0.04/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.04/0.12	% Command    : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 240 THM
0.13/0.33	% Computer : n023.cluster.edu
0.13/0.33	% Model    : x86_64 x86_64
0.13/0.33	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.33	% Memory   : 8042.1875MB
0.13/0.33	% OS       : Linux 3.10.0-693.el7.x86_64
0.13/0.34	% CPULimit   : 1920
0.13/0.34	% WCLimit    : 240
0.13/0.34	% DateTime   : Wed Jul 30 02:19:34 EDT 2025
0.13/0.34	% CPUTime    : 
0.20/0.48	Running higher-order theorem proving
0.20/0.50	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.OIMAA4A9TE/E---3.1_8814.p
0.46/240.02	# Version: 3.0.0-ho
0.46/240.02	# Preprocessing class: HSMSSLSSLLLCHFA.
0.46/240.02	# Scheduled 4 strats onto 8 cores with 240 seconds (1920 total)
0.46/240.02	# Starting new_ho_10 with 1200s (5) cores
0.46/240.02	# Starting sh5l with 240s (1) cores
0.46/240.02	# Starting new_bool_1 with 240s (1) cores
0.46/240.02	# Starting new_bool_2 with 240s (1) cores
0.46/240.02	# new_bool_2 with pid 8901 completed with status 0
0.46/240.02	# Result found by new_bool_2
0.46/240.02	# Preprocessing class: HSMSSLSSLLLCHFA.
0.46/240.02	# Scheduled 4 strats onto 8 cores with 240 seconds (1920 total)
0.46/240.02	# Starting new_ho_10 with 1200s (5) cores
0.46/240.02	# Starting sh5l with 240s (1) cores
0.46/240.02	# Starting new_bool_1 with 240s (1) cores
0.46/240.02	# Starting new_bool_2 with 240s (1) cores
0.46/240.02	# SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
0.46/240.02	# Search class: HGHSM-FSLM31-SHFMMMBN
0.46/240.02	# Scheduled 6 strats onto 1 cores with 240 seconds (240 total)
0.46/240.02	# Starting ho_unfolding_3 with 130s (1) cores
0.46/240.02	# ho_unfolding_3 with pid 8905 completed with status 0
0.46/240.02	# Result found by ho_unfolding_3
0.46/240.02	# Preprocessing class: HSMSSLSSLLLCHFA.
0.46/240.02	# Scheduled 4 strats onto 8 cores with 240 seconds (1920 total)
0.46/240.02	# Starting new_ho_10 with 1200s (5) cores
0.46/240.02	# Starting sh5l with 240s (1) cores
0.46/240.02	# Starting new_bool_1 with 240s (1) cores
0.46/240.02	# Starting new_bool_2 with 240s (1) cores
0.46/240.02	# SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
0.46/240.02	# Search class: HGHSM-FSLM31-SHFMMMBN
0.46/240.02	# Scheduled 6 strats onto 1 cores with 240 seconds (240 total)
0.46/240.02	# Starting ho_unfolding_3 with 130s (1) cores
0.46/240.02	# Preprocessing time       : 0.005 s
0.46/240.02	# Presaturation interreduction done
0.46/240.02	
0.46/240.02	# Proof found!
0.46/240.02	# SZS status Theorem
0.46/240.02	# SZS output start CNFRefutation
0.46/240.02	thf(decl_23, type, in: $i > $i > $o).
0.46/240.02	thf(decl_24, type, exu: ($i > $o) > $o).
0.46/240.02	thf(decl_25, type, setextAx: $o).
0.46/240.02	thf(decl_26, type, emptyset: $i).
0.46/240.02	thf(decl_27, type, emptysetAx: $o).
0.46/240.02	thf(decl_28, type, setadjoin: $i > $i > $i).
0.46/240.02	thf(decl_29, type, setadjoinAx: $o).
0.46/240.02	thf(decl_30, type, powerset: $i > $i).
0.46/240.02	thf(decl_31, type, powersetAx: $o).
0.46/240.02	thf(decl_32, type, setunion: $i > $i).
0.46/240.02	thf(decl_33, type, setunionAx: $o).
0.46/240.02	thf(decl_34, type, omega: $i).
0.46/240.02	thf(decl_35, type, omega0Ax: $o).
0.46/240.02	thf(decl_36, type, omegaSAx: $o).
0.46/240.02	thf(decl_37, type, omegaIndAx: $o).
0.46/240.02	thf(decl_38, type, replAx: $o).
0.46/240.02	thf(decl_39, type, foundationAx: $o).
0.46/240.02	thf(decl_40, type, wellorderingAx: $o).
0.46/240.02	thf(decl_41, type, descr: ($i > $o) > $i).
0.46/240.02	thf(decl_42, type, descrp: $o).
0.46/240.02	thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
0.46/240.02	thf(decl_44, type, dsetconstrI: $o).
0.46/240.02	thf(decl_45, type, dsetconstrEL: $o).
0.46/240.02	thf(decl_46, type, dsetconstrER: $o).
0.46/240.02	thf(decl_47, type, exuE1: $o).
0.46/240.02	thf(decl_48, type, prop2set: $o > $i).
0.46/240.02	thf(decl_49, type, prop2setE: $o).
0.46/240.02	thf(decl_50, type, emptysetE: $o).
0.46/240.02	thf(decl_51, type, emptysetimpfalse: $o).
0.46/240.02	thf(decl_52, type, notinemptyset: $o).
0.46/240.02	thf(decl_53, type, exuE3e: $o).
0.46/240.02	thf(decl_54, type, setext: $o).
0.46/240.02	thf(decl_55, type, emptyI: $o).
0.46/240.02	thf(decl_56, type, noeltsimpempty: $o).
0.46/240.02	thf(decl_57, type, setbeta: $o).
0.46/240.02	thf(decl_58, type, nonempty: $i > $o).
0.46/240.02	thf(decl_59, type, nonemptyE1: $o).
0.46/240.02	thf(decl_60, type, nonemptyI: $o).
0.46/240.02	thf(decl_61, type, nonemptyI1: $o).
0.46/240.02	thf(decl_62, type, setadjoinIL: $o).
0.46/240.02	thf(decl_63, type, emptyinunitempty: $o).
0.46/240.02	thf(decl_64, type, setadjoinIR: $o).
0.46/240.02	thf(decl_65, type, setadjoinE: $o).
0.46/240.02	thf(decl_66, type, setadjoinOr: $o).
0.46/240.02	thf(decl_67, type, setoftrueEq: $o).
0.46/240.02	thf(decl_68, type, powersetI: $o).
0.46/240.02	thf(decl_69, type, emptyinPowerset: $o).
0.46/240.02	thf(decl_70, type, emptyInPowerset: $o).
0.46/240.02	thf(decl_71, type, powersetE: $o).
0.46/240.02	thf(decl_72, type, setunionI: $o).
0.46/240.02	thf(decl_73, type, setunionE: $o).
0.46/240.02	thf(decl_74, type, subPowSU: $o).
0.46/240.02	thf(decl_75, type, exuE2: $o).
0.46/240.02	thf(decl_76, type, nonemptyImpWitness: $o).
0.46/240.02	thf(decl_77, type, uniqinunit: $o).
0.46/240.02	thf(decl_78, type, notinsingleton: $o).
0.46/240.02	thf(decl_79, type, eqinunit: $o).
0.46/240.02	thf(decl_80, type, singletonsswitch: $o).
0.46/240.02	thf(decl_81, type, upairsetE: $o).
0.46/240.02	thf(decl_82, type, upairsetIL: $o).
0.46/240.02	thf(decl_83, type, upairsetIR: $o).
0.46/240.02	thf(decl_84, type, emptyE1: $o).
0.46/240.02	thf(decl_85, type, vacuousDall: $o).
0.46/240.02	thf(decl_86, type, quantDeMorgan1: $o).
0.46/240.02	thf(decl_87, type, quantDeMorgan2: $o).
0.46/240.02	thf(decl_88, type, quantDeMorgan3: $o).
0.46/240.02	thf(decl_89, type, quantDeMorgan4: $o).
0.46/240.02	thf(decl_90, type, prop2setI: $o).
0.46/240.02	thf(decl_92, type, prop2set2propI: $o).
0.46/240.02	thf(decl_93, type, notdexE: $o).
0.46/240.02	thf(decl_94, type, notdallE: $o).
0.46/240.02	thf(decl_95, type, exuI1: $o).
0.46/240.02	thf(decl_96, type, exuI3: $o).
0.46/240.02	thf(decl_97, type, exuI2: $o).
0.46/240.02	thf(decl_98, type, inCongP: $o).
0.46/240.02	thf(decl_99, type, in__Cong: $o).
0.46/240.02	thf(decl_100, type, exuE3u: $o).
0.46/240.02	thf(decl_101, type, exu__Cong: $o).
0.46/240.02	thf(decl_102, type, emptyset__Cong: $o).
0.46/240.02	thf(decl_103, type, setadjoin__Cong: $o).
0.46/240.02	thf(decl_104, type, powerset__Cong: $o).
0.46/240.02	thf(decl_105, type, setunion__Cong: $o).
0.46/240.02	thf(decl_106, type, omega__Cong: $o).
0.46/240.02	thf(decl_107, type, exuEu: $o).
0.46/240.02	thf(decl_108, type, descr__Cong: $o).
0.46/240.02	thf(decl_109, type, dsetconstr__Cong: $o).
0.46/240.02	thf(decl_110, type, subset: $i > $i > $o).
0.46/240.02	thf(decl_113, type, subsetI1: $o).
0.46/240.02	thf(decl_114, type, eqimpsubset2: $o).
0.46/240.02	thf(decl_115, type, epred1_0: $o).
0.46/240.02	thf(decl_116, type, esk1_2: $i > $i > $i).
0.46/240.02	thf(decl_117, type, esk2_2: $i > $i > $i).
0.46/240.02	thf(decl_118, type, esk3_2: $i > $i > $i).
0.46/240.02	thf(decl_119, type, esk4_1: $i > $i).
0.46/240.02	thf(decl_120, type, esk5_2: ($i > $i > $o) > $i > $i).
0.46/240.02	thf(decl_121, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
0.46/240.02	thf(decl_122, type, esk7_2: ($i > $i > $o) > $i > $i).
0.46/240.02	thf(decl_123, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
0.46/240.02	thf(decl_124, type, esk9_1: $i > $i).
0.46/240.02	thf(decl_125, type, esk10_2: ($i > $o) > $i > $i).
0.46/240.02	thf(decl_126, type, esk11_2: ($i > $o) > $i > $i).
0.46/240.02	thf(decl_127, type, esk12_1: ($i > $o) > $i).
0.46/240.02	thf(decl_128, type, esk13_2: ($i > $o) > $i > $i).
0.46/240.02	thf(decl_129, type, esk14_1: ($i > $o) > $i).
0.46/240.02	thf(decl_130, type, esk15_2: $i > $i > $i).
0.46/240.02	thf(decl_131, type, esk16_2: $i > $i > $i).
0.46/240.02	thf(decl_132, type, esk17_1: $i > $i).
0.46/240.02	thf(decl_133, type, esk18_1: $i > $i).
0.46/240.02	thf(decl_134, type, esk19_1: $i > $i).
0.46/240.02	thf(decl_135, type, esk20_2: $i > $i > $i).
0.46/240.02	thf(decl_136, type, esk21_3: $i > $i > $o > $i).
0.46/240.02	thf(decl_137, type, esk22_2: ($i > $o) > $i > $i).
0.46/240.02	thf(decl_138, type, esk23_1: ($i > $o) > $i).
0.46/240.02	thf(decl_139, type, esk24_1: $i > $i).
0.46/240.02	thf(decl_140, type, esk25_2: $i > ($i > $o) > $i).
0.46/240.02	thf(decl_141, type, esk26_2: $i > ($i > $o) > $i).
0.46/240.02	thf(decl_142, type, esk27_2: $i > ($i > $o) > $i).
0.46/240.02	thf(decl_143, type, esk28_2: $i > ($i > $o) > $i).
0.46/240.02	thf(decl_144, type, esk29_2: $i > ($i > $o) > $i).
0.46/240.02	thf(decl_145, type, esk30_2: $i > ($i > $o) > $i).
0.46/240.02	thf(decl_146, type, esk31_2: ($i > $o) > $i > $i).
0.46/240.02	thf(decl_147, type, esk32_1: ($i > $o) > $i).
0.46/240.02	thf(decl_148, type, esk33_1: ($i > $o) > $i).
0.46/240.02	thf(decl_149, type, esk34_1: ($i > $o) > $i).
0.46/240.02	thf(decl_150, type, esk35_1: ($i > $o) > $i).
0.46/240.02	thf(decl_151, type, esk36_2: ($i > $o) > $i > $i).
0.46/240.02	thf(decl_152, type, esk37_1: ($i > $o) > $i).
0.46/240.02	thf(decl_153, type, esk38_2: ($i > $o) > $i > $i).
0.46/240.02	thf(decl_154, type, esk39_2: ($i > $o) > ($i > $o) > $i).
0.46/240.02	thf(decl_155, type, esk40_2: ($i > $o) > ($i > $o) > $i).
0.46/240.02	thf(decl_156, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
0.46/240.02	thf(decl_157, type, esk42_2: ($i > $o) > ($i > $o) > $i).
0.46/240.02	thf(decl_158, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
0.46/240.02	thf(decl_159, type, esk44_2: ($i > $o) > ($i > $o) > $i).
0.46/240.02	thf(decl_160, type, esk45_2: ($i > $o) > $i > $i).
0.46/240.02	thf(decl_161, type, esk46_2: ($i > $o) > ($i > $o) > $i).
0.46/240.02	thf(decl_162, type, esk47_2: ($i > $o) > ($i > $o) > $i).
0.46/240.02	thf(decl_163, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
0.46/240.02	thf(decl_164, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
0.46/240.02	thf(decl_165, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
0.46/240.02	thf(decl_166, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
0.46/240.02	thf(decl_167, type, esk52_2: $i > $i > $i).
0.46/240.02	thf(decl_168, type, esk53_0: $i).
0.46/240.02	thf(decl_169, type, esk54_0: $i).
0.46/240.02	thf(decl_170, type, esk55_0: $i).
0.46/240.02	thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', nonempty)).
0.46/240.02	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', exuE3e)).
0.46/240.02	thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', exu)).
0.46/240.02	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', descrp)).
0.46/240.02	thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', exuE2)).
0.46/240.02	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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', replAx)).
0.46/240.02	thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', exu__Cong)).
0.46/240.02	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', exuI3)).
0.46/240.02	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', exuEu)).
0.46/240.02	thf(subset, axiom, ((subset)=(^[X4:$i, X5:$i]:(![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', subset)).
0.46/240.02	thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', descr__Cong)).
0.46/240.02	thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', exuE3u)).
0.46/240.02	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.OIMAA4A9TE/E---3.1_8814.p', exuI2)).
0.46/240.02	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.OIMAA4A9TE/E---3.1_8814.p', exuI1)).
0.46/240.02	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', nonemptyI)).
0.46/240.02	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', exuE1)).
0.46/240.02	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', nonemptyI1)).
0.46/240.02	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', setoftrueEq)).
0.46/240.02	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', dsetconstrEL)).
0.46/240.02	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', dsetconstrI)).
0.46/240.02	thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.OIMAA4A9TE/E---3.1_8814.p', emptyE1)).
0.46/240.02	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', eqimpsubset2)).
0.46/240.02	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', subsetI1)).
0.46/240.02	thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', dsetconstr__Cong)).
0.46/240.02	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', nonemptyImpWitness)).
0.46/240.02	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', nonemptyE1)).
0.46/240.02	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', setbeta)).
0.46/240.02	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', dsetconstrER)).
0.46/240.02	thf(eqimpsubset1, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>(((omegaIndAx)=>((((((((dsetconstrER)=>((exuE1)=>(((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((((emptyI)=>(((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>(((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>(((setoftrueEq)=>(((emptyinPowerset)=>(((((setunionE)=>((subPowSU)=>((exuE2)=>((((notinsingleton)=>((eqinunit)=>((((((emptyE1)=>((((((quantDeMorgan4)=>(((((((exuI3)=>((((((((((((exuEu)=>(((((eqimpsubset2)=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5))))<=(subsetI1))<=(dsetconstr__Cong))<=(descr__Cong)))<=(omega__Cong))<=(setunion__Cong))<=(powerset__Cong))<=(setadjoin__Cong))<=(emptyset__Cong))<=(exu__Cong))<=(exuE3u))<=(in__Cong))<=(inCongP))<=(exuI2)))<=(exuI1))<=(notdallE))<=(notdexE))<=(prop2set2propI))<=(prop2setI)))<=(quantDeMorgan3))<=(quantDeMorgan2))<=(quantDeMorgan1))<=(vacuousDall)))<=(upairsetIR))<=(upairsetIL))<=(upairsetE))<=(singletonsswitch))))<=(uniqinunit))<=(nonemptyImpWitness)))))<=(setunionI))<=(powersetE))<=(emptyInPowerset)))<=(powersetI)))<=(setadjoinOr)))))<=(setadjoinIL))))))<=(noeltsimpempty)))<=(setext))<=(exuE3e)))))<=(prop2setE))))<=(dsetconstrEL))<=(dsetconstrI))<=(descrp))<=(wellorderingAx))<=(foundationAx))<=(replAx)))<=(omegaSAx)))))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', eqimpsubset1)).
0.46/240.02	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', omegaSAx)).
0.46/240.02	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', emptyInPowerset)).
0.46/240.02	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', powersetI)).
0.46/240.02	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', setadjoinOr)).
0.46/240.02	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', setadjoinIL)).
0.46/240.02	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', noeltsimpempty)).
0.46/240.02	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', emptyinPowerset)).
0.46/240.02	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.OIMAA4A9TE/E---3.1_8814.p', setext)).
0.46/240.02	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.OIMAA4A9TE/E---3.1_8814.p', setunionE)).
0.46/240.02	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', prop2setE)).
0.46/240.02	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', subPowSU)).
0.46/240.02	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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', wellorderingAx)).
0.46/240.02	thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', foundationAx)).
0.46/240.02	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', notinsingleton)).
0.46/240.02	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', eqinunit)).
0.46/240.02	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', emptyinunitempty)).
0.46/240.02	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', quantDeMorgan4)).
0.46/240.02	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', setadjoinIR)).
0.46/240.02	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', omega__Cong)).
0.46/240.02	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', setunion__Cong)).
0.46/240.02	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', powerset__Cong)).
0.46/240.02	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.OIMAA4A9TE/E---3.1_8814.p', setadjoin__Cong)).
0.46/240.02	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', emptyset__Cong)).
0.46/240.02	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.OIMAA4A9TE/E---3.1_8814.p', in__Cong)).
0.46/240.02	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.OIMAA4A9TE/E---3.1_8814.p', inCongP)).
0.46/240.02	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', notdallE)).
0.46/240.02	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', notdexE)).
0.46/240.02	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', prop2setI)).
0.46/240.02	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', quantDeMorgan3)).
0.46/240.02	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', quantDeMorgan2)).
0.46/240.02	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', quantDeMorgan1)).
0.46/240.02	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', vacuousDall)).
0.46/240.02	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', upairsetIR)).
0.46/240.02	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', upairsetIL)).
0.46/240.02	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', upairsetE)).
0.46/240.02	thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', setadjoinE)).
0.46/240.02	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', singletonsswitch)).
0.46/240.02	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', uniqinunit)).
0.46/240.02	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', setunionI)).
0.46/240.02	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', powersetE)).
0.46/240.02	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', emptyI)).
0.46/240.02	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', notinemptyset)).
0.46/240.02	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', emptysetimpfalse)).
0.46/240.02	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', emptysetE)).
0.46/240.02	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', omegaIndAx)).
0.46/240.02	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', omega0Ax)).
0.46/240.02	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', setunionAx)).
0.46/240.02	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', powersetAx)).
0.46/240.02	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', setadjoinAx)).
0.46/240.02	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', emptysetAx)).
0.46/240.02	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.OIMAA4A9TE/E---3.1_8814.p', setextAx)).
0.46/240.02	thf(c_0_80, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
0.46/240.02	thf(c_0_81, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
0.46/240.02	thf(c_0_82, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])).
0.46/240.02	thf(c_0_83, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
0.46/240.02	thf(c_0_84, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
0.46/240.02	thf(c_0_85, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
0.46/240.02	thf(c_0_86, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
0.46/240.02	thf(c_0_87, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
0.46/240.02	thf(c_0_88, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
0.46/240.02	thf(c_0_89, plain, ((subset)=(^[Z0/* 19 */:$i, Z1:$i]:(![X2:$i]:(((in @ X2 @ Z0)=>(in @ X2 @ Z1)))))), inference(fof_simplification,[status(thm)],[subset])).
0.46/240.02	thf(c_0_90, plain, ((descr__Cong)<=>![X1:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
0.46/240.02	thf(c_0_91, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
0.46/240.02	thf(c_0_92, 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])).
0.46/240.02	thf(c_0_93, 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])).
0.46/240.02	thf(c_0_94, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
0.46/240.02	thf(c_0_95, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
0.46/240.02	thf(c_0_96, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_80])).
0.46/240.02	thf(c_0_97, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
0.46/240.02	thf(c_0_98, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X243:$i]:((((X1 @ X243))&![X244:$i]:((((X1 @ X244))=>((X243)=(X244)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_81, c_0_82])).
0.46/240.02	thf(c_0_99, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
0.46/240.02	thf(c_0_100, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
0.46/240.02	thf(c_0_101, plain, ((descrp)=(![X1:$i > $o]:(((?[X239:$i]:((((X1 @ X239))&![X240:$i]:((((X1 @ X240))=>((X239)=(X240)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_83, c_0_82])).
0.46/240.02	thf(c_0_102, plain, ((exuE2)=(![X1:$i > $o]:(((?[X245:$i]:((((X1 @ X245))&![X246:$i]:((((X1 @ X246))=>((X245)=(X246)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_84, c_0_82])).
0.46/240.02	thf(c_0_103, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X237:$i]:((((X6 @ X2 @ X237))&![X238:$i]:((((X6 @ X2 @ X238))=>((X237)=(X238)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_85, c_0_82])).
0.46/240.02	thf(c_0_104, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X255:$i]:((((X1 @ X255))&![X256:$i]:((((X1 @ X256))=>((X255)=(X256)))))))<=>(?[X257:$i]:((((X17 @ X257))&![X258:$i]:((((X17 @ X258))=>((X257)=(X258)))))))))))), inference(apply_def,[status(thm)],[c_0_86, c_0_82])).
0.46/240.02	thf(c_0_105, plain, ((emptyE1)<=>![X4:$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])).
0.46/240.02	thf(c_0_106, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X249:$i]:((((X1 @ X249))&![X250:$i]:((((X1 @ X250))=>((X249)=(X250)))))))))))), inference(apply_def,[status(thm)],[c_0_87, c_0_82])).
0.46/240.02	thf(c_0_107, plain, ((exuEu)=(![X1:$i > $o]:(((?[X259:$i]:((((X1 @ X259))&![X260:$i]:((((X1 @ X260))=>((X259)=(X260)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_88, c_0_82])).
0.46/240.02	thf(c_0_108, axiom, ((eqimpsubset2)=(![X4:$i, X5:$i]:((((X4)=(X5))=>(![X266:$i]:(((in @ X266 @ X5)=>(in @ X266 @ X4)))))))), inference(apply_def,[status(thm)],[eqimpsubset2, c_0_89])).
0.46/240.02	thf(c_0_109, axiom, ((subsetI1)=(![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X265:$i]:(((in @ X265 @ X4)=>(in @ X265 @ X5)))))))), inference(apply_def,[status(thm)],[subsetI1, c_0_89])).
0.46/240.02	thf(c_0_110, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
0.46/240.02	thf(c_0_111, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X261:$i]:((((X1 @ X261))&![X262:$i]:((((X1 @ X262))=>((X261)=(X262)))))))=>((?[X263:$i]:((((X17 @ X263))&![X264:$i]:((((X17 @ X264))=>((X263)=(X264)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_90, c_0_82])).
0.46/240.02	thf(c_0_112, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X253:$i]:((((X1 @ X253))&![X254:$i]:((((X1 @ X254))=>((X253)=(X254)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_91, c_0_82])).
0.46/240.02	thf(c_0_113, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X251:$i]:((((X1 @ X251))&![X252:$i]:((((X1 @ X252))=>((X251)=(X252))))))))))), inference(apply_def,[status(thm)],[c_0_92, c_0_82])).
0.46/240.02	thf(c_0_114, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X247:$i]:((((X1 @ X247))&![X248:$i]:((((X1 @ X248))=>((X247)=(X248))))))))))), inference(apply_def,[status(thm)],[c_0_93, c_0_82])).
0.46/240.02	thf(c_0_115, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_80])).
0.46/240.02	thf(c_0_116, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_94, c_0_80])).
0.46/240.02	thf(c_0_117, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_80])).
0.46/240.02	thf(c_0_118, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
0.46/240.02	thf(c_0_119, plain, ((exuE1)=(![X1:$i > $o]:(((?[X241:$i]:((((X1 @ X241))&![X242:$i]:((((X1 @ X242))=>((X241)=(X242)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_95, c_0_82])).
0.46/240.02	thf(c_0_120, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
0.46/240.02	thf(c_0_121, plain, ((epred1_0)<=>![X482:$i]:(?[X483:$i]:((((![X484:$i]:(((in @ X484 @ X483)=>![X485:$i]:(((in @ X485 @ X484)=>(in @ X485 @ X482)))))&![X486:$i, X487:$i]:((((in @ X486 @ X482)&(in @ X487 @ X482))=>(![X488:$i]:(((in @ X488 @ X483)=>((in @ X486 @ X488)<=>(in @ X487 @ X488))))=>((X486)=(X487))))))&![X489:$i, X490:$i]:((((in @ X489 @ X483)&(in @ X490 @ X483))=>(![X491:$i]:(((in @ X491 @ X489)=>(in @ X491 @ X490)))|![X492:$i]:(((in @ X492 @ X490)=>(in @ X492 @ X489)))))))&![X493:$i]:(((![X494:$i]:(((in @ X494 @ X493)=>(in @ X494 @ X482)))&?[X495:$i]:((in @ X495 @ X493)))=>?[X496:$i, X497:$i]:(((((in @ X496 @ X483)&(in @ X497 @ X493))&~(?[X498:$i]:(((in @ X498 @ X496)&(in @ X498 @ X493)))))&![X499:$i]:(((in @ X499 @ X483)=>(![X500:$i]:(((in @ X500 @ X499)=>(in @ X500 @ X496)))|(in @ X497 @ X499)))))))))))), introduced(definition)).
0.46/240.02	thf(c_0_122, negated_conjecture, ~((![X267:$i, X268:$i]:((![X269:$i]:(((in @ X269 @ X267)<=>(in @ X269 @ X268)))=>((X267)=(X268))))=>(![X270:$i]:(~(in @ X270 @ emptyset))=>(![X271:$i, X272:$i, X273:$i]:(((in @ X273 @ (setadjoin @ X271 @ X272))<=>(((X273)=(X271))|(in @ X273 @ X272))))=>(![X274:$i, X275:$i]:(((in @ X275 @ (powerset @ X274))<=>![X276:$i]:(((in @ X276 @ X275)=>(in @ X276 @ X274)))))=>(![X277:$i, X278:$i]:(((in @ X278 @ (setunion @ X277))<=>?[X279:$i]:(((in @ X278 @ X279)&(in @ X279 @ X277)))))=>((in @ emptyset @ omega)=>(![X513:$i]:(((in @ X513 @ omega)=>(in @ (setadjoin @ X513 @ X513) @ omega)))=>(![X280:$i]:((((in @ emptyset @ X280)&![X281:$i]:((((in @ X281 @ omega)&(in @ X281 @ X280))=>(in @ (setadjoin @ X281 @ X281) @ X280))))=>![X282:$i]:(((in @ X282 @ omega)=>(in @ X282 @ X280)))))=>(![X505:$i > $i > $o, X506:$i]:((![X507:$i]:(((in @ X507 @ X506)=>?[X508:$i]:(((X505 @ X507 @ X508)&![X509:$i]:(((X505 @ X507 @ X509)=>((X508)=(X509))))))))=>?[X510:$i]:(![X511:$i]:(((in @ X511 @ X510)<=>?[X512:$i]:(((in @ X512 @ X506)&(X505 @ X512 @ X511))))))))=>(![X501:$i]:((?[X502:$i]:((in @ X502 @ X501))=>?[X503:$i]:(((in @ X503 @ X501)&~(?[X504:$i]:(((in @ X504 @ X503)&(in @ X504 @ X501))))))))=>((epred1_0)=>(![X479:$i > $o]:((?[X480:$i]:(((X479 @ X480)&![X481:$i]:(((X479 @ X481)=>((X480)=(X481))))))=>(X479 @ (descr @ (^[Z0/* 3 */:$i]:((X479 @ Z0)))))))=>(![X476:$i, X477:$i > $o, X478:$i]:(((in @ X478 @ X476)=>((X477 @ X478)=>(in @ X478 @ (dsetconstr @ X476 @ (^[Z0/* 3 */:$i]:((X477 @ Z0))))))))=>(![X473:$i, X474:$i > $o, X475:$i]:(((in @ X475 @ (dsetconstr @ X473 @ (^[Z0/* 3 */:$i]:((X474 @ Z0)))))=>(in @ X475 @ X473)))=>(![X283:$i, X284:$i > $o, X285:$i]:(((in @ X285 @ (dsetconstr @ X283 @ (^[Z0/* 3 */:$i]:((X284 @ Z0)))))=>(X284 @ X285)))=>(![X286:$i > $o]:((?[X287:$i]:(((X286 @ X287)&![X288:$i]:(((X286 @ X288)=>((X287)=(X288))))))=>?[X289:$i]:(((X286 @ X289)&![X290:$i]:(((X286 @ X290)=>((X289)=(X290))))))))=>(![X471:$o, X472:$i]:(((in @ X472 @ (prop2set @ ((X471))))=>(X471)))=>(![X291:$i]:(((in @ X291 @ emptyset)=>![X292:$o]:((X292))))=>(![X293:$i]:(~(in @ X293 @ emptyset))=>(![X294:$i]:(~(in @ X294 @ emptyset))=>(![X467:$i > $o]:((?[X468:$i]:(((X467 @ X468)&![X469:$i]:(((X467 @ X469)=>((X468)=(X469))))))=>?[X470:$i]:((X467 @ X470))))=>(![X463:$i, X464:$i]:((![X465:$i]:(((in @ X465 @ X463)=>(in @ X465 @ X464)))=>(![X466:$i]:(((in @ X466 @ X464)=>(in @ X466 @ X463)))=>((X463)=(X464)))))=>(![X295:$i]:((![X296:$i]:(~(in @ X296 @ X295))=>((X295)=(emptyset))))=>(![X461:$i]:((![X462:$i]:(~(in @ X462 @ X461))=>((X461)=(emptyset))))=>(![X297:$i, X298:$i > $o, X299:$i]:(((in @ X299 @ X297)=>((in @ X299 @ (dsetconstr @ X297 @ (^[Z0/* 3 */:$i]:((X298 @ Z0)))))<=>(X298 @ X299))))=>(![X300:$i]:((((X300)!=(emptyset))=>?[X301:$i]:((in @ X301 @ X300))))=>(![X302:$i, X303:$i > $o, X304:$i]:(((in @ X304 @ X302)=>((X303 @ X304)=>((dsetconstr @ X302 @ (^[Z0/* 3 */:$i]:((X303 @ Z0))))!=(emptyset)))))=>(![X305:$i]:((?[X306:$i]:((in @ X306 @ X305))=>((X305)!=(emptyset))))=>(![X459:$i, X460:$i]:((in @ X459 @ (setadjoin @ X459 @ X460)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X307:$i, X308:$i, X309:$i]:(((in @ X309 @ X308)=>(in @ X309 @ (setadjoin @ X307 @ X308))))=>(![X310:$i, X311:$i, X312:$i]:(((in @ X312 @ (setadjoin @ X310 @ X311))=>![X313:$o]:(((((X312)=(X310))=>(X313))=>(((in @ X312 @ X311)=>(X313))=>(X313))))))=>(![X456:$i, X457:$i, X458:$i]:(((in @ X458 @ (setadjoin @ X456 @ X457))=>(((X458)=(X456))|(in @ X458 @ X457))))=>(![X314:$i]:(((dsetconstr @ X314 @ (^[Z0/* 3 */:$i]:(($true))))=(X314)))=>(![X453:$i, X454:$i]:((![X455:$i]:(((in @ X455 @ X454)=>(in @ X455 @ X453)))=>(in @ X454 @ (powerset @ X453))))=>(![X315:$i]:((in @ emptyset @ (powerset @ X315)))=>(![X452:$i]:((in @ emptyset @ (powerset @ X452)))=>(![X449:$i, X450:$i, X451:$i]:(((in @ X450 @ (powerset @ X449))=>((in @ X451 @ X450)=>(in @ X451 @ X449))))=>(![X446:$i, X447:$i, X448:$i]:(((in @ X447 @ X448)=>((in @ X448 @ X446)=>(in @ X447 @ (setunion @ X446)))))=>(![X316:$i, X317:$i]:(((in @ X317 @ (setunion @ X316))=>![X318:$o]:((![X319:$i]:(((in @ X317 @ X319)=>((in @ X319 @ X316)=>(X318))))=>(X318)))))=>(![X320:$i, X321:$i]:(((in @ X321 @ X320)=>(in @ X321 @ (powerset @ (setunion @ X320)))))=>(![X322:$i > $o]:((?[X323:$i]:(((X322 @ X323)&![X324:$i]:(((X322 @ X324)=>((X323)=(X324))))))=>?[X325:$i]:(![X326:$i]:(((X322 @ X326)<=>((X326)=(X325)))))))=>(![X444:$i]:((((X444)!=(emptyset))=>?[X445:$i]:((in @ X445 @ X444))))=>(![X442:$i, X443:$i]:(((in @ X442 @ (setadjoin @ X443 @ emptyset))=>((X442)=(X443))))=>(![X327:$i, X328:$i]:((((X327)!=(X328))=>~(in @ X328 @ (setadjoin @ X327 @ emptyset))))=>(![X329:$i, X330:$i]:((((X329)=(X330))=>(in @ X329 @ (setadjoin @ X330 @ emptyset))))=>(![X440:$i, X441:$i]:(((in @ X440 @ (setadjoin @ X441 @ emptyset))=>(in @ X441 @ (setadjoin @ X440 @ emptyset))))=>(![X437:$i, X438:$i, X439:$i]:(((in @ X439 @ (setadjoin @ X437 @ (setadjoin @ X438 @ emptyset)))=>(((X439)=(X437))|((X439)=(X438)))))=>(![X435:$i, X436:$i]:((in @ X435 @ (setadjoin @ X435 @ (setadjoin @ X436 @ emptyset))))=>(![X433:$i, X434:$i]:((in @ X434 @ (setadjoin @ X433 @ (setadjoin @ X434 @ emptyset))))=>(![X331:$i, X332:$i > $o]:((?[X333:$i]:(((in @ X333 @ X331)&(X332 @ X333)))=>((dsetconstr @ X331 @ (^[Z0/* 3 */:$i]:((X332 @ Z0))))!=(emptyset))))=>(![X431:$i > $o, X432:$i]:(((in @ X432 @ emptyset)=>(X431 @ X432)))=>(![X427:$i, X428:$i > $o]:((~(![X429:$i]:(((in @ X429 @ X427)=>(X428 @ X429))))=>?[X430:$i]:(((in @ X430 @ X427)&~(X428 @ X430)))))=>(![X423:$i, X424:$i > $o]:((![X425:$i]:(((in @ X425 @ X423)=>~(X424 @ X425)))=>~(?[X426:$i]:(((in @ X426 @ X423)&(X424 @ X426))))))=>(![X419:$i, X420:$i > $o]:((~(?[X421:$i]:(((in @ X421 @ X419)&(X420 @ X421))))=>![X422:$i]:(((in @ X422 @ X419)=>~(X420 @ X422)))))=>(![X334:$i, X335:$i > $o]:((?[X336:$i]:(((in @ X336 @ X334)&~(X335 @ X336)))=>~(![X337:$i]:(((in @ X337 @ X334)=>(X335 @ X337))))))=>(![X418:$o]:(((X418)=>(in @ emptyset @ (prop2set @ ((X418))))))=>((prop2set2propI)=>(![X414:$i, X415:$i > $o]:((~(?[X416:$i]:(((in @ X416 @ X414)&(X415 @ X416))))=>![X417:$i]:(((in @ X417 @ X414)=>~(X415 @ X417)))))=>(![X410:$i, X411:$i > $o]:((~(![X412:$i]:(((in @ X412 @ X410)=>(X411 @ X412))))=>?[X413:$i]:(((in @ X413 @ X410)&~(X411 @ X413)))))=>(![X405:$i > $o]:((?[X406:$i]:(((X405 @ X406)&![X407:$i]:(((X405 @ X407)=>((X406)=(X407))))))=>?[X408:$i]:(((X405 @ X408)&![X409:$i]:(((X405 @ X409)=>((X408)=(X409))))))))=>(![X338:$i > $o]:((?[X339:$i]:((X338 @ X339))=>(![X340:$i, X341:$i]:(((X338 @ X340)=>((X338 @ X341)=>((X340)=(X341)))))=>?[X342:$i]:(((X338 @ X342)&![X343:$i]:(((X338 @ X343)=>((X342)=(X343)))))))))=>(![X400:$i > $o]:((?[X401:$i]:(![X402:$i]:(((X400 @ X402)<=>((X402)=(X401)))))=>?[X403:$i]:(((X400 @ X403)&![X404:$i]:(((X400 @ X404)=>((X403)=(X404))))))))=>(![X396:$i, X397:$i]:((((X396)=(X397))=>![X398:$i, X399:$i]:((((X398)=(X399))=>((in @ X398 @ X396)=>(in @ X399 @ X397))))))=>(![X392:$i, X393:$i]:((((X392)=(X393))=>![X394:$i, X395:$i]:((((X394)=(X395))=>((in @ X394 @ X392)<=>(in @ X395 @ X393))))))=>(![X387:$i > $o]:((?[X388:$i]:(((X387 @ X388)&![X389:$i]:(((X387 @ X389)=>((X388)=(X389))))))=>![X390:$i, X391:$i]:(((X387 @ X390)=>((X387 @ X391)=>((X390)=(X391)))))))=>(![X379:$i > $o, X380:$i > $o]:((![X381:$i, X382:$i]:((((X381)=(X382))=>((X379 @ X381)<=>(X380 @ X382))))=>(?[X383:$i]:(((X379 @ X383)&![X384:$i]:(((X379 @ X384)=>((X383)=(X384))))))<=>?[X385:$i]:(((X380 @ X385)&![X386:$i]:(((X380 @ X386)=>((X385)=(X386)))))))))=>(((emptyset)=(emptyset))=>(![X375:$i, X376:$i]:((((X375)=(X376))=>![X377:$i, X378:$i]:((((X377)=(X378))=>((setadjoin @ X375 @ X377)=(setadjoin @ X376 @ X378))))))=>(![X373:$i, X374:$i]:((((X373)=(X374))=>((powerset @ X373)=(powerset @ X374))))=>(![X371:$i, X372:$i]:((((X371)=(X372))=>((setunion @ X371)=(setunion @ X372))))=>(((omega)=(omega))=>(![X344:$i > $o]:((?[X345:$i]:(((X344 @ X345)&![X346:$i]:(((X344 @ X346)=>((X345)=(X346))))))=>![X347:$i, X348:$i]:(((X344 @ X347)=>((X344 @ X348)=>((X347)=(X348)))))))=>(![X363:$i > $o, X364:$i > $o]:((![X365:$i, X366:$i]:((((X365)=(X366))=>((X363 @ X365)<=>(X364 @ X366))))=>(?[X367:$i]:(((X363 @ X367)&![X368:$i]:(((X363 @ X368)=>((X367)=(X368))))))=>(?[X369:$i]:(((X364 @ X369)&![X370:$i]:(((X364 @ X370)=>((X369)=(X370))))))=>((descr @ (^[Z0/* 3 */:$i]:((X363 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X364 @ Z0)))))))))=>(![X357:$i, X358:$i]:((((X357)=(X358))=>![X359:$i > $o, X360:$i > $o]:((![X361:$i]:(((in @ X361 @ X357)=>![X362:$i]:(((in @ X362 @ X358)=>(((X361)=(X362))=>((X359 @ X361)<=>(X360 @ X362)))))))=>((dsetconstr @ X357 @ (^[Z0/* 3 */:$i]:((X359 @ Z0))))=(dsetconstr @ X358 @ (^[Z0/* 3 */:$i]:((X360 @ Z0)))))))))=>(![X353:$i, X354:$i]:((![X355:$i]:(((in @ X355 @ X353)=>(in @ X355 @ X354)))=>![X356:$i]:(((in @ X356 @ X353)=>(in @ X356 @ X354)))))=>(![X349:$i, X350:$i]:((((X349)=(X350))=>![X351:$i]:(((in @ X351 @ X350)=>(in @ X351 @ X349)))))=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X352:$i]:(((in @ X352 @ X4)=>(in @ X352 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[eqimpsubset1]), omegaSAx]), emptyInPowerset]), c_0_96]), powersetI]), c_0_97]), setadjoinOr]), setadjoinIL]), noeltsimpempty]), emptyinPowerset]), setext]), c_0_98]), setunionE]), prop2setE]), c_0_99]), c_0_100]), subPowSU]), c_0_101]), wellorderingAx]), c_0_102]), foundationAx]), c_0_103]), notinsingleton]), eqinunit]), c_0_104]), emptyinunitempty]), c_0_105]), quantDeMorgan4]), c_0_106]), c_0_107]), c_0_108]), c_0_89]), c_0_109]), c_0_110]), setadjoinIR]), c_0_111]), omega__Cong]), setunion__Cong]), powerset__Cong]), setadjoin__Cong]), emptyset__Cong]), c_0_112]), in__Cong]), inCongP]), c_0_113]), c_0_114]), notdallE]), notdexE]), prop2setI]), quantDeMorgan3]), quantDeMorgan2]), quantDeMorgan1]), vacuousDall]), upairsetIR]), upairsetIL]), upairsetE]), setadjoinE]), singletonsswitch]), uniqinunit]), c_0_115]), setunionI]), powersetE]), c_0_116]), c_0_117]), c_0_118]), emptyI]), notinemptyset]), emptysetimpfalse]), emptysetE]), c_0_119]), c_0_120]), omegaIndAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])]), c_0_121])).
0.46/240.02	thf(c_0_123, negated_conjecture, ![X514:$i, X515:$i, X517:$i, X518:$i, X519:$i, X520:$i, X521:$i, X522:$i, X523:$i, X524:$i, X525:$i, X527:$i, X528:$i, X530:$i, X531:$i, X532:$i, X533:$i, X534:$i, X536:$i, X537:$i > $i > $o, X538:$i, X540:$i, X543:$i, X545:$i, X546:$i, X547:$i, X548:$i, X550:$i, X551:$i > $o, X552:$i, X554:$i, X555:$i > $o, X556:$i, X557:$i, X558:$i > $o, X559:$i, X560:$i, X561:$i > $o, X562:$i, X563:$i > $o, X564:$i, X567:$i, X568:$o, X569:$i, X570:$i, X571:$o, X572:$i, X573:$i, X574:$i > $o, X575:$i, X578:$i, X579:$i, X582:$i, X584:$i, X586:$i, X587:$i > $o, X588:$i, X589:$i, X591:$i, X592:$i > $o, X593:$i, X594:$i, X595:$i, X596:$i, X597:$i, X598:$i, X599:$i, X600:$i, X601:$i, X602:$i, X603:$i, X604:$o, X605:$i, X606:$i, X607:$i, X608:$i, X609:$i, X610:$i, X612:$i, X613:$i, X614:$i, X615:$i, X616:$i, X617:$i, X618:$i, X619:$i, X620:$i, X621:$i, X622:$o, X624:$i, X625:$i, X626:$i > $o, X627:$i, X630:$i, X631:$i, X632:$i, X634:$i, X635:$i, X636:$i, X637:$i, X638:$i, X639:$i, X640:$i, X641:$i, X642:$i, X643:$i, X644:$i, X645:$i, X646:$i, X647:$i, X648:$i, X649:$i, X650:$i > $o, X651:$i, X652:$i > $o, X653:$i, X654:$i, X655:$i > $o, X656:$i, X658:$i, X659:$i > $o, X661:$i, X662:$i, X663:$i > $o, X665:$i, X666:$i, X667:$i > $o, X668:$i, X670:$o, X671:$i, X672:$i > $o, X674:$i, X675:$i, X676:$i > $o, X677:$i, X679:$i > $o, X680:$i, X683:$i, X684:$i > $o, X685:$i, X689:$i, X690:$i > $o, X691:$i, X694:$i, X695:$i, X696:$i, X697:$i, X698:$i, X699:$i, X700:$i, X701:$i, X702:$i, X703:$i > $o, X704:$i, X706:$i, X707:$i, X708:$i > $o, X709:$i > $o, X712:$i, X715:$i, X716:$i, X719:$i, X720:$i, X721:$i, X722:$i, X723:$i, X724:$i, X725:$i, X726:$i, X727:$i, X728:$i > $o, X729:$i, X731:$i, X732:$i, X733:$i > $o, X734:$i > $o, X737:$i, X739:$i, X741:$i, X742:$i, X743:$i > $o, X744:$i > $o, X747:$i, X748:$i, X750:$i, X751:$i, X752:$i, X753:$i]:((((~(in @ (esk1_2 @ X514 @ X515) @ X514)|~(in @ (esk1_2 @ X514 @ X515) @ X515)|((X514)=(X515)))&((in @ (esk1_2 @ X514 @ X515) @ X514)|(in @ (esk1_2 @ X514 @ X515) @ X515)|((X514)=(X515))))&(~(in @ X517 @ emptyset)&(((~(in @ X520 @ (setadjoin @ X518 @ X519))|(((X520)=(X518))|(in @ X520 @ X519)))&((((X520)!=(X518))|(in @ X520 @ (setadjoin @ X518 @ X519)))&(~(in @ X520 @ X519)|(in @ X520 @ (setadjoin @ X518 @ X519)))))&(((~(in @ X522 @ (powerset @ X521))|(~(in @ X523 @ X522)|(in @ X523 @ X521)))&(((in @ (esk2_2 @ X524 @ X525) @ X525)|(in @ X525 @ (powerset @ X524)))&(~(in @ (esk2_2 @ X524 @ X525) @ X524)|(in @ X525 @ (powerset @ X524)))))&(((((in @ X528 @ (esk3_2 @ X527 @ X528))|~(in @ X528 @ (setunion @ X527)))&((in @ (esk3_2 @ X527 @ X528) @ X527)|~(in @ X528 @ (setunion @ X527))))&(~(in @ X531 @ X532)|~(in @ X532 @ X530)|(in @ X531 @ (setunion @ X530))))&((in @ emptyset @ omega)&((~(in @ X533 @ omega)|(in @ (setadjoin @ X533 @ X533) @ omega))&(((((in @ (esk4_1 @ X534) @ omega)|~(in @ emptyset @ X534)|(~(in @ X536 @ omega)|(in @ X536 @ X534)))&((in @ (esk4_1 @ X534) @ X534)|~(in @ emptyset @ X534)|(~(in @ X536 @ omega)|(in @ X536 @ X534))))&(~(in @ (setadjoin @ (esk4_1 @ X534) @ (esk4_1 @ X534)) @ X534)|~(in @ emptyset @ X534)|(~(in @ X536 @ omega)|(in @ X536 @ X534))))&((((((in @ (esk8_3 @ X537 @ X538 @ X543) @ X538)|~(in @ X543 @ (esk7_2 @ X537 @ X538))|(in @ (esk5_2 @ X537 @ X538) @ X538))&((X537 @ (esk8_3 @ X537 @ X538 @ X543) @ X543)|~(in @ X543 @ (esk7_2 @ X537 @ X538))|(in @ (esk5_2 @ X537 @ X538) @ X538)))&(~(in @ X546 @ X538)|~(X537 @ X546 @ X545)|(in @ X545 @ (esk7_2 @ X537 @ X538))|(in @ (esk5_2 @ X537 @ X538) @ X538)))&(((((in @ (esk8_3 @ X537 @ X538 @ X543) @ X538)|~(in @ X543 @ (esk7_2 @ X537 @ X538))|((X537 @ (esk5_2 @ X537 @ X538) @ (esk6_3 @ X537 @ X538 @ X540))|~(X537 @ (esk5_2 @ X537 @ X538) @ X540)))&((X537 @ (esk8_3 @ X537 @ X538 @ X543) @ X543)|~(in @ X543 @ (esk7_2 @ X537 @ X538))|((X537 @ (esk5_2 @ X537 @ X538) @ (esk6_3 @ X537 @ X538 @ X540))|~(X537 @ (esk5_2 @ X537 @ X538) @ X540))))&(~(in @ X546 @ X538)|~(X537 @ X546 @ X545)|(in @ X545 @ (esk7_2 @ X537 @ X538))|((X537 @ (esk5_2 @ X537 @ X538) @ (esk6_3 @ X537 @ X538 @ X540))|~(X537 @ (esk5_2 @ X537 @ X538) @ X540))))&((((in @ (esk8_3 @ X537 @ X538 @ X543) @ X538)|~(in @ X543 @ (esk7_2 @ X537 @ X538))|(((X540)!=(esk6_3 @ X537 @ X538 @ X540))|~(X537 @ (esk5_2 @ X537 @ X538) @ X540)))&((X537 @ (esk8_3 @ X537 @ X538 @ X543) @ X543)|~(in @ X543 @ (esk7_2 @ X537 @ X538))|(((X540)!=(esk6_3 @ X537 @ X538 @ X540))|~(X537 @ (esk5_2 @ X537 @ X538) @ X540))))&(~(in @ X546 @ X538)|~(X537 @ X546 @ X545)|(in @ X545 @ (esk7_2 @ X537 @ X538))|(((X540)!=(esk6_3 @ X537 @ X538 @ X540))|~(X537 @ (esk5_2 @ X537 @ X538) @ X540))))))&((((in @ (esk9_1 @ X547) @ X547)|~(in @ X548 @ X547))&(~(in @ X550 @ (esk9_1 @ X547))|~(in @ X550 @ X547)|~(in @ X548 @ X547)))&((epred1_0)&((((X551 @ (esk10_2 @ X551 @ X552))|~(X551 @ X552)|(X551 @ (descr @ (^[Z0/* 3 */:$i]:((X551 @ Z0))))))&(((X552)!=(esk10_2 @ X551 @ X552))|~(X551 @ X552)|(X551 @ (descr @ (^[Z0/* 3 */:$i]:((X551 @ Z0)))))))&((~(in @ X556 @ X554)|(~(X555 @ X556)|(in @ X556 @ (dsetconstr @ X554 @ (^[Z0/* 3 */:$i]:((X555 @ Z0)))))))&((~(in @ X559 @ (dsetconstr @ X557 @ (^[Z0/* 3 */:$i]:((X558 @ Z0)))))|(in @ X559 @ X557))&((~(in @ X562 @ (dsetconstr @ X560 @ (^[Z0/* 3 */:$i]:((X561 @ Z0)))))|(X561 @ X562))&(((((X563 @ (esk12_1 @ X563))|((X563 @ (esk11_2 @ X563 @ X564))|~(X563 @ X564)))&(~(X563 @ X567)|((esk12_1 @ X563)=(X567))|((X563 @ (esk11_2 @ X563 @ X564))|~(X563 @ X564))))&(((X563 @ (esk12_1 @ X563))|(((X564)!=(esk11_2 @ X563 @ X564))|~(X563 @ X564)))&(~(X563 @ X567)|((esk12_1 @ X563)=(X567))|(((X564)!=(esk11_2 @ X563 @ X564))|~(X563 @ X564)))))&((~(in @ X569 @ (prop2set @ ((X568))))|(X568))&((~(in @ X570 @ emptyset)|(X571))&(~(in @ X572 @ emptyset)&(~(in @ X573 @ emptyset)&((((X574 @ (esk13_2 @ X574 @ X575))|~(X574 @ X575)|(X574 @ (esk14_1 @ X574)))&(((X575)!=(esk13_2 @ X574 @ X575))|~(X574 @ X575)|(X574 @ (esk14_1 @ X574))))&(((((in @ (esk16_2 @ X578 @ X579) @ X579)|((X578)=(X579))|(in @ (esk15_2 @ X578 @ X579) @ X578))&(~(in @ (esk16_2 @ X578 @ X579) @ X578)|((X578)=(X579))|(in @ (esk15_2 @ X578 @ X579) @ X578)))&(((in @ (esk16_2 @ X578 @ X579) @ X579)|((X578)=(X579))|~(in @ (esk15_2 @ X578 @ X579) @ X579))&(~(in @ (esk16_2 @ X578 @ X579) @ X578)|((X578)=(X579))|~(in @ (esk15_2 @ X578 @ X579) @ X579))))&(((in @ (esk17_1 @ X582) @ X582)|((X582)=(emptyset)))&(((in @ (esk18_1 @ X584) @ X584)|((X584)=(emptyset)))&(((~(in @ X588 @ (dsetconstr @ X586 @ (^[Z0/* 3 */:$i]:((X587 @ Z0)))))|(X587 @ X588)|~(in @ X588 @ X586))&(~(X587 @ X588)|(in @ X588 @ (dsetconstr @ X586 @ (^[Z0/* 3 */:$i]:((X587 @ Z0)))))|~(in @ X588 @ X586)))&((((X589)=(emptyset))|(in @ (esk19_1 @ X589) @ X589))&((~(in @ X593 @ X591)|(~(X592 @ X593)|((dsetconstr @ X591 @ (^[Z0/* 3 */:$i]:((X592 @ Z0))))!=(emptyset))))&((~(in @ X595 @ X594)|((X594)!=(emptyset)))&((in @ X596 @ (setadjoin @ X596 @ X597))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X600 @ X599)|(in @ X600 @ (setadjoin @ X598 @ X599)))&(((((in @ X603 @ 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X646 @ emptyset)))&((in @ X648 @ (setadjoin @ X647 @ (setadjoin @ X648 @ emptyset)))&((~(in @ X651 @ X649)|~(X650 @ X651)|((dsetconstr @ X649 @ (^[Z0/* 3 */:$i]:((X650 @ Z0))))!=(emptyset)))&((~(in @ X653 @ emptyset)|(X652 @ X653))&((((in @ (esk25_2 @ X654 @ X655) @ X654)|(~(in @ X656 @ X654)|(X655 @ X656)))&(~(X655 @ (esk25_2 @ X654 @ X655))|(~(in @ X656 @ X654)|(X655 @ X656))))&((((in @ (esk26_2 @ X658 @ X659) @ X658)|(~(in @ X661 @ X658)|~(X659 @ X661)))&((X659 @ (esk26_2 @ X658 @ X659))|(~(in @ X661 @ X658)|~(X659 @ X661))))&((((in @ (esk27_2 @ X662 @ X663) @ X662)|(~(in @ X665 @ X662)|~(X663 @ X665)))&((X663 @ (esk27_2 @ X662 @ X663))|(~(in @ X665 @ X662)|~(X663 @ X665))))&((((in @ (esk28_2 @ X666 @ X667) @ X666)|(~(in @ X668 @ X666)|(X667 @ X668)))&(~(X667 @ (esk28_2 @ X666 @ X667))|(~(in @ X668 @ X666)|(X667 @ X668))))&((~(X670)|(in @ emptyset @ (prop2set @ ((X670)))))&((prop2set2propI)&((((in @ (esk29_2 @ X671 @ X672) @ X671)|(~(in @ X674 @ X671)|~(X672 @ X674)))&((X672 @ 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X684)=(X689))|((esk33_1 @ X684)!=(esk34_1 @ X684))|~(X684 @ X685)))))&(((((X690 @ (esk37_1 @ X690))|(~(X690 @ (esk36_2 @ X690 @ X691))|((esk36_2 @ X690 @ X691)!=(X691))))&(~(X690 @ X694)|((esk37_1 @ X690)=(X694))|(~(X690 @ (esk36_2 @ X690 @ X691))|((esk36_2 @ X690 @ X691)!=(X691)))))&(((X690 @ (esk37_1 @ X690))|((X690 @ (esk36_2 @ X690 @ X691))|((esk36_2 @ X690 @ X691)=(X691))))&(~(X690 @ X694)|((esk37_1 @ X690)=(X694))|((X690 @ (esk36_2 @ X690 @ X691))|((esk36_2 @ X690 @ X691)=(X691))))))&((((X695)!=(X696))|(((X697)!=(X698))|(~(in @ X697 @ X695)|(in @ X698 @ X696))))&(((~(in @ X701 @ X699)|(in @ X702 @ X700)|((X701)!=(X702))|((X699)!=(X700)))&(~(in @ X702 @ X700)|(in @ X701 @ X699)|((X701)!=(X702))|((X699)!=(X700))))&((((X703 @ (esk38_2 @ X703 @ X704))|~(X703 @ X704)|(~(X703 @ X706)|(~(X703 @ X707)|((X706)=(X707)))))&(((X704)!=(esk38_2 @ X703 @ X704))|~(X703 @ X704)|(~(X703 @ X706)|(~(X703 @ X707)|((X706)=(X707))))))&(((((((X709 @ (esk42_2 @ X708 @ X709))|((X708 @ (esk41_3 @ X708 @ 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X719)|((esk44_2 @ X708 @ X709)=(X719))|(((X716)!=(esk43_3 @ X708 @ X709 @ X716))|~(X709 @ X716))|((esk39_2 @ X708 @ X709)=(esk40_2 @ X708 @ X709))))))&((((((X709 @ (esk42_2 @ X708 @ X709))|((X708 @ (esk41_3 @ X708 @ X709 @ X712))|~(X708 @ X712))|(~(X708 @ (esk39_2 @ X708 @ X709))|~(X709 @ (esk40_2 @ X708 @ X709))))&(~(X709 @ X715)|((esk42_2 @ X708 @ X709)=(X715))|((X708 @ (esk41_3 @ X708 @ X709 @ X712))|~(X708 @ X712))|(~(X708 @ (esk39_2 @ X708 @ X709))|~(X709 @ (esk40_2 @ X708 @ X709)))))&(((X709 @ (esk42_2 @ X708 @ X709))|(((X712)!=(esk41_3 @ X708 @ X709 @ X712))|~(X708 @ X712))|(~(X708 @ (esk39_2 @ X708 @ X709))|~(X709 @ (esk40_2 @ X708 @ X709))))&(~(X709 @ X715)|((esk42_2 @ X708 @ X709)=(X715))|(((X712)!=(esk41_3 @ X708 @ X709 @ X712))|~(X708 @ X712))|(~(X708 @ (esk39_2 @ X708 @ X709))|~(X709 @ (esk40_2 @ X708 @ X709))))))&((((X708 @ (esk44_2 @ X708 @ X709))|((X709 @ (esk43_3 @ X708 @ X709 @ X716))|~(X709 @ X716))|(~(X708 @ (esk39_2 @ X708 @ X709))|~(X709 @ (esk40_2 @ X708 @ X709))))&(~(X708 @ X719)|((esk44_2 @ X708 @ X709)=(X719))|((X709 @ (esk43_3 @ X708 @ X709 @ X716))|~(X709 @ X716))|(~(X708 @ (esk39_2 @ X708 @ X709))|~(X709 @ (esk40_2 @ X708 @ X709)))))&(((X708 @ (esk44_2 @ X708 @ X709))|(((X716)!=(esk43_3 @ X708 @ X709 @ X716))|~(X709 @ X716))|(~(X708 @ (esk39_2 @ X708 @ X709))|~(X709 @ (esk40_2 @ X708 @ X709))))&(~(X708 @ X719)|((esk44_2 @ X708 @ X709)=(X719))|(((X716)!=(esk43_3 @ X708 @ X709 @ X716))|~(X709 @ X716))|(~(X708 @ (esk39_2 @ X708 @ X709))|~(X709 @ (esk40_2 @ X708 @ X709)))))))&(((((X709 @ (esk42_2 @ X708 @ X709))|((X708 @ (esk41_3 @ X708 @ X709 @ X712))|~(X708 @ X712))|((X708 @ (esk39_2 @ X708 @ X709))|(X709 @ (esk40_2 @ X708 @ X709))))&(~(X709 @ X715)|((esk42_2 @ X708 @ X709)=(X715))|((X708 @ (esk41_3 @ X708 @ X709 @ X712))|~(X708 @ X712))|((X708 @ (esk39_2 @ X708 @ X709))|(X709 @ (esk40_2 @ X708 @ X709)))))&(((X709 @ (esk42_2 @ X708 @ X709))|(((X712)!=(esk41_3 @ X708 @ X709 @ X712))|~(X708 @ X712))|((X708 @ (esk39_2 @ X708 @ X709))|(X709 @ (esk40_2 @ X708 @ X709))))&(~(X709 @ X715)|((esk42_2 @ X708 @ X709)=(X715))|(((X712)!=(esk41_3 @ X708 @ X709 @ X712))|~(X708 @ X712))|((X708 @ (esk39_2 @ X708 @ X709))|(X709 @ (esk40_2 @ X708 @ X709))))))&((((X708 @ (esk44_2 @ X708 @ X709))|((X709 @ (esk43_3 @ X708 @ X709 @ X716))|~(X709 @ X716))|((X708 @ (esk39_2 @ X708 @ X709))|(X709 @ (esk40_2 @ X708 @ X709))))&(~(X708 @ X719)|((esk44_2 @ X708 @ X709)=(X719))|((X709 @ (esk43_3 @ X708 @ X709 @ X716))|~(X709 @ X716))|((X708 @ (esk39_2 @ X708 @ X709))|(X709 @ (esk40_2 @ X708 @ X709)))))&(((X708 @ (esk44_2 @ X708 @ X709))|(((X716)!=(esk43_3 @ X708 @ X709 @ X716))|~(X709 @ X716))|((X708 @ (esk39_2 @ X708 @ X709))|(X709 @ (esk40_2 @ X708 @ X709))))&(~(X708 @ X719)|((esk44_2 @ X708 @ X709)=(X719))|(((X716)!=(esk43_3 @ X708 @ X709 @ X716))|~(X709 @ X716))|((X708 @ (esk39_2 @ X708 @ X709))|(X709 @ (esk40_2 @ X708 @ X709)))))))))&(((emptyset)=(emptyset))&((((X720)!=(X721))|(((X722)!=(X723))|((setadjoin @ X720 @ X722)=(setadjoin @ X721 @ X723))))&((((X724)!=(X725))|((powerset @ X724)=(powerset @ X725)))&((((X726)!=(X727))|((setunion @ X726)=(setunion @ X727)))&(((omega)=(omega))&((((X728 @ (esk45_2 @ X728 @ X729))|~(X728 @ X729)|(~(X728 @ X731)|(~(X728 @ X732)|((X731)=(X732)))))&(((X729)!=(esk45_2 @ X728 @ X729))|~(X728 @ X729)|(~(X728 @ X731)|(~(X728 @ X732)|((X731)=(X732))))))&((((((X734 @ (esk49_3 @ X733 @ X734 @ X739))|~(X734 @ X739)|((descr @ (^[Z0/* 3 */:$i]:((X733 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X734 @ Z0)))))|((X733 @ (esk48_3 @ X733 @ X734 @ X737))|~(X733 @ X737))|((esk46_2 @ X733 @ X734)=(esk47_2 @ X733 @ X734)))&(((X739)!=(esk49_3 @ X733 @ X734 @ X739))|~(X734 @ X739)|((descr @ (^[Z0/* 3 */:$i]:((X733 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X734 @ Z0)))))|((X733 @ (esk48_3 @ X733 @ X734 @ X737))|~(X733 @ X737))|((esk46_2 @ X733 @ X734)=(esk47_2 @ X733 @ X734))))&(((X734 @ (esk49_3 @ X733 @ X734 @ X739))|~(X734 @ X739)|((descr @ (^[Z0/* 3 */:$i]:((X733 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X734 @ Z0)))))|(((X737)!=(esk48_3 @ X733 @ X734 @ X737))|~(X733 @ X737))|((esk46_2 @ X733 @ X734)=(esk47_2 @ X733 @ X734)))&(((X739)!=(esk49_3 @ X733 @ X734 @ X739))|~(X734 @ X739)|((descr @ (^[Z0/* 3 */:$i]:((X733 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X734 @ Z0)))))|(((X737)!=(esk48_3 @ X733 @ X734 @ X737))|~(X733 @ X737))|((esk46_2 @ X733 @ X734)=(esk47_2 @ X733 @ X734)))))&(((((X734 @ (esk49_3 @ X733 @ X734 @ X739))|~(X734 @ X739)|((descr @ (^[Z0/* 3 */:$i]:((X733 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X734 @ Z0)))))|((X733 @ (esk48_3 @ X733 @ X734 @ X737))|~(X733 @ X737))|(~(X733 @ (esk46_2 @ X733 @ X734))|~(X734 @ (esk47_2 @ X733 @ X734))))&(((X739)!=(esk49_3 @ X733 @ X734 @ X739))|~(X734 @ X739)|((descr @ (^[Z0/* 3 */:$i]:((X733 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X734 @ Z0)))))|((X733 @ (esk48_3 @ X733 @ X734 @ X737))|~(X733 @ X737))|(~(X733 @ (esk46_2 @ X733 @ X734))|~(X734 @ (esk47_2 @ X733 @ X734)))))&(((X734 @ (esk49_3 @ X733 @ X734 @ X739))|~(X734 @ X739)|((descr @ (^[Z0/* 3 */:$i]:((X733 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X734 @ Z0)))))|(((X737)!=(esk48_3 @ X733 @ X734 @ X737))|~(X733 @ X737))|(~(X733 @ (esk46_2 @ X733 @ X734))|~(X734 @ (esk47_2 @ X733 @ X734))))&(((X739)!=(esk49_3 @ X733 @ X734 @ X739))|~(X734 @ X739)|((descr @ (^[Z0/* 3 */:$i]:((X733 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X734 @ Z0)))))|(((X737)!=(esk48_3 @ X733 @ X734 @ X737))|~(X733 @ X737))|(~(X733 @ (esk46_2 @ X733 @ X734))|~(X734 @ (esk47_2 @ X733 @ X734))))))&((((X734 @ (esk49_3 @ X733 @ X734 @ X739))|~(X734 @ X739)|((descr @ (^[Z0/* 3 */:$i]:((X733 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X734 @ Z0)))))|((X733 @ (esk48_3 @ X733 @ X734 @ X737))|~(X733 @ X737))|((X733 @ (esk46_2 @ X733 @ X734))|(X734 @ (esk47_2 @ X733 @ X734))))&(((X739)!=(esk49_3 @ X733 @ X734 @ X739))|~(X734 @ X739)|((descr @ (^[Z0/* 3 */:$i]:((X733 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X734 @ Z0)))))|((X733 @ (esk48_3 @ X733 @ X734 @ X737))|~(X733 @ X737))|((X733 @ (esk46_2 @ X733 @ X734))|(X734 @ (esk47_2 @ X733 @ X734)))))&(((X734 @ (esk49_3 @ X733 @ X734 @ X739))|~(X734 @ X739)|((descr @ (^[Z0/* 3 */:$i]:((X733 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X734 @ Z0)))))|(((X737)!=(esk48_3 @ X733 @ X734 @ X737))|~(X733 @ X737))|((X733 @ (esk46_2 @ X733 @ X734))|(X734 @ (esk47_2 @ X733 @ X734))))&(((X739)!=(esk49_3 @ X733 @ X734 @ X739))|~(X734 @ X739)|((descr @ (^[Z0/* 3 */:$i]:((X733 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X734 @ Z0)))))|(((X737)!=(esk48_3 @ X733 @ X734 @ X737))|~(X733 @ X737))|((X733 @ (esk46_2 @ X733 @ X734))|(X734 @ (esk47_2 @ X733 @ X734))))))))&((((in @ (esk50_4 @ X741 @ X742 @ X743 @ X744) @ X741)|((dsetconstr @ X741 @ (^[Z0/* 3 */:$i]:((X743 @ Z0))))=(dsetconstr @ X742 @ (^[Z0/* 3 */:$i]:((X744 @ Z0)))))|((X741)!=(X742)))&(((in @ (esk51_4 @ X741 @ X742 @ X743 @ X744) @ X742)|((dsetconstr @ X741 @ (^[Z0/* 3 */:$i]:((X743 @ Z0))))=(dsetconstr @ X742 @ (^[Z0/* 3 */:$i]:((X744 @ Z0)))))|((X741)!=(X742)))&((((esk50_4 @ X741 @ X742 @ X743 @ X744)=(esk51_4 @ X741 @ X742 @ X743 @ X744))|((dsetconstr @ X741 @ (^[Z0/* 3 */:$i]:((X743 @ Z0))))=(dsetconstr @ X742 @ (^[Z0/* 3 */:$i]:((X744 @ Z0)))))|((X741)!=(X742)))&((~(X743 @ (esk50_4 @ X741 @ X742 @ X743 @ X744))|~(X744 @ (esk51_4 @ X741 @ X742 @ X743 @ X744))|((dsetconstr @ X741 @ (^[Z0/* 3 */:$i]:((X743 @ Z0))))=(dsetconstr @ X742 @ (^[Z0/* 3 */:$i]:((X744 @ Z0)))))|((X741)!=(X742)))&((X743 @ (esk50_4 @ X741 @ X742 @ X743 @ X744))|(X744 @ (esk51_4 @ X741 @ X742 @ X743 @ X744))|((dsetconstr @ X741 @ (^[Z0/* 3 */:$i]:((X743 @ Z0))))=(dsetconstr @ X742 @ (^[Z0/* 3 */:$i]:((X744 @ Z0)))))|((X741)!=(X742)))))))&((((in @ (esk52_2 @ X747 @ X748) @ X747)|(~(in @ X750 @ X747)|(in @ X750 @ X748)))&(~(in @ (esk52_2 @ X747 @ X748) @ X748)|(~(in @ X750 @ X747)|(in @ X750 @ X748))))&((((X751)!=(X752))|(~(in @ X753 @ X752)|(in @ X753 @ X751)))&(((esk53_0)=(esk54_0))&((in @ esk55_0 @ esk53_0)&~(in @ esk55_0 @ esk54_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[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_122])])])])])])).
0.46/240.02	thf(c_0_124, negated_conjecture, ~((in @ esk55_0 @ esk54_0)), inference(split_conjunct,[status(thm)],[c_0_123])).
0.46/240.02	thf(c_0_125, negated_conjecture, ((esk53_0)=(esk54_0)), inference(split_conjunct,[status(thm)],[c_0_123])).
0.46/240.02	thf(c_0_126, negated_conjecture, (in @ esk55_0 @ esk53_0), inference(split_conjunct,[status(thm)],[c_0_123])).
0.46/240.02	thf(c_0_127, negated_conjecture, ~((in @ esk55_0 @ esk53_0)), inference(rw,[status(thm)],[c_0_124, c_0_125])).
0.46/240.02	thf(c_0_128, negated_conjecture, ($false), inference(sr,[status(thm)],[c_0_126, c_0_127]), ['proof']).
0.46/240.02	# SZS output end CNFRefutation
0.46/240.02	# Parsed axioms                        : 173
0.46/240.02	# Removed by relevancy pruning/SinE    : 93
0.46/240.02	# Initial clauses                      : 188
0.46/240.02	# Removed in clause preprocessing      : 13
0.46/240.02	# Initial clauses in saturation        : 175
0.46/240.02	# Processed clauses                    : 6
0.46/240.02	# ...of these trivial                  : 0
0.46/240.02	# ...subsumed                          : 0
0.46/240.02	# ...remaining for further processing  : 5
0.46/240.02	# Other redundant clauses eliminated   : 0
0.46/240.02	# Clauses deleted for lack of memory   : 0
0.46/240.02	# Backward-subsumed                    : 0
0.46/240.02	# Backward-rewritten                   : 0
0.46/240.02	# Generated clauses                    : 0
0.46/240.02	# ...of the previous two non-redundant : 0
0.46/240.02	# ...aggressively subsumed             : 0
0.46/240.02	# Contextual simplify-reflections      : 0
0.46/240.02	# Paramodulations                      : 0
0.46/240.02	# Factorizations                       : 0
0.46/240.02	# NegExts                              : 0
0.46/240.02	# Equation resolutions                 : 0
0.46/240.02	# Disequality decompositions           : 0
0.46/240.02	# Total rewrite steps                  : 1
0.46/240.02	# ...of those cached                   : 0
0.46/240.02	# Propositional unsat checks           : 0
0.46/240.02	#    Propositional check models        : 0
0.46/240.02	#    Propositional check unsatisfiable : 0
0.46/240.02	#    Propositional clauses             : 0
0.46/240.02	#    Propositional clauses after purity: 0
0.46/240.02	#    Propositional unsat core size     : 0
0.46/240.02	#    Propositional preprocessing time  : 0.000
0.46/240.02	#    Propositional encoding time       : 0.000
0.46/240.02	#    Propositional solver time         : 0.000
0.46/240.02	#    Success case prop preproc time    : 0.000
0.46/240.02	#    Success case prop encoding time   : 0.000
0.46/240.02	#    Success case prop solver time     : 0.000
0.46/240.02	# Current number of processed clauses  : 5
0.46/240.02	#    Positive orientable unit clauses  : 4
0.46/240.02	#    Positive unorientable unit clauses: 0
0.46/240.02	#    Negative unit clauses             : 1
0.46/240.02	#    Non-unit-clauses                  : 0
0.46/240.02	# Current number of unprocessed clauses: 169
0.46/240.02	# ...number of literals in the above   : 615
0.46/240.02	# Current number of archived formulas  : 0
0.46/240.02	# Current number of archived clauses   : 0
0.46/240.02	# Clause-clause subsumption calls (NU) : 0
0.46/240.02	# Rec. Clause-clause subsumption calls : 0
0.46/240.02	# Non-unit clause-clause subsumptions  : 0
0.46/240.02	# Unit Clause-clause subsumption calls : 0
0.46/240.02	# Rewrite failures with RHS unbound    : 0
0.46/240.02	# BW rewrite match attempts            : 0
0.46/240.02	# BW rewrite match successes           : 0
0.46/240.02	# Condensation attempts                : 6
0.46/240.02	# Condensation successes               : 0
0.46/240.02	# Termbank termtop insertions          : 21593
0.46/240.02	# Search garbage collected termcells   : 7781
0.46/240.02	
0.46/240.02	# -------------------------------------------------
0.46/240.02	# User time                : 0.023 s
0.46/240.02	# System time              : 0.008 s
0.46/240.02	# Total time               : 0.031 s
0.46/240.02	# Maximum resident set size: 4356 pages
0.46/240.02	
0.46/240.02	# -------------------------------------------------
0.46/240.02	# User time                : 0.028 s
0.46/240.02	# System time              : 0.011 s
0.46/240.02	# Total time               : 0.039 s
0.46/240.02	# Maximum resident set size: 1916 pages
0.46/240.02	% E exiting
0.46/240.03	% E exiting
0.46/240.03	EOF
