%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU562^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:26:43 AM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU562^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n019.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Sep 29 13:50:32 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running higher-order theorem proving
% 0.09/0.23 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p
% 0.19/0.27 % Version: 3.5.1-ho
% 0.19/0.27 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.19/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.19/0.27 % Starting sh5l with 300s (1) cores
% 0.19/0.27 % Starting new_bool_1 with 300s (1) cores
% 0.19/0.27 % Starting new_bool_2 with 300s (1) cores
% 0.19/0.27 % new_bool_2 with pid 799294 completed with status 0
% 0.19/0.27 % Result found by new_bool_2
% 0.19/0.27 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.19/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.19/0.27 % Starting sh5l with 300s (1) cores
% 0.19/0.27 % Starting new_bool_1 with 300s (1) cores
% 0.19/0.27 % Starting new_bool_2 with 300s (1) cores
% 0.19/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.19/0.27 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/0.27 % Search class: HGHSM-FSLM31-SHFMMMBN
% 0.19/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.19/0.27 % SubtermCWHack with pid 799295 completed with status 0
% 0.19/0.27 % Result found by SubtermCWHack
% 0.19/0.27 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.19/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.19/0.27 % Starting sh5l with 300s (1) cores
% 0.19/0.27 % Starting new_bool_1 with 300s (1) cores
% 0.19/0.27 % Starting new_bool_2 with 300s (1) cores
% 0.19/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.19/0.27 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/0.27 % Search class: HGHSM-FSLM31-SHFMMMBN
% 0.19/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.19/0.27 % Preprocessing time : 0.002 s
% 0.19/0.27
% 0.19/0.27 % Proof found!
% 0.19/0.27 % SZS status Theorem
% 0.19/0.27 % SZS output start CNFRefutation
% 0.19/0.27 thf(decl_23, type, in: $i > $i > $o).
% 0.19/0.27 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.19/0.27 thf(decl_25, type, setextAx: $o).
% 0.19/0.27 thf(decl_26, type, emptyset: $i).
% 0.19/0.27 thf(decl_27, type, emptysetAx: $o).
% 0.19/0.27 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.19/0.27 thf(decl_29, type, setadjoinAx: $o).
% 0.19/0.27 thf(decl_30, type, powerset: $i > $i).
% 0.19/0.27 thf(decl_31, type, powersetAx: $o).
% 0.19/0.27 thf(decl_32, type, setunion: $i > $i).
% 0.19/0.27 thf(decl_33, type, setunionAx: $o).
% 0.19/0.27 thf(decl_34, type, omega: $i).
% 0.19/0.27 thf(decl_35, type, omega0Ax: $o).
% 0.19/0.27 thf(decl_36, type, omegaSAx: $o).
% 0.19/0.27 thf(decl_37, type, omegaIndAx: $o).
% 0.19/0.27 thf(decl_38, type, replAx: $o).
% 0.19/0.27 thf(decl_39, type, foundationAx: $o).
% 0.19/0.27 thf(decl_40, type, wellorderingAx: $o).
% 0.19/0.27 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.19/0.27 thf(decl_42, type, descrp: $o).
% 0.19/0.27 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.19/0.27 thf(decl_44, type, dsetconstrI: $o).
% 0.19/0.27 thf(decl_45, type, dsetconstrEL: $o).
% 0.19/0.27 thf(decl_46, type, dsetconstrER: $o).
% 0.19/0.27 thf(decl_47, type, exuE1: $o).
% 0.19/0.27 thf(decl_48, type, prop2set: $o > $i).
% 0.19/0.27 thf(decl_49, type, prop2setE: $o).
% 0.19/0.27 thf(decl_50, type, emptysetE: $o).
% 0.19/0.27 thf(decl_51, type, emptysetimpfalse: $o).
% 0.19/0.27 thf(decl_52, type, notinemptyset: $o).
% 0.19/0.27 thf(decl_53, type, exuE3e: $o).
% 0.19/0.27 thf(decl_54, type, setext: $o).
% 0.19/0.27 thf(decl_55, type, emptyI: $o).
% 0.19/0.27 thf(decl_56, type, noeltsimpempty: $o).
% 0.19/0.27 thf(decl_57, type, setbeta: $o).
% 0.19/0.27 thf(decl_58, type, nonempty: $i > $o).
% 0.19/0.27 thf(decl_59, type, nonemptyE1: $o).
% 0.19/0.27 thf(decl_60, type, nonemptyI: $o).
% 0.19/0.27 thf(decl_61, type, nonemptyI1: $o).
% 0.19/0.27 thf(decl_62, type, setadjoinIL: $o).
% 0.19/0.27 thf(decl_63, type, emptyinunitempty: $o).
% 0.19/0.27 thf(decl_64, type, setadjoinIR: $o).
% 0.19/0.27 thf(decl_65, type, setadjoinE: $o).
% 0.19/0.27 thf(decl_66, type, setadjoinOr: $o).
% 0.19/0.27 thf(decl_67, type, setoftrueEq: $o).
% 0.19/0.27 thf(decl_68, type, powersetI: $o).
% 0.19/0.27 thf(decl_69, type, emptyinPowerset: $o).
% 0.19/0.27 thf(decl_70, type, emptyInPowerset: $o).
% 0.19/0.27 thf(decl_71, type, powersetE: $o).
% 0.19/0.27 thf(decl_72, type, setunionI: $o).
% 0.19/0.27 thf(decl_73, type, setunionE: $o).
% 0.19/0.27 thf(decl_74, type, subPowSU: $o).
% 0.19/0.27 thf(decl_75, type, exuE2: $o).
% 0.19/0.27 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.19/0.27 thf(decl_77, type, uniqinunit: $o).
% 0.19/0.27 thf(decl_78, type, notinsingleton: $o).
% 0.19/0.27 thf(decl_79, type, eqinunit: $o).
% 0.19/0.27 thf(decl_80, type, singletonsswitch: $o).
% 0.19/0.27 thf(decl_81, type, upairsetE: $o).
% 0.19/0.27 thf(decl_82, type, upairsetIL: $o).
% 0.19/0.27 thf(decl_83, type, upairsetIR: $o).
% 0.19/0.27 thf(decl_84, type, emptyE1: $o).
% 0.19/0.27 thf(decl_85, type, vacuousDall: $o).
% 0.19/0.27 thf(decl_86, type, quantDeMorgan1: $o).
% 0.19/0.27 thf(decl_87, type, quantDeMorgan2: $o).
% 0.19/0.27 thf(decl_88, type, quantDeMorgan3: $o).
% 0.19/0.27 thf(decl_89, type, quantDeMorgan4: $o).
% 0.19/0.27 thf(decl_90, type, prop2setI: $o).
% 0.19/0.27 thf(decl_92, type, prop2set2propI: $o).
% 0.19/0.27 thf(decl_93, type, notdexE: $o).
% 0.19/0.27 thf(decl_94, type, notdallE: $o).
% 0.19/0.27 thf(decl_95, type, exuI1: $o).
% 0.19/0.27 thf(decl_96, type, exuI3: $o).
% 0.19/0.27 thf(decl_97, type, exuI2: $o).
% 0.19/0.27 thf(decl_98, type, inCongP: $o).
% 0.19/0.27 thf(decl_99, type, in__Cong: $o).
% 0.19/0.27 thf(decl_100, type, exuE3u: $o).
% 0.19/0.27 thf(decl_101, type, exu__Cong: $o).
% 0.19/0.27 thf(decl_102, type, emptyset__Cong: $o).
% 0.19/0.27 thf(decl_103, type, setadjoin__Cong: $o).
% 0.19/0.27 thf(decl_104, type, powerset__Cong: $o).
% 0.19/0.27 thf(decl_105, type, setunion__Cong: $o).
% 0.19/0.27 thf(decl_106, type, omega__Cong: $o).
% 0.19/0.27 thf(decl_107, type, exuEu: $o).
% 0.19/0.27 thf(decl_108, type, descr__Cong: $o).
% 0.19/0.27 thf(decl_109, type, dsetconstr__Cong: $o).
% 0.19/0.27 thf(decl_110, type, subset: $i > $i > $o).
% 0.19/0.27 thf(decl_113, type, subsetI1: $o).
% 0.19/0.27 thf(decl_114, type, eqimpsubset2: $o).
% 0.19/0.27 thf(decl_115, type, eqimpsubset1: $o).
% 0.19/0.27 thf(decl_116, type, epred1_0: $o).
% 0.19/0.27 thf(decl_117, type, esk1_2: $i > $i > $i).
% 0.19/0.27 thf(decl_118, type, esk2_2: $i > $i > $i).
% 0.19/0.27 thf(decl_119, type, esk3_2: $i > $i > $i).
% 0.19/0.27 thf(decl_120, type, esk4_1: $i > $i).
% 0.19/0.27 thf(decl_121, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.19/0.27 thf(decl_122, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.19/0.27 thf(decl_123, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.19/0.27 thf(decl_124, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.19/0.27 thf(decl_125, type, esk9_1: $i > $i).
% 0.19/0.27 thf(decl_126, type, esk10_2: ($i > $o) > $i > $i).
% 0.19/0.27 thf(decl_127, type, esk11_2: ($i > $o) > $i > $i).
% 0.19/0.27 thf(decl_128, type, esk12_1: ($i > $o) > $i).
% 0.19/0.27 thf(decl_129, type, esk13_2: ($i > $o) > $i > $i).
% 0.19/0.27 thf(decl_130, type, esk14_1: ($i > $o) > $i).
% 0.19/0.27 thf(decl_131, type, esk15_2: $i > $i > $i).
% 0.19/0.27 thf(decl_132, type, esk16_2: $i > $i > $i).
% 0.19/0.27 thf(decl_133, type, esk17_1: $i > $i).
% 0.19/0.27 thf(decl_134, type, esk18_1: $i > $i).
% 0.19/0.27 thf(decl_135, type, esk19_1: $i > $i).
% 0.19/0.27 thf(decl_136, type, esk20_2: $i > $i > $i).
% 0.19/0.27 thf(decl_137, type, esk21_3: $i > $i > $o > $i).
% 0.19/0.27 thf(decl_138, type, esk22_2: ($i > $o) > $i > $i).
% 0.19/0.27 thf(decl_139, type, esk23_1: ($i > $o) > $i).
% 0.19/0.27 thf(decl_140, type, esk24_1: $i > $i).
% 0.19/0.27 thf(decl_141, type, esk25_2: $i > ($i > $o) > $i).
% 0.19/0.27 thf(decl_142, type, esk26_2: $i > ($i > $o) > $i).
% 0.19/0.27 thf(decl_143, type, esk27_2: $i > ($i > $o) > $i).
% 0.19/0.27 thf(decl_144, type, esk28_2: $i > ($i > $o) > $i).
% 0.19/0.27 thf(decl_145, type, esk29_2: $i > ($i > $o) > $i).
% 0.19/0.27 thf(decl_146, type, esk30_2: $i > ($i > $o) > $i).
% 0.19/0.27 thf(decl_147, type, esk31_2: ($i > $o) > $i > $i).
% 0.19/0.27 thf(decl_148, type, esk32_1: ($i > $o) > $i).
% 0.19/0.27 thf(decl_149, type, esk33_1: ($i > $o) > $i).
% 0.19/0.27 thf(decl_150, type, esk34_1: ($i > $o) > $i).
% 0.19/0.27 thf(decl_151, type, esk35_1: ($i > $o) > $i).
% 0.19/0.27 thf(decl_152, type, esk36_2: ($i > $o) > $i > $i).
% 0.19/0.27 thf(decl_153, type, esk37_1: ($i > $o) > $i).
% 0.19/0.27 thf(decl_154, type, esk38_2: ($i > $o) > $i > $i).
% 0.19/0.27 thf(decl_155, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 0.19/0.27 thf(decl_156, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 0.19/0.27 thf(decl_157, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.19/0.27 thf(decl_158, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 0.19/0.27 thf(decl_159, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.19/0.27 thf(decl_160, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 0.19/0.27 thf(decl_161, type, esk45_2: ($i > $o) > $i > $i).
% 0.19/0.27 thf(decl_162, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 0.19/0.27 thf(decl_163, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 0.19/0.27 thf(decl_164, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.19/0.27 thf(decl_165, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.19/0.27 thf(decl_166, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.19/0.27 thf(decl_167, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.19/0.27 thf(decl_168, type, esk52_2: $i > $i > $i).
% 0.19/0.27 thf(decl_169, type, esk53_0: $i).
% 0.19/0.27 thf(decl_170, type, esk54_0: $i).
% 0.19/0.27 thf(decl_171, type, esk55_0: $i).
% 0.19/0.27 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', exuE3u)).
% 0.19/0.27 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', exu)).
% 0.19/0.27 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', exu__Cong)).
% 0.19/0.27 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', exuEu)).
% 0.19/0.27 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', descr__Cong)).
% 0.19/0.27 thf(subset, axiom, ((subset)=(^[X4:$i, X5:$i]:(![X2:$i]:((((in @ X2 @ X4))=>((in @ X2 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', subset)).
% 0.19/0.27 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.HE86sOTfKU/E---3.1_799278.p', exuE1)).
% 0.19/0.27 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', descrp)).
% 0.19/0.27 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', nonemptyI)).
% 0.19/0.27 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', nonempty)).
% 0.19/0.27 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', exuE3e)).
% 0.19/0.27 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', exuE2)).
% 0.19/0.27 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', exuI3)).
% 0.19/0.27 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', exuI2)).
% 0.19/0.27 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.HE86sOTfKU/E---3.1_799278.p', exuI1)).
% 0.19/0.27 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', replAx)).
% 0.19/0.27 thf(subsetI2, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', subsetI2)).
% 0.19/0.27 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', dsetconstr__Cong)).
% 0.19/0.27 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', subsetI1)).
% 0.19/0.27 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', eqimpsubset2)).
% 0.19/0.27 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', dsetconstrER)).
% 0.19/0.27 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', eqimpsubset1)).
% 0.19/0.27 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', dsetconstrEL)).
% 0.19/0.27 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', dsetconstrI)).
% 0.19/0.27 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', nonemptyE1)).
% 0.19/0.27 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', setbeta)).
% 0.19/0.27 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', nonemptyI1)).
% 0.19/0.27 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', setoftrueEq)).
% 0.19/0.27 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', nonemptyImpWitness)).
% 0.19/0.27 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.HE86sOTfKU/E---3.1_799278.p', emptyE1)).
% 0.19/0.27 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', emptyset__Cong)).
% 0.19/0.27 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.HE86sOTfKU/E---3.1_799278.p', setadjoin__Cong)).
% 0.19/0.27 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', powerset__Cong)).
% 0.19/0.27 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', setunion__Cong)).
% 0.19/0.27 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', omega__Cong)).
% 0.19/0.27 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', emptysetimpfalse)).
% 0.19/0.27 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', emptysetE)).
% 0.19/0.27 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', prop2setE)).
% 0.19/0.27 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', notinemptyset)).
% 0.19/0.27 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', noeltsimpempty)).
% 0.19/0.27 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', emptyI)).
% 0.19/0.27 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', setext)).
% 0.19/0.27 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', powersetI)).
% 0.19/0.27 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', setadjoinOr)).
% 0.19/0.27 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', setadjoinE)).
% 0.19/0.27 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', setadjoinIR)).
% 0.19/0.27 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', emptyinunitempty)).
% 0.19/0.27 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', setadjoinIL)).
% 0.19/0.27 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', emptyinPowerset)).
% 0.19/0.27 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', subPowSU)).
% 0.19/0.27 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', setunionE)).
% 0.19/0.27 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', setunionI)).
% 0.19/0.27 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', powersetE)).
% 0.19/0.27 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', emptyInPowerset)).
% 0.19/0.27 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', uniqinunit)).
% 0.19/0.27 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', upairsetIR)).
% 0.19/0.27 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', upairsetIL)).
% 0.19/0.27 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', upairsetE)).
% 0.19/0.27 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', singletonsswitch)).
% 0.19/0.27 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', eqinunit)).
% 0.19/0.27 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', notinsingleton)).
% 0.19/0.27 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', vacuousDall)).
% 0.19/0.27 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', notdallE)).
% 0.19/0.27 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', notdexE)).
% 0.19/0.27 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', prop2setI)).
% 0.19/0.27 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', quantDeMorgan4)).
% 0.19/0.27 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', quantDeMorgan3)).
% 0.19/0.27 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', quantDeMorgan2)).
% 0.19/0.27 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', quantDeMorgan1)).
% 0.19/0.27 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', inCongP)).
% 0.19/0.27 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', in__Cong)).
% 0.19/0.27 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.HE86sOTfKU/E---3.1_799278.p', wellorderingAx)).
% 0.19/0.27 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.HE86sOTfKU/E---3.1_799278.p', foundationAx)).
% 0.19/0.27 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', omegaIndAx)).
% 0.19/0.27 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', omegaSAx)).
% 0.19/0.27 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', omega0Ax)).
% 0.19/0.27 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', setunionAx)).
% 0.19/0.27 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', powersetAx)).
% 0.19/0.27 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', setadjoinAx)).
% 0.19/0.27 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', emptysetAx)).
% 0.19/0.27 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.HE86sOTfKU/E---3.1_799278.p', setextAx)).
% 0.19/0.27 thf(c_0_81, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 0.19/0.27 thf(c_0_82, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.19/0.27 thf(c_0_83, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.19/0.27 thf(c_0_84, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 0.19/0.27 thf(c_0_85, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))=>((exu @ (^[Z0:$i]:((X17 @ Z0))))=>((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 0.19/0.27 thf(c_0_86, plain, ((subset)=(^[Z0:$i, Z1:$i]:(![X2:$i]:((((in @ X2 @ Z0))=>((in @ X2 @ Z1))))))), inference(fof_simplification,[status(thm)],[subset])).
% 0.19/0.27 thf(c_0_87, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.19/0.27 thf(c_0_88, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.19/0.27 thf(c_0_89, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.19/0.27 thf(c_0_90, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.19/0.27 thf(c_0_91, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.19/0.27 thf(c_0_92, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.19/0.27 thf(c_0_93, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.19/0.27 thf(c_0_94, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.19/0.27 thf(c_0_95, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 0.19/0.27 thf(c_0_96, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.19/0.27 thf(c_0_97, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[subsetI2])).
% 0.19/0.27 thf(c_0_98, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X256:$i]:(((((X1 @ X256)))&(![X257:$i]:(((((X1 @ X257)))=>(((X256)=(X257))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_81, c_0_82])).
% 0.19/0.27 thf(c_0_99, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X258:$i]:(((((X1 @ X258)))&(![X259:$i]:(((((X1 @ X259)))=>(((X258)=(X259))))))))))<=>((?[X260:$i]:(((((X17 @ X260)))&(![X261:$i]:(((((X17 @ X261)))=>(((X260)=(X261)))))))))))))))), inference(apply_def,[status(thm)],[c_0_83, c_0_82])).
% 0.19/0.27 thf(c_0_100, plain, ((exuEu)=(![X1:$i > $o]:((((?[X262:$i]:(((((X1 @ X262)))&(![X263:$i]:(((((X1 @ X263)))=>(((X262)=(X263))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_84, c_0_82])).
% 0.19/0.27 thf(c_0_101, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X264:$i]:(((((X1 @ X264)))&(![X265:$i]:(((((X1 @ X265)))=>(((X264)=(X265))))))))))=>((((?[X266:$i]:(((((X17 @ X266)))&(![X267:$i]:(((((X17 @ X267)))=>(((X266)=(X267))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_85, c_0_82])).
% 0.19/0.27 thf(c_0_102, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 0.19/0.27 thf(c_0_103, axiom, ((subsetI1)=(![X4:$i, X5:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((in @ X2 @ X5)))))=>((![X268:$i]:((((in @ X268 @ X4))=>((in @ X268 @ X5)))))))))), inference(apply_def,[status(thm)],[subsetI1, c_0_86])).
% 0.19/0.27 thf(c_0_104, plain, ((exuE1)=(![X1:$i > $o]:((((?[X244:$i]:(((((X1 @ X244)))&(![X245:$i]:(((((X1 @ X245)))=>(((X244)=(X245))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_87, c_0_82])).
% 0.19/0.27 thf(c_0_105, axiom, ((eqimpsubset2)=(![X4:$i, X5:$i]:(((((X4)=(X5)))=>((![X269:$i]:((((in @ X269 @ X5))=>((in @ X269 @ X4)))))))))), inference(apply_def,[status(thm)],[eqimpsubset2, c_0_86])).
% 0.19/0.27 thf(c_0_106, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.19/0.27 thf(c_0_107, axiom, ((eqimpsubset1)=(![X4:$i, X5:$i]:(((((X4)=(X5)))=>((![X270:$i]:((((in @ X270 @ X4))=>((in @ X270 @ X5)))))))))), inference(apply_def,[status(thm)],[eqimpsubset1, c_0_86])).
% 0.19/0.27 thf(c_0_108, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.19/0.27 thf(c_0_109, plain, ((descrp)=(![X1:$i > $o]:((((?[X242:$i]:(((((X1 @ X242)))&(![X243:$i]:(((((X1 @ X243)))=>(((X242)=(X243))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_88, c_0_82])).
% 0.19/0.27 thf(c_0_110, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.19/0.27 thf(c_0_111, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_89, c_0_90])).
% 0.19/0.27 thf(c_0_112, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_90])).
% 0.19/0.27 thf(c_0_113, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.19/0.27 thf(c_0_114, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X246:$i]:(((((X1 @ X246)))&(![X247:$i]:(((((X1 @ X247)))=>(((X246)=(X247))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_91, c_0_82])).
% 0.19/0.27 thf(c_0_115, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_90])).
% 0.19/0.27 thf(c_0_116, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.19/0.27 thf(c_0_117, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_90])).
% 0.19/0.27 thf(c_0_118, plain, ((exuE2)=(![X1:$i > $o]:((((?[X248:$i]:(((((X1 @ X248)))&(![X249:$i]:(((((X1 @ X249)))=>(((X248)=(X249))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_92, c_0_82])).
% 0.19/0.27 thf(c_0_119, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
% 0.19/0.27 thf(c_0_120, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X252:$i]:(((((X1 @ X252)))&(![X253:$i]:(((((X1 @ X253)))=>(((X252)=(X253)))))))))))))))), inference(apply_def,[status(thm)],[c_0_93, c_0_82])).
% 0.19/0.27 thf(c_0_121, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X254:$i]:(((((X1 @ X254)))&(![X255:$i]:(((((X1 @ X255)))=>(((X254)=(X255)))))))))))))), inference(apply_def,[status(thm)],[c_0_94, c_0_82])).
% 0.19/0.27 thf(c_0_122, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X250:$i]:(((((X1 @ X250)))&(![X251:$i]:(((((X1 @ X251)))=>(((X250)=(X251)))))))))))))), inference(apply_def,[status(thm)],[c_0_95, c_0_82])).
% 0.19/0.27 thf(c_0_123, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X240:$i]:(((((X6 @ X2 @ X240)))&(![X241:$i]:(((((X6 @ X2 @ X241)))=>(((X240)=(X241)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_96, c_0_82])).
% 0.19/0.27 thf(c_0_124, plain, ((epred1_0)<=>![X300:$i]:(?[X301:$i]:((((![X302:$i]:(((in @ X302 @ X301)=>![X303:$i]:(((in @ X303 @ X302)=>(in @ X303 @ X300)))))&![X304:$i, X305:$i]:((((in @ X304 @ X300)&(in @ X305 @ X300))=>(![X306:$i]:(((in @ X306 @ X301)=>((in @ X304 @ X306)<=>(in @ X305 @ X306))))=>((X304)=(X305))))))&![X307:$i, X308:$i]:((((in @ X307 @ X301)&(in @ X308 @ X301))=>(![X309:$i]:(((in @ X309 @ X307)=>(in @ X309 @ X308)))|![X310:$i]:(((in @ X310 @ X308)=>(in @ X310 @ X307)))))))&![X311:$i]:(((![X312:$i]:(((in @ X312 @ X311)=>(in @ X312 @ X300)))&?[X313:$i]:((in @ X313 @ X311)))=>?[X314:$i, X315:$i]:(((((in @ X314 @ X301)&(in @ X315 @ X311))&~(?[X316:$i]:(((in @ X316 @ X314)&(in @ X316 @ X311)))))&![X317:$i]:(((in @ X317 @ X301)=>(![X318:$i]:(((in @ X318 @ X317)=>(in @ X318 @ X314)))|(in @ X315 @ X317)))))))))))), introduced(definition)).
% 0.19/0.27 thf(c_0_125, negated_conjecture, ~((![X271:$i, X272:$i]:((![X273:$i]:(((in @ X273 @ X271)<=>(in @ X273 @ X272)))=>((X271)=(X272))))=>(![X274:$i]:(~(in @ X274 @ emptyset))=>(![X275:$i, X276:$i, X277:$i]:(((in @ X277 @ (setadjoin @ X275 @ X276))<=>(((X277)=(X275))|(in @ X277 @ X276))))=>(![X278:$i, X279:$i]:(((in @ X279 @ (powerset @ X278))<=>![X280:$i]:(((in @ X280 @ X279)=>(in @ X280 @ X278)))))=>(![X281:$i, X282:$i]:(((in @ X282 @ (setunion @ X281))<=>?[X283:$i]:(((in @ X282 @ X283)&(in @ X283 @ X281)))))=>((in @ emptyset @ omega)=>(![X284:$i]:(((in @ X284 @ omega)=>(in @ (setadjoin @ X284 @ X284) @ omega)))=>(![X285:$i]:((((in @ emptyset @ X285)&![X286:$i]:((((in @ X286 @ omega)&(in @ X286 @ X285))=>(in @ (setadjoin @ X286 @ X286) @ X285))))=>![X287:$i]:(((in @ X287 @ omega)=>(in @ X287 @ X285)))))=>(![X288:$i > $i > $o, X289:$i]:((![X290:$i]:(((in @ X290 @ X289)=>?[X291:$i]:(((X288 @ X290 @ X291)&![X292:$i]:(((X288 @ X290 @ X292)=>((X291)=(X292))))))))=>?[X293:$i]:(![X294:$i]:(((in @ X294 @ X293)<=>?[X295:$i]:(((in @ X295 @ X289)&(X288 @ X295 @ X294))))))))=>(![X296:$i]:((?[X297:$i]:((in @ X297 @ X296))=>?[X298:$i]:(((in @ X298 @ X296)&~(?[X299:$i]:(((in @ X299 @ X298)&(in @ X299 @ X296))))))))=>((epred1_0)=>(![X319:$i > $o]:((?[X320:$i]:(((X319 @ X320)&![X321:$i]:(((X319 @ X321)=>((X320)=(X321))))))=>(X319 @ (descr @ (^[Z0:$i]:((X319 @ Z0)))))))=>(![X322:$i, X323:$i > $o, X324:$i]:(((in @ X324 @ X322)=>((X323 @ X324)=>(in @ X324 @ (dsetconstr @ X322 @ (^[Z0:$i]:((X323 @ Z0))))))))=>(![X325:$i, X326:$i > $o, X327:$i]:(((in @ X327 @ (dsetconstr @ X325 @ (^[Z0:$i]:((X326 @ Z0)))))=>(in @ X327 @ X325)))=>(![X328:$i, X329:$i > $o, X330:$i]:(((in @ X330 @ (dsetconstr @ X328 @ (^[Z0:$i]:((X329 @ Z0)))))=>(X329 @ X330)))=>(![X331:$i > $o]:((?[X332:$i]:(((X331 @ X332)&![X333:$i]:(((X331 @ X333)=>((X332)=(X333))))))=>?[X334:$i]:(((X331 @ X334)&![X335:$i]:(((X331 @ X335)=>((X334)=(X335))))))))=>(![X336:$o, X337:$i]:(((in @ X337 @ (prop2set @ ((X336))))=>(X336)))=>(![X338:$i]:(((in @ X338 @ emptyset)=>![X339:$o]:((X339))))=>(![X340:$i]:(~(in @ X340 @ emptyset))=>(![X341:$i]:(~(in @ X341 @ emptyset))=>(![X342:$i > $o]:((?[X343:$i]:(((X342 @ X343)&![X344:$i]:(((X342 @ X344)=>((X343)=(X344))))))=>?[X345:$i]:((X342 @ X345))))=>(![X346:$i, X347:$i]:((![X348:$i]:(((in @ X348 @ X346)=>(in @ X348 @ X347)))=>(![X349:$i]:(((in @ X349 @ X347)=>(in @ X349 @ X346)))=>((X346)=(X347)))))=>(![X350:$i]:((![X351:$i]:(~(in @ X351 @ X350))=>((X350)=(emptyset))))=>(![X352:$i]:((![X353:$i]:(~(in @ X353 @ X352))=>((X352)=(emptyset))))=>(![X354:$i, X355:$i > $o, X356:$i]:(((in @ X356 @ X354)=>((in @ X356 @ (dsetconstr @ X354 @ (^[Z0:$i]:((X355 @ Z0)))))<=>(X355 @ X356))))=>(![X357:$i]:((((X357)!=(emptyset))=>?[X358:$i]:((in @ X358 @ X357))))=>(![X359:$i, X360:$i > $o, X361:$i]:(((in @ X361 @ X359)=>((X360 @ X361)=>((dsetconstr @ X359 @ (^[Z0:$i]:((X360 @ Z0))))!=(emptyset)))))=>(![X362:$i]:((?[X363:$i]:((in @ X363 @ X362))=>((X362)!=(emptyset))))=>(![X364:$i, X365:$i]:((in @ X364 @ (setadjoin @ X364 @ X365)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X366:$i, X367:$i, X368:$i]:(((in @ X368 @ X367)=>(in @ X368 @ (setadjoin @ X366 @ X367))))=>(![X369:$i, X370:$i, X371:$i]:(((in @ X371 @ (setadjoin @ X369 @ X370))=>![X372:$o]:(((((X371)=(X369))=>(X372))=>(((in @ X371 @ X370)=>(X372))=>(X372))))))=>(![X373:$i, X374:$i, X375:$i]:(((in @ X375 @ (setadjoin @ X373 @ X374))=>(((X375)=(X373))|(in @ X375 @ X374))))=>(![X376:$i]:(((dsetconstr @ X376 @ (^[Z0:$i]:(($true))))=(X376)))=>(![X377:$i, X378:$i]:((![X379:$i]:(((in @ X379 @ X378)=>(in @ X379 @ X377)))=>(in @ X378 @ (powerset @ X377))))=>(![X380:$i]:((in @ emptyset @ (powerset @ X380)))=>(![X381:$i]:((in @ emptyset @ (powerset @ X381)))=>(![X382:$i, X383:$i, X384:$i]:(((in @ X383 @ (powerset @ X382))=>((in @ X384 @ X383)=>(in @ X384 @ X382))))=>(![X385:$i, X386:$i, X387:$i]:(((in @ X386 @ X387)=>((in @ X387 @ X385)=>(in @ X386 @ (setunion @ X385)))))=>(![X388:$i, X389:$i]:(((in @ X389 @ (setunion @ X388))=>![X390:$o]:((![X391:$i]:(((in @ X389 @ X391)=>((in @ X391 @ X388)=>(X390))))=>(X390)))))=>(![X392:$i, X393:$i]:(((in @ X393 @ X392)=>(in @ X393 @ (powerset @ (setunion @ X392)))))=>(![X394:$i > $o]:((?[X395:$i]:(((X394 @ X395)&![X396:$i]:(((X394 @ X396)=>((X395)=(X396))))))=>?[X397:$i]:(![X398:$i]:(((X394 @ X398)<=>((X398)=(X397)))))))=>(![X399:$i]:((((X399)!=(emptyset))=>?[X400:$i]:((in @ X400 @ X399))))=>(![X401:$i, X402:$i]:(((in @ X401 @ (setadjoin @ X402 @ emptyset))=>((X401)=(X402))))=>(![X403:$i, X404:$i]:((((X403)!=(X404))=>~(in @ X404 @ (setadjoin @ X403 @ emptyset))))=>(![X405:$i, X406:$i]:((((X405)=(X406))=>(in @ X405 @ (setadjoin @ X406 @ emptyset))))=>(![X407:$i, X408:$i]:(((in @ X407 @ (setadjoin @ X408 @ emptyset))=>(in @ X408 @ (setadjoin @ X407 @ emptyset))))=>(![X409:$i, X410:$i, X411:$i]:(((in @ X411 @ (setadjoin @ X409 @ (setadjoin @ X410 @ emptyset)))=>(((X411)=(X409))|((X411)=(X410)))))=>(![X412:$i, X413:$i]:((in @ X412 @ (setadjoin @ X412 @ (setadjoin @ X413 @ emptyset))))=>(![X414:$i, X415:$i]:((in @ X415 @ (setadjoin @ X414 @ (setadjoin @ X415 @ emptyset))))=>(![X416:$i, X417:$i > $o]:((?[X418:$i]:(((in @ X418 @ X416)&(X417 @ X418)))=>((dsetconstr @ X416 @ (^[Z0:$i]:((X417 @ Z0))))!=(emptyset))))=>(![X419:$i > $o, X420:$i]:(((in @ X420 @ emptyset)=>(X419 @ X420)))=>(![X421:$i, X422:$i > $o]:((~(![X423:$i]:(((in @ X423 @ X421)=>(X422 @ X423))))=>?[X424:$i]:(((in @ X424 @ X421)&~(X422 @ X424)))))=>(![X425:$i, X426:$i > $o]:((![X427:$i]:(((in @ X427 @ X425)=>~(X426 @ X427)))=>~(?[X428:$i]:(((in @ X428 @ X425)&(X426 @ X428))))))=>(![X429:$i, X430:$i > $o]:((~(?[X431:$i]:(((in @ X431 @ X429)&(X430 @ X431))))=>![X432:$i]:(((in @ X432 @ X429)=>~(X430 @ X432)))))=>(![X433:$i, X434:$i > $o]:((?[X435:$i]:(((in @ X435 @ X433)&~(X434 @ X435)))=>~(![X436:$i]:(((in @ X436 @ X433)=>(X434 @ X436))))))=>(![X437:$o]:(((X437)=>(in @ emptyset @ (prop2set @ ((X437))))))=>((prop2set2propI)=>(![X438:$i, X439:$i > $o]:((~(?[X440:$i]:(((in @ X440 @ X438)&(X439 @ X440))))=>![X441:$i]:(((in @ X441 @ X438)=>~(X439 @ X441)))))=>(![X442:$i, X443:$i > $o]:((~(![X444:$i]:(((in @ X444 @ X442)=>(X443 @ X444))))=>?[X445:$i]:(((in @ X445 @ X442)&~(X443 @ X445)))))=>(![X446:$i > $o]:((?[X447:$i]:(((X446 @ X447)&![X448:$i]:(((X446 @ X448)=>((X447)=(X448))))))=>?[X449:$i]:(((X446 @ X449)&![X450:$i]:(((X446 @ X450)=>((X449)=(X450))))))))=>(![X451:$i > $o]:((?[X452:$i]:((X451 @ X452))=>(![X453:$i, X454:$i]:(((X451 @ X453)=>((X451 @ X454)=>((X453)=(X454)))))=>?[X455:$i]:(((X451 @ X455)&![X456:$i]:(((X451 @ X456)=>((X455)=(X456)))))))))=>(![X457:$i > $o]:((?[X458:$i]:(![X459:$i]:(((X457 @ X459)<=>((X459)=(X458)))))=>?[X460:$i]:(((X457 @ X460)&![X461:$i]:(((X457 @ X461)=>((X460)=(X461))))))))=>(![X462:$i, X463:$i]:((((X462)=(X463))=>![X464:$i, X465:$i]:((((X464)=(X465))=>((in @ X464 @ X462)=>(in @ X465 @ X463))))))=>(![X466:$i, X467:$i]:((((X466)=(X467))=>![X468:$i, X469:$i]:((((X468)=(X469))=>((in @ X468 @ X466)<=>(in @ X469 @ X467))))))=>(![X470:$i > $o]:((?[X471:$i]:(((X470 @ X471)&![X472:$i]:(((X470 @ X472)=>((X471)=(X472))))))=>![X473:$i, X474:$i]:(((X470 @ X473)=>((X470 @ X474)=>((X473)=(X474)))))))=>(![X475:$i > $o, X476:$i > $o]:((![X477:$i, X478:$i]:((((X477)=(X478))=>((X475 @ X477)<=>(X476 @ X478))))=>(?[X479:$i]:(((X475 @ X479)&![X480:$i]:(((X475 @ X480)=>((X479)=(X480))))))<=>?[X481:$i]:(((X476 @ X481)&![X482:$i]:(((X476 @ X482)=>((X481)=(X482)))))))))=>(((emptyset)=(emptyset))=>(![X483:$i, X484:$i]:((((X483)=(X484))=>![X485:$i, X486:$i]:((((X485)=(X486))=>((setadjoin @ X483 @ X485)=(setadjoin @ X484 @ X486))))))=>(![X487:$i, X488:$i]:((((X487)=(X488))=>((powerset @ X487)=(powerset @ X488))))=>(![X489:$i, X490:$i]:((((X489)=(X490))=>((setunion @ X489)=(setunion @ X490))))=>(((omega)=(omega))=>(![X491:$i > $o]:((?[X492:$i]:(((X491 @ X492)&![X493:$i]:(((X491 @ X493)=>((X492)=(X493))))))=>![X494:$i, X495:$i]:(((X491 @ X494)=>((X491 @ X495)=>((X494)=(X495)))))))=>(![X496:$i > $o, X497:$i > $o]:((![X498:$i, X499:$i]:((((X498)=(X499))=>((X496 @ X498)<=>(X497 @ X499))))=>(?[X500:$i]:(((X496 @ X500)&![X501:$i]:(((X496 @ X501)=>((X500)=(X501))))))=>(?[X502:$i]:(((X497 @ X502)&![X503:$i]:(((X497 @ X503)=>((X502)=(X503))))))=>((descr @ (^[Z0:$i]:((X496 @ Z0))))=(descr @ (^[Z0:$i]:((X497 @ Z0)))))))))=>(![X504:$i, X505:$i]:((((X504)=(X505))=>![X506:$i > $o, X507:$i > $o]:((![X508:$i]:(((in @ X508 @ X504)=>![X509:$i]:(((in @ X509 @ X505)=>(((X508)=(X509))=>((X506 @ X508)<=>(X507 @ X509)))))))=>((dsetconstr @ X504 @ (^[Z0:$i]:((X506 @ Z0))))=(dsetconstr @ X505 @ (^[Z0:$i]:((X507 @ Z0)))))))))=>(![X510:$i, X511:$i]:((![X512:$i]:(((in @ X512 @ X510)=>(in @ X512 @ X511)))=>![X513:$i]:(((in @ X513 @ X510)=>(in @ X513 @ X511)))))=>(![X514:$i, X515:$i]:((((X514)=(X515))=>![X516:$i]:(((in @ X516 @ X515)=>(in @ X516 @ X514)))))=>(![X517:$i, X518:$i]:((((X517)=(X518))=>![X519:$i]:(((in @ X519 @ X517)=>(in @ X519 @ X518)))))=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>![X520:$i]:(((in @ X520 @ X4)=>(in @ X520 @ 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(apply_def,[status(thm)],[c_0_97, c_0_98]), c_0_99]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_100]), emptysetimpfalse]), c_0_101]), emptysetE]), c_0_102]), prop2setE]), c_0_103]), c_0_104]), c_0_105]), c_0_106]), c_0_107]), c_0_108]), c_0_86]), c_0_109]), c_0_110]), notinemptyset]), c_0_111]), c_0_112]), c_0_113]), noeltsimpempty]), emptyI]), setext]), c_0_114]), c_0_115]), powersetI]), c_0_116]), setadjoinOr]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), emptyinPowerset]), c_0_117]), c_0_118]), subPowSU]), setunionE]), setunionI]), powersetE]), emptyInPowerset]), uniqinunit]), c_0_119]), upairsetIR]), upairsetIL]), upairsetE]), singletonsswitch]), eqinunit]), notinsingleton]), vacuousDall]), notdallE]), notdexE]), prop2setI]), quantDeMorgan4]), quantDeMorgan3]), quantDeMorgan2]), quantDeMorgan1]), c_0_120]), c_0_121]), inCongP]), in__Cong]), c_0_122]), wellorderingAx]), foundationAx]), c_0_123]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])]), c_0_124])).
% 0.19/0.27 thf(c_0_126, negated_conjecture, ![X521:$i, X522:$i, X524:$i, X525:$i, X526:$i, X527:$i, X528:$i, X529:$i, X530:$i, X531:$i, X532:$i, X534:$i, X535:$i, X537:$i, X538:$i, X539:$i, X540:$i, X541:$i, X543:$i, X544:$i > $i > $o, X545:$i, X547:$i, X550:$i, X552:$i, X553:$i, X554:$i, X555:$i, X557:$i, X558:$i > $o, X559:$i, X561:$i, X562:$i > $o, X563:$i, X564:$i, X565:$i > $o, X566:$i, X567:$i, X568:$i > $o, X569:$i, X570:$i > $o, X571:$i, X574:$i, X575:$o, X576:$i, X577:$i, X578:$o, X579:$i, X580:$i, X581:$i > $o, X582:$i, X585:$i, X586:$i, X589:$i, X591:$i, X593:$i, X594:$i > $o, X595:$i, X596:$i, X598:$i, X599:$i > $o, X600:$i, X601:$i, X602:$i, X603:$i, X604:$i, X605:$i, X606:$i, X607:$i, X608:$i, X609:$i, X610:$i, X611:$o, X612:$i, X613:$i, X614:$i, X615:$i, X616:$i, X617:$i, X619:$i, X620:$i, X621:$i, X622:$i, X623:$i, X624:$i, X625:$i, X626:$i, X627:$i, X628:$i, X629:$o, X631:$i, X632:$i, X633:$i > $o, X634:$i, X637:$i, X638:$i, X639:$i, X641:$i, X642:$i, X643:$i, X644:$i, X645:$i, X646:$i, X647:$i, X648:$i, X649:$i, X650:$i, X651:$i, X652:$i, X653:$i, X654:$i, X655:$i, X656:$i, X657:$i > $o, X658:$i, X659:$i > $o, X660:$i, X661:$i, X662:$i > $o, X663:$i, X665:$i, X666:$i > $o, X668:$i, X669:$i, X670:$i > $o, X672:$i, X673:$i, X674:$i > $o, X675:$i, X677:$o, X678:$i, X679:$i > $o, X681:$i, X682:$i, X683:$i > $o, X684:$i, X686:$i > $o, X687:$i, X690:$i, X691:$i > $o, X692:$i, X696:$i, X697:$i > $o, X698:$i, X701:$i, X702:$i, X703:$i, X704:$i, X705:$i, X706:$i, X707:$i, X708:$i, X709:$i, X710:$i > $o, X711:$i, X713:$i, X714:$i, X715:$i > $o, X716:$i > $o, X719:$i, X722:$i, X723:$i, X726:$i, X727:$i, X728:$i, X729:$i, X730:$i, X731:$i, X732:$i, X733:$i, X734:$i, X735:$i > $o, X736:$i, X738:$i, X739:$i, X740:$i > $o, X741:$i > $o, X744:$i, X746:$i, X748:$i, X749:$i, X750:$i > $o, X751:$i > $o, X754:$i, X755:$i, X757:$i, X758:$i, X759:$i, X760:$i, X761:$i, X762:$i, X763:$i, X766:$i]:((((~(in @ (esk1_2 @ X521 @ X522) @ X521)|~(in @ (esk1_2 @ X521 @ X522) @ X522)|((X521)=(X522)))&((in @ (esk1_2 @ X521 @ X522) @ X521)|(in @ (esk1_2 @ X521 @ X522) @ X522)|((X521)=(X522))))&(~(in @ X524 @ emptyset)&(((~(in @ X527 @ (setadjoin @ X525 @ X526))|(((X527)=(X525))|(in @ X527 @ X526)))&((((X527)!=(X525))|(in @ X527 @ (setadjoin @ X525 @ X526)))&(~(in @ X527 @ X526)|(in @ X527 @ (setadjoin @ X525 @ X526)))))&(((~(in @ X529 @ (powerset @ X528))|(~(in @ X530 @ X529)|(in @ X530 @ X528)))&(((in @ (esk2_2 @ X531 @ X532) @ X532)|(in @ X532 @ (powerset @ X531)))&(~(in @ (esk2_2 @ X531 @ X532) @ X531)|(in @ X532 @ (powerset @ X531)))))&(((((in @ X535 @ (esk3_2 @ X534 @ X535))|~(in @ X535 @ (setunion @ X534)))&((in @ (esk3_2 @ X534 @ X535) @ X534)|~(in @ X535 @ (setunion @ X534))))&(~(in @ X538 @ X539)|~(in @ X539 @ X537)|(in @ X538 @ (setunion @ X537))))&((in @ emptyset @ omega)&((~(in @ X540 @ omega)|(in @ (setadjoin @ X540 @ X540) @ omega))&(((((in @ (esk4_1 @ X541) @ omega)|~(in @ emptyset @ X541)|(~(in @ X543 @ omega)|(in @ X543 @ X541)))&((in @ (esk4_1 @ X541) @ X541)|~(in @ emptyset @ X541)|(~(in @ X543 @ omega)|(in @ X543 @ X541))))&(~(in @ (setadjoin @ (esk4_1 @ X541) @ (esk4_1 @ X541)) @ X541)|~(in @ emptyset @ X541)|(~(in @ X543 @ omega)|(in @ X543 @ X541))))&((((((in @ (esk8_3 @ X544 @ X545 @ X550) @ X545)|~(in @ X550 @ (esk7_2 @ X544 @ X545))|(in @ (esk5_2 @ X544 @ X545) @ X545))&((X544 @ (esk8_3 @ X544 @ X545 @ X550) @ X550)|~(in @ X550 @ (esk7_2 @ X544 @ X545))|(in @ (esk5_2 @ X544 @ X545) @ X545)))&(~(in @ X553 @ X545)|~(X544 @ X553 @ X552)|(in @ X552 @ (esk7_2 @ X544 @ X545))|(in @ (esk5_2 @ X544 @ X545) @ X545)))&(((((in @ (esk8_3 @ X544 @ X545 @ X550) @ X545)|~(in @ X550 @ (esk7_2 @ X544 @ X545))|((X544 @ (esk5_2 @ X544 @ X545) @ (esk6_3 @ X544 @ X545 @ X547))|~(X544 @ (esk5_2 @ X544 @ X545) @ X547)))&((X544 @ (esk8_3 @ X544 @ X545 @ X550) @ X550)|~(in @ X550 @ (esk7_2 @ X544 @ X545))|((X544 @ (esk5_2 @ X544 @ X545) @ (esk6_3 @ X544 @ X545 @ X547))|~(X544 @ (esk5_2 @ X544 @ X545) @ X547))))&(~(in @ X553 @ 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X744))|~(X740 @ X744))|(~(X740 @ (esk46_2 @ X740 @ X741))|~(X741 @ (esk47_2 @ X740 @ X741))))&(((X746)!=(esk49_3 @ X740 @ X741 @ X746))|~(X741 @ X746)|((descr @ (^[Z0:$i]:((X740 @ Z0))))=(descr @ (^[Z0:$i]:((X741 @ Z0)))))|(((X744)!=(esk48_3 @ X740 @ X741 @ X744))|~(X740 @ X744))|(~(X740 @ (esk46_2 @ X740 @ X741))|~(X741 @ (esk47_2 @ X740 @ X741))))))&((((X741 @ (esk49_3 @ X740 @ X741 @ X746))|~(X741 @ X746)|((descr @ (^[Z0:$i]:((X740 @ Z0))))=(descr @ (^[Z0:$i]:((X741 @ Z0)))))|((X740 @ (esk48_3 @ X740 @ X741 @ X744))|~(X740 @ X744))|((X740 @ (esk46_2 @ X740 @ X741))|(X741 @ (esk47_2 @ X740 @ X741))))&(((X746)!=(esk49_3 @ X740 @ X741 @ X746))|~(X741 @ X746)|((descr @ (^[Z0:$i]:((X740 @ Z0))))=(descr @ (^[Z0:$i]:((X741 @ Z0)))))|((X740 @ (esk48_3 @ X740 @ X741 @ X744))|~(X740 @ X744))|((X740 @ (esk46_2 @ X740 @ X741))|(X741 @ (esk47_2 @ X740 @ X741)))))&(((X741 @ (esk49_3 @ X740 @ X741 @ X746))|~(X741 @ X746)|((descr @ (^[Z0:$i]:((X740 @ Z0))))=(descr @ (^[Z0:$i]:((X741 @ Z0)))))|(((X744)!=(esk48_3 @ X740 @ X741 @ X744))|~(X740 @ X744))|((X740 @ (esk46_2 @ X740 @ X741))|(X741 @ (esk47_2 @ X740 @ X741))))&(((X746)!=(esk49_3 @ X740 @ X741 @ X746))|~(X741 @ X746)|((descr @ (^[Z0:$i]:((X740 @ Z0))))=(descr @ (^[Z0:$i]:((X741 @ Z0)))))|(((X744)!=(esk48_3 @ X740 @ X741 @ X744))|~(X740 @ X744))|((X740 @ (esk46_2 @ X740 @ X741))|(X741 @ (esk47_2 @ X740 @ X741))))))))&((((in @ (esk50_4 @ X748 @ X749 @ X750 @ X751) @ X748)|((dsetconstr @ X748 @ (^[Z0:$i]:((X750 @ Z0))))=(dsetconstr @ X749 @ (^[Z0:$i]:((X751 @ Z0)))))|((X748)!=(X749)))&(((in @ (esk51_4 @ X748 @ X749 @ X750 @ X751) @ X749)|((dsetconstr @ X748 @ (^[Z0:$i]:((X750 @ Z0))))=(dsetconstr @ X749 @ (^[Z0:$i]:((X751 @ Z0)))))|((X748)!=(X749)))&((((esk50_4 @ X748 @ X749 @ X750 @ X751)=(esk51_4 @ X748 @ X749 @ X750 @ X751))|((dsetconstr @ X748 @ (^[Z0:$i]:((X750 @ Z0))))=(dsetconstr @ X749 @ (^[Z0:$i]:((X751 @ Z0)))))|((X748)!=(X749)))&((~(X750 @ (esk50_4 @ X748 @ X749 @ X750 @ X751))|~(X751 @ (esk51_4 @ X748 @ X749 @ X750 @ X751))|((dsetconstr @ X748 @ (^[Z0:$i]:((X750 @ Z0))))=(dsetconstr @ X749 @ (^[Z0:$i]:((X751 @ Z0)))))|((X748)!=(X749)))&((X750 @ (esk50_4 @ X748 @ X749 @ X750 @ X751))|(X751 @ (esk51_4 @ X748 @ X749 @ X750 @ X751))|((dsetconstr @ X748 @ (^[Z0:$i]:((X750 @ Z0))))=(dsetconstr @ X749 @ (^[Z0:$i]:((X751 @ Z0)))))|((X748)!=(X749)))))))&((((in @ (esk52_2 @ X754 @ X755) @ X754)|(~(in @ X757 @ X754)|(in @ X757 @ X755)))&(~(in @ (esk52_2 @ X754 @ X755) @ X755)|(~(in @ X757 @ X754)|(in @ X757 @ X755))))&((((X758)!=(X759))|(~(in @ X760 @ X759)|(in @ X760 @ X758)))&((((X761)!=(X762))|(~(in @ X763 @ X761)|(in @ X763 @ X762)))&((~(in @ X766 @ esk53_0)|(in @ X766 @ esk54_0))&((in @ esk55_0 @ esk53_0)&~(in @ esk55_0 @ esk54_0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_125])])])])])])).
% 0.19/0.27 thf(c_0_127, negated_conjecture, ~((in @ esk55_0 @ esk54_0)), inference(split_conjunct,[status(thm)],[c_0_126])).
% 0.19/0.27 thf(c_0_128, negated_conjecture, ![X2:$i]:(((in @ X2 @ esk54_0)|~((in @ X2 @ esk53_0)))), inference(split_conjunct,[status(thm)],[c_0_126])).
% 0.19/0.27 thf(c_0_129, negated_conjecture, (in @ esk55_0 @ esk53_0), inference(split_conjunct,[status(thm)],[c_0_126])).
% 0.19/0.27 thf(c_0_130, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127, c_0_128]), c_0_129])]), ['proof']).
% 0.19/0.27 % SZS output end CNFRefutation
% 0.19/0.27 % Parsed axioms : 175
% 0.19/0.27 % Removed by relevancy pruning/SinE : 94
% 0.19/0.27 % Initial clauses : 189
% 0.19/0.27 % Removed in clause preprocessing : 14
% 0.19/0.27 % Initial clauses in saturation : 175
% 0.19/0.27 % Processed clauses : 20
% 0.19/0.27 % ...of these trivial : 1
% 0.19/0.27 % ...subsumed : 5
% 0.19/0.27 % ...remaining for further processing : 14
% 0.19/0.27 % Other redundant clauses eliminated : 1
% 0.19/0.27 % Clauses deleted for lack of memory : 0
% 0.19/0.27 % Backward-subsumed : 0
% 0.19/0.27 % Backward-rewritten : 1
% 0.19/0.27 % Generated clauses : 2
% 0.19/0.27 % ...of the previous two non-redundant : 1
% 0.19/0.27 % ...aggressively subsumed : 0
% 0.19/0.27 % Contextual simplify-reflections : 0
% 0.19/0.27 % Paramodulations : 1
% 0.19/0.27 % Factorizations : 0
% 0.19/0.27 % NegExts : 0
% 0.19/0.27 % Equation resolutions : 1
% 0.19/0.27 % Disequality decompositions : 0
% 0.19/0.27 % Total rewrite steps : 3
% 0.19/0.27 % ...of those cached : 0
% 0.19/0.27 % Propositional unsat checks : 0
% 0.19/0.27 % Propositional check models : 0
% 0.19/0.27 % Propositional check unsatisfiable : 0
% 0.19/0.27 % Propositional clauses : 0
% 0.19/0.27 % Propositional clauses after purity: 0
% 0.19/0.27 % Propositional unsat core size : 0
% 0.19/0.27 % Propositional preprocessing time : 0.000
% 0.19/0.27 % Propositional encoding time : 0.000
% 0.19/0.27 % Propositional solver time : 0.000
% 0.19/0.27 % Success case prop preproc time : 0.000
% 0.19/0.27 % Success case prop encoding time : 0.000
% 0.19/0.27 % Success case prop solver time : 0.000
% 0.19/0.27 % Current number of processed clauses : 12
% 0.19/0.27 % Positive orientable unit clauses : 8
% 0.19/0.27 % Positive unorientable unit clauses: 0
% 0.19/0.27 % Negative unit clauses : 3
% 0.19/0.27 % Non-unit-clauses : 1
% 0.19/0.27 % Current number of unprocessed clauses: 156
% 0.19/0.27 % ...number of literals in the above : 600
% 0.19/0.27 % Current number of archived formulas : 0
% 0.19/0.27 % Current number of archived clauses : 1
% 0.19/0.27 % Clause-clause subsumption calls (NU) : 0
% 0.19/0.27 % Rec. Clause-clause subsumption calls : 0
% 0.19/0.27 % Non-unit clause-clause subsumptions : 0
% 0.19/0.27 % Unit Clause-clause subsumption calls : 0
% 0.19/0.27 % Rewrite failures with RHS unbound : 0
% 0.19/0.27 % BW rewrite match attempts : 1
% 0.19/0.27 % BW rewrite match successes : 1
% 0.19/0.27 % Condensation attempts : 0
% 0.19/0.27 % Condensation successes : 0
% 0.19/0.27 % Termbank termtop insertions : 20387
% 0.19/0.27 % Search garbage collected termcells : 7828
% 0.19/0.27
% 0.19/0.27 % -------------------------------------------------
% 0.19/0.27 % User time : 0.019 s
% 0.19/0.27 % System time : 0.006 s
% 0.19/0.27 % Total time : 0.024 s
% 0.19/0.27 % Maximum resident set size: 6368 pages
% 0.19/0.27
% 0.19/0.27 % -------------------------------------------------
% 0.19/0.27 % User time : 0.024 s
% 0.19/0.27 % System time : 0.010 s
% 0.19/0.27 % Total time : 0.034 s
% 0.19/0.27 % Maximum resident set size: 5120 pages
% 0.19/0.27 % E exiting
%------------------------------------------------------------------------------