%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU579^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:26:47 AM UTC 2026
% Result : Theorem 1.20s 0.51s
% Output : CNFRefutation 1.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU579^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n007.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 13:49:55 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.25 Running higher-order theorem proving
% 0.08/0.27 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p
% 1.20/0.51 % Version: 3.5.1-ho
% 1.20/0.51 % Preprocessing class: HSMMSLSSLLLCHFA.
% 1.20/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.20/0.51 % Starting ehoh_best3_avoidappvar with 1500s (5) cores
% 1.20/0.51 % Starting ehoh_best3_rw with 300s (1) cores
% 1.20/0.51 % Starting almost_fo_3 with 300s (1) cores
% 1.20/0.51 % Starting new_ho_13 with 300s (1) cores
% 1.20/0.51 % ehoh_best3_rw with pid 3397855 completed with status 0
% 1.20/0.51 % Result found by ehoh_best3_rw
% 1.20/0.51 % Preprocessing class: HSMMSLSSLLLCHFA.
% 1.20/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.20/0.51 % Starting ehoh_best3_avoidappvar with 1500s (5) cores
% 1.20/0.51 % Starting ehoh_best3_rw with 300s (1) cores
% 1.20/0.51 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf120_gu_RUU_F100_L01000)
% 1.20/0.51 % SinE strategy is gf120_gu_RUU_F100_L01000
% 1.20/0.51 % Search class: HGHSM-FSLM31-SHFMMSBN
% 1.20/0.51 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 1.20/0.51 % Starting SubtermCWHack with 28s (1) cores
% 1.20/0.51 % SubtermCWHack with pid 3397858 completed with status 0
% 1.20/0.51 % Result found by SubtermCWHack
% 1.20/0.51 % Preprocessing class: HSMMSLSSLLLCHFA.
% 1.20/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.20/0.51 % Starting ehoh_best3_avoidappvar with 1500s (5) cores
% 1.20/0.51 % Starting ehoh_best3_rw with 300s (1) cores
% 1.20/0.51 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf120_gu_RUU_F100_L01000)
% 1.20/0.51 % SinE strategy is gf120_gu_RUU_F100_L01000
% 1.20/0.51 % Search class: HGHSM-FSLM31-SHFMMSBN
% 1.20/0.51 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 1.20/0.51 % Starting SubtermCWHack with 28s (1) cores
% 1.20/0.51 % Preprocessing time : 0.002 s
% 1.20/0.51
% 1.20/0.51 % Proof found!
% 1.20/0.51 % SZS status Theorem
% 1.20/0.51 % SZS output start CNFRefutation
% 1.20/0.51 thf(decl_23, type, in: $i > $i > $o).
% 1.20/0.51 thf(decl_24, type, exu: ($i > $o) > $o).
% 1.20/0.51 thf(decl_25, type, setextAx: $o).
% 1.20/0.51 thf(decl_26, type, emptyset: $i).
% 1.20/0.51 thf(decl_27, type, emptysetAx: $o).
% 1.20/0.51 thf(decl_28, type, setadjoin: $i > $i > $i).
% 1.20/0.51 thf(decl_29, type, setadjoinAx: $o).
% 1.20/0.51 thf(decl_30, type, powerset: $i > $i).
% 1.20/0.51 thf(decl_31, type, powersetAx: $o).
% 1.20/0.51 thf(decl_32, type, setunion: $i > $i).
% 1.20/0.51 thf(decl_33, type, setunionAx: $o).
% 1.20/0.51 thf(decl_34, type, omega: $i).
% 1.20/0.51 thf(decl_35, type, omega0Ax: $o).
% 1.20/0.51 thf(decl_36, type, omegaSAx: $o).
% 1.20/0.51 thf(decl_37, type, omegaIndAx: $o).
% 1.20/0.51 thf(decl_38, type, replAx: $o).
% 1.20/0.51 thf(decl_39, type, foundationAx: $o).
% 1.20/0.51 thf(decl_40, type, wellorderingAx: $o).
% 1.20/0.51 thf(decl_41, type, descr: ($i > $o) > $i).
% 1.20/0.51 thf(decl_42, type, descrp: $o).
% 1.20/0.51 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 1.20/0.51 thf(decl_44, type, dsetconstrI: $o).
% 1.20/0.51 thf(decl_45, type, dsetconstrEL: $o).
% 1.20/0.51 thf(decl_46, type, dsetconstrER: $o).
% 1.20/0.51 thf(decl_47, type, exuE1: $o).
% 1.20/0.51 thf(decl_48, type, prop2set: $o > $i).
% 1.20/0.51 thf(decl_49, type, prop2setE: $o).
% 1.20/0.51 thf(decl_50, type, emptysetE: $o).
% 1.20/0.51 thf(decl_51, type, emptysetimpfalse: $o).
% 1.20/0.51 thf(decl_52, type, notinemptyset: $o).
% 1.20/0.51 thf(decl_53, type, exuE3e: $o).
% 1.20/0.51 thf(decl_54, type, setext: $o).
% 1.20/0.51 thf(decl_55, type, emptyI: $o).
% 1.20/0.51 thf(decl_56, type, noeltsimpempty: $o).
% 1.20/0.51 thf(decl_57, type, setbeta: $o).
% 1.20/0.51 thf(decl_58, type, nonempty: $i > $o).
% 1.20/0.51 thf(decl_59, type, nonemptyE1: $o).
% 1.20/0.51 thf(decl_60, type, nonemptyI: $o).
% 1.20/0.51 thf(decl_61, type, nonemptyI1: $o).
% 1.20/0.51 thf(decl_62, type, setadjoinIL: $o).
% 1.20/0.51 thf(decl_63, type, emptyinunitempty: $o).
% 1.20/0.51 thf(decl_64, type, setadjoinIR: $o).
% 1.20/0.51 thf(decl_65, type, setadjoinE: $o).
% 1.20/0.51 thf(decl_66, type, setadjoinOr: $o).
% 1.20/0.51 thf(decl_67, type, setoftrueEq: $o).
% 1.20/0.51 thf(decl_68, type, powersetI: $o).
% 1.20/0.51 thf(decl_69, type, emptyinPowerset: $o).
% 1.20/0.51 thf(decl_70, type, emptyInPowerset: $o).
% 1.20/0.51 thf(decl_71, type, powersetE: $o).
% 1.20/0.51 thf(decl_72, type, setunionI: $o).
% 1.20/0.51 thf(decl_73, type, setunionE: $o).
% 1.20/0.51 thf(decl_74, type, subPowSU: $o).
% 1.20/0.51 thf(decl_75, type, exuE2: $o).
% 1.20/0.51 thf(decl_76, type, nonemptyImpWitness: $o).
% 1.20/0.51 thf(decl_77, type, uniqinunit: $o).
% 1.20/0.51 thf(decl_78, type, notinsingleton: $o).
% 1.20/0.51 thf(decl_79, type, eqinunit: $o).
% 1.20/0.51 thf(decl_80, type, singletonsswitch: $o).
% 1.20/0.51 thf(decl_81, type, upairsetE: $o).
% 1.20/0.51 thf(decl_82, type, upairsetIL: $o).
% 1.20/0.51 thf(decl_83, type, upairsetIR: $o).
% 1.20/0.51 thf(decl_84, type, emptyE1: $o).
% 1.20/0.51 thf(decl_85, type, vacuousDall: $o).
% 1.20/0.51 thf(decl_86, type, quantDeMorgan1: $o).
% 1.20/0.51 thf(decl_87, type, quantDeMorgan2: $o).
% 1.20/0.51 thf(decl_88, type, quantDeMorgan3: $o).
% 1.20/0.51 thf(decl_89, type, quantDeMorgan4: $o).
% 1.20/0.51 thf(decl_90, type, prop2setI: $o).
% 1.20/0.51 thf(decl_92, type, prop2set2propI: $o).
% 1.20/0.51 thf(decl_93, type, notdexE: $o).
% 1.20/0.51 thf(decl_94, type, notdallE: $o).
% 1.20/0.51 thf(decl_95, type, exuI1: $o).
% 1.20/0.51 thf(decl_96, type, exuI3: $o).
% 1.20/0.51 thf(decl_97, type, exuI2: $o).
% 1.20/0.51 thf(decl_98, type, inCongP: $o).
% 1.20/0.51 thf(decl_99, type, in__Cong: $o).
% 1.20/0.51 thf(decl_100, type, exuE3u: $o).
% 1.20/0.51 thf(decl_101, type, exu__Cong: $o).
% 1.20/0.51 thf(decl_102, type, emptyset__Cong: $o).
% 1.20/0.51 thf(decl_103, type, setadjoin__Cong: $o).
% 1.20/0.51 thf(decl_104, type, powerset__Cong: $o).
% 1.20/0.51 thf(decl_105, type, setunion__Cong: $o).
% 1.20/0.51 thf(decl_106, type, omega__Cong: $o).
% 1.20/0.51 thf(decl_107, type, exuEu: $o).
% 1.20/0.51 thf(decl_108, type, descr__Cong: $o).
% 1.20/0.51 thf(decl_109, type, dsetconstr__Cong: $o).
% 1.20/0.51 thf(decl_110, type, subset: $i > $i > $o).
% 1.20/0.51 thf(decl_113, type, subsetI1: $o).
% 1.20/0.51 thf(decl_114, type, eqimpsubset2: $o).
% 1.20/0.51 thf(decl_115, type, eqimpsubset1: $o).
% 1.20/0.51 thf(decl_116, type, subsetI2: $o).
% 1.20/0.51 thf(decl_117, type, emptysetsubset: $o).
% 1.20/0.51 thf(decl_118, type, subsetE: $o).
% 1.20/0.51 thf(decl_119, type, subsetE2: $o).
% 1.20/0.51 thf(decl_120, type, notsubsetI: $o).
% 1.20/0.51 thf(decl_121, type, notequalI1: $o).
% 1.20/0.51 thf(decl_122, type, notequalI2: $o).
% 1.20/0.51 thf(decl_123, type, subsetRefl: $o).
% 1.20/0.51 thf(decl_124, type, subsetTrans: $o).
% 1.20/0.51 thf(decl_125, type, setadjoinSub: $o).
% 1.20/0.51 thf(decl_126, type, setadjoinSub2: $o).
% 1.20/0.51 thf(decl_127, type, subset2powerset: $o).
% 1.20/0.51 thf(decl_128, type, setextsub: $o).
% 1.20/0.51 thf(decl_129, type, subsetemptysetimpeq: $o).
% 1.20/0.51 thf(decl_130, type, powersetI1: $o).
% 1.20/0.51 thf(decl_131, type, powersetE1: $o).
% 1.20/0.51 thf(decl_132, type, inPowerset: $o).
% 1.20/0.51 thf(decl_133, type, epred1_0: $o).
% 1.20/0.51 thf(decl_134, type, esk1_2: $i > $i > $i).
% 1.20/0.51 thf(decl_135, type, esk2_2: $i > $i > $i).
% 1.20/0.51 thf(decl_136, type, esk3_2: $i > $i > $i).
% 1.20/0.51 thf(decl_137, type, esk4_1: $i > $i).
% 1.20/0.51 thf(decl_138, type, esk5_2: ($i > $i > $o) > $i > $i).
% 1.20/0.51 thf(decl_139, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 1.20/0.51 thf(decl_140, type, esk7_2: ($i > $i > $o) > $i > $i).
% 1.20/0.51 thf(decl_141, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 1.20/0.51 thf(decl_142, type, esk9_1: $i > $i).
% 1.20/0.51 thf(decl_143, type, esk10_2: ($i > $o) > $i > $i).
% 1.20/0.51 thf(decl_144, type, esk11_2: ($i > $o) > $i > $i).
% 1.20/0.51 thf(decl_145, type, esk12_1: ($i > $o) > $i).
% 1.20/0.51 thf(decl_146, type, esk13_2: ($i > $o) > $i > $i).
% 1.20/0.51 thf(decl_147, type, esk14_1: ($i > $o) > $i).
% 1.20/0.51 thf(decl_148, type, esk15_2: $i > $i > $i).
% 1.20/0.51 thf(decl_149, type, esk16_2: $i > $i > $i).
% 1.20/0.51 thf(decl_150, type, esk17_1: $i > $i).
% 1.20/0.51 thf(decl_151, type, esk18_1: $i > $i).
% 1.20/0.51 thf(decl_152, type, esk19_1: $i > $i).
% 1.20/0.51 thf(decl_153, type, esk20_2: $i > $i > $i).
% 1.20/0.51 thf(decl_154, type, esk21_3: $i > $i > $o > $i).
% 1.20/0.51 thf(decl_155, type, esk22_2: ($i > $o) > $i > $i).
% 1.20/0.51 thf(decl_156, type, esk23_1: ($i > $o) > $i).
% 1.20/0.51 thf(decl_157, type, esk24_1: $i > $i).
% 1.20/0.51 thf(decl_158, type, esk25_2: $i > ($i > $o) > $i).
% 1.20/0.51 thf(decl_159, type, esk26_2: $i > ($i > $o) > $i).
% 1.20/0.51 thf(decl_160, type, esk27_2: $i > ($i > $o) > $i).
% 1.20/0.51 thf(decl_161, type, esk28_2: $i > ($i > $o) > $i).
% 1.20/0.51 thf(decl_162, type, esk29_2: $i > ($i > $o) > $i).
% 1.20/0.51 thf(decl_163, type, esk30_2: $i > ($i > $o) > $i).
% 1.20/0.51 thf(decl_164, type, esk31_2: ($i > $o) > $i > $i).
% 1.20/0.51 thf(decl_165, type, esk32_1: ($i > $o) > $i).
% 1.20/0.51 thf(decl_166, type, esk33_1: ($i > $o) > $i).
% 1.20/0.51 thf(decl_167, type, esk34_1: ($i > $o) > $i).
% 1.20/0.51 thf(decl_168, type, esk35_1: ($i > $o) > $i).
% 1.20/0.51 thf(decl_169, type, esk36_2: ($i > $o) > $i > $i).
% 1.20/0.51 thf(decl_170, type, esk37_1: ($i > $o) > $i).
% 1.20/0.51 thf(decl_171, type, esk38_2: ($i > $o) > $i > $i).
% 1.20/0.51 thf(decl_172, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 1.20/0.51 thf(decl_173, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 1.20/0.51 thf(decl_174, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.20/0.51 thf(decl_175, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 1.20/0.51 thf(decl_176, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.20/0.51 thf(decl_177, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 1.20/0.51 thf(decl_178, type, esk45_2: ($i > $o) > $i > $i).
% 1.20/0.51 thf(decl_179, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 1.20/0.51 thf(decl_180, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 1.20/0.51 thf(decl_181, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.20/0.51 thf(decl_182, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.20/0.51 thf(decl_183, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 1.20/0.51 thf(decl_184, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 1.20/0.51 thf(decl_185, type, esk52_2: $i > $i > $i).
% 1.20/0.51 thf(decl_186, type, esk53_2: $i > $i > $i).
% 1.20/0.51 thf(decl_187, type, esk54_0: $i).
% 1.20/0.51 thf(decl_188, type, esk55_0: $i).
% 1.20/0.51 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', exuE3e)).
% 1.20/0.51 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', exu)).
% 1.20/0.51 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', nonempty)).
% 1.20/0.51 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', exuE2)).
% 1.20/0.51 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', nonemptyI)).
% 1.20/0.51 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', exuE3u)).
% 1.20/0.51 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', exuI2)).
% 1.20/0.51 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', exuI3)).
% 1.20/0.51 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', exuI1)).
% 1.20/0.51 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', exu__Cong)).
% 1.20/0.51 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', descr__Cong)).
% 1.20/0.51 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', exuEu)).
% 1.20/0.51 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', exuE1)).
% 1.20/0.51 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', descrp)).
% 1.20/0.51 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', replAx)).
% 1.20/0.51 thf(powersetsubset, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', powersetsubset)).
% 1.20/0.51 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', setbeta)).
% 1.20/0.51 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', nonemptyE1)).
% 1.20/0.51 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', nonemptyI1)).
% 1.20/0.51 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', setoftrueEq)).
% 1.20/0.51 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', nonemptyImpWitness)).
% 1.20/0.51 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', emptyE1)).
% 1.20/0.51 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', dsetconstr__Cong)).
% 1.20/0.51 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', dsetconstrER)).
% 1.20/0.51 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', dsetconstrEL)).
% 1.20/0.51 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', dsetconstrI)).
% 1.20/0.51 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', subsetE)).
% 1.20/0.51 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', subsetI1)).
% 1.20/0.51 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', eqimpsubset2)).
% 1.20/0.51 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', eqimpsubset1)).
% 1.20/0.51 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', subsetE2)).
% 1.20/0.51 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', notsubsetI)).
% 1.20/0.51 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', notequalI1)).
% 1.20/0.51 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', notequalI2)).
% 1.20/0.51 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', subsetRefl)).
% 1.20/0.51 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', subsetTrans)).
% 1.20/0.51 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', setadjoinSub)).
% 1.20/0.51 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', setadjoinSub2)).
% 1.20/0.51 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', subset2powerset)).
% 1.20/0.51 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', setextsub)).
% 1.20/0.51 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', noeltsimpempty)).
% 1.20/0.51 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', subsetemptysetimpeq)).
% 1.20/0.51 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', emptyI)).
% 1.20/0.51 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', powersetI1)).
% 1.20/0.51 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', setext)).
% 1.20/0.51 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', powersetE1)).
% 1.20/0.51 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', emptysetE)).
% 1.20/0.51 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', inPowerset)).
% 1.20/0.51 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', notinemptyset)).
% 1.20/0.51 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', emptysetimpfalse)).
% 1.20/0.51 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', setadjoinOr)).
% 1.20/0.51 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', setadjoinE)).
% 1.20/0.51 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', setadjoinIR)).
% 1.20/0.51 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', emptyinunitempty)).
% 1.20/0.51 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', setadjoinIL)).
% 1.20/0.51 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', subPowSU)).
% 1.20/0.51 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', setunionE)).
% 1.20/0.51 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', setunionI)).
% 1.20/0.51 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', powersetE)).
% 1.20/0.51 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', emptyInPowerset)).
% 1.20/0.51 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', emptyinPowerset)).
% 1.20/0.51 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', powersetI)).
% 1.20/0.51 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', upairsetIL)).
% 1.20/0.51 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', upairsetE)).
% 1.20/0.51 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', singletonsswitch)).
% 1.20/0.51 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', eqinunit)).
% 1.20/0.51 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', notinsingleton)).
% 1.20/0.51 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', uniqinunit)).
% 1.20/0.51 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', upairsetIR)).
% 1.20/0.51 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', prop2setI)).
% 1.20/0.51 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', quantDeMorgan4)).
% 1.20/0.51 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', quantDeMorgan3)).
% 1.20/0.51 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', quantDeMorgan2)).
% 1.20/0.51 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', quantDeMorgan1)).
% 1.20/0.51 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', vacuousDall)).
% 1.20/0.51 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', notdexE)).
% 1.20/0.51 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', in__Cong)).
% 1.20/0.51 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', inCongP)).
% 1.20/0.51 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', notdallE)).
% 1.20/0.51 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', omega__Cong)).
% 1.20/0.51 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', setunion__Cong)).
% 1.20/0.51 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', powerset__Cong)).
% 1.20/0.51 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', setadjoin__Cong)).
% 1.20/0.51 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', emptyset__Cong)).
% 1.20/0.51 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', subsetI2)).
% 1.20/0.51 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', emptysetsubset)).
% 1.20/0.51 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', prop2setE)).
% 1.20/0.51 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', wellorderingAx)).
% 1.20/0.51 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', foundationAx)).
% 1.20/0.51 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', omegaIndAx)).
% 1.20/0.51 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', omegaSAx)).
% 1.20/0.51 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', omega0Ax)).
% 1.20/0.51 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', setunionAx)).
% 1.20/0.51 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', powersetAx)).
% 1.20/0.51 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', setadjoinAx)).
% 1.20/0.51 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', emptysetAx)).
% 1.20/0.51 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.RkcKcMZhiz/E---3.1_3397841.p', setextAx)).
% 1.20/0.51 thf(c_0_97, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 1.20/0.51 thf(c_0_98, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 1.20/0.51 thf(c_0_99, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 1.20/0.51 thf(c_0_100, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 1.20/0.51 thf(c_0_101, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 1.20/0.51 thf(c_0_102, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 1.20/0.51 thf(c_0_103, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 1.20/0.51 thf(c_0_104, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 1.20/0.51 thf(c_0_105, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 1.20/0.51 thf(c_0_106, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 1.20/0.51 thf(c_0_107, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))=>((exu @ (^[Z0:$i]:((X17 @ Z0))))=>((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 1.20/0.51 thf(c_0_108, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 1.20/0.51 thf(c_0_109, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 1.20/0.51 thf(c_0_110, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 1.20/0.51 thf(c_0_111, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 1.20/0.51 thf(c_0_112, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[powersetsubset])).
% 1.20/0.51 thf(c_0_113, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 1.20/0.51 thf(c_0_114, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X282:$i]:(((((X1 @ X282)))&(![X283:$i]:(((((X1 @ X283)))=>(((X282)=(X283))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_97, c_0_98])).
% 1.20/0.51 thf(c_0_115, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_99])).
% 1.20/0.51 thf(c_0_116, plain, ((exuE2)=(![X1:$i > $o]:((((?[X284:$i]:(((((X1 @ X284)))&(![X285:$i]:(((((X1 @ X285)))=>(((X284)=(X285))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_100, c_0_98])).
% 1.20/0.51 thf(c_0_117, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_99])).
% 1.20/0.51 thf(c_0_118, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_101, c_0_99])).
% 1.20/0.51 thf(c_0_119, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 1.20/0.51 thf(c_0_120, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_99])).
% 1.20/0.51 thf(c_0_121, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
% 1.20/0.51 thf(c_0_122, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X292:$i]:(((((X1 @ X292)))&(![X293:$i]:(((((X1 @ X293)))=>(((X292)=(X293))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_102, c_0_98])).
% 1.20/0.51 thf(c_0_123, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X290:$i]:(((((X1 @ X290)))&(![X291:$i]:(((((X1 @ X291)))=>(((X290)=(X291)))))))))))))), inference(apply_def,[status(thm)],[c_0_103, c_0_98])).
% 1.20/0.51 thf(c_0_124, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X288:$i]:(((((X1 @ X288)))&(![X289:$i]:(((((X1 @ X289)))=>(((X288)=(X289)))))))))))))))), inference(apply_def,[status(thm)],[c_0_104, c_0_98])).
% 1.20/0.51 thf(c_0_125, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X286:$i]:(((((X1 @ X286)))&(![X287:$i]:(((((X1 @ X287)))=>(((X286)=(X287)))))))))))))), inference(apply_def,[status(thm)],[c_0_105, c_0_98])).
% 1.20/0.51 thf(c_0_126, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X294:$i]:(((((X1 @ X294)))&(![X295:$i]:(((((X1 @ X295)))=>(((X294)=(X295))))))))))<=>((?[X296:$i]:(((((X17 @ X296)))&(![X297:$i]:(((((X17 @ X297)))=>(((X296)=(X297)))))))))))))))), inference(apply_def,[status(thm)],[c_0_106, c_0_98])).
% 1.20/0.51 thf(c_0_127, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X300:$i]:(((((X1 @ X300)))&(![X301:$i]:(((((X1 @ X301)))=>(((X300)=(X301))))))))))=>((((?[X302:$i]:(((((X17 @ X302)))&(![X303:$i]:(((((X17 @ X303)))=>(((X302)=(X303))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_107, c_0_98])).
% 1.20/0.51 thf(c_0_128, plain, ((exuEu)=(![X1:$i > $o]:((((?[X298:$i]:(((((X1 @ X298)))&(![X299:$i]:(((((X1 @ X299)))=>(((X298)=(X299))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_108, c_0_98])).
% 1.20/0.51 thf(c_0_129, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 1.20/0.51 thf(c_0_130, plain, ((exuE1)=(![X1:$i > $o]:((((?[X280:$i]:(((((X1 @ X280)))&(![X281:$i]:(((((X1 @ X281)))=>(((X280)=(X281))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_109, c_0_98])).
% 1.20/0.51 thf(c_0_131, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 1.20/0.51 thf(c_0_132, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 1.20/0.51 thf(c_0_133, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 1.20/0.51 thf(c_0_134, plain, ((descrp)=(![X1:$i > $o]:((((?[X278:$i]:(((((X1 @ X278)))&(![X279:$i]:(((((X1 @ X279)))=>(((X278)=(X279))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_110, c_0_98])).
% 1.20/0.51 thf(c_0_135, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X276:$i]:(((((X6 @ X2 @ X276)))&(![X277:$i]:(((((X6 @ X2 @ X277)))=>(((X276)=(X277)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_111, c_0_98])).
% 1.20/0.51 thf(c_0_136, plain, ((epred1_0)<=>![X333:$i]:(?[X334:$i]:((((![X335:$i]:(((in @ X335 @ X334)=>![X336:$i]:(((in @ X336 @ X335)=>(in @ X336 @ X333)))))&![X337:$i, X338:$i]:((((in @ X337 @ X333)&(in @ X338 @ X333))=>(![X339:$i]:(((in @ X339 @ X334)=>((in @ X337 @ X339)<=>(in @ X338 @ X339))))=>((X337)=(X338))))))&![X340:$i, X341:$i]:((((in @ X340 @ X334)&(in @ X341 @ X334))=>(![X342:$i]:(((in @ X342 @ X340)=>(in @ X342 @ X341)))|![X343:$i]:(((in @ X343 @ X341)=>(in @ X343 @ X340)))))))&![X344:$i]:(((![X345:$i]:(((in @ X345 @ X344)=>(in @ X345 @ X333)))&?[X346:$i]:((in @ X346 @ X344)))=>?[X347:$i, X348:$i]:(((((in @ X347 @ X334)&(in @ X348 @ X344))&~(?[X349:$i]:(((in @ X349 @ X347)&(in @ X349 @ X344)))))&![X350:$i]:(((in @ X350 @ X334)=>(![X351:$i]:(((in @ X351 @ X350)=>(in @ X351 @ X347)))|(in @ X348 @ X350)))))))))))), introduced(definition)).
% 1.20/0.51 thf(c_0_137, negated_conjecture, ~((![X304:$i, X305:$i]:((![X306:$i]:(((in @ X306 @ X304)<=>(in @ X306 @ X305)))=>((X304)=(X305))))=>(![X307:$i]:(~(in @ X307 @ emptyset))=>(![X308:$i, X309:$i, X310:$i]:(((in @ X310 @ (setadjoin @ X308 @ X309))<=>(((X310)=(X308))|(in @ X310 @ X309))))=>(![X311:$i, X312:$i]:(((in @ X312 @ (powerset @ X311))<=>![X313:$i]:(((in @ X313 @ X312)=>(in @ X313 @ X311)))))=>(![X314:$i, X315:$i]:(((in @ X315 @ (setunion @ X314))<=>?[X316:$i]:(((in @ X315 @ X316)&(in @ X316 @ X314)))))=>((in @ emptyset @ omega)=>(![X317:$i]:(((in @ X317 @ omega)=>(in @ (setadjoin @ X317 @ X317) @ omega)))=>(![X318:$i]:((((in @ emptyset @ X318)&![X319:$i]:((((in @ X319 @ omega)&(in @ X319 @ X318))=>(in @ (setadjoin @ X319 @ X319) @ X318))))=>![X320:$i]:(((in @ X320 @ omega)=>(in @ X320 @ X318)))))=>(![X321:$i > $i > $o, X322:$i]:((![X323:$i]:(((in @ X323 @ X322)=>?[X324:$i]:(((X321 @ X323 @ X324)&![X325:$i]:(((X321 @ X323 @ X325)=>((X324)=(X325))))))))=>?[X326:$i]:(![X327:$i]:(((in @ X327 @ X326)<=>?[X328:$i]:(((in @ X328 @ X322)&(X321 @ X328 @ X327))))))))=>(![X329:$i]:((?[X330:$i]:((in @ X330 @ X329))=>?[X331:$i]:(((in @ X331 @ X329)&~(?[X332:$i]:(((in @ X332 @ X331)&(in @ X332 @ X329))))))))=>((epred1_0)=>(![X352:$i > $o]:((?[X353:$i]:(((X352 @ X353)&![X354:$i]:(((X352 @ X354)=>((X353)=(X354))))))=>(X352 @ (descr @ (^[Z0:$i]:(X352 @ Z0))))))=>(![X355:$i, X356:$i > $o, X357:$i]:(((in @ X357 @ X355)=>((X356 @ X357)=>(in @ X357 @ (dsetconstr @ X355 @ X356)))))=>(![X358:$i, X359:$i > $o, X360:$i]:(((in @ X360 @ (dsetconstr @ X358 @ X359))=>(in @ X360 @ X358)))=>(![X361:$i, X362:$i > $o, X363:$i]:(((in @ X363 @ (dsetconstr @ X361 @ X362))=>(X362 @ X363)))=>(![X364:$i > $o]:((?[X365:$i]:(((X364 @ X365)&![X366:$i]:(((X364 @ X366)=>((X365)=(X366))))))=>?[X367:$i]:(((X364 @ X367)&![X368:$i]:(((X364 @ X368)=>((X367)=(X368))))))))=>(![X369:$o, X370:$i]:(((in @ X370 @ (prop2set @ ((X369))))=>(X369)))=>(![X371:$i]:(((in @ X371 @ emptyset)=>![X372:$o]:((X372))))=>(![X373:$i]:(((in @ X373 @ emptyset)=>~($true)))=>(![X374:$i]:(~(in @ X374 @ emptyset))=>(![X375:$i > $o]:((?[X376:$i]:(((X375 @ X376)&![X377:$i]:(((X375 @ X377)=>((X376)=(X377))))))=>?[X378:$i]:((X375 @ X378))))=>(![X379:$i, X380:$i]:((![X381:$i]:(((in @ X381 @ X379)=>(in @ X381 @ X380)))=>(![X382:$i]:(((in @ X382 @ X380)=>(in @ X382 @ X379)))=>((X379)=(X380)))))=>(![X383:$i]:((![X384:$i]:(~(in @ X384 @ X383))=>((X383)=(emptyset))))=>(![X385:$i]:((![X386:$i]:(~(in @ X386 @ X385))=>((X385)=(emptyset))))=>(![X387:$i, X388:$i > $o, X389:$i]:(((in @ X389 @ X387)=>((in @ X389 @ (dsetconstr @ X387 @ X388))<=>(X388 @ X389))))=>(![X390:$i]:((((X390)!=(emptyset))=>?[X391:$i]:((in @ X391 @ X390))))=>(![X392:$i, X393:$i > $o, X394:$i]:(((in @ X394 @ X392)=>((X393 @ X394)=>((dsetconstr @ X392 @ X393)!=(emptyset)))))=>(![X395:$i]:((?[X396:$i]:((in @ X396 @ X395))=>((X395)!=(emptyset))))=>(![X397:$i, X398:$i]:((in @ X397 @ (setadjoin @ X397 @ X398)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X399:$i, X400:$i, X401:$i]:(((in @ X401 @ X400)=>(in @ X401 @ (setadjoin @ X399 @ X400))))=>(![X402:$i, X403:$i, X404:$i]:(((in @ X404 @ (setadjoin @ X402 @ X403))=>![X405:$o]:(((((X404)=(X402))=>(X405))=>(((in @ X404 @ X403)=>(X405))=>(X405))))))=>(![X406:$i, X407:$i, X408:$i]:(((in @ X408 @ (setadjoin @ X406 @ X407))=>(((X408)=(X406))|(in @ X408 @ X407))))=>(![X409:$i]:(((dsetconstr @ X409 @ (^[Z0:$i]:($true)))=(X409)))=>(![X410:$i, X411:$i]:((![X412:$i]:(((in @ X412 @ X411)=>(in @ X412 @ X410)))=>(in @ X411 @ (powerset @ X410))))=>(![X413:$i]:((in @ emptyset @ (powerset @ X413)))=>(![X414:$i]:((in @ emptyset @ (powerset @ X414)))=>(![X415:$i, X416:$i, X417:$i]:(((in @ X416 @ (powerset @ X415))=>((in @ X417 @ X416)=>(in @ X417 @ X415))))=>(![X418:$i, X419:$i, X420:$i]:(((in @ X419 @ X420)=>((in @ X420 @ X418)=>(in @ X419 @ (setunion @ X418)))))=>(![X421:$i, X422:$i]:(((in @ X422 @ (setunion @ X421))=>![X423:$o]:((![X424:$i]:(((in @ X422 @ X424)=>((in @ X424 @ X421)=>(X423))))=>(X423)))))=>(![X425:$i, X426:$i]:(((in @ X426 @ X425)=>(in @ X426 @ (powerset @ (setunion @ X425)))))=>(![X427:$i > $o]:((?[X428:$i]:(((X427 @ X428)&![X429:$i]:(((X427 @ X429)=>((X428)=(X429))))))=>?[X430:$i]:(![X431:$i]:(((X427 @ X431)<=>((X431)=(X430)))))))=>(![X432:$i]:((((X432)!=(emptyset))=>?[X433:$i]:(((in @ X433 @ X432)&$true))))=>(![X434:$i, X435:$i]:(((in @ X434 @ (setadjoin @ X435 @ emptyset))=>((X434)=(X435))))=>(![X436:$i, X437:$i]:((((X436)!=(X437))=>~(in @ X437 @ (setadjoin @ X436 @ emptyset))))=>(![X438:$i, X439:$i]:((((X438)=(X439))=>(in @ X438 @ (setadjoin @ X439 @ emptyset))))=>(![X440:$i, X441:$i]:(((in @ X440 @ (setadjoin @ X441 @ emptyset))=>(in @ X441 @ (setadjoin @ X440 @ emptyset))))=>(![X442:$i, X443:$i, X444:$i]:(((in @ X444 @ (setadjoin @ X442 @ (setadjoin @ X443 @ emptyset)))=>(((X444)=(X442))|((X444)=(X443)))))=>(![X445:$i, X446:$i]:((in @ X445 @ (setadjoin @ X445 @ (setadjoin @ X446 @ emptyset))))=>(![X447:$i, X448:$i]:((in @ X448 @ (setadjoin @ X447 @ (setadjoin @ X448 @ emptyset))))=>(![X449:$i, X450:$i > $o]:((?[X451:$i]:(((in @ X451 @ X449)&(X450 @ X451)))=>(((dsetconstr @ X449 @ X450)=(emptyset))=>~($true))))=>(![X452:$i > $o, X453:$i]:(((in @ X453 @ emptyset)=>(X452 @ X453)))=>(![X454:$i, X455:$i > $o]:((~(![X456:$i]:(((in @ X456 @ X454)=>(X455 @ X456))))=>?[X457:$i]:(((in @ X457 @ X454)&~((X455 @ X457))))))=>(![X458:$i, X459:$i > $o]:((![X460:$i]:(((in @ X460 @ X458)=>~((X459 @ X460))))=>~(?[X461:$i]:(((in @ X461 @ X458)&(X459 @ X461))))))=>(![X462:$i, X463:$i > $o]:((~(?[X464:$i]:(((in @ X464 @ X462)&(X463 @ X464))))=>![X465:$i]:(((in @ X465 @ X462)=>~((X463 @ X465))))))=>(![X466:$i, X467:$i > $o]:((?[X468:$i]:(((in @ X468 @ X466)&~((X467 @ X468))))=>~(![X469:$i]:(((in @ X469 @ X466)=>(X467 @ X469))))))=>(![X470:$o]:(((X470)=>(in @ emptyset @ (prop2set @ ((X470))))))=>((prop2set2propI)=>(![X471:$i, X472:$i > $o]:((~(?[X473:$i]:(((in @ X473 @ X471)&(X472 @ X473))))=>![X474:$i]:(((in @ X474 @ X471)=>~((X472 @ X474))))))=>(![X475:$i, X476:$i > $o]:((~(![X477:$i]:(((in @ X477 @ X475)=>(X476 @ X477))))=>?[X478:$i]:(((in @ X478 @ X475)&~((X476 @ X478))))))=>(![X479:$i > $o]:((?[X480:$i]:(((X479 @ X480)&![X481:$i]:(((X479 @ X481)=>((X480)=(X481))))))=>?[X482:$i]:(((X479 @ X482)&![X483:$i]:(((X479 @ X483)=>((X482)=(X483))))))))=>(![X484:$i > $o]:((?[X485:$i]:((X484 @ X485))=>(![X486:$i, X487:$i]:(((X484 @ X486)=>((X484 @ X487)=>((X486)=(X487)))))=>?[X488:$i]:(((X484 @ X488)&![X489:$i]:(((X484 @ X489)=>((X488)=(X489)))))))))=>(![X490:$i > $o]:((?[X491:$i]:(![X492:$i]:(((X490 @ X492)<=>((X492)=(X491)))))=>?[X493:$i]:(((X490 @ X493)&![X494:$i]:(((X490 @ X494)=>((X493)=(X494))))))))=>(![X495:$i, X496:$i]:((((X495)=(X496))=>![X497:$i, X498:$i]:((((X497)=(X498))=>((in @ X497 @ X495)=>(in @ X498 @ X496))))))=>(![X499:$i, X500:$i]:((((X499)=(X500))=>![X501:$i, X502:$i]:((((X501)=(X502))=>((in @ X501 @ X499)<=>(in @ X502 @ X500))))))=>(![X503:$i > $o]:((?[X504:$i]:(((X503 @ X504)&![X505:$i]:(((X503 @ X505)=>((X504)=(X505))))))=>![X506:$i, X507:$i]:(((X503 @ X506)=>((X503 @ X507)=>((X506)=(X507)))))))=>(![X508:$i > $o, X509:$i > $o]:((![X510:$i, X511:$i]:((((X510)=(X511))=>((X508 @ X510)<=>(X509 @ X511))))=>(?[X512:$i]:(((X508 @ X512)&![X513:$i]:(((X508 @ X513)=>((X512)=(X513))))))<=>?[X514:$i]:(((X509 @ X514)&![X515:$i]:(((X509 @ X515)=>((X514)=(X515)))))))))=>(((emptyset)=(emptyset))=>(![X516:$i, X517:$i]:((((X516)=(X517))=>![X518:$i, X519:$i]:((((X518)=(X519))=>((setadjoin @ X516 @ X518)=(setadjoin @ X517 @ X519))))))=>(![X520:$i, X521:$i]:((((X520)=(X521))=>((powerset @ X520)=(powerset @ X521))))=>(![X522:$i, X523:$i]:((((X522)=(X523))=>((setunion @ X522)=(setunion @ X523))))=>(((omega)=(omega))=>(![X524:$i > $o]:((?[X525:$i]:(((X524 @ X525)&![X526:$i]:(((X524 @ X526)=>((X525)=(X526))))))=>![X527:$i, X528:$i]:(((X524 @ X527)=>((X524 @ X528)=>((X527)=(X528)))))))=>(![X529:$i > $o, X530:$i > $o]:((![X531:$i, X532:$i]:((((X531)=(X532))=>((X529 @ X531)<=>(X530 @ X532))))=>(?[X533:$i]:(((X529 @ X533)&![X534:$i]:(((X529 @ X534)=>((X533)=(X534))))))=>(?[X535:$i]:(((X530 @ X535)&![X536:$i]:(((X530 @ X536)=>((X535)=(X536))))))=>((descr @ X529)=(descr @ X530))))))=>(![X537:$i, X538:$i]:((((X537)=(X538))=>![X539:$i > $o, X540:$i > $o]:((![X541:$i]:(((in @ X541 @ X537)=>![X542:$i]:(((in @ X542 @ X538)=>(((X541)=(X542))=>((X539 @ X541)<=>(X540 @ X542)))))))=>((dsetconstr @ X537 @ X539)=(dsetconstr @ X538 @ X540))))))=>(![X543:$i, X544:$i]:((![X545:$i]:(((in @ X545 @ X543)=>(in @ X545 @ X544)))=>(subset @ X543 @ X544)))=>(![X546:$i, X547:$i]:((((X546)=(X547))=>(subset @ X547 @ X546)))=>(![X548:$i, X549:$i]:((((X548)=(X549))=>(subset @ X548 @ X549)))=>(![X550:$i, X551:$i]:((![X552:$i]:(((in @ X552 @ X550)=>(in @ X552 @ X551)))=>(subset @ X550 @ X551)))=>(![X553:$i]:((subset @ emptyset @ X553))=>(![X554:$i, X555:$i, X556:$i]:(((subset @ X554 @ X555)=>((in @ X556 @ X554)=>(in @ X556 @ X555))))=>(![X557:$i, X558:$i, X559:$i]:(((subset @ X557 @ X558)=>(~(in @ X559 @ X558)=>~(in @ X559 @ X557))))=>(![X560:$i, X561:$i, X562:$i]:(((in @ X562 @ X560)=>(~(in @ X562 @ X561)=>~(subset @ X560 @ X561))))=>(![X563:$i, X564:$i]:((~(subset @ X563 @ X564)=>((X563)!=(X564))))=>(![X565:$i, X566:$i, X567:$i]:(((in @ X567 @ X565)=>(~(in @ X567 @ X566)=>((X565)!=(X566)))))=>(![X568:$i]:((subset @ X568 @ X568))=>(![X569:$i, X570:$i, X571:$i]:(((subset @ X569 @ X570)=>((subset @ X570 @ X571)=>(subset @ X569 @ X571))))=>(![X572:$i, X573:$i]:((subset @ X573 @ (setadjoin @ X572 @ X573)))=>(![X574:$i, X575:$i, X576:$i]:(((subset @ X574 @ X576)=>(subset @ X574 @ (setadjoin @ X575 @ X576))))=>(![X577:$i, X578:$i]:(((subset @ X577 @ X578)=>(in @ X577 @ (powerset @ X578))))=>(![X579:$i, X580:$i]:(((subset @ X579 @ X580)=>((subset @ X580 @ X579)=>((X579)=(X580)))))=>(![X581:$i]:(((subset @ X581 @ emptyset)=>((X581)=(emptyset))))=>(![X582:$i, X583:$i]:(((subset @ X583 @ X582)=>(in @ X583 @ (powerset @ X582))))=>(![X584:$i, X585:$i]:(((in @ X585 @ (powerset @ X584))=>(subset @ X585 @ X584)))=>(![X586:$i]:((in @ X586 @ (powerset @ X586)))=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_112, subsetE]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), c_0_113]), setextsub]), noeltsimpempty]), subsetemptysetimpeq]), emptyI]), powersetI1]), setext]), powersetE1]), emptysetE]), inPowerset]), c_0_114]), notinemptyset]), emptysetimpfalse]), c_0_115]), c_0_116]), setadjoinOr]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), c_0_117]), c_0_118]), c_0_119]), subPowSU]), setunionE]), setunionI]), powersetE]), emptyInPowerset]), emptyinPowerset]), powersetI]), upairsetIL]), upairsetE]), singletonsswitch]), eqinunit]), notinsingleton]), uniqinunit]), c_0_120]), upairsetIR]), prop2setI]), quantDeMorgan4]), quantDeMorgan3]), quantDeMorgan2]), quantDeMorgan1]), vacuousDall]), c_0_121]), notdexE]), c_0_122]), in__Cong]), inCongP]), c_0_123]), c_0_124]), c_0_125]), notdallE]), c_0_126]), c_0_127]), c_0_128]), omega__Cong]), setunion__Cong]), powerset__Cong]), setadjoin__Cong]), emptyset__Cong]), subsetI2]), c_0_129]), emptysetsubset]), prop2setE]), c_0_130]), c_0_131]), c_0_132]), c_0_133]), c_0_134]), wellorderingAx]), foundationAx]), c_0_135]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_136])).
% 1.20/0.51 thf(c_0_138, negated_conjecture, ![X587:$i, X588:$i, X590:$i, X591:$i, X592:$i, X593:$i, X594:$i, X595:$i, X596:$i, X597:$i, X598:$i, X600:$i, X601:$i, X603:$i, X604:$i, X605:$i, X606:$i, X607:$i, X609:$i, X610:$i > $i > $o, X611:$i, X613:$i, X616:$i, X618:$i, X619:$i, X620:$i, X621:$i, X623:$i, X624:$i > $o, X625:$i, X627:$i, X628:$i > $o, X629:$i, X630:$i, X631:$i > $o, X632:$i, X633:$i, X634:$i > $o, X635:$i, X636:$i > $o, X637:$i, X640:$i, X641:$o, X642:$i, X643:$i, X644:$o, X645:$i, X646:$i, X647:$i > $o, X648:$i, X651:$i, X652:$i, X655:$i, X657:$i, X659:$i, X660:$i > $o, X661:$i, X662:$i, X664:$i, X665:$i > $o, X666:$i, X667:$i, X668:$i, X669:$i, X670:$i, X671:$i, X672:$i, X673:$i, X674:$i, X675:$i, X676:$i, X677:$o, X678:$i, X679:$i, X680:$i, X681:$i, X682:$i, X683:$i, X685:$i, X686:$i, X687:$i, X688:$i, X689:$i, X690:$i, X691:$i, X692:$i, X693:$i, X694:$i, X695:$o, X697:$i, X698:$i, X699:$i > $o, X700:$i, X703:$i, X704:$i, X705:$i, X707:$i, X708:$i, X709:$i, X710:$i, X711:$i, X712:$i, X713:$i, X714:$i, X715:$i, X716:$i, X717:$i, X718:$i, X719:$i, X720:$i, X721:$i, X722:$i, X723:$i > $o, X724:$i, X725:$i > $o, X726:$i, X727:$i, X728:$i > $o, X729:$i, X731:$i, X732:$i > $o, X734:$i, X735:$i, X736:$i > $o, X738:$i, X739:$i, X740:$i > $o, X741:$i, X743:$o, X744:$i, X745:$i > $o, X747:$i, X748:$i, X749:$i > $o, X750:$i, X752:$i > $o, X753:$i, X756:$i, X757:$i > $o, X758:$i, X762:$i, X763:$i > $o, X764:$i, X767:$i, X768:$i, X769:$i, X770:$i, X771:$i, X772:$i, X773:$i, X774:$i, X775:$i, X776:$i > $o, X777:$i, X779:$i, X780:$i, X781:$i > $o, X782:$i > $o, X785:$i, X788:$i, X789:$i, X792:$i, X793:$i, X794:$i, X795:$i, X796:$i, X797:$i, X798:$i, X799:$i, X800:$i, X801:$i > $o, X802:$i, X804:$i, X805:$i, X806:$i > $o, X807:$i > $o, X810:$i, X812:$i, X814:$i, X815:$i, X816:$i > $o, X817:$i > $o, X820:$i, X821:$i, X823:$i, X824:$i, X825:$i, X826:$i, X827:$i, X828:$i, X830:$i, X831:$i, X832:$i, X833:$i, X834:$i, X835:$i, X836:$i, X837:$i, X838:$i, X839:$i, X840:$i, X841:$i, X842:$i, X843:$i, X844:$i, X845:$i, X846:$i, X847:$i, X848:$i, X849:$i, X850:$i, X851:$i, X852:$i, X853:$i, X854:$i, X855:$i, X856:$i, X857:$i, X858:$i, X859:$i, X860:$i, X861:$i, X862:$i, X863:$i]:((((~(in @ (esk1_2 @ X587 @ X588) @ X587)|~(in @ (esk1_2 @ X587 @ X588) @ X588)|((X587)=(X588)))&((in @ (esk1_2 @ X587 @ X588) @ X587)|(in @ (esk1_2 @ X587 @ X588) @ X588)|((X587)=(X588))))&(~(in @ X590 @ emptyset)&(((~(in @ X593 @ (setadjoin @ X591 @ X592))|(((X593)=(X591))|(in @ X593 @ X592)))&((((X593)!=(X591))|(in @ X593 @ (setadjoin @ X591 @ X592)))&(~(in @ X593 @ X592)|(in @ X593 @ (setadjoin @ X591 @ X592)))))&(((~(in @ X595 @ (powerset @ X594))|(~(in @ X596 @ X595)|(in @ X596 @ X594)))&(((in @ (esk2_2 @ X597 @ X598) @ X598)|(in @ X598 @ (powerset @ X597)))&(~(in @ (esk2_2 @ X597 @ X598) @ X597)|(in @ X598 @ (powerset @ X597)))))&(((((in @ X601 @ (esk3_2 @ X600 @ X601))|~(in @ X601 @ (setunion @ X600)))&((in @ (esk3_2 @ X600 @ X601) @ X600)|~(in @ X601 @ (setunion @ X600))))&(~(in @ X604 @ X605)|~(in @ X605 @ X603)|(in @ X604 @ (setunion @ X603))))&((in @ emptyset @ omega)&((~(in @ X606 @ omega)|(in @ (setadjoin @ X606 @ X606) @ omega))&(((((in @ (esk4_1 @ X607) @ omega)|~(in @ emptyset @ X607)|(~(in @ X609 @ omega)|(in @ X609 @ X607)))&((in @ (esk4_1 @ X607) @ X607)|~(in @ emptyset @ X607)|(~(in @ X609 @ omega)|(in @ X609 @ X607))))&(~(in @ (setadjoin @ (esk4_1 @ X607) @ (esk4_1 @ X607)) @ X607)|~(in @ emptyset @ X607)|(~(in @ X609 @ omega)|(in @ X609 @ X607))))&((((((in @ (esk8_3 @ X610 @ X611 @ X616) @ X611)|~(in @ X616 @ (esk7_2 @ X610 @ X611))|(in @ (esk5_2 @ X610 @ X611) @ X611))&((X610 @ (esk8_3 @ X610 @ X611 @ X616) @ X616)|~(in @ X616 @ (esk7_2 @ X610 @ X611))|(in @ (esk5_2 @ X610 @ X611) @ X611)))&(~(in @ X619 @ X611)|~(X610 @ X619 @ X618)|(in @ X618 @ (esk7_2 @ X610 @ X611))|(in @ (esk5_2 @ X610 @ X611) @ X611)))&(((((in @ (esk8_3 @ X610 @ X611 @ X616) @ X611)|~(in @ X616 @ (esk7_2 @ X610 @ X611))|((X610 @ (esk5_2 @ X610 @ X611) @ (esk6_3 @ X610 @ X611 @ X613))|~(X610 @ (esk5_2 @ X610 @ X611) @ X613)))&((X610 @ (esk8_3 @ X610 @ X611 @ X616) @ X616)|~(in @ X616 @ (esk7_2 @ X610 @ X611))|((X610 @ (esk5_2 @ X610 @ X611) @ (esk6_3 @ X610 @ X611 @ X613))|~(X610 @ (esk5_2 @ X610 @ X611) @ X613))))&(~(in @ X619 @ X611)|~(X610 @ X619 @ X618)|(in @ X618 @ (esk7_2 @ X610 @ X611))|((X610 @ (esk5_2 @ X610 @ X611) @ (esk6_3 @ X610 @ X611 @ X613))|~(X610 @ (esk5_2 @ X610 @ X611) @ X613))))&((((in @ (esk8_3 @ X610 @ X611 @ X616) @ X611)|~(in @ X616 @ (esk7_2 @ X610 @ X611))|(((X613)!=(esk6_3 @ X610 @ X611 @ X613))|~(X610 @ (esk5_2 @ X610 @ X611) @ X613)))&((X610 @ (esk8_3 @ X610 @ X611 @ X616) @ X616)|~(in @ X616 @ (esk7_2 @ X610 @ X611))|(((X613)!=(esk6_3 @ X610 @ X611 @ X613))|~(X610 @ (esk5_2 @ X610 @ X611) @ X613))))&(~(in @ X619 @ X611)|~(X610 @ X619 @ X618)|(in @ X618 @ (esk7_2 @ X610 @ X611))|(((X613)!=(esk6_3 @ X610 @ X611 @ X613))|~(X610 @ (esk5_2 @ X610 @ X611) @ X613))))))&((((in @ (esk9_1 @ X620) @ X620)|~(in @ X621 @ X620))&(~(in @ X623 @ (esk9_1 @ X620))|~(in @ X623 @ X620)|~(in @ X621 @ X620)))&((epred1_0)&((((X624 @ (esk10_2 @ X624 @ X625))|~(X624 @ X625)|(X624 @ (descr @ X624)))&(((X625)!=(esk10_2 @ X624 @ X625))|~(X624 @ X625)|(X624 @ (descr @ X624))))&((~(in @ X629 @ X627)|(~(X628 @ X629)|(in @ X629 @ (dsetconstr @ X627 @ X628))))&((~(in @ X632 @ (dsetconstr @ X630 @ X631))|(in @ X632 @ X630))&((~(in @ X635 @ (dsetconstr @ X633 @ X634))|(X634 @ X635))&(((((X636 @ (esk12_1 @ X636))|((X636 @ (esk11_2 @ X636 @ X637))|~(X636 @ X637)))&(~(X636 @ X640)|((esk12_1 @ X636)=(X640))|((X636 @ (esk11_2 @ X636 @ X637))|~(X636 @ X637))))&(((X636 @ (esk12_1 @ X636))|(((X637)!=(esk11_2 @ X636 @ X637))|~(X636 @ X637)))&(~(X636 @ X640)|((esk12_1 @ X636)=(X640))|(((X637)!=(esk11_2 @ X636 @ X637))|~(X636 @ X637)))))&((~(in @ X642 @ (prop2set @ ((X641))))|(X641))&((~(in @ X643 @ emptyset)|(X644))&((~(in @ X645 @ emptyset)|~($true))&(~(in @ X646 @ emptyset)&((((X647 @ (esk13_2 @ X647 @ X648))|~(X647 @ X648)|(X647 @ (esk14_1 @ X647)))&(((X648)!=(esk13_2 @ X647 @ X648))|~(X647 @ X648)|(X647 @ (esk14_1 @ X647))))&(((((in @ (esk16_2 @ X651 @ X652) @ X652)|((X651)=(X652))|(in @ (esk15_2 @ X651 @ X652) @ X651))&(~(in @ (esk16_2 @ X651 @ X652) @ X651)|((X651)=(X652))|(in @ (esk15_2 @ X651 @ X652) @ X651)))&(((in @ (esk16_2 @ X651 @ X652) @ X652)|((X651)=(X652))|~(in @ (esk15_2 @ X651 @ X652) @ X652))&(~(in @ (esk16_2 @ X651 @ X652) @ X651)|((X651)=(X652))|~(in @ (esk15_2 @ X651 @ X652) @ X652))))&(((in @ (esk17_1 @ X655) @ X655)|((X655)=(emptyset)))&(((in @ (esk18_1 @ X657) @ X657)|((X657)=(emptyset)))&(((~(in @ X661 @ (dsetconstr @ X659 @ X660))|(X660 @ X661)|~(in @ X661 @ X659))&(~(X660 @ X661)|(in @ X661 @ (dsetconstr @ X659 @ X660))|~(in @ X661 @ X659)))&((((X662)=(emptyset))|(in @ (esk19_1 @ X662) @ X662))&((~(in @ X666 @ X664)|(~(X665 @ X666)|((dsetconstr @ X664 @ X665)!=(emptyset))))&((~(in @ X668 @ X667)|((X667)!=(emptyset)))&((in @ X669 @ (setadjoin @ X669 @ X670))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X673 @ X672)|(in @ X673 @ (setadjoin @ X671 @ X672)))&(((((in @ X676 @ X675)|(X677)|((X676)=(X674))|~(in @ X676 @ (setadjoin @ X674 @ X675)))&(~(X677)|(X677)|((X676)=(X674))|~(in @ X676 @ (setadjoin @ X674 @ X675))))&(((in @ X676 @ X675)|(X677)|~(X677)|~(in @ X676 @ (setadjoin @ X674 @ X675)))&(~(X677)|(X677)|~(X677)|~(in @ X676 @ (setadjoin @ X674 @ X675)))))&((~(in @ X680 @ (setadjoin @ X678 @ X679))|(((X680)=(X678))|(in @ X680 @ X679)))&(((dsetconstr @ X681 @ (^[Z0:$i]:($true)))=(X681))&((((in @ (esk20_2 @ X682 @ X683) @ X683)|(in @ X683 @ (powerset @ X682)))&(~(in @ (esk20_2 @ X682 @ X683) @ X682)|(in @ X683 @ (powerset @ X682))))&((in @ emptyset @ (powerset @ X685))&((in @ emptyset @ (powerset @ X686))&((~(in @ X688 @ (powerset @ X687))|(~(in @ X689 @ X688)|(in @ X689 @ X687)))&((~(in @ X691 @ X692)|(~(in @ X692 @ X690)|(in @ X691 @ (setunion @ X690))))&((((in @ X694 @ (esk21_3 @ X693 @ X694 @ X695))|(X695)|~(in @ X694 @ (setunion @ X693)))&(((in @ (esk21_3 @ X693 @ X694 @ X695) @ X693)|(X695)|~(in @ X694 @ (setunion @ X693)))&(~(X695)|(X695)|~(in @ X694 @ (setunion @ X693)))))&((~(in @ X698 @ X697)|(in @ X698 @ (powerset @ (setunion @ X697))))&((((~(X699 @ X703)|((X703)=(esk23_1 @ X699))|((X699 @ (esk22_2 @ X699 @ X700))|~(X699 @ X700)))&(((X704)!=(esk23_1 @ X699))|(X699 @ X704)|((X699 @ (esk22_2 @ X699 @ X700))|~(X699 @ X700))))&((~(X699 @ X703)|((X703)=(esk23_1 @ X699))|(((X700)!=(esk22_2 @ X699 @ X700))|~(X699 @ X700)))&(((X704)!=(esk23_1 @ X699))|(X699 @ X704)|(((X700)!=(esk22_2 @ X699 @ X700))|~(X699 @ X700)))))&((((in @ (esk24_1 @ X705) @ X705)|((X705)=(emptyset)))&(($true)|((X705)=(emptyset))))&((~(in @ X707 @ (setadjoin @ X708 @ emptyset))|((X707)=(X708)))&((((X709)=(X710))|~(in @ X710 @ (setadjoin @ X709 @ emptyset)))&((((X711)!=(X712))|(in @ X711 @ (setadjoin @ X712 @ emptyset)))&((~(in @ X713 @ (setadjoin @ X714 @ emptyset))|(in @ X714 @ (setadjoin @ X713 @ emptyset)))&((~(in @ X717 @ (setadjoin @ X715 @ (setadjoin @ X716 @ emptyset)))|(((X717)=(X715))|((X717)=(X716))))&((in @ X718 @ (setadjoin @ X718 @ (setadjoin @ X719 @ emptyset)))&((in @ X721 @ (setadjoin @ X720 @ (setadjoin @ X721 @ emptyset)))&((~(in @ X724 @ X722)|~(X723 @ X724)|(((dsetconstr @ X722 @ X723)!=(emptyset))|~($true)))&((~(in @ X726 @ emptyset)|(X725 @ X726))&((((in @ (esk25_2 @ X727 @ X728) @ X727)|(~(in @ X729 @ X727)|(X728 @ X729)))&(~(X728 @ (esk25_2 @ X727 @ X728))|(~(in @ X729 @ X727)|(X728 @ X729))))&((((in @ (esk26_2 @ X731 @ X732) @ X731)|(~(in @ X734 @ X731)|~(X732 @ X734)))&((X732 @ (esk26_2 @ X731 @ X732))|(~(in @ X734 @ X731)|~(X732 @ X734))))&((((in @ (esk27_2 @ X735 @ X736) @ X735)|(~(in @ X738 @ X735)|~(X736 @ X738)))&((X736 @ (esk27_2 @ X735 @ X736))|(~(in @ X738 @ X735)|~(X736 @ X738))))&((((in @ (esk28_2 @ X739 @ X740) @ X739)|(~(in @ X741 @ X739)|(X740 @ X741)))&(~(X740 @ (esk28_2 @ X739 @ X740))|(~(in @ X741 @ X739)|(X740 @ X741))))&((~(X743)|(in @ emptyset @ (prop2set @ ((X743)))))&((prop2set2propI)&((((in @ (esk29_2 @ X744 @ X745) @ X744)|(~(in @ X747 @ X744)|~(X745 @ X747)))&((X745 @ (esk29_2 @ X744 @ X745))|(~(in @ X747 @ X744)|~(X745 @ X747))))&((((in @ (esk30_2 @ X748 @ X749) @ X748)|(~(in @ X750 @ X748)|(X749 @ X750)))&(~(X749 @ (esk30_2 @ X748 @ X749))|(~(in @ X750 @ X748)|(X749 @ X750))))&(((((X752 @ (esk32_1 @ X752))|((X752 @ (esk31_2 @ X752 @ X753))|~(X752 @ X753)))&(~(X752 @ X756)|((esk32_1 @ X752)=(X756))|((X752 @ (esk31_2 @ X752 @ X753))|~(X752 @ X753))))&(((X752 @ (esk32_1 @ X752))|(((X753)!=(esk31_2 @ X752 @ X753))|~(X752 @ X753)))&(~(X752 @ X756)|((esk32_1 @ X752)=(X756))|(((X753)!=(esk31_2 @ X752 @ X753))|~(X752 @ X753)))))&(((((X757 @ (esk35_1 @ X757))|(X757 @ (esk33_1 @ X757))|~(X757 @ X758))&(~(X757 @ X762)|((esk35_1 @ X757)=(X762))|(X757 @ (esk33_1 @ X757))|~(X757 @ X758)))&((((X757 @ (esk35_1 @ X757))|(X757 @ (esk34_1 @ X757))|~(X757 @ X758))&(~(X757 @ X762)|((esk35_1 @ X757)=(X762))|(X757 @ (esk34_1 @ X757))|~(X757 @ X758)))&(((X757 @ (esk35_1 @ X757))|((esk33_1 @ X757)!=(esk34_1 @ X757))|~(X757 @ X758))&(~(X757 @ X762)|((esk35_1 @ X757)=(X762))|((esk33_1 @ X757)!=(esk34_1 @ X757))|~(X757 @ X758)))))&(((((X763 @ (esk37_1 @ X763))|(~(X763 @ (esk36_2 @ X763 @ X764))|((esk36_2 @ X763 @ X764)!=(X764))))&(~(X763 @ X767)|((esk37_1 @ X763)=(X767))|(~(X763 @ (esk36_2 @ X763 @ X764))|((esk36_2 @ X763 @ X764)!=(X764)))))&(((X763 @ (esk37_1 @ X763))|((X763 @ (esk36_2 @ X763 @ X764))|((esk36_2 @ X763 @ X764)=(X764))))&(~(X763 @ X767)|((esk37_1 @ X763)=(X767))|((X763 @ (esk36_2 @ X763 @ X764))|((esk36_2 @ X763 @ X764)=(X764))))))&((((X768)!=(X769))|(((X770)!=(X771))|(~(in @ X770 @ X768)|(in @ X771 @ X769))))&(((~(in @ X774 @ X772)|(in @ X775 @ X773)|((X774)!=(X775))|((X772)!=(X773)))&(~(in @ X775 @ X773)|(in @ X774 @ X772)|((X774)!=(X775))|((X772)!=(X773))))&((((X776 @ (esk38_2 @ X776 @ X777))|~(X776 @ X777)|(~(X776 @ X779)|(~(X776 @ X780)|((X779)=(X780)))))&(((X777)!=(esk38_2 @ X776 @ X777))|~(X776 @ X777)|(~(X776 @ X779)|(~(X776 @ X780)|((X779)=(X780))))))&(((((((X782 @ (esk42_2 @ X781 @ X782))|((X781 @ (esk41_3 @ X781 @ X782 @ X785))|~(X781 @ X785))|((esk39_2 @ X781 @ X782)=(esk40_2 @ X781 @ X782)))&(~(X782 @ X788)|((esk42_2 @ X781 @ X782)=(X788))|((X781 @ (esk41_3 @ X781 @ X782 @ X785))|~(X781 @ X785))|((esk39_2 @ X781 @ X782)=(esk40_2 @ X781 @ X782))))&(((X782 @ (esk42_2 @ X781 @ X782))|(((X785)!=(esk41_3 @ X781 @ X782 @ X785))|~(X781 @ X785))|((esk39_2 @ X781 @ X782)=(esk40_2 @ X781 @ X782)))&(~(X782 @ X788)|((esk42_2 @ X781 @ X782)=(X788))|(((X785)!=(esk41_3 @ X781 @ X782 @ X785))|~(X781 @ X785))|((esk39_2 @ X781 @ X782)=(esk40_2 @ X781 @ X782)))))&((((X781 @ (esk44_2 @ X781 @ X782))|((X782 @ (esk43_3 @ X781 @ X782 @ X789))|~(X782 @ X789))|((esk39_2 @ X781 @ X782)=(esk40_2 @ X781 @ X782)))&(~(X781 @ X792)|((esk44_2 @ X781 @ X782)=(X792))|((X782 @ (esk43_3 @ X781 @ X782 @ X789))|~(X782 @ X789))|((esk39_2 @ X781 @ X782)=(esk40_2 @ X781 @ X782))))&(((X781 @ (esk44_2 @ X781 @ X782))|(((X789)!=(esk43_3 @ X781 @ X782 @ X789))|~(X782 @ X789))|((esk39_2 @ X781 @ X782)=(esk40_2 @ X781 @ X782)))&(~(X781 @ X792)|((esk44_2 @ X781 @ X782)=(X792))|(((X789)!=(esk43_3 @ X781 @ X782 @ X789))|~(X782 @ X789))|((esk39_2 @ X781 @ X782)=(esk40_2 @ X781 @ X782))))))&((((((X782 @ (esk42_2 @ X781 @ X782))|((X781 @ (esk41_3 @ X781 @ X782 @ X785))|~(X781 @ X785))|(~(X781 @ (esk39_2 @ X781 @ X782))|~(X782 @ (esk40_2 @ X781 @ X782))))&(~(X782 @ X788)|((esk42_2 @ X781 @ X782)=(X788))|((X781 @ (esk41_3 @ X781 @ X782 @ X785))|~(X781 @ X785))|(~(X781 @ (esk39_2 @ X781 @ X782))|~(X782 @ (esk40_2 @ X781 @ X782)))))&(((X782 @ (esk42_2 @ X781 @ X782))|(((X785)!=(esk41_3 @ X781 @ X782 @ X785))|~(X781 @ X785))|(~(X781 @ (esk39_2 @ X781 @ X782))|~(X782 @ (esk40_2 @ X781 @ X782))))&(~(X782 @ X788)|((esk42_2 @ X781 @ X782)=(X788))|(((X785)!=(esk41_3 @ X781 @ X782 @ X785))|~(X781 @ X785))|(~(X781 @ (esk39_2 @ X781 @ X782))|~(X782 @ (esk40_2 @ X781 @ X782))))))&((((X781 @ (esk44_2 @ X781 @ X782))|((X782 @ (esk43_3 @ X781 @ X782 @ X789))|~(X782 @ X789))|(~(X781 @ (esk39_2 @ X781 @ X782))|~(X782 @ (esk40_2 @ X781 @ X782))))&(~(X781 @ X792)|((esk44_2 @ X781 @ X782)=(X792))|((X782 @ (esk43_3 @ X781 @ X782 @ X789))|~(X782 @ X789))|(~(X781 @ (esk39_2 @ X781 @ X782))|~(X782 @ (esk40_2 @ X781 @ X782)))))&(((X781 @ (esk44_2 @ X781 @ X782))|(((X789)!=(esk43_3 @ X781 @ X782 @ X789))|~(X782 @ X789))|(~(X781 @ (esk39_2 @ X781 @ X782))|~(X782 @ (esk40_2 @ X781 @ X782))))&(~(X781 @ X792)|((esk44_2 @ X781 @ X782)=(X792))|(((X789)!=(esk43_3 @ X781 @ X782 @ X789))|~(X782 @ X789))|(~(X781 @ (esk39_2 @ X781 @ X782))|~(X782 @ (esk40_2 @ X781 @ X782)))))))&(((((X782 @ (esk42_2 @ X781 @ X782))|((X781 @ (esk41_3 @ X781 @ X782 @ X785))|~(X781 @ X785))|((X781 @ (esk39_2 @ X781 @ X782))|(X782 @ (esk40_2 @ X781 @ X782))))&(~(X782 @ X788)|((esk42_2 @ X781 @ X782)=(X788))|((X781 @ (esk41_3 @ X781 @ X782 @ X785))|~(X781 @ X785))|((X781 @ (esk39_2 @ X781 @ X782))|(X782 @ (esk40_2 @ X781 @ X782)))))&(((X782 @ (esk42_2 @ X781 @ X782))|(((X785)!=(esk41_3 @ X781 @ X782 @ X785))|~(X781 @ X785))|((X781 @ (esk39_2 @ X781 @ X782))|(X782 @ (esk40_2 @ X781 @ X782))))&(~(X782 @ X788)|((esk42_2 @ X781 @ X782)=(X788))|(((X785)!=(esk41_3 @ X781 @ X782 @ X785))|~(X781 @ X785))|((X781 @ (esk39_2 @ X781 @ X782))|(X782 @ (esk40_2 @ X781 @ X782))))))&((((X781 @ (esk44_2 @ X781 @ X782))|((X782 @ (esk43_3 @ X781 @ X782 @ X789))|~(X782 @ X789))|((X781 @ (esk39_2 @ X781 @ X782))|(X782 @ (esk40_2 @ X781 @ X782))))&(~(X781 @ X792)|((esk44_2 @ X781 @ X782)=(X792))|((X782 @ (esk43_3 @ X781 @ X782 @ X789))|~(X782 @ X789))|((X781 @ (esk39_2 @ X781 @ X782))|(X782 @ (esk40_2 @ X781 @ X782)))))&(((X781 @ (esk44_2 @ X781 @ X782))|(((X789)!=(esk43_3 @ X781 @ X782 @ X789))|~(X782 @ X789))|((X781 @ (esk39_2 @ X781 @ X782))|(X782 @ (esk40_2 @ X781 @ X782))))&(~(X781 @ X792)|((esk44_2 @ X781 @ X782)=(X792))|(((X789)!=(esk43_3 @ X781 @ X782 @ X789))|~(X782 @ X789))|((X781 @ (esk39_2 @ X781 @ X782))|(X782 @ (esk40_2 @ X781 @ X782)))))))))&(((emptyset)=(emptyset))&((((X793)!=(X794))|(((X795)!=(X796))|((setadjoin @ X793 @ X795)=(setadjoin @ X794 @ X796))))&((((X797)!=(X798))|((powerset @ X797)=(powerset @ X798)))&((((X799)!=(X800))|((setunion @ X799)=(setunion @ X800)))&(((omega)=(omega))&((((X801 @ (esk45_2 @ X801 @ X802))|~(X801 @ X802)|(~(X801 @ X804)|(~(X801 @ X805)|((X804)=(X805)))))&(((X802)!=(esk45_2 @ X801 @ X802))|~(X801 @ X802)|(~(X801 @ X804)|(~(X801 @ X805)|((X804)=(X805))))))&((((((X807 @ (esk49_3 @ X806 @ X807 @ X812))|~(X807 @ X812)|((descr @ X806)=(descr @ X807))|((X806 @ (esk48_3 @ X806 @ X807 @ X810))|~(X806 @ X810))|((esk46_2 @ X806 @ X807)=(esk47_2 @ X806 @ X807)))&(((X812)!=(esk49_3 @ X806 @ X807 @ X812))|~(X807 @ X812)|((descr @ X806)=(descr @ X807))|((X806 @ (esk48_3 @ X806 @ X807 @ X810))|~(X806 @ X810))|((esk46_2 @ X806 @ X807)=(esk47_2 @ X806 @ X807))))&(((X807 @ (esk49_3 @ X806 @ X807 @ X812))|~(X807 @ X812)|((descr @ X806)=(descr @ X807))|(((X810)!=(esk48_3 @ X806 @ X807 @ X810))|~(X806 @ X810))|((esk46_2 @ X806 @ X807)=(esk47_2 @ X806 @ X807)))&(((X812)!=(esk49_3 @ X806 @ X807 @ X812))|~(X807 @ X812)|((descr @ X806)=(descr @ X807))|(((X810)!=(esk48_3 @ X806 @ X807 @ X810))|~(X806 @ X810))|((esk46_2 @ X806 @ X807)=(esk47_2 @ X806 @ X807)))))&(((((X807 @ (esk49_3 @ X806 @ X807 @ X812))|~(X807 @ X812)|((descr @ X806)=(descr @ X807))|((X806 @ (esk48_3 @ X806 @ X807 @ X810))|~(X806 @ X810))|(~(X806 @ (esk46_2 @ X806 @ X807))|~(X807 @ (esk47_2 @ X806 @ X807))))&(((X812)!=(esk49_3 @ X806 @ X807 @ X812))|~(X807 @ X812)|((descr @ X806)=(descr @ X807))|((X806 @ (esk48_3 @ X806 @ X807 @ X810))|~(X806 @ X810))|(~(X806 @ (esk46_2 @ X806 @ X807))|~(X807 @ (esk47_2 @ X806 @ X807)))))&(((X807 @ (esk49_3 @ X806 @ X807 @ X812))|~(X807 @ X812)|((descr @ X806)=(descr @ X807))|(((X810)!=(esk48_3 @ X806 @ X807 @ X810))|~(X806 @ X810))|(~(X806 @ (esk46_2 @ X806 @ X807))|~(X807 @ (esk47_2 @ X806 @ X807))))&(((X812)!=(esk49_3 @ X806 @ X807 @ X812))|~(X807 @ X812)|((descr @ X806)=(descr @ X807))|(((X810)!=(esk48_3 @ X806 @ X807 @ X810))|~(X806 @ X810))|(~(X806 @ (esk46_2 @ X806 @ X807))|~(X807 @ (esk47_2 @ X806 @ X807))))))&((((X807 @ (esk49_3 @ X806 @ X807 @ X812))|~(X807 @ X812)|((descr @ X806)=(descr @ X807))|((X806 @ (esk48_3 @ X806 @ X807 @ X810))|~(X806 @ X810))|((X806 @ (esk46_2 @ X806 @ X807))|(X807 @ (esk47_2 @ X806 @ X807))))&(((X812)!=(esk49_3 @ X806 @ X807 @ X812))|~(X807 @ X812)|((descr @ X806)=(descr @ X807))|((X806 @ (esk48_3 @ X806 @ X807 @ X810))|~(X806 @ X810))|((X806 @ (esk46_2 @ X806 @ X807))|(X807 @ (esk47_2 @ X806 @ X807)))))&(((X807 @ (esk49_3 @ X806 @ X807 @ X812))|~(X807 @ X812)|((descr @ X806)=(descr @ X807))|(((X810)!=(esk48_3 @ X806 @ X807 @ X810))|~(X806 @ X810))|((X806 @ (esk46_2 @ X806 @ X807))|(X807 @ (esk47_2 @ X806 @ X807))))&(((X812)!=(esk49_3 @ X806 @ X807 @ X812))|~(X807 @ X812)|((descr @ X806)=(descr @ X807))|(((X810)!=(esk48_3 @ X806 @ X807 @ X810))|~(X806 @ X810))|((X806 @ (esk46_2 @ X806 @ X807))|(X807 @ (esk47_2 @ X806 @ X807))))))))&((((in @ (esk50_4 @ X814 @ X815 @ X816 @ X817) @ X814)|((dsetconstr @ X814 @ X816)=(dsetconstr @ X815 @ X817))|((X814)!=(X815)))&(((in @ (esk51_4 @ X814 @ X815 @ X816 @ X817) @ X815)|((dsetconstr @ X814 @ X816)=(dsetconstr @ X815 @ X817))|((X814)!=(X815)))&((((esk50_4 @ X814 @ X815 @ X816 @ X817)=(esk51_4 @ X814 @ X815 @ X816 @ X817))|((dsetconstr @ X814 @ X816)=(dsetconstr @ X815 @ X817))|((X814)!=(X815)))&((~(X816 @ (esk50_4 @ X814 @ X815 @ X816 @ X817))|~(X817 @ (esk51_4 @ X814 @ X815 @ X816 @ X817))|((dsetconstr @ X814 @ X816)=(dsetconstr @ X815 @ X817))|((X814)!=(X815)))&((X816 @ (esk50_4 @ X814 @ X815 @ X816 @ X817))|(X817 @ (esk51_4 @ X814 @ X815 @ X816 @ X817))|((dsetconstr @ X814 @ X816)=(dsetconstr @ X815 @ X817))|((X814)!=(X815)))))))&((((in @ (esk52_2 @ X820 @ X821) @ X820)|(subset @ X820 @ X821))&(~(in @ (esk52_2 @ X820 @ X821) @ X821)|(subset @ X820 @ X821)))&((((X823)!=(X824))|(subset @ X824 @ X823))&((((X825)!=(X826))|(subset @ X825 @ X826))&((((in @ (esk53_2 @ X827 @ X828) @ X827)|(subset @ X827 @ X828))&(~(in @ (esk53_2 @ X827 @ X828) @ X828)|(subset @ X827 @ X828)))&((subset @ emptyset @ X830)&((~(subset @ X831 @ X832)|(~(in @ X833 @ X831)|(in @ X833 @ X832)))&((~(subset @ X834 @ X835)|((in @ X836 @ X835)|~(in @ X836 @ X834)))&((~(in @ X839 @ X837)|((in @ X839 @ X838)|~(subset @ X837 @ X838)))&(((subset @ X840 @ X841)|((X840)!=(X841)))&((~(in @ X844 @ X842)|((in @ X844 @ X843)|((X842)!=(X843))))&((subset @ X845 @ X845)&((~(subset @ X846 @ X847)|(~(subset @ X847 @ X848)|(subset @ X846 @ X848)))&((subset @ X850 @ (setadjoin @ X849 @ X850))&((~(subset @ X851 @ X853)|(subset @ X851 @ (setadjoin @ X852 @ X853)))&((~(subset @ X854 @ X855)|(in @ X854 @ (powerset @ X855)))&((~(subset @ X856 @ X857)|(~(subset @ X857 @ X856)|((X856)=(X857))))&((~(subset @ X858 @ emptyset)|((X858)=(emptyset)))&((~(subset @ X860 @ X859)|(in @ X860 @ (powerset @ X859)))&((~(in @ X862 @ (powerset @ X861))|(subset @ X862 @ X861))&((in @ X863 @ (powerset @ X863))&((subset @ esk54_0 @ esk55_0)&~(subset @ (powerset @ esk54_0) @ (powerset @ esk55_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_137])])])])])])])).
% 1.20/0.51 thf(c_0_139, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ X3)|~((in @ (esk52_2 @ X2 @ X3) @ X3)))), inference(split_conjunct,[status(thm)],[c_0_138])).
% 1.20/0.51 thf(c_0_140, negated_conjecture, ![X2:$i, X3:$i]:(((in @ X2 @ (powerset @ X3))|~((subset @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_138])).
% 1.20/0.51 thf(c_0_141, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((subset @ X2 @ X4)|~((subset @ X2 @ X3))|~((subset @ X3 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_138])).
% 1.20/0.51 thf(c_0_142, negated_conjecture, (subset @ esk54_0 @ esk55_0), inference(split_conjunct,[status(thm)],[c_0_138])).
% 1.20/0.51 thf(c_0_143, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ (powerset @ X3))|~((subset @ (esk52_2 @ X2 @ (powerset @ X3)) @ X3)))), inference(spm,[status(thm)],[c_0_139, c_0_140])).
% 1.20/0.51 thf(c_0_144, negated_conjecture, ![X2:$i]:(((subset @ X2 @ esk55_0)|~((subset @ X2 @ esk54_0)))), inference(spm,[status(thm)],[c_0_141, c_0_142])).
% 1.20/0.51 thf(c_0_145, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ X3)|~((in @ X2 @ (powerset @ X3))))), inference(split_conjunct,[status(thm)],[c_0_138])).
% 1.20/0.51 thf(c_0_146, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (esk52_2 @ X2 @ X3) @ X2)|(subset @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_138])).
% 1.20/0.51 thf(c_0_147, negated_conjecture, ![X2:$i]:(((subset @ X2 @ (powerset @ esk55_0))|~((subset @ (esk52_2 @ X2 @ (powerset @ esk55_0)) @ esk54_0)))), inference(spm,[status(thm)],[c_0_143, c_0_144])).
% 1.20/0.51 thf(c_0_148, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ (esk52_2 @ (powerset @ X2) @ X3) @ X2)|(subset @ (powerset @ X2) @ X3))), inference(spm,[status(thm)],[c_0_145, c_0_146])).
% 1.20/0.51 thf(c_0_149, negated_conjecture, ~((subset @ (powerset @ esk54_0) @ (powerset @ esk55_0))), inference(split_conjunct,[status(thm)],[c_0_138])).
% 1.20/0.51 thf(c_0_150, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_147, c_0_148]), c_0_149]), ['proof']).
% 1.20/0.51 % SZS output end CNFRefutation
% 1.20/0.51 % Parsed axioms : 208
% 1.20/0.51 % Removed by relevancy pruning/SinE : 111
% 1.20/0.51 % Initial clauses : 207
% 1.20/0.51 % Removed in clause preprocessing : 14
% 1.20/0.51 % Initial clauses in saturation : 193
% 1.20/0.51 % Processed clauses : 1072
% 1.20/0.51 % ...of these trivial : 6
% 1.20/0.51 % ...subsumed : 545
% 1.20/0.51 % ...remaining for further processing : 521
% 1.20/0.51 % Other redundant clauses eliminated : 9
% 1.20/0.51 % Clauses deleted for lack of memory : 0
% 1.20/0.51 % Backward-subsumed : 7
% 1.20/0.51 % Backward-rewritten : 6
% 1.20/0.51 % Generated clauses : 17554
% 1.20/0.51 % ...of the previous two non-redundant : 16945
% 1.20/0.51 % ...aggressively subsumed : 0
% 1.20/0.51 % Contextual simplify-reflections : 0
% 1.20/0.51 % Paramodulations : 17543
% 1.20/0.51 % Factorizations : 2
% 1.20/0.51 % NegExts : 0
% 1.20/0.51 % Equation resolutions : 9
% 1.20/0.51 % Disequality decompositions : 0
% 1.20/0.51 % Total rewrite steps : 775
% 1.20/0.51 % ...of those cached : 670
% 1.20/0.51 % Propositional unsat checks : 0
% 1.20/0.51 % Propositional check models : 0
% 1.20/0.51 % Propositional check unsatisfiable : 0
% 1.20/0.51 % Propositional clauses : 0
% 1.20/0.51 % Propositional clauses after purity: 0
% 1.20/0.51 % Propositional unsat core size : 0
% 1.20/0.51 % Propositional preprocessing time : 0.000
% 1.20/0.51 % Propositional encoding time : 0.000
% 1.20/0.51 % Propositional solver time : 0.000
% 1.20/0.51 % Success case prop preproc time : 0.000
% 1.20/0.51 % Success case prop encoding time : 0.000
% 1.20/0.51 % Success case prop solver time : 0.000
% 1.20/0.51 % Current number of processed clauses : 500
% 1.20/0.51 % Positive orientable unit clauses : 35
% 1.20/0.51 % Positive unorientable unit clauses: 0
% 1.20/0.51 % Negative unit clauses : 2
% 1.20/0.51 % Non-unit-clauses : 463
% 1.20/0.51 % Current number of unprocessed clauses: 16008
% 1.20/0.51 % ...number of literals in the above : 56842
% 1.20/0.51 % Current number of archived formulas : 0
% 1.20/0.51 % Current number of archived clauses : 13
% 1.20/0.51 % Clause-clause subsumption calls (NU) : 25537
% 1.20/0.51 % Rec. Clause-clause subsumption calls : 18020
% 1.20/0.51 % Non-unit clause-clause subsumptions : 511
% 1.20/0.51 % Unit Clause-clause subsumption calls : 522
% 1.20/0.51 % Rewrite failures with RHS unbound : 0
% 1.20/0.51 % BW rewrite match attempts : 17
% 1.20/0.51 % BW rewrite match successes : 4
% 1.20/0.51 % Condensation attempts : 0
% 1.20/0.51 % Condensation successes : 0
% 1.20/0.51 % Termbank termtop insertions : 346473
% 1.20/0.51 % Search garbage collected termcells : 10346
% 1.20/0.51
% 1.20/0.51 % -------------------------------------------------
% 1.20/0.51 % User time : 0.182 s
% 1.20/0.51 % System time : 0.019 s
% 1.20/0.51 % Total time : 0.201 s
% 1.20/0.51 % Maximum resident set size: 6140 pages
% 1.20/0.51
% 1.20/0.51 % -------------------------------------------------
% 1.20/0.51 % User time : 0.188 s
% 1.20/0.51 % System time : 0.023 s
% 1.20/0.51 % Total time : 0.211 s
% 1.20/0.51 % Maximum resident set size: 4864 pages
% 1.20/0.51 % E exiting
%------------------------------------------------------------------------------