.57	thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', symdiffE)).
118.52/15.57	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', setminusSubset1)).
118.52/15.57	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', setminusLsub)).
118.52/15.57	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', setminusELneg)).
118.52/15.57	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', binunionLsub)).
118.52/15.57	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', binunionE)).
118.52/15.57	thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', binunionEcases)).
118.52/15.57	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', powersetsubset)).
118.52/15.57	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', powersetE1)).
118.52/15.57	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', powersetI1)).
118.52/15.57	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', subsetemptysetimpeq)).
118.52/15.57	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', setextsub)).
118.52/15.57	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', setadjoinSub2)).
118.52/15.57	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', subsetE)).
118.52/15.57	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', eqimpsubset1)).
118.52/15.57	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', omega__Cong)).
118.52/15.57	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', setunion__Cong)).
118.52/15.57	thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', setadjoin__Cong)).
118.52/15.57	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', emptyset__Cong)).
118.52/15.57	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', notdallE)).
118.52/15.57	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', prop2setI)).
118.52/15.57	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', quantDeMorgan4)).
118.52/15.57	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', quantDeMorgan1)).
118.52/15.57	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', upairsetIR)).
118.52/15.57	thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', in__Cong)).
118.52/15.57	thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', inCongP)).
118.52/15.57	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', notdexE)).
118.52/15.57	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', quantDeMorgan3)).
118.52/15.57	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', quantDeMorgan2)).
118.52/15.57	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', vacuousDall)).
118.52/15.57	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', upairsetE)).
118.52/15.57	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', singletonsswitch)).
118.52/15.57	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', uniqinunit)).
118.52/15.57	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', setunionI)).
118.52/15.57	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', powersetE)).
118.52/15.57	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', emptyInPowerset)).
118.52/15.57	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', powersetI)).
118.52/15.57	thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', setadjoinE)).
118.52/15.57	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', setadjoinIL)).
118.52/15.57	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', noeltsimpempty)).
118.52/15.57	thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', setext)).
118.52/15.57	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', notinemptyset)).
118.52/15.57	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', prop2setE)).
118.52/15.57	thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', wellorderingAx)).
118.52/15.57	thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', foundationAx)).
118.52/15.57	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', omegaIndAx)).
118.52/15.57	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', omegaSAx)).
118.52/15.57	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', omega0Ax)).
118.52/15.57	thf(cartprod, axiom, ((cartprod)=(^[X4:$i, X5:$i]:(dsetconstr @ (powerset @ (powerset @ (binunion @ X4 @ X5))) @ (^[X2:$i]:(?[X3:$i]:(((in @ X3 @ X4)&?[X14:$i]:(((in @ X14 @ X5)&((X2)=(kpair @ X3 @ X14))))))))))), file('/export/starexec/sandbox/tmp/tmp.kc8VksXJ0R/E---3.1_25752.p', cartprod)).
118.52/15.57	thf(c_0_147, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
118.52/15.57	thf(c_0_148, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
118.52/15.57	thf(c_0_149, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
118.52/15.57	thf(c_0_150, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
118.52/15.57	thf(c_0_151, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
118.52/15.57	thf(c_0_152, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
118.52/15.57	thf(c_0_153, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
118.52/15.57	thf(c_0_154, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0/* 3 */:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
118.52/15.57	thf(c_0_155, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
118.52/15.57	thf(c_0_156, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
118.52/15.57	thf(c_0_157, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>((exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
118.52/15.57	thf(c_0_158, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
118.52/15.57	thf(c_0_159, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
118.52/15.57	thf(c_0_160, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
118.52/15.57	thf(c_0_161, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
118.52/15.57	thf(c_0_162, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
118.52/15.57	thf(c_0_163, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
118.52/15.57	thf(c_0_164, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
118.52/15.57	thf(c_0_165, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
118.52/15.57	thf(c_0_166, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
118.52/15.57	thf(c_0_167, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
118.52/15.57	thf(c_0_168, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
118.52/15.57	thf(c_0_169, plain, ((epred1_0)<=>![X426:$i]:(?[X427:$i]:((((![X428:$i]:(((in @ X428 @ X427)=>![X429:$i]:(((in @ X429 @ X428)=>(in @ X429 @ X426)))))&![X430:$i, X431:$i]:((((in @ X430 @ X426)&(in @ X431 @ X426))=>(![X432:$i]:(((in @ X432 @ X427)=>((in @ X430 @ X432)<=>(in @ X431 @ X432))))=>((X430)=(X431))))))&![X433:$i, X434:$i]:((((in @ X433 @ X427)&(in @ X434 @ X427))=>(![X435:$i]:(((in @ X435 @ X433)=>(in @ X435 @ X434)))|![X436:$i]:(((in @ X436 @ X434)=>(in @ X436 @ X433)))))))&![X437:$i]:(((![X438:$i]:(((in @ X438 @ X437)=>(in @ X438 @ X426)))&?[X439:$i]:((in @ X439 @ X437)))=>?[X440:$i, X441:$i]:(((((in @ X440 @ X427)&(in @ X441 @ X437))&~(?[X442:$i]:(((in @ X442 @ X440)&(in @ X442 @ X437)))))&![X443:$i]:(((in @ X443 @ X427)=>(![X444:$i]:(((in @ X444 @ X443)=>(in @ X444 @ X440)))|(in @ X441 @ X443)))))))))))), introduced(definition)).
118.52/15.57	thf(c_0_170, negated_conjecture, ~((![X808:$i, X809:$i]:((![X810:$i]:(((in @ X810 @ X808)<=>(in @ X810 @ X809)))=>((X808)=(X809))))=>(![X807:$i]:(~(in @ X807 @ emptyset))=>(![X804:$i, X805:$i, X806:$i]:(((in @ X806 @ (setadjoin @ X804 @ X805))<=>(((X806)=(X804))|(in @ X806 @ X805))))=>(![X801:$i, X802:$i]:(((in @ X802 @ (powerset @ X801))<=>![X803:$i]:(((in @ X803 @ X802)=>(in @ X803 @ X801)))))=>(![X798:$i, X799:$i]:(((in @ X799 @ (setunion @ X798))<=>?[X800:$i]:(((in @ X799 @ X800)&(in @ X800 @ X798)))))=>((in @ emptyset @ omega)=>(![X418:$i]:(((in @ X418 @ omega)=>(in @ (setadjoin @ X418 @ X418) @ omega)))=>(![X419:$i]:((((in @ emptyset @ X419)&![X420:$i]:((((in @ X420 @ omega)&(in @ X420 @ X419))=>(in @ (setadjoin @ X420 @ X420) @ X419))))=>![X421:$i]:(((in @ X421 @ omega)=>(in @ X421 @ X419)))))=>(![X792:$i > $i > $o, X793:$i]:((![X794:$i]:(((in @ X794 @ X793)=>(exu @ (X792 @ X794))))=>?[X795:$i]:(![X796:$i]:(((in @ X796 @ X795)<=>?[X797:$i]:(((in @ X797 @ X793)&(X792 @ X797 @ X796))))))))=>(![X422:$i]:((?[X423:$i]:((in @ X423 @ X422))=>?[X424:$i]:(((in @ X424 @ X422)&~(?[X425:$i]:(((in @ X425 @ X424)&(in @ X425 @ X422))))))))=>((epred1_0)=>(![X445:$i > $o]:(((exu @ X445)=>(X445 @ (descr @ (^[Z0/* 17 */:$i]:(X445 @ Z0))))))=>(![X789:$i, X790:$i > $o, X791:$i]:(((in @ X791 @ X789)=>((X790 @ X791)=>(in @ X791 @ (dsetconstr @ X789 @ X790)))))=>(![X786:$i, X787:$i > $o, X788:$i]:(((in @ X788 @ (dsetconstr @ X786 @ X787))=>(in @ X788 @ X786)))=>(![X783:$i, X784:$i > $o, X785:$i]:(((in @ X785 @ (dsetconstr @ X783 @ X784))=>(X784 @ X785)))=>(![X780:$i > $o]:(((exu @ X780)=>?[X781:$i]:(((X780 @ X781)&![X782:$i]:(((X780 @ X782)=>((X781)=(X782))))))))=>(![X446:$o, X447:$i]:(((in @ X447 @ (prop2set @ ((X446))))=>(X446)))=>(![X778:$i]:(((in @ X778 @ emptyset)=>![X779:$o]:((X779))))=>(![X777:$i]:(((in @ X777 @ emptyset)=>~($true)))=>(![X448:$i]:(~(in @ X448 @ emptyset))=>(![X449:$i > $o]:(((exu @ X449)=>?[X450:$i]:((X449 @ X450))))=>(![X451:$i, X452:$i]:((![X453:$i]:(((in @ X453 @ X451)=>(in @ X453 @ X452)))=>(![X454:$i]:(((in @ X454 @ X452)=>(in @ X454 @ X451)))=>((X451)=(X452)))))=>(![X775:$i]:((![X776:$i]:(~(in @ X776 @ X775))=>((X775)=(emptyset))))=>(![X455:$i]:((![X456:$i]:(~(in @ X456 @ X455))=>((X455)=(emptyset))))=>(![X457:$i, X458:$i > $o, X459:$i]:(((in @ X459 @ X457)=>((in @ X459 @ (dsetconstr @ X457 @ X458))<=>(X458 @ X459))))=>(![X773:$i]:(((nonempty @ X773)=>?[X774:$i]:((in @ X774 @ X773))))=>(![X770:$i, X771:$i > $o, X772:$i]:(((in @ X772 @ X770)=>((X771 @ X772)=>(nonempty @ (dsetconstr @ X770 @ X771)))))=>(![X768:$i]:((?[X769:$i]:((in @ X769 @ X768))=>(nonempty @ X768)))=>(![X460:$i, X461:$i]:((in @ X460 @ (setadjoin @ X460 @ X461)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X765:$i, X766:$i, X767:$i]:(((in @ X767 @ X766)=>(in @ X767 @ (setadjoin @ X765 @ X766))))=>(![X462:$i, X463:$i, X464:$i]:(((in @ X464 @ (setadjoin @ X462 @ X463))=>![X465:$o]:(((((X464)=(X462))=>(X465))=>(((in @ X464 @ X463)=>(X465))=>(X465))))))=>(![X762:$i, X763:$i, X764:$i]:(((in @ X764 @ (setadjoin @ X762 @ X763))=>(((X764)=(X762))|(in @ X764 @ X763))))=>(![X761:$i]:(((dsetconstr @ X761 @ (^[Z0/* 1 */:$i]:($true)))=(X761)))=>(![X466:$i, X467:$i]:((![X468:$i]:(((in @ X468 @ X467)=>(in @ X468 @ X466)))=>(in @ X467 @ (powerset @ X466))))=>(![X760:$i]:((in @ emptyset @ (powerset @ X760)))=>(![X469:$i]:((in @ emptyset @ (powerset @ X469)))=>(![X470:$i, X471:$i, X472:$i]:(((in @ X471 @ (powerset @ X470))=>((in @ X472 @ X471)=>(in @ X472 @ X470))))=>(![X473:$i, X474:$i, X475:$i]:(((in @ X474 @ X475)=>((in @ X475 @ X473)=>(in @ X474 @ (setunion @ X473)))))=>(![X756:$i, X757:$i]:(((in @ X757 @ (setunion @ X756))=>![X758:$o]:((![X759:$i]:(((in @ X757 @ X759)=>((in @ X759 @ X756)=>(X758))))=>(X758)))))=>(![X754:$i, X755:$i]:(((in @ X755 @ X754)=>(in @ X755 @ (powerset @ (setunion @ X754)))))=>(![X476:$i > $o]:(((exu @ X476)=>?[X477:$i]:(![X478:$i]:(((X476 @ X478)<=>((X478)=(X477)))))))=>(![X752:$i]:(((nonempty @ X752)=>?[X753:$i]:(((in @ X753 @ X752)&$true))))=>(![X479:$i, X480:$i]:(((in @ X479 @ (setadjoin @ X480 @ emptyset))=>((X479)=(X480))))=>(![X750:$i, X751:$i]:((((X750)!=(X751))=>~(in @ X751 @ (setadjoin @ X750 @ emptyset))))=>(![X748:$i, X749:$i]:((((X748)=(X749))=>(in @ X748 @ (setadjoin @ X749 @ emptyset))))=>(![X481:$i, X482:$i]:(((in @ X481 @ (setadjoin @ X482 @ emptyset))=>(in @ X482 @ (setadjoin @ X481 @ emptyset))))=>(![X483:$i, X484:$i, X485:$i]:(((in @ X485 @ (setadjoin @ X483 @ (setadjoin @ X484 @ emptyset)))=>(((X485)=(X483))|((X485)=(X484)))))=>(![X746:$i, X747:$i]:((in @ X746 @ (setadjoin @ X746 @ (setadjoin @ X747 @ emptyset))))=>(![X744:$i, X745:$i]:((in @ X745 @ (setadjoin @ X744 @ (setadjoin @ X745 @ emptyset))))=>(![X486:$i, X487:$i > $o]:((?[X488:$i]:(((in @ X488 @ X486)&(X487 @ X488)))=>(((dsetconstr @ X486 @ X487)=(emptyset))=>~($true))))=>(![X489:$i > $o, X490:$i]:(((in @ X490 @ emptyset)=>(X489 @ 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setextAx]), upairsetIL]), eqinunit]), notinsingleton]), subsetI1]), nonemptyImpWitness]), subPowSU]), eqimpsubset2]), setunionE]), emptyinPowerset]), c_0_147]), subsetI2]), setadjoinOr]), setadjoinIR]), emptysetsubset]), emptyinunitempty]), nonemptyI1]), c_0_148]), subsetE2]), nonemptyE1]), emptyI]), c_0_149]), emptysetimpfalse]), notsubsetI]), emptysetE]), c_0_150]), c_0_151]), notequalI1]), c_0_152]), disjointsetsI1]), c_0_153]), notequalI2]), c_0_154]), c_0_155]), setunionAx]), powersetAx]), setadjoinAx]), subsetRefl]), emptysetAx]), subsetTrans]), setadjoinSub]), subset2powerset]), inPowerset]), c_0_156]), binunionIL]), upairset2IR]), powerset__Cong]), binunionIR]), binintersectI]), binintersectSubset5]), binintersectEL]), binintersectLsub]), binintersectSubset3]), setminusSubset2]), bs114d]), binintersectER]), binintersectSubset2]), binunionRsub]), binintersectRsub]), binintersectSubset4]), binintersectSubset1]), setminusI]), setminusEL]), setminusER]), setminusERneg]), setminusILneg]), setminusIRneg]), c_0_157]), symdiffI1]), symdiffI2]), symdiffIneg1]), secondinupair]), setukpairIR]), kpairp]), upairsubunion]), ubforcartprodlem3]), ubforcartprodlem2]), ubforcartprodlem1]), upairinpowunion]), upairset2E]), singletoninpowunion]), singletoninpowerset]), singletonsubset]), kpairiskpair]), setukpairIL]), symdiffIneg2]), symdiffE]), setminusSubset1]), setminusLsub]), setminusELneg]), binunionLsub]), binunionE]), binunionEcases]), c_0_158]), powersetsubset]), powersetE1]), powersetI1]), subsetemptysetimpeq]), setextsub]), setadjoinSub2]), subsetE]), eqimpsubset1]), c_0_159]), c_0_160]), omega__Cong]), setunion__Cong]), setadjoin__Cong]), emptyset__Cong]), c_0_161]), notdallE]), prop2setI]), quantDeMorgan4]), quantDeMorgan1]), upairsetIR]), in__Cong]), inCongP]), c_0_162]), c_0_163]), notdexE]), quantDeMorgan3]), quantDeMorgan2]), vacuousDall]), c_0_164]), upairsetE]), singletonsswitch]), uniqinunit]), c_0_165]), setunionI]), powersetE]), emptyInPowerset]), powersetI]), setadjoinE]), setadjoinIL]), c_0_166]), noeltsimpempty]), setext]), c_0_167]), notinemptyset]), prop2setE]), c_0_168]), wellorderingAx]), foundationAx]), omegaIndAx]), omegaSAx]), omega0Ax])])]), c_0_169])).
118.52/15.57	thf(c_0_171, plain, ![X811:$i, X812:$i]:(((cartprod @ X811 @ X812)=(dsetconstr @ (powerset @ (powerset @ (binunion @ X811 @ X812))) @ (^[Z0/* 5 */:$i]:(?[X3:$i]:(((in @ X3 @ X811)&?[X14:$i]:(((in @ X14 @ X812)&((Z0)=(kpair @ X3 @ X14))))))))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[cartprod])])).
118.52/15.57	thf(c_0_172, negated_conjecture, ![X815:$i, X816:$i, X818:$i, X819:$i, X820:$i, X821:$i, X822:$i, X823:$i, X824:$i, X825:$i, X826:$i, X828:$i, X829:$i, X831:$i, X832:$i, X833:$i, X834:$i, X835:$i, X837:$i, X838:$i > $i > $o, X839:$i, X842:$i, X844:$i, X845:$i, X846:$i, X847:$i, X849:$i, X850:$i > $o, X851:$i, X852:$i > $o, X853:$i, X854:$i, X855:$i > $o, X856:$i, X857:$i, X858:$i > $o, X859:$i, X860:$i > $o, X862:$i, X863:$o, X864:$i, X865:$i, X866:$o, X867:$i, X868:$i, X869:$i > $o, X871:$i, X872:$i, X875:$i, X877:$i, X879:$i, X880:$i > $o, X881:$i, X882:$i, X884:$i, X885:$i > $o, X886:$i, X887:$i, X888:$i, X889:$i, X890:$i, X891:$i, X892:$i, X893:$i, X894:$i, X895:$i, X896:$i, X897:$o, X898:$i, X899:$i, X900:$i, X901:$i, X902:$i, X903:$i, X905:$i, X906:$i, X907:$i, X908:$i, X909:$i, X910:$i, X911:$i, X912:$i, X913:$i, X914:$i, X915:$o, X917:$i, X918:$i, X919:$i > $o, X921:$i, X922:$i, X923:$i, X925:$i, X926:$i, X927:$i, X928:$i, X929:$i, X930:$i, X931:$i, X932:$i, X933:$i, X934:$i, X935:$i, X936:$i, X937:$i, X938:$i, X939:$i, X940:$i, X941:$i > $o, X942:$i, X943:$i > $o, X944:$i, X945:$i, X946:$i > $o, X947:$i, X949:$i, X950:$i > $o, X952:$i, X953:$i, X954:$i > $o, X956:$i, X957:$i, X958:$i > $o, X959:$i, X961:$o, X962:$i, X963:$i > $o, X965:$i, X966:$i, X967:$i > $o, X968:$i, X970:$i > $o, X971:$i, X973:$i > $o, X974:$i, X977:$i > $o, X978:$i, X980:$i, X981:$i, X982:$i, X983:$i, X984:$i, X985:$i, X986:$i, X987:$i, X988:$i > $o, X989:$i, X990:$i, X991:$i > $o, X992:$i > $o, X995:$i, X996:$i, X997:$i, X998:$i, X999:$i, X1000:$i, X1001:$i, X1002:$i, X1003:$i > $o, X1004:$i, X1005:$i, X1006:$i > $o, X1007:$i > $o, X1010:$i, X1011:$i, X1012:$i > $o, X1013:$i > $o, X1016:$i, X1017:$i, X1019:$i, X1020:$i, X1021:$i, X1022:$i, X1023:$i, X1024:$i, X1026:$i, X1027:$i, X1028:$i, X1029:$i, X1030:$i, X1031:$i, X1032:$i, X1033:$i, X1034:$i, X1035:$i, X1036:$i, X1037:$i, X1038:$i, X1039:$i, X1040:$i, X1041:$i, X1042:$i, X1043:$i, X1044:$i, X1045:$i, X1046:$i, X1047:$i, X1048:$i, X1049:$i, X1050:$i, X1051:$i, X1052:$i, X1053:$i, X1054:$i, X1055:$i, X1056:$i, X1057:$i, X1058:$i, X1059:$i, X1060:$i, X1061:$i, X1062:$i, X1063:$i > $o, X1064:$i, X1065:$i > $o, X1066:$i, X1067:$i, X1068:$i, X1069:$i, X1070:$i, X1071:$i, X1072:$i, X1073:$i, X1074:$i, X1075:$i, X1076:$i, X1077:$o, X1078:$i, X1079:$i, X1080:$i, X1081:$i, X1082:$i, X1083:$i, X1084:$i, X1085:$i, X1086:$i, X1087:$i, X1088:$i, X1089:$i, X1090:$i, X1091:$i, X1092:$i, X1093:$i, X1094:$i, X1095:$i, X1096:$i, X1097:$i, X1098:$i, X1099:$i, X1100:$i, X1101:$i, X1102:$i, X1103:$i, X1104:$i, X1106:$i, X1107:$i, X1108:$i, X1109:$i, X1110:$i, X1111:$i, X1112:$i, X1113:$i, X1114:$i, X1115:$i, X1116:$i, X1117:$i, X1118:$i, X1119:$i, X1120:$i, X1121:$i, X1122:$i, X1123:$i, X1124:$i, X1125:$i, X1126:$i, X1127:$i, X1128:$i, X1129:$i, X1130:$i, X1131:$i, X1132:$i, X1133:$i, X1134:$i, X1135:$i, X1136:$i, X1137:$i, X1138:$i, X1139:$i, X1140:$i, X1141:$i, X1142:$i, X1143:$i, X1144:$i, X1145:$o, X1146:$i, X1147:$i, X1148:$i, X1149:$i, X1150:$i, X1151:$i, X1152:$i, X1153:$i, X1154:$i, X1155:$i, X1156:$i, X1157:$i, X1158:$i, X1159:$i, X1160:$i, X1161:$i, X1162:$i, X1163:$i, X1164:$i, X1165:$i, X1166:$i, X1167:$i, X1168:$i, X1169:$i, X1170:$i, X1171:$i, X1172:$i, X1173:$i, X1174:$i, X1175:$i, X1176:$i, X1177:$i, X1178:$i, X1179:$i, X1180:$i, X1181:$i, X1182:$i, X1183:$i, X1184:$i, X1185:$i, X1186:$i, X1187:$i, X1188:$i, X1189:$i, X1190:$i, X1191:$i, X1192:$i, X1193:$i, X1194:$i, X1195:$i, X1196:$i, X1197:$i]:((((~(in @ (esk1_2 @ X815 @ X816) @ X815)|~(in @ (esk1_2 @ X815 @ X816) @ X816)|((X815)=(X816)))&((in @ (esk1_2 @ X815 @ X816) @ X815)|(in @ (esk1_2 @ X815 @ X816) @ X816)|((X815)=(X816))))&(~(in @ X818 @ emptyset)&(((~(in @ X821 @ (setadjoin @ X819 @ X820))|(((X821)=(X819))|(in @ X821 @ X820)))&((((X821)!=(X819))|(in @ X821 @ (setadjoin @ X819 @ X820)))&(~(in @ X821 @ X820)|(in @ X821 @ (setadjoin @ X819 @ X820)))))&(((~(in @ X823 @ (powerset @ X822))|(~(in @ X824 @ X823)|(in @ X824 @ X822)))&(((in @ (esk2_2 @ X825 @ X826) @ X826)|(in @ X826 @ (powerset @ X825)))&(~(in @ (esk2_2 @ X825 @ X826) @ X825)|(in @ X826 @ (powerset @ X825)))))&(((((in @ X829 @ (esk3_2 @ X828 @ X829))|~(in @ X829 @ (setunion @ X828)))&((in @ (esk3_2 @ X828 @ X829) @ X828)|~(in @ X829 @ (setunion @ X828))))&(~(in @ X832 @ X833)|~(in @ X833 @ X831)|(in @ X832 @ (setunion @ X831))))&((in @ emptyset @ omega)&((~(in @ X834 @ omega)|(in @ (setadjoin @ X834 @ X834) @ omega))&(((((in @ (esk4_1 @ X835) @ omega)|~(in @ emptyset @ X835)|(~(in @ X837 @ omega)|(in @ X837 @ X835)))&((in @ (esk4_1 @ X835) @ X835)|~(in @ emptyset @ X835)|(~(in @ X837 @ omega)|(in @ X837 @ X835))))&(~(in @ (setadjoin @ (esk4_1 @ X835) @ (esk4_1 @ X835)) @ X835)|~(in @ emptyset @ X835)|(~(in @ X837 @ omega)|(in @ X837 @ X835))))&((((((in @ (esk7_3 @ X838 @ X839 @ X842) @ X839)|~(in @ X842 @ (esk6_2 @ X838 @ X839))|(in @ (esk5_2 @ X838 @ X839) @ X839))&((X838 @ (esk7_3 @ X838 @ X839 @ X842) @ X842)|~(in @ X842 @ (esk6_2 @ X838 @ X839))|(in @ (esk5_2 @ X838 @ X839) @ X839)))&(~(in @ X845 @ X839)|~(X838 @ X845 @ X844)|(in @ X844 @ (esk6_2 @ X838 @ X839))|(in @ (esk5_2 @ X838 @ X839) @ X839)))&((((in @ (esk7_3 @ X838 @ X839 @ X842) @ X839)|~(in @ X842 @ (esk6_2 @ X838 @ X839))|~(exu @ (X838 @ (esk5_2 @ X838 @ X839))))&((X838 @ (esk7_3 @ X838 @ X839 @ X842) @ X842)|~(in @ X842 @ (esk6_2 @ X838 @ X839))|~(exu @ (X838 @ (esk5_2 @ X838 @ X839)))))&(~(in @ X845 @ X839)|~(X838 @ X845 @ X844)|(in @ X844 @ (esk6_2 @ X838 @ X839))|~(exu @ (X838 @ (esk5_2 @ X838 @ X839))))))&((((in @ (esk8_1 @ X846) @ X846)|~(in @ X847 @ X846))&(~(in @ X849 @ (esk8_1 @ X846))|~(in @ X849 @ X846)|~(in @ X847 @ X846)))&((epred1_0)&((~(exu @ X850)|(X850 @ (descr @ X850)))&((~(in @ X853 @ X851)|(~(X852 @ X853)|(in @ X853 @ (dsetconstr @ X851 @ X852))))&((~(in @ X856 @ (dsetconstr @ X854 @ X855))|(in @ X856 @ X854))&((~(in @ X859 @ (dsetconstr @ X857 @ X858))|(X858 @ X859))&((((X860 @ (esk9_1 @ X860))|~(exu @ X860))&(~(X860 @ X862)|((esk9_1 @ X860)=(X862))|~(exu @ X860)))&((~(in @ X864 @ (prop2set @ ((X863))))|(X863))&((~(in @ X865 @ emptyset)|(X866))&((~(in @ X867 @ emptyset)|~($true))&(~(in @ X868 @ emptyset)&((~(exu @ X869)|(X869 @ (esk10_1 @ X869)))&(((((in @ (esk12_2 @ X871 @ X872) @ X872)|((X871)=(X872))|(in @ (esk11_2 @ X871 @ X872) @ X871))&(~(in @ (esk12_2 @ X871 @ X872) @ X871)|((X871)=(X872))|(in @ (esk11_2 @ X871 @ X872) @ X871)))&(((in @ (esk12_2 @ X871 @ X872) @ X872)|((X871)=(X872))|~(in @ (esk11_2 @ X871 @ X872) @ X872))&(~(in @ (esk12_2 @ X871 @ X872) @ X871)|((X871)=(X872))|~(in @ (esk11_2 @ X871 @ X872) @ X872))))&(((in @ (esk13_1 @ X875) @ X875)|((X875)=(emptyset)))&(((in @ (esk14_1 @ X877) @ X877)|((X877)=(emptyset)))&(((~(in @ X881 @ (dsetconstr @ X879 @ X880))|(X880 @ X881)|~(in @ X881 @ X879))&(~(X880 @ X881)|(in @ X881 @ (dsetconstr @ X879 @ X880))|~(in @ X881 @ X879)))&((~(nonempty @ X882)|(in @ (esk15_1 @ X882) @ X882))&((~(in @ X886 @ X884)|(~(X885 @ X886)|(nonempty @ (dsetconstr @ X884 @ X885))))&((~(in @ X888 @ X887)|(nonempty @ X887))&((in @ X889 @ (setadjoin @ X889 @ X890))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X893 @ X892)|(in @ X893 @ (setadjoin @ X891 @ X892)))&(((((in @ X896 @ X895)|(X897)|((X896)=(X894))|~(in @ X896 @ (setadjoin @ X894 @ X895)))&(~(X897)|(X897)|((X896)=(X894))|~(in @ X896 @ (setadjoin @ X894 @ X895))))&(((in @ X896 @ X895)|(X897)|~(X897)|~(in @ X896 @ (setadjoin @ X894 @ X895)))&(~(X897)|(X897)|~(X897)|~(in @ X896 @ (setadjoin @ X894 @ X895)))))&((~(in @ X900 @ (setadjoin @ X898 @ X899))|(((X900)=(X898))|(in @ X900 @ X899)))&(((dsetconstr @ X901 @ (^[Z0/* 1 */:$i]:($true)))=(X901))&((((in @ (esk16_2 @ X902 @ X903) @ X903)|(in @ X903 @ (powerset @ X902)))&(~(in @ (esk16_2 @ X902 @ X903) @ X902)|(in @ X903 @ (powerset @ X902))))&((in @ emptyset @ (powerset @ X905))&((in @ emptyset @ (powerset @ X906))&((~(in @ X908 @ (powerset @ X907))|(~(in @ X909 @ X908)|(in @ X909 @ X907)))&((~(in @ X911 @ X912)|(~(in @ X912 @ X910)|(in @ X911 @ (setunion @ X910))))&((((in @ X914 @ (esk17_3 @ X913 @ X914 @ X915))|(X915)|~(in @ X914 @ (setunion @ X913)))&(((in @ (esk17_3 @ X913 @ X914 @ X915) @ X913)|(X915)|~(in @ X914 @ (setunion @ X913)))&(~(X915)|(X915)|~(in @ X914 @ (setunion @ X913)))))&((~(in @ X918 @ X917)|(in @ X918 @ (powerset @ (setunion @ X917))))&(((~(X919 @ X921)|((X921)=(esk18_1 @ X919))|~(exu @ X919))&(((X922)!=(esk18_1 @ X919))|(X919 @ X922)|~(exu @ X919)))&((((in @ (esk19_1 @ X923) @ X923)|~(nonempty @ X923))&(($true)|~(nonempty @ X923)))&((~(in @ X925 @ (setadjoin @ X926 @ emptyset))|((X925)=(X926)))&((((X927)=(X928))|~(in @ X928 @ (setadjoin @ X927 @ emptyset)))&((((X929)!=(X930))|(in @ X929 @ (setadjoin @ X930 @ emptyset)))&((~(in @ X931 @ (setadjoin @ X932 @ emptyset))|(in @ X932 @ (setadjoin @ X931 @ emptyset)))&((~(in @ X935 @ (setadjoin @ X933 @ (setadjoin @ X934 @ emptyset)))|(((X935)=(X933))|((X935)=(X934))))&((in @ X936 @ (setadjoin @ X936 @ (setadjoin @ X937 @ emptyset)))&((in @ X939 @ (setadjoin @ X938 @ (setadjoin @ X939 @ emptyset)))&((~(in @ X942 @ X940)|~(X941 @ X942)|(((dsetconstr @ X940 @ X941)!=(emptyset))|~($true)))&((~(in @ X944 @ emptyset)|(X943 @ X944))&((((in @ (esk20_2 @ X945 @ X946) @ X945)|(~(in @ X947 @ X945)|(X946 @ X947)))&(~(X946 @ (esk20_2 @ X945 @ X946))|(~(in @ X947 @ X945)|(X946 @ X947))))&((((in @ (esk21_2 @ X949 @ X950) @ X949)|(~(in @ X952 @ X949)|~(X950 @ X952)))&((X950 @ (esk21_2 @ X949 @ X950))|(~(in @ X952 @ X949)|~(X950 @ X952))))&((((in @ (esk22_2 @ X953 @ X954) @ X953)|(~(in @ X956 @ X953)|~(X954 @ X956)))&((X954 @ (esk22_2 @ X953 @ X954))|(~(in @ X956 @ X953)|~(X954 @ X956))))&((((in @ (esk23_2 @ X957 @ X958) @ X957)|(~(in @ X959 @ X957)|(X958 @ X959)))&(~(X958 @ (esk23_2 @ X957 @ X958))|(~(in @ X959 @ X957)|(X958 @ X959))))&((~(X961)|(in @ emptyset @ (prop2set @ ((X961)))))&((prop2set2propI)&((((in @ (esk24_2 @ X962 @ X963) @ X962)|(~(in @ X965 @ X962)|~(X963 @ X965)))&((X963 @ (esk24_2 @ X962 @ X963))|(~(in @ X965 @ X962)|~(X963 @ X965))))&((((in @ (esk25_2 @ X966 @ X967) @ X966)|(~(in @ X968 @ X966)|(X967 @ X968)))&(~(X967 @ (esk25_2 @ X966 @ X967))|(~(in @ X968 @ X966)|(X967 @ X968))))&((((X970 @ (esk26_2 @ X970 @ X971))|~(X970 @ X971)|(exu @ X970))&(((X971)!=(esk26_2 @ X970 @ X971))|~(X970 @ X971)|(exu @ X970)))&((((X973 @ (esk27_1 @ X973))|(exu @ X973)|~(X973 @ X974))&(((X973 @ (esk28_1 @ X973))|(exu @ X973)|~(X973 @ X974))&(((esk27_1 @ X973)!=(esk28_1 @ X973))|(exu @ X973)|~(X973 @ X974))))&(((~(X977 @ (esk29_2 @ X977 @ X978))|((esk29_2 @ X977 @ X978)!=(X978))|(exu @ X977))&((X977 @ (esk29_2 @ X977 @ X978))|((esk29_2 @ X977 @ X978)=(X978))|(exu @ X977)))&((((X980)!=(X981))|(((X982)!=(X983))|(~(in @ X982 @ X980)|(in @ X983 @ X981))))&(((~(in @ X986 @ X984)|(in @ X987 @ X985)|((X986)!=(X987))|((X984)!=(X985)))&(~(in @ X987 @ X985)|(in @ X986 @ X984)|((X986)!=(X987))|((X984)!=(X985))))&((~(exu @ X988)|(~(X988 @ X989)|(~(X988 @ X990)|((X989)=(X990)))))&((((~(exu @ X991)|(exu @ X992)|((esk30_2 @ X991 @ X992)=(esk31_2 @ X991 @ X992)))&(~(exu @ X992)|(exu @ X991)|((esk30_2 @ X991 @ X992)=(esk31_2 @ X991 @ X992))))&(((~(exu @ X991)|(exu @ X992)|(~(X991 @ (esk30_2 @ X991 @ X992))|~(X992 @ (esk31_2 @ X991 @ X992))))&(~(exu @ X992)|(exu @ X991)|(~(X991 @ (esk30_2 @ X991 @ X992))|~(X992 @ (esk31_2 @ X991 @ X992)))))&((~(exu @ X991)|(exu @ X992)|((X991 @ (esk30_2 @ X991 @ X992))|(X992 @ (esk31_2 @ X991 @ X992))))&(~(exu @ X992)|(exu @ X991)|((X991 @ (esk30_2 @ X991 @ X992))|(X992 @ (esk31_2 @ X991 @ X992)))))))&(((emptyset)=(emptyset))&((((X995)!=(X996))|(((X997)!=(X998))|((setadjoin @ X995 @ X997)=(setadjoin @ X996 @ X998))))&((((X999)!=(X1000))|((powerset @ X999)=(powerset @ X1000)))&((((X1001)!=(X1002))|((setunion @ X1001)=(setunion @ X1002)))&(((omega)=(omega))&((~(exu @ X1003)|(~(X1003 @ X1004)|(~(X1003 @ X1005)|((X1004)=(X1005)))))&(((((esk32_2 @ X1006 @ X1007)=(esk33_2 @ X1006 @ X1007))|(~(exu @ X1006)|(~(exu @ X1007)|((descr @ X1006)=(descr @ X1007)))))&((~(X1006 @ (esk32_2 @ X1006 @ X1007))|~(X1007 @ (esk33_2 @ X1006 @ X1007))|(~(exu @ X1006)|(~(exu @ X1007)|((descr @ X1006)=(descr @ X1007)))))&((X1006 @ (esk32_2 @ X1006 @ X1007))|(X1007 @ (esk33_2 @ X1006 @ X1007))|(~(exu @ X1006)|(~(exu @ X1007)|((descr @ X1006)=(descr @ X1007)))))))&((((in @ (esk34_4 @ X1010 @ X1011 @ X1012 @ X1013) @ X1010)|((dsetconstr @ X1010 @ X1012)=(dsetconstr @ X1011 @ X1013))|((X1010)!=(X1011)))&(((in @ (esk35_4 @ X1010 @ X1011 @ X1012 @ X1013) @ X1011)|((dsetconstr @ X1010 @ X1012)=(dsetconstr @ X1011 @ X1013))|((X1010)!=(X1011)))&((((esk34_4 @ X1010 @ X1011 @ X1012 @ X1013)=(esk35_4 @ X1010 @ X1011 @ X1012 @ X1013))|((dsetconstr @ X1010 @ X1012)=(dsetconstr @ X1011 @ X1013))|((X1010)!=(X1011)))&((~(X1012 @ (esk34_4 @ X1010 @ X1011 @ X1012 @ X1013))|~(X1013 @ (esk35_4 @ X1010 @ X1011 @ X1012 @ X1013))|((dsetconstr @ X1010 @ X1012)=(dsetconstr @ X1011 @ X1013))|((X1010)!=(X1011)))&((X1012 @ (esk34_4 @ X1010 @ X1011 @ X1012 @ X1013))|(X1013 @ (esk35_4 @ X1010 @ X1011 @ X1012 @ X1013))|((dsetconstr @ X1010 @ X1012)=(dsetconstr @ X1011 @ X1013))|((X1010)!=(X1011)))))))&((((in @ (esk36_2 @ X1016 @ X1017) @ X1016)|(subset @ X1016 @ X1017))&(~(in @ (esk36_2 @ X1016 @ X1017) @ X1017)|(subset @ X1016 @ X1017)))&((((X1019)!=(X1020))|(subset @ X1020 @ X1019))&((((X1021)!=(X1022))|(subset @ X1021 @ X1022))&((((in @ (esk37_2 @ X1023 @ X1024) @ X1023)|(subset @ X1023 @ X1024))&(~(in @ (esk37_2 @ X1023 @ X1024) @ X1024)|(subset @ X1023 @ X1024)))&((subset @ emptyset @ X1026)&((~(subset @ X1027 @ X1028)|(~(in @ X1029 @ X1027)|(in @ X1029 @ X1028)))&((~(subset @ X1030 @ X1031)|((in @ X1032 @ X1031)|~(in @ X1032 @ X1030)))&((~(in @ X1035 @ X1033)|((in @ X1035 @ X1034)|~(subset @ X1033 @ X1034)))&(((subset @ X1036 @ X1037)|((X1036)!=(X1037)))&((~(in @ X1040 @ X1038)|((in @ X1040 @ X1039)|((X1038)!=(X1039))))&((subset @ X1041 @ X1041)&((~(subset @ X1042 @ X1043)|(~(subset @ X1043 @ X1044)|(subset @ X1042 @ X1044)))&((subset @ X1046 @ (setadjoin @ X1045 @ X1046))&((~(subset @ X1047 @ X1049)|(subset @ X1047 @ (setadjoin @ X1048 @ X1049)))&((~(subset @ X1050 @ X1051)|(in @ X1050 @ (powerset @ X1051)))&((~(subset @ X1052 @ X1053)|(~(subset @ X1053 @ X1052)|((X1052)=(X1053))))&((~(subset @ X1054 @ emptyset)|((X1054)=(emptyset)))&((~(subset @ X1056 @ X1055)|(in @ X1056 @ (powerset @ X1055)))&((~(in @ X1058 @ (powerset @ X1057))|(subset @ X1058 @ X1057))&((in @ X1059 @ (powerset @ X1059))&((~(subset @ X1060 @ X1061)|(subset @ (powerset @ X1060) @ (powerset @ X1061)))&((in @ (dsetconstr @ X1062 @ X1063) @ (powerset @ X1062))&((subset @ (dsetconstr @ X1064 @ X1065) @ X1064)&((~(in @ X1068 @ X1066)|(in @ X1068 @ (binunion @ X1066 @ X1067)))&((in @ X1070 @ (setadjoin @ X1069 @ (setadjoin @ X1070 @ emptyset)))&((~(in @ X1073 @ X1072)|(in @ X1073 @ (binunion @ X1071 @ X1072)))&(((((in @ X1076 @ X1075)|(X1077)|(in @ X1076 @ X1074)|~(in @ X1076 @ (binunion @ X1074 @ X1075)))&(~(X1077)|(X1077)|(in @ X1076 @ X1074)|~(in @ X1076 @ (binunion @ X1074 @ X1075))))&(((in @ X1076 @ X1075)|(X1077)|~(X1077)|~(in @ X1076 @ (binunion @ X1074 @ X1075)))&(~(X1077)|(X1077)|~(X1077)|~(in @ X1076 @ (binunion @ X1074 @ X1075)))))&((~(in @ X1080 @ (binunion @ X1078 @ X1079))|((in @ X1080 @ X1078)|(in @ X1080 @ X1079)))&((subset @ X1081 @ (binunion @ X1081 @ X1082))&((subset @ X1084 @ (binunion @ X1083 @ X1084))&((~(in @ X1087 @ X1085)|(~(in @ X1087 @ X1086)|(in @ X1087 @ (binintersect @ X1085 @ X1086))))&((~(subset @ X1090 @ X1088)|(~(subset @ X1090 @ X1089)|(subset @ X1090 @ (binintersect @ X1088 @ X1089))))&((~(in @ X1093 @ (binintersect @ X1091 @ X1092))|(in @ X1093 @ X1091))&((subset @ (binintersect @ X1094 @ X1095) @ X1094)&((~(subset @ X1096 @ X1097)|((binintersect @ X1096 @ X1097)=(X1096)))&((((binintersect @ X1098 @ X1099)!=(X1099))|(subset @ X1099 @ X1098))&((~(in @ X1102 @ (binintersect @ X1100 @ X1101))|(in @ X1102 @ X1101))&((((in @ (esk38_2 @ X1103 @ X1104) @ X1103)|((binintersect @ X1103 @ X1104)=(emptyset)))&((in @ (esk38_2 @ X1103 @ X1104) @ X1104)|((binintersect @ X1103 @ X1104)=(emptyset))))&((subset @ (binintersect @ X1106 @ X1107) @ X1107)&((~(subset @ X1109 @ X1108)|((binintersect @ X1108 @ X1109)=(X1109)))&((((binintersect @ X1110 @ X1111)!=(X1110))|(subset @ X1110 @ X1111))&(((binintersect @ X1112 @ (binunion @ X1113 @ X1114))=(binunion @ (binintersect @ X1112 @ X1113) @ (binintersect @ X1112 @ X1114)))&((~(in @ X1117 @ X1115)|((in @ X1117 @ X1116)|(in @ X1117 @ (setminus @ X1115 @ X1116))))&((~(in @ X1120 @ (setminus @ X1118 @ X1119))|(in @ X1120 @ X1118))&((~(in @ X1123 @ (setminus @ X1121 @ X1122))|~(in @ X1123 @ X1122))&((~(subset @ X1124 @ X1125)|((setminus @ X1124 @ X1125)=(emptyset)))&(((in @ X1128 @ (setminus @ X1126 @ X1127))|(~(in @ X1128 @ X1126)|(in @ X1128 @ X1127)))&(((in @ X1131 @ (setminus @ X1129 @ X1130))|((in @ X1131 @ X1130)|~(in @ X1131 @ X1129)))&(((in @ X1134 @ X1132)|~(in @ X1134 @ (setminus @ X1132 @ X1133)))&((~(in @ X1137 @ X1136)|~(in @ X1137 @ (setminus @ X1135 @ X1136)))&((subset @ (setminus @ X1138 @ X1139) @ X1138)&((((setminus @ X1140 @ X1141)!=(emptyset))|(subset @ X1140 @ X1141))&((((~(in @ X1144 @ X1142)|(X1145)|(in @ X1144 @ X1142)|~(in @ X1144 @ (symdiff @ X1142 @ X1143)))&(((in @ X1144 @ X1143)|(X1145)|(in @ X1144 @ X1142)|~(in @ X1144 @ (symdiff @ X1142 @ X1143)))&(~(X1145)|(X1145)|(in @ X1144 @ X1142)|~(in @ X1144 @ (symdiff @ X1142 @ X1143)))))&(((~(in @ X1144 @ X1142)|(X1145)|~(in @ X1144 @ X1143)|~(in @ X1144 @ (symdiff @ X1142 @ X1143)))&(((in @ X1144 @ X1143)|(X1145)|~(in @ X1144 @ X1143)|~(in @ X1144 @ (symdiff @ X1142 @ X1143)))&(~(X1145)|(X1145)|~(in @ X1144 @ X1143)|~(in @ X1144 @ (symdiff @ X1142 @ X1143)))))&((~(in @ X1144 @ X1142)|(X1145)|~(X1145)|~(in @ X1144 @ (symdiff @ X1142 @ X1143)))&(((in @ X1144 @ X1143)|(X1145)|~(X1145)|~(in @ X1144 @ (symdiff @ X1142 @ X1143)))&(~(X1145)|(X1145)|~(X1145)|~(in @ X1144 @ (symdiff @ X1142 @ X1143)))))))&((~(in @ X1148 @ X1146)|((in @ X1148 @ X1147)|(in @ X1148 @ (symdiff @ X1146 @ X1147))))&(((in @ X1151 @ X1149)|(~(in @ X1151 @ X1150)|(in @ X1151 @ (symdiff @ X1149 @ X1150))))&((~(in @ X1154 @ X1152)|(~(in @ X1154 @ X1153)|~(in @ X1154 @ (symdiff @ X1152 @ X1153))))&(((in @ X1157 @ X1155)|((in @ X1157 @ X1156)|~(in @ X1157 @ (symdiff @ X1155 @ X1156))))&((in @ X1159 @ (setadjoin @ X1158 @ (setadjoin @ X1159 @ emptyset)))&((in @ X1160 @ (setunion @ (setadjoin @ (setadjoin @ X1160 @ emptyset) @ (setadjoin @ (setadjoin @ X1160 @ (setadjoin @ X1161 @ emptyset)) @ emptyset))))&((in @ X1163 @ (setunion @ (setadjoin @ (setadjoin @ X1162 @ emptyset) @ (setadjoin @ (setadjoin @ X1162 @ (setadjoin @ X1163 @ emptyset)) @ emptyset))))&((iskpair @ (setadjoin @ (setadjoin @ X1164 @ emptyset) @ (setadjoin @ (setadjoin @ X1164 @ (setadjoin @ X1165 @ emptyset)) @ emptyset)))&((iskpair @ (kpair @ X1166 @ X1167))&((~(in @ X1169 @ X1168)|(subset @ (setadjoin @ X1169 @ emptyset) @ X1168))&((~(in @ X1171 @ X1170)|(in @ (setadjoin @ X1171 @ emptyset) @ (powerset @ X1170)))&((~(in @ X1174 @ X1172)|(in @ (setadjoin @ X1174 @ emptyset) @ (powerset @ (binunion @ X1172 @ X1173))))&((~(in @ X1177 @ (setadjoin @ X1175 @ (setadjoin @ X1176 @ emptyset)))|(((X1177)=(X1175))|((X1177)=(X1176))))&((~(in @ X1180 @ X1178)|(~(in @ X1181 @ X1179)|(subset @ (setadjoin @ X1180 @ (setadjoin @ X1181 @ emptyset)) @ (binunion @ X1178 @ X1179))))&((~(in @ X1184 @ X1182)|(~(in @ X1185 @ X1183)|(in @ (setadjoin @ X1184 @ (setadjoin @ X1185 @ emptyset)) @ (powerset @ (binunion @ X1182 @ X1183)))))&((~(in @ X1188 @ X1186)|(~(in @ X1189 @ X1187)|(subset @ (setadjoin @ (setadjoin @ X1188 @ emptyset) @ (setadjoin @ (setadjoin @ X1188 @ (setadjoin @ X1189 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X1186 @ X1187)))))&((~(in @ X1192 @ X1190)|(~(in @ X1193 @ X1191)|(in @ (setadjoin @ (setadjoin @ X1192 @ emptyset) @ (setadjoin @ (setadjoin @ X1192 @ (setadjoin @ X1193 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1190 @ X1191))))))&((~(in @ X1196 @ X1194)|(~(in @ X1197 @ X1195)|(in @ (kpair @ X1196 @ X1197) @ (powerset @ (powerset @ (binunion @ X1194 @ X1195))))))&((in @ esk41_0 @ esk39_0)&((in @ esk42_0 @ esk40_0)&~(in @ (kpair @ esk41_0 @ esk42_0) @ (cartprod @ esk39_0 @ esk40_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_170])])])])])])])).
118.52/15.57	thf(c_0_173, plain, ![X1202:$i, X1203:$i]:(((cartprod @ X1202 @ X1203)=(dsetconstr @ (powerset @ (powerset @ (binunion @ X1202 @ X1203))) @ (^[Z0/* 5 */:$i]:(?[X3:$i]:(((in @ X3 @ X1202)&?[X14:$i]:(((in @ X14 @ X1203)&((Z0)=(kpair @ X3 @ X14))))))))))), inference(variable_rename,[status(thm)],[c_0_171])).
118.52/15.57	thf(c_0_174, plain, ![X1228:$i, X2:$i, X3:$i]:(((epred3_2 @ X3 @ X2 @ X1228)<=>?[X1226:$i]:(((in @ X1226 @ X2)&?[X1227:$i]:(((in @ X1227 @ X3)&((X1228)=(kpair @ X1226 @ X1227)))))))), introduced(definition)).
118.52/15.57	thf(c_0_175, negated_conjecture, ![X1:$i > $o, X2:$i, X3:$i]:(((in @ X2 @ (dsetconstr @ X3 @ X1))|~((X1 @ X2))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_172])).
118.52/15.57	thf(c_0_176, plain, ![X3:$i, X2:$i]:(((cartprod @ X2 @ X3)=(dsetconstr @ (powerset @ (powerset @ (binunion @ X2 @ X3))) @ (epred3_2 @ X3 @ X2)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_173]), c_0_174])).
118.52/15.57	thf(c_0_177, negated_conjecture, ~((in @ (kpair @ esk41_0 @ esk42_0) @ (cartprod @ esk39_0 @ esk40_0))), inference(split_conjunct,[status(thm)],[c_0_172])).
118.52/15.57	thf(c_0_178, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:(((in @ X2 @ (cartprod @ X3 @ X4))|~((in @ X2 @ (powerset @ (powerset @ (binunion @ X3 @ X4)))))|~((epred3_2 @ X4 @ X3 @ X2)))), inference(spm,[status(thm)],[c_0_175, c_0_176])).
118.52/15.57	thf(c_0_179, plain, ![X1230:$i, X1231:$i, X1232:$i, X1235:$i, X1236:$i, X1237:$i, X1238:$i, X1239:$i]:(((((in @ (esk48_3 @ X1230 @ X1231 @ X1232) @ X1231)|~(epred3_2 @ X1232 @ X1231 @ X1230))&(((in @ (esk49_3 @ X1230 @ X1231 @ X1232) @ X1232)|~(epred3_2 @ X1232 @ X1231 @ X1230))&(((X1230)=(kpair @ (esk48_3 @ X1230 @ X1231 @ X1232) @ (esk49_3 @ X1230 @ X1231 @ X1232)))|~(epred3_2 @ X1232 @ X1231 @ X1230))))&(~(in @ X1238 @ X1236)|(~(in @ X1239 @ X1237)|((X1235)!=(kpair @ X1238 @ X1239)))|(epred3_2 @ X1237 @ X1236 @ X1235)))), 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)],[])])])])])])])).
118.52/15.57	thf(c_0_180, negated_conjecture, (~((in @ (kpair @ esk41_0 @ esk42_0) @ (powerset @ (powerset @ (binunion @ esk39_0 @ esk40_0)))))|~((epred3_2 @ esk40_0 @ esk39_0 @ (kpair @ esk41_0 @ esk42_0)))), inference(spm,[status(thm)],[c_0_177, c_0_178])).
118.52/15.57	thf(c_0_181, negated_conjecture, ![X2:$i, X3:$i, X4:$i, X5:$i]:(((in @ (kpair @ X2 @ X4) @ (powerset @ (powerset @ (binunion @ X3 @ X5))))|~((in @ X2 @ X3))|~((in @ X4 @ X5)))), inference(split_conjunct,[status(thm)],[c_0_172])).
118.52/15.57	thf(c_0_182, negated_conjecture, (in @ esk42_0 @ esk40_0), inference(split_conjunct,[status(thm)],[c_0_172])).
118.52/15.57	thf(c_0_183, negated_conjecture, (in @ esk41_0 @ esk39_0), inference(split_conjunct,[status(thm)],[c_0_172])).
118.52/15.57	thf(c_0_184, plain, ![X7:$i, X3:$i, X2:$i, X5:$i, X4:$i]:(((epred3_2 @ X5 @ X3 @ X7)|~((in @ X2 @ X3))|~((in @ X4 @ X5))|((X7)!=(kpair @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_179])).
118.52/15.57	thf(c_0_185, negated_conjecture, ~((epred3_2 @ esk40_0 @ esk39_0 @ (kpair @ esk41_0 @ esk42_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180, c_0_181]), c_0_182]), c_0_183])])).
118.52/15.57	thf(c_0_186, plain, ![X2:$i, X5:$i, X4:$i, X3:$i]:(((epred3_2 @ X2 @ X3 @ (kpair @ X4 @ X5))|~((in @ X5 @ X2))|~((in @ X4 @ X3)))), inference(er,[status(thm)],[c_0_184])).
118.52/15.57	thf(c_0_187, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185, c_0_186]), c_0_182]), c_0_183])]), ['proof']).
118.52/15.57	# SZS output end CNFRefutation
118.52/15.57	# Parsed axioms                        : 321
118.52/15.57	# Removed by relevancy pruning/SinE    : 173
118.52/15.57	# Initial clauses                      : 234
118.52/15.57	# Removed in clause preprocessing      : 25
118.52/15.57	# Initial clauses in saturation        : 209
118.52/15.57	# Processed clauses                    : 4727
118.52/15.57	# ...of these trivial                  : 118
118.52/15.57	# ...subsumed                          : 1554
118.52/15.57	# ...remaining for further processing  : 3055
118.52/15.57	# Other redundant clauses eliminated   : 90
118.52/15.57	# Clauses deleted for lack of memory   : 0
118.52/15.57	# Backward-subsumed                    : 439
118.52/15.57	# Backward-rewritten                   : 47
118.52/15.57	# Generated clauses                    : 497346
118.52/15.57	# ...of the previous two non-redundant : 492938
118.52/15.57	# ...aggressively subsumed             : 0
118.52/15.57	# Contextual simplify-reflections      : 10
118.52/15.57	# Paramodulations                      : 497135
118.52/15.57	# Factorizations                       : 110
118.52/15.57	# NegExts                              : 0
118.52/15.57	# Equation resolutions                 : 90
118.52/15.57	# Disequality decompositions           : 0
118.52/15.57	# Total rewrite steps                  : 8994
118.52/15.57	# ...of those cached                   : 8018
118.52/15.57	# Propositional unsat checks           : 0
118.52/15.57	#    Propositional check models        : 0
118.52/15.57	#    Propositional check unsatisfiable : 0
118.52/15.57	#    Propositional clauses             : 0
118.52/15.57	#    Propositional clauses after purity: 0
118.52/15.57	#    Propositional unsat core size     : 0
118.52/15.57	#    Propositional preprocessing time  : 0.000
118.52/15.57	#    Propositional encoding time       : 0.000
118.52/15.57	#    Propositional solver time         : 0.000
118.52/15.57	#    Success case prop preproc time    : 0.000
118.52/15.57	#    Success case prop encoding time   : 0.000
118.52/15.57	#    Success case prop solver time     : 0.000
118.52/15.57	# Current number of processed clauses  : 2373
118.52/15.57	#    Positive orientable unit clauses  : 171
118.52/15.57	#    Positive unorientable unit clauses: 0
118.52/15.57	#    Negative unit clauses             : 125
118.52/15.57	#    Non-unit-clauses                  : 2077
118.52/15.57	# Current number of unprocessed clauses: 486990
118.52/15.57	# ...number of literals in the above   : 2114932
118.52/15.57	# Current number of archived formulas  : 0
118.52/15.57	# Current number of archived clauses   : 670
118.52/15.57	# Clause-clause subsumption calls (NU) : 593691
118.52/15.57	# Rec. Clause-clause subsumption calls : 302595
118.52/15.57	# Non-unit clause-clause subsumptions  : 711
118.52/15.57	# Unit Clause-clause subsumption calls : 21499
118.52/15.57	# Rewrite failures with RHS unbound    : 0
118.52/15.57	# BW rewrite match attempts            : 270
118.52/15.57	# BW rewrite match successes           : 44
118.52/15.57	# Condensation attempts                : 4727
118.52/15.57	# Condensation successes               : 26
118.52/15.57	# Termbank termtop insertions          : 9987275
118.52/15.57	# Search garbage collected termcells   : 12942
118.52/15.57	
118.52/15.57	# -------------------------------------------------
118.52/15.57	# User time                : 14.195 s
118.52/15.57	# System time              : 0.472 s
118.52/15.57	# Total time               : 14.667 s
118.52/15.57	# Maximum resident set size: 5048 pages
118.52/15.57	
118.52/15.57	# -------------------------------------------------
118.52/15.57	# User time                : 14.203 s
118.52/15.57	# System time              : 0.476 s
118.52/15.57	# Total time               : 14.680 s
118.52/15.57	# Maximum resident set size: 2096 pages
118.52/15.57	% E exiting
118.52/15.57	% E exiting
118.52/15.57	EOF