%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU589^1 : 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 08:24:37 AM UTC 2026
% Result : Theorem 0.67s 0.38s
% Output : CNFRefutation 0.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU589^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n007.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 13:51:11 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.22/0.27 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.ZMWwgKxIQS/E---3.1_3400031.p
% 0.67/0.38 % Version: 3.5.1-ho
% 0.67/0.38 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.67/0.38 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.67/0.38 % Starting ehoh_best5 with 300s (1) cores
% 0.67/0.38 % Starting almost_fo_3_lam with 300s (1) cores
% 0.67/0.38 % Starting new_bool_5 with 300s (1) cores
% 0.67/0.38 % Starting pre_casc_3 with 300s (1) cores
% 0.67/0.38 % Starting ho_unfolding_8 with 300s (1) cores
% 0.67/0.38 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.67/0.38 % Starting new_bool_3 with 300s (1) cores
% 0.67/0.38 % Starting new_ho_5 with 300s (1) cores
% 0.67/0.38 % pre_casc_3 with pid 3400047 completed with status 9
% 0.67/0.38 % ho_unfolding_8 with pid 3400048 completed with status 0
% 0.67/0.38 % Result found by ho_unfolding_8
% 0.67/0.38 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.67/0.38 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.67/0.38 % Starting ehoh_best5 with 300s (1) cores
% 0.67/0.38 % Starting almost_fo_3_lam with 300s (1) cores
% 0.67/0.38 % Starting new_bool_5 with 300s (1) cores
% 0.67/0.38 % Starting pre_casc_3 with 300s (1) cores
% 0.67/0.38 % Starting ho_unfolding_8 with 300s (1) cores
% 0.67/0.38 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.67/0.38 % No SInE strategy applied
% 0.67/0.38 % Search class: HGHSM-FSLM31-MHFMMSBN
% 0.67/0.38 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.67/0.38 % Starting SubtermCWHack with 28s (1) cores
% 0.67/0.38 % SubtermCWHack with pid 3400071 completed with status 0
% 0.67/0.38 % Result found by SubtermCWHack
% 0.67/0.38 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.67/0.38 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.67/0.38 % Starting ehoh_best5 with 300s (1) cores
% 0.67/0.38 % Starting almost_fo_3_lam with 300s (1) cores
% 0.67/0.38 % Starting new_bool_5 with 300s (1) cores
% 0.67/0.38 % Starting pre_casc_3 with 300s (1) cores
% 0.67/0.38 % Starting ho_unfolding_8 with 300s (1) cores
% 0.67/0.38 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.67/0.38 % No SInE strategy applied
% 0.67/0.38 % Search class: HGHSM-FSLM31-MHFMMSBN
% 0.67/0.38 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.67/0.38 % Starting SubtermCWHack with 28s (1) cores
% 0.67/0.38 % Preprocessing time : 0.004 s
% 0.67/0.38
% 0.67/0.38 % Proof found!
% 0.67/0.38 % SZS status Theorem
% 0.67/0.38 % SZS output start CNFRefutation
% 0.67/0.38 thf(decl_23, type, in: $i > $i > $o).
% 0.67/0.38 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.67/0.38 thf(decl_25, type, setextAx: $o).
% 0.67/0.38 thf(decl_26, type, emptyset: $i).
% 0.67/0.38 thf(decl_27, type, emptysetAx: $o).
% 0.67/0.38 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.67/0.38 thf(decl_29, type, setadjoinAx: $o).
% 0.67/0.38 thf(decl_30, type, powerset: $i > $i).
% 0.67/0.38 thf(decl_31, type, powersetAx: $o).
% 0.67/0.38 thf(decl_32, type, setunion: $i > $i).
% 0.67/0.38 thf(decl_33, type, setunionAx: $o).
% 0.67/0.38 thf(decl_34, type, omega: $i).
% 0.67/0.38 thf(decl_35, type, omega0Ax: $o).
% 0.67/0.38 thf(decl_36, type, omegaSAx: $o).
% 0.67/0.38 thf(decl_37, type, omegaIndAx: $o).
% 0.67/0.38 thf(decl_38, type, replAx: $o).
% 0.67/0.38 thf(decl_39, type, foundationAx: $o).
% 0.67/0.38 thf(decl_40, type, wellorderingAx: $o).
% 0.67/0.38 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.67/0.38 thf(decl_42, type, descrp: $o).
% 0.67/0.38 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.67/0.38 thf(decl_44, type, dsetconstrI: $o).
% 0.67/0.38 thf(decl_45, type, dsetconstrEL: $o).
% 0.67/0.38 thf(decl_46, type, dsetconstrER: $o).
% 0.67/0.38 thf(decl_47, type, exuE1: $o).
% 0.67/0.38 thf(decl_48, type, prop2set: $o > $i).
% 0.67/0.38 thf(decl_49, type, prop2setE: $o).
% 0.67/0.38 thf(decl_50, type, emptysetE: $o).
% 0.67/0.38 thf(decl_51, type, emptysetimpfalse: $o).
% 0.67/0.38 thf(decl_52, type, notinemptyset: $o).
% 0.67/0.39 thf(decl_53, type, exuE3e: $o).
% 0.67/0.39 thf(decl_54, type, setext: $o).
% 0.67/0.39 thf(decl_55, type, emptyI: $o).
% 0.67/0.39 thf(decl_56, type, noeltsimpempty: $o).
% 0.67/0.39 thf(decl_57, type, setbeta: $o).
% 0.67/0.39 thf(decl_58, type, nonempty: $i > $o).
% 0.67/0.39 thf(decl_59, type, nonemptyE1: $o).
% 0.67/0.39 thf(decl_60, type, nonemptyI: $o).
% 0.67/0.39 thf(decl_61, type, nonemptyI1: $o).
% 0.67/0.39 thf(decl_62, type, setadjoinIL: $o).
% 0.67/0.39 thf(decl_63, type, emptyinunitempty: $o).
% 0.67/0.39 thf(decl_64, type, setadjoinIR: $o).
% 0.67/0.39 thf(decl_65, type, setadjoinE: $o).
% 0.67/0.39 thf(decl_66, type, setadjoinOr: $o).
% 0.67/0.39 thf(decl_67, type, setoftrueEq: $o).
% 0.67/0.39 thf(decl_68, type, powersetI: $o).
% 0.67/0.39 thf(decl_69, type, emptyinPowerset: $o).
% 0.67/0.39 thf(decl_70, type, emptyInPowerset: $o).
% 0.67/0.39 thf(decl_71, type, powersetE: $o).
% 0.67/0.39 thf(decl_72, type, setunionI: $o).
% 0.67/0.39 thf(decl_73, type, setunionE: $o).
% 0.67/0.39 thf(decl_74, type, subPowSU: $o).
% 0.67/0.39 thf(decl_75, type, exuE2: $o).
% 0.67/0.39 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.67/0.39 thf(decl_77, type, uniqinunit: $o).
% 0.67/0.39 thf(decl_78, type, notinsingleton: $o).
% 0.67/0.39 thf(decl_79, type, eqinunit: $o).
% 0.67/0.39 thf(decl_80, type, singletonsswitch: $o).
% 0.67/0.39 thf(decl_81, type, upairsetE: $o).
% 0.67/0.39 thf(decl_82, type, upairsetIL: $o).
% 0.67/0.39 thf(decl_83, type, upairsetIR: $o).
% 0.67/0.39 thf(decl_84, type, emptyE1: $o).
% 0.67/0.39 thf(decl_85, type, vacuousDall: $o).
% 0.67/0.39 thf(decl_86, type, quantDeMorgan1: $o).
% 0.67/0.39 thf(decl_87, type, quantDeMorgan2: $o).
% 0.67/0.39 thf(decl_88, type, quantDeMorgan3: $o).
% 0.67/0.39 thf(decl_89, type, quantDeMorgan4: $o).
% 0.67/0.39 thf(decl_90, type, prop2setI: $o).
% 0.67/0.39 thf(decl_91, type, set2prop: $i > $o).
% 0.67/0.39 thf(decl_92, type, prop2set2propI: $o).
% 0.67/0.39 thf(decl_93, type, notdexE: $o).
% 0.67/0.39 thf(decl_94, type, notdallE: $o).
% 0.67/0.39 thf(decl_95, type, exuI1: $o).
% 0.67/0.39 thf(decl_96, type, exuI3: $o).
% 0.67/0.39 thf(decl_97, type, exuI2: $o).
% 0.67/0.39 thf(decl_98, type, inCongP: $o).
% 0.67/0.39 thf(decl_99, type, in__Cong: $o).
% 0.67/0.39 thf(decl_100, type, exuE3u: $o).
% 0.67/0.39 thf(decl_101, type, exu__Cong: $o).
% 0.67/0.39 thf(decl_102, type, emptyset__Cong: $o).
% 0.67/0.39 thf(decl_103, type, setadjoin__Cong: $o).
% 0.67/0.39 thf(decl_104, type, powerset__Cong: $o).
% 0.67/0.39 thf(decl_105, type, setunion__Cong: $o).
% 0.67/0.39 thf(decl_106, type, omega__Cong: $o).
% 0.67/0.39 thf(decl_107, type, exuEu: $o).
% 0.67/0.39 thf(decl_108, type, descr__Cong: $o).
% 0.67/0.39 thf(decl_109, type, dsetconstr__Cong: $o).
% 0.67/0.39 thf(decl_110, type, subset: $i > $i > $o).
% 0.67/0.39 thf(decl_113, type, subsetI1: $o).
% 0.67/0.39 thf(decl_114, type, eqimpsubset2: $o).
% 0.67/0.39 thf(decl_115, type, eqimpsubset1: $o).
% 0.67/0.39 thf(decl_116, type, subsetI2: $o).
% 0.67/0.39 thf(decl_117, type, emptysetsubset: $o).
% 0.67/0.39 thf(decl_118, type, subsetE: $o).
% 0.67/0.39 thf(decl_119, type, subsetE2: $o).
% 0.67/0.39 thf(decl_120, type, notsubsetI: $o).
% 0.67/0.39 thf(decl_121, type, notequalI1: $o).
% 0.67/0.39 thf(decl_122, type, notequalI2: $o).
% 0.67/0.39 thf(decl_123, type, subsetRefl: $o).
% 0.67/0.39 thf(decl_124, type, subsetTrans: $o).
% 0.67/0.39 thf(decl_125, type, setadjoinSub: $o).
% 0.67/0.39 thf(decl_126, type, setadjoinSub2: $o).
% 0.67/0.39 thf(decl_127, type, subset2powerset: $o).
% 0.67/0.39 thf(decl_128, type, setextsub: $o).
% 0.67/0.39 thf(decl_129, type, subsetemptysetimpeq: $o).
% 0.67/0.39 thf(decl_130, type, powersetI1: $o).
% 0.67/0.39 thf(decl_131, type, powersetE1: $o).
% 0.67/0.39 thf(decl_132, type, inPowerset: $o).
% 0.67/0.39 thf(decl_133, type, powersetsubset: $o).
% 0.67/0.39 thf(decl_134, type, sepInPowerset: $o).
% 0.67/0.39 thf(decl_135, type, sepSubset: $o).
% 0.67/0.39 thf(decl_136, type, binunion: $i > $i > $i).
% 0.67/0.39 thf(decl_137, type, binunionIL: $o).
% 0.67/0.39 thf(decl_138, type, upairset2IR: $o).
% 0.67/0.39 thf(decl_139, type, binunionIR: $o).
% 0.67/0.39 thf(decl_140, type, binunionEcases: $o).
% 0.67/0.39 thf(decl_141, type, binunionE: $o).
% 0.67/0.39 thf(decl_142, type, binunionLsub: $o).
% 0.67/0.39 thf(decl_143, type, binunionRsub: $o).
% 0.67/0.39 thf(decl_144, type, binintersect: $i > $i > $i).
% 0.67/0.39 thf(decl_145, type, epred1_0: $o).
% 0.67/0.39 thf(decl_146, type, esk1_2: $i > $i > $i).
% 0.67/0.39 thf(decl_147, type, esk2_2: $i > $i > $i).
% 0.67/0.39 thf(decl_148, type, esk3_2: $i > $i > $i).
% 0.67/0.39 thf(decl_149, type, esk4_1: $i > $i).
% 0.67/0.39 thf(decl_150, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.67/0.39 thf(decl_151, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.67/0.39 thf(decl_152, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.67/0.39 thf(decl_153, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.67/0.39 thf(decl_154, type, esk9_1: $i > $i).
% 0.67/0.39 thf(decl_155, type, esk10_2: ($i > $o) > $i > $i).
% 0.67/0.39 thf(decl_156, type, esk11_2: ($i > $o) > $i > $i).
% 0.67/0.39 thf(decl_157, type, esk12_1: ($i > $o) > $i).
% 0.67/0.39 thf(decl_158, type, esk13_2: ($i > $o) > $i > $i).
% 0.67/0.39 thf(decl_159, type, esk14_1: ($i > $o) > $i).
% 0.67/0.39 thf(decl_160, type, esk15_2: $i > $i > $i).
% 0.67/0.39 thf(decl_161, type, esk16_2: $i > $i > $i).
% 0.67/0.39 thf(decl_162, type, esk17_1: $i > $i).
% 0.67/0.39 thf(decl_163, type, esk18_1: $i > $i).
% 0.67/0.39 thf(decl_164, type, esk19_1: $i > $i).
% 0.67/0.39 thf(decl_165, type, esk20_2: $i > $i > $i).
% 0.67/0.39 thf(decl_166, type, esk21_3: $i > $i > $o > $i).
% 0.67/0.39 thf(decl_167, type, esk22_2: ($i > $o) > $i > $i).
% 0.67/0.39 thf(decl_168, type, esk23_1: ($i > $o) > $i).
% 0.67/0.39 thf(decl_169, type, esk24_1: $i > $i).
% 0.67/0.39 thf(decl_170, type, esk25_2: $i > ($i > $o) > $i).
% 0.67/0.39 thf(decl_171, type, esk26_2: $i > ($i > $o) > $i).
% 0.67/0.39 thf(decl_172, type, esk27_2: $i > ($i > $o) > $i).
% 0.67/0.39 thf(decl_173, type, esk28_2: $i > ($i > $o) > $i).
% 0.67/0.39 thf(decl_174, type, esk29_2: $i > ($i > $o) > $i).
% 0.67/0.39 thf(decl_175, type, esk30_2: $i > ($i > $o) > $i).
% 0.67/0.39 thf(decl_176, type, esk31_2: ($i > $o) > $i > $i).
% 0.67/0.39 thf(decl_177, type, esk32_1: ($i > $o) > $i).
% 0.67/0.39 thf(decl_178, type, esk33_1: ($i > $o) > $i).
% 0.67/0.39 thf(decl_179, type, esk34_1: ($i > $o) > $i).
% 0.67/0.39 thf(decl_180, type, esk35_1: ($i > $o) > $i).
% 0.67/0.39 thf(decl_181, type, esk36_2: ($i > $o) > $i > $i).
% 0.67/0.39 thf(decl_182, type, esk37_1: ($i > $o) > $i).
% 0.67/0.39 thf(decl_183, type, esk38_2: ($i > $o) > $i > $i).
% 0.67/0.39 thf(decl_184, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 0.67/0.39 thf(decl_185, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 0.67/0.39 thf(decl_186, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.67/0.39 thf(decl_187, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 0.67/0.39 thf(decl_188, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.67/0.39 thf(decl_189, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 0.67/0.39 thf(decl_190, type, esk45_2: ($i > $o) > $i > $i).
% 0.67/0.39 thf(decl_191, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 0.67/0.39 thf(decl_192, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 0.67/0.39 thf(decl_193, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.67/0.39 thf(decl_194, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.67/0.39 thf(decl_195, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.67/0.39 thf(decl_196, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.67/0.39 thf(decl_197, type, esk52_2: $i > $i > $i).
% 0.67/0.39 thf(decl_198, type, esk53_2: $i > $i > $i).
% 0.67/0.39 thf(decl_199, type, esk54_0: $i).
% 0.67/0.39 thf(decl_200, type, esk55_0: $i).
% 0.67/0.39 thf(decl_201, type, esk56_0: $i).
% 0.67/0.39 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', replAx)).
% 0.67/0.39 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', exu)).
% 0.67/0.39 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', descrp)).
% 0.67/0.39 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', exuE1)).
% 0.67/0.39 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', exuE3e)).
% 0.67/0.39 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', nonempty)).
% 0.67/0.39 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', nonemptyI)).
% 0.67/0.39 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', exuE2)).
% 0.67/0.39 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.ZMWwgKxIQS/E---3.1_3400031.p', exuI1)).
% 0.67/0.39 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', exuI3)).
% 0.67/0.39 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', exuI2)).
% 0.67/0.39 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.ZMWwgKxIQS/E---3.1_3400031.p', exuE3u)).
% 0.67/0.39 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', exu__Cong)).
% 0.67/0.39 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', exuEu)).
% 0.67/0.39 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', descr__Cong)).
% 0.67/0.39 thf(binintersectI, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', binintersectI)).
% 0.67/0.39 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', dsetconstrI)).
% 0.67/0.39 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', dsetconstrEL)).
% 0.67/0.39 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', dsetconstrER)).
% 0.67/0.39 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', setbeta)).
% 0.67/0.39 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', nonemptyE1)).
% 0.67/0.39 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', nonemptyI1)).
% 0.67/0.39 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', setoftrueEq)).
% 0.67/0.39 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', nonemptyImpWitness)).
% 0.67/0.39 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.ZMWwgKxIQS/E---3.1_3400031.p', emptyE1)).
% 0.67/0.39 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', dsetconstr__Cong)).
% 0.67/0.39 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', sepInPowerset)).
% 0.67/0.39 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', sepSubset)).
% 0.67/0.39 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', setextAx)).
% 0.67/0.39 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', emptysetAx)).
% 0.67/0.39 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', setadjoinAx)).
% 0.67/0.39 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', powersetAx)).
% 0.67/0.39 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', setunionAx)).
% 0.67/0.39 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', omega0Ax)).
% 0.67/0.39 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', omegaSAx)).
% 0.67/0.39 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', omegaIndAx)).
% 0.67/0.39 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', foundationAx)).
% 0.67/0.39 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.ZMWwgKxIQS/E---3.1_3400031.p', wellorderingAx)).
% 0.67/0.39 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', prop2setE)).
% 0.67/0.39 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', emptysetE)).
% 0.67/0.39 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', emptysetimpfalse)).
% 0.67/0.39 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', notinemptyset)).
% 0.67/0.39 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', setext)).
% 0.67/0.39 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', emptyI)).
% 0.67/0.39 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', noeltsimpempty)).
% 0.67/0.39 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', setadjoinIL)).
% 0.67/0.39 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', emptyinunitempty)).
% 0.67/0.39 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', setadjoinIR)).
% 0.67/0.39 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.ZMWwgKxIQS/E---3.1_3400031.p', setadjoinE)).
% 0.67/0.39 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', setadjoinOr)).
% 0.67/0.39 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', powersetI)).
% 0.67/0.39 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', emptyinPowerset)).
% 0.67/0.39 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', emptyInPowerset)).
% 0.67/0.39 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', powersetE)).
% 0.67/0.39 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', setunionI)).
% 0.67/0.39 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.ZMWwgKxIQS/E---3.1_3400031.p', setunionE)).
% 0.67/0.39 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', subPowSU)).
% 0.67/0.39 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', uniqinunit)).
% 0.67/0.39 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', notinsingleton)).
% 0.67/0.39 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', eqinunit)).
% 0.67/0.39 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', singletonsswitch)).
% 0.67/0.39 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', upairsetE)).
% 0.67/0.39 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', upairsetIL)).
% 0.67/0.39 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', upairsetIR)).
% 0.67/0.39 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', vacuousDall)).
% 0.67/0.39 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', quantDeMorgan1)).
% 0.67/0.39 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', quantDeMorgan2)).
% 0.67/0.39 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', quantDeMorgan3)).
% 0.67/0.39 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', quantDeMorgan4)).
% 0.67/0.39 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', prop2setI)).
% 0.67/0.39 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', prop2set2propI)).
% 0.67/0.39 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', notdexE)).
% 0.67/0.39 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', notdallE)).
% 0.67/0.39 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', inCongP)).
% 0.67/0.39 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', in__Cong)).
% 0.67/0.39 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', emptyset__Cong)).
% 0.67/0.39 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', setadjoin__Cong)).
% 0.67/0.39 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', powerset__Cong)).
% 0.67/0.39 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', setunion__Cong)).
% 0.67/0.39 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', omega__Cong)).
% 0.67/0.39 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', subsetI1)).
% 0.67/0.39 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', eqimpsubset2)).
% 0.67/0.39 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', eqimpsubset1)).
% 0.67/0.39 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', subsetI2)).
% 0.67/0.39 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', emptysetsubset)).
% 0.67/0.39 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', subsetE)).
% 0.67/0.39 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', subsetE2)).
% 0.67/0.39 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', notsubsetI)).
% 0.67/0.39 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', notequalI1)).
% 0.67/0.39 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', notequalI2)).
% 0.67/0.39 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', subsetRefl)).
% 0.67/0.39 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', subsetTrans)).
% 0.67/0.39 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', setadjoinSub)).
% 0.67/0.39 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', setadjoinSub2)).
% 0.67/0.39 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', subset2powerset)).
% 0.67/0.39 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', setextsub)).
% 0.67/0.39 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', subsetemptysetimpeq)).
% 0.67/0.39 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', powersetI1)).
% 0.67/0.39 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', powersetE1)).
% 0.67/0.39 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', inPowerset)).
% 0.67/0.39 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', powersetsubset)).
% 0.67/0.39 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', binunionIL)).
% 0.67/0.39 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', upairset2IR)).
% 0.67/0.39 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', binunionIR)).
% 0.67/0.39 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', binunionEcases)).
% 0.67/0.39 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', binunionE)).
% 0.67/0.39 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', binunionLsub)).
% 0.67/0.39 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', binunionRsub)).
% 0.67/0.39 thf(binintersect, axiom, ((binintersect)=(^[X4:$i, X5:$i]:(dsetconstr @ X4 @ (^[X2:$i]:((in @ X2 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ZMWwgKxIQS/E---3.1_3400031.p', binintersect)).
% 0.67/0.39 thf(c_0_109, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.67/0.39 thf(c_0_110, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.67/0.39 thf(c_0_111, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.67/0.39 thf(c_0_112, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.67/0.39 thf(c_0_113, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.67/0.39 thf(c_0_114, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.67/0.39 thf(c_0_115, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.67/0.39 thf(c_0_116, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.67/0.39 thf(c_0_117, 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])).
% 0.67/0.39 thf(c_0_118, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.67/0.39 thf(c_0_119, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.67/0.39 thf(c_0_120, 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])).
% 0.67/0.39 thf(c_0_121, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.67/0.39 thf(c_0_122, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 0.67/0.39 thf(c_0_123, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 0.67/0.39 thf(c_0_124, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[binintersectI])).
% 0.67/0.39 thf(c_0_125, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X304:$i]:(((((X6 @ X2 @ X304)))&(![X305:$i]:(((((X6 @ X2 @ X305)))=>(((X304)=(X305)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_109, c_0_110])).
% 0.67/0.39 thf(c_0_126, plain, ((descrp)=(![X1:$i > $o]:((((?[X306:$i]:(((((X1 @ X306)))&(![X307:$i]:(((((X1 @ X307)))=>(((X306)=(X307))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_111, c_0_110])).
% 0.67/0.39 thf(c_0_127, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.67/0.39 thf(c_0_128, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.67/0.39 thf(c_0_129, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.67/0.39 thf(c_0_130, plain, ((exuE1)=(![X1:$i > $o]:((((?[X308:$i]:(((((X1 @ X308)))&(![X309:$i]:(((((X1 @ X309)))=>(((X308)=(X309))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_112, c_0_110])).
% 0.67/0.39 thf(c_0_131, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X310:$i]:(((((X1 @ X310)))&(![X311:$i]:(((((X1 @ X311)))=>(((X310)=(X311))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_113, c_0_110])).
% 0.67/0.39 thf(c_0_132, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.67/0.39 thf(c_0_133, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_114])).
% 0.67/0.39 thf(c_0_134, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_115, c_0_114])).
% 0.67/0.39 thf(c_0_135, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_114])).
% 0.67/0.39 thf(c_0_136, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.67/0.39 thf(c_0_137, plain, ((exuE2)=(![X1:$i > $o]:((((?[X312:$i]:(((((X1 @ X312)))&(![X313:$i]:(((((X1 @ X313)))=>(((X312)=(X313))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_116, c_0_110])).
% 0.67/0.39 thf(c_0_138, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_114])).
% 0.67/0.39 thf(c_0_139, 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])).
% 0.67/0.39 thf(c_0_140, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X314:$i]:(((((X1 @ X314)))&(![X315:$i]:(((((X1 @ X315)))=>(((X314)=(X315)))))))))))))), inference(apply_def,[status(thm)],[c_0_117, c_0_110])).
% 0.67/0.39 thf(c_0_141, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X316:$i]:(((((X1 @ X316)))&(![X317:$i]:(((((X1 @ X317)))=>(((X316)=(X317)))))))))))))))), inference(apply_def,[status(thm)],[c_0_118, c_0_110])).
% 0.67/0.39 thf(c_0_142, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X318:$i]:(((((X1 @ X318)))&(![X319:$i]:(((((X1 @ X319)))=>(((X318)=(X319)))))))))))))), inference(apply_def,[status(thm)],[c_0_119, c_0_110])).
% 0.67/0.39 thf(c_0_143, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X320:$i]:(((((X1 @ X320)))&(![X321:$i]:(((((X1 @ X321)))=>(((X320)=(X321))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_120, c_0_110])).
% 0.67/0.39 thf(c_0_144, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X322:$i]:(((((X1 @ X322)))&(![X323:$i]:(((((X1 @ X323)))=>(((X322)=(X323))))))))))<=>((?[X324:$i]:(((((X17 @ X324)))&(![X325:$i]:(((((X17 @ X325)))=>(((X324)=(X325)))))))))))))))), inference(apply_def,[status(thm)],[c_0_121, c_0_110])).
% 0.67/0.39 thf(c_0_145, plain, ((exuEu)=(![X1:$i > $o]:((((?[X326:$i]:(((((X1 @ X326)))&(![X327:$i]:(((((X1 @ X327)))=>(((X326)=(X327))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_122, c_0_110])).
% 0.67/0.39 thf(c_0_146, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X328:$i]:(((((X1 @ X328)))&(![X329:$i]:(((((X1 @ X329)))=>(((X328)=(X329))))))))))=>((((?[X330:$i]:(((((X17 @ X330)))&(![X331:$i]:(((((X17 @ X331)))=>(((X330)=(X331))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_123, c_0_110])).
% 0.67/0.39 thf(c_0_147, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 0.67/0.39 thf(c_0_148, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 0.67/0.39 thf(c_0_149, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 0.67/0.39 thf(c_0_150, plain, ((epred1_0)<=>![X361:$i]:(?[X362:$i]:((((![X363:$i]:(((in @ X363 @ X362)=>![X364:$i]:(((in @ X364 @ X363)=>(in @ X364 @ X361)))))&![X365:$i, X366:$i]:((((in @ X365 @ X361)&(in @ X366 @ X361))=>(![X367:$i]:(((in @ X367 @ X362)=>((in @ X365 @ X367)<=>(in @ X366 @ X367))))=>((X365)=(X366))))))&![X368:$i, X369:$i]:((((in @ X368 @ X362)&(in @ X369 @ X362))=>(![X370:$i]:(((in @ X370 @ X368)=>(in @ X370 @ X369)))|![X371:$i]:(((in @ X371 @ X369)=>(in @ X371 @ X368)))))))&![X372:$i]:(((![X373:$i]:(((in @ X373 @ X372)=>(in @ X373 @ X361)))&?[X374:$i]:((in @ X374 @ X372)))=>?[X375:$i, X376:$i]:(((((in @ X375 @ X362)&(in @ X376 @ X372))&~(?[X377:$i]:(((in @ X377 @ X375)&(in @ X377 @ X372)))))&![X378:$i]:(((in @ X378 @ X362)=>(![X379:$i]:(((in @ X379 @ X378)=>(in @ X379 @ X375)))|(in @ X376 @ X378)))))))))))), introduced(definition)).
% 0.67/0.39 thf(c_0_151, negated_conjecture, ~((![X332:$i, X333:$i]:((![X334:$i]:(((in @ X334 @ X332)<=>(in @ X334 @ X333)))=>((X332)=(X333))))=>(![X335:$i]:(~(in @ X335 @ emptyset))=>(![X336:$i, X337:$i, X338:$i]:(((in @ X338 @ (setadjoin @ X336 @ X337))<=>(((X338)=(X336))|(in @ X338 @ X337))))=>(![X339:$i, X340:$i]:(((in @ X340 @ (powerset @ X339))<=>![X341:$i]:(((in @ X341 @ X340)=>(in @ X341 @ X339)))))=>(![X342:$i, X343:$i]:(((in @ X343 @ (setunion @ X342))<=>?[X344:$i]:(((in @ X343 @ X344)&(in @ X344 @ X342)))))=>((in @ emptyset @ omega)=>(![X345:$i]:(((in @ X345 @ omega)=>(in @ (setadjoin @ X345 @ X345) @ omega)))=>(![X346:$i]:((((in @ emptyset @ X346)&![X347:$i]:((((in @ X347 @ omega)&(in @ X347 @ X346))=>(in @ (setadjoin @ X347 @ X347) @ X346))))=>![X348:$i]:(((in @ X348 @ omega)=>(in @ X348 @ X346)))))=>(![X349:$i > $i > $o, X350:$i]:((![X351:$i]:(((in @ X351 @ X350)=>?[X352:$i]:(((X349 @ X351 @ X352)&![X353:$i]:(((X349 @ X351 @ X353)=>((X352)=(X353))))))))=>?[X354:$i]:(![X355:$i]:(((in @ X355 @ X354)<=>?[X356:$i]:(((in @ X356 @ X350)&(X349 @ X356 @ X355))))))))=>(![X357:$i]:((?[X358:$i]:((in @ X358 @ X357))=>?[X359:$i]:(((in @ X359 @ X357)&~(?[X360:$i]:(((in @ X360 @ X359)&(in @ X360 @ X357))))))))=>((epred1_0)=>(![X380:$i > $o]:((?[X381:$i]:(((X380 @ X381)&![X382:$i]:(((X380 @ X382)=>((X381)=(X382))))))=>(X380 @ (descr @ (^[Z0:$i]:(X380 @ Z0))))))=>(![X383:$i, X384:$i > $o, X385:$i]:(((in @ X385 @ X383)=>((X384 @ X385)=>(in @ X385 @ (dsetconstr @ X383 @ X384)))))=>(![X386:$i, X387:$i > $o, X388:$i]:(((in @ X388 @ (dsetconstr @ X386 @ X387))=>(in @ X388 @ X386)))=>(![X389:$i, X390:$i > $o, X391:$i]:(((in @ X391 @ (dsetconstr @ X389 @ X390))=>(X390 @ X391)))=>(![X392:$i > $o]:((?[X393:$i]:(((X392 @ X393)&![X394:$i]:(((X392 @ X394)=>((X393)=(X394))))))=>?[X395:$i]:(((X392 @ X395)&![X396:$i]:(((X392 @ X396)=>((X395)=(X396))))))))=>(![X397:$o, X398:$i]:(((in @ X398 @ (prop2set @ ((X397))))=>(X397)))=>(![X399:$i]:(((in @ X399 @ emptyset)=>![X400:$o]:((X400))))=>(![X401:$i]:(((in @ X401 @ emptyset)=>~($true)))=>(![X402:$i]:(~(in @ X402 @ emptyset))=>(![X403:$i > $o]:((?[X404:$i]:(((X403 @ X404)&![X405:$i]:(((X403 @ X405)=>((X404)=(X405))))))=>?[X406:$i]:((X403 @ X406))))=>(![X407:$i, X408:$i]:((![X409:$i]:(((in @ X409 @ X407)=>(in @ X409 @ X408)))=>(![X410:$i]:(((in @ X410 @ X408)=>(in @ X410 @ X407)))=>((X407)=(X408)))))=>(![X411:$i]:((![X412:$i]:(~(in @ X412 @ X411))=>((X411)=(emptyset))))=>(![X413:$i]:((![X414:$i]:(~(in @ X414 @ X413))=>((X413)=(emptyset))))=>(![X415:$i, X416:$i > $o, X417:$i]:(((in @ X417 @ X415)=>((in @ X417 @ (dsetconstr @ X415 @ X416))<=>(X416 @ X417))))=>(![X418:$i]:((((X418)!=(emptyset))=>?[X419:$i]:((in @ X419 @ X418))))=>(![X420:$i, X421:$i > $o, X422:$i]:(((in @ X422 @ X420)=>((X421 @ X422)=>((dsetconstr @ X420 @ X421)!=(emptyset)))))=>(![X423:$i]:((?[X424:$i]:((in @ X424 @ X423))=>((X423)!=(emptyset))))=>(![X425:$i, X426:$i]:((in @ X425 @ (setadjoin @ X425 @ X426)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X427:$i, X428:$i, X429:$i]:(((in @ X429 @ X428)=>(in @ X429 @ (setadjoin @ X427 @ X428))))=>(![X430:$i, X431:$i, X432:$i]:(((in @ X432 @ (setadjoin @ X430 @ X431))=>![X433:$o]:(((((X432)=(X430))=>(X433))=>(((in @ X432 @ X431)=>(X433))=>(X433))))))=>(![X434:$i, X435:$i, X436:$i]:(((in @ X436 @ (setadjoin @ X434 @ X435))=>(((X436)=(X434))|(in @ X436 @ X435))))=>(![X437:$i]:(((dsetconstr @ X437 @ (^[Z0:$i]:($true)))=(X437)))=>(![X438:$i, X439:$i]:((![X440:$i]:(((in @ X440 @ X439)=>(in @ X440 @ X438)))=>(in @ X439 @ (powerset @ X438))))=>(![X441:$i]:((in @ emptyset @ (powerset @ X441)))=>(![X442:$i]:((in @ emptyset @ (powerset @ X442)))=>(![X443:$i, X444:$i, X445:$i]:(((in @ X444 @ (powerset @ X443))=>((in @ X445 @ X444)=>(in @ X445 @ X443))))=>(![X446:$i, X447:$i, X448:$i]:(((in @ X447 @ X448)=>((in @ X448 @ X446)=>(in @ X447 @ (setunion @ X446)))))=>(![X449:$i, X450:$i]:(((in @ X450 @ (setunion @ X449))=>![X451:$o]:((![X452:$i]:(((in @ X450 @ X452)=>((in @ X452 @ X449)=>(X451))))=>(X451)))))=>(![X453:$i, X454:$i]:(((in @ X454 @ X453)=>(in @ X454 @ (powerset @ (setunion @ X453)))))=>(![X455:$i > $o]:((?[X456:$i]:(((X455 @ X456)&![X457:$i]:(((X455 @ X457)=>((X456)=(X457))))))=>?[X458:$i]:(![X459:$i]:(((X455 @ X459)<=>((X459)=(X458)))))))=>(![X460:$i]:((((X460)!=(emptyset))=>?[X461:$i]:(((in @ X461 @ X460)&$true))))=>(![X462:$i, X463:$i]:(((in @ X462 @ (setadjoin @ X463 @ emptyset))=>((X462)=(X463))))=>(![X464:$i, X465:$i]:((((X464)!=(X465))=>~(in @ X465 @ (setadjoin @ X464 @ emptyset))))=>(![X466:$i, X467:$i]:((((X466)=(X467))=>(in @ X466 @ (setadjoin @ X467 @ emptyset))))=>(![X468:$i, X469:$i]:(((in @ X468 @ (setadjoin @ X469 @ emptyset))=>(in @ X469 @ (setadjoin @ X468 @ emptyset))))=>(![X470:$i, X471:$i, X472:$i]:(((in @ X472 @ (setadjoin @ X470 @ (setadjoin @ X471 @ emptyset)))=>(((X472)=(X470))|((X472)=(X471)))))=>(![X473:$i, X474:$i]:((in @ X473 @ (setadjoin @ X473 @ (setadjoin @ X474 @ emptyset))))=>(![X475:$i, X476:$i]:((in @ X476 @ (setadjoin @ X475 @ (setadjoin @ X476 @ emptyset))))=>(![X477:$i, X478:$i > $o]:((?[X479:$i]:(((in @ X479 @ X477)&(X478 @ X479)))=>(((dsetconstr @ X477 @ X478)=(emptyset))=>~($true))))=>(![X480:$i > $o, X481:$i]:(((in @ X481 @ emptyset)=>(X480 @ X481)))=>(![X482:$i, X483:$i > $o]:((~(![X484:$i]:(((in @ X484 @ X482)=>(X483 @ X484))))=>?[X485:$i]:(((in @ X485 @ X482)&~((X483 @ X485))))))=>(![X486:$i, X487:$i > $o]:((![X488:$i]:(((in @ X488 @ X486)=>~((X487 @ X488))))=>~(?[X489:$i]:(((in @ X489 @ X486)&(X487 @ X489))))))=>(![X490:$i, X491:$i > $o]:((~(?[X492:$i]:(((in @ X492 @ X490)&(X491 @ X492))))=>![X493:$i]:(((in @ X493 @ X490)=>~((X491 @ X493))))))=>(![X494:$i, X495:$i > $o]:((?[X496:$i]:(((in @ X496 @ X494)&~((X495 @ X496))))=>~(![X497:$i]:(((in @ X497 @ X494)=>(X495 @ X497))))))=>(![X498:$o]:(((X498)=>(in @ emptyset @ (prop2set @ ((X498))))))=>(![X499:$o]:(((X499)=>(set2prop @ (prop2set @ ((X499))))))=>(![X500:$i, X501:$i > $o]:((~(?[X502:$i]:(((in @ X502 @ X500)&(X501 @ X502))))=>![X503:$i]:(((in @ X503 @ X500)=>~((X501 @ X503))))))=>(![X504:$i, X505:$i > $o]:((~(![X506:$i]:(((in @ X506 @ X504)=>(X505 @ X506))))=>?[X507:$i]:(((in @ X507 @ X504)&~((X505 @ X507))))))=>(![X508:$i > $o]:((?[X509:$i]:(((X508 @ X509)&![X510:$i]:(((X508 @ X510)=>((X509)=(X510))))))=>?[X511:$i]:(((X508 @ X511)&![X512:$i]:(((X508 @ X512)=>((X511)=(X512))))))))=>(![X513:$i > $o]:((?[X514:$i]:((X513 @ X514))=>(![X515:$i, X516:$i]:(((X513 @ X515)=>((X513 @ X516)=>((X515)=(X516)))))=>?[X517:$i]:(((X513 @ X517)&![X518:$i]:(((X513 @ X518)=>((X517)=(X518)))))))))=>(![X519:$i > $o]:((?[X520:$i]:(![X521:$i]:(((X519 @ X521)<=>((X521)=(X520)))))=>?[X522:$i]:(((X519 @ X522)&![X523:$i]:(((X519 @ X523)=>((X522)=(X523))))))))=>(![X524:$i, X525:$i]:((((X524)=(X525))=>![X526:$i, X527:$i]:((((X526)=(X527))=>((in @ X526 @ X524)=>(in @ X527 @ X525))))))=>(![X528:$i, X529:$i]:((((X528)=(X529))=>![X530:$i, X531:$i]:((((X530)=(X531))=>((in @ X530 @ X528)<=>(in @ X531 @ X529))))))=>(![X532:$i > $o]:((?[X533:$i]:(((X532 @ X533)&![X534:$i]:(((X532 @ X534)=>((X533)=(X534))))))=>![X535:$i, X536:$i]:(((X532 @ X535)=>((X532 @ X536)=>((X535)=(X536)))))))=>(![X537:$i > $o, X538:$i > $o]:((![X539:$i, X540:$i]:((((X539)=(X540))=>((X537 @ X539)<=>(X538 @ X540))))=>(?[X541:$i]:(((X537 @ X541)&![X542:$i]:(((X537 @ X542)=>((X541)=(X542))))))<=>?[X543:$i]:(((X538 @ X543)&![X544:$i]:(((X538 @ X544)=>((X543)=(X544)))))))))=>(((emptyset)=(emptyset))=>(![X545:$i, X546:$i]:((((X545)=(X546))=>![X547:$i, X548:$i]:((((X547)=(X548))=>((setadjoin @ X545 @ X547)=(setadjoin @ X546 @ X548))))))=>(![X549:$i, X550:$i]:((((X549)=(X550))=>((powerset @ X549)=(powerset @ X550))))=>(![X551:$i, X552:$i]:((((X551)=(X552))=>((setunion @ X551)=(setunion @ X552))))=>(((omega)=(omega))=>(![X553:$i > $o]:((?[X554:$i]:(((X553 @ X554)&![X555:$i]:(((X553 @ X555)=>((X554)=(X555))))))=>![X556:$i, X557:$i]:(((X553 @ X556)=>((X553 @ X557)=>((X556)=(X557)))))))=>(![X558:$i > $o, X559:$i > $o]:((![X560:$i, X561:$i]:((((X560)=(X561))=>((X558 @ X560)<=>(X559 @ X561))))=>(?[X562:$i]:(((X558 @ X562)&![X563:$i]:(((X558 @ X563)=>((X562)=(X563))))))=>(?[X564:$i]:(((X559 @ X564)&![X565:$i]:(((X559 @ X565)=>((X564)=(X565))))))=>((descr @ X558)=(descr @ X559))))))=>(![X566:$i, X567:$i]:((((X566)=(X567))=>![X568:$i > $o, X569:$i > $o]:((![X570:$i]:(((in @ X570 @ X566)=>![X571:$i]:(((in @ X571 @ X567)=>(((X570)=(X571))=>((X568 @ X570)<=>(X569 @ X571)))))))=>((dsetconstr @ X566 @ X568)=(dsetconstr @ X567 @ X569))))))=>(![X572:$i, X573:$i]:((![X574:$i]:(((in @ X574 @ X572)=>(in @ X574 @ X573)))=>(subset @ X572 @ X573)))=>(![X575:$i, X576:$i]:((((X575)=(X576))=>(subset @ X576 @ X575)))=>(![X577:$i, X578:$i]:((((X577)=(X578))=>(subset @ X577 @ X578)))=>(![X579:$i, X580:$i]:((![X581:$i]:(((in @ X581 @ X579)=>(in @ X581 @ X580)))=>(subset @ X579 @ X580)))=>(![X582:$i]:((subset @ emptyset @ X582))=>(![X583:$i, X584:$i, X585:$i]:(((subset @ X583 @ X584)=>((in @ X585 @ X583)=>(in @ X585 @ X584))))=>(![X586:$i, X587:$i, X588:$i]:(((subset @ X586 @ X587)=>(~(in @ X588 @ X587)=>~(in @ X588 @ X586))))=>(![X589:$i, X590:$i, X591:$i]:(((in @ X591 @ X589)=>(~(in @ X591 @ X590)=>~(subset @ X589 @ X590))))=>(![X592:$i, X593:$i]:((~(subset @ X592 @ X593)=>((X592)!=(X593))))=>(![X594:$i, X595:$i, X596:$i]:(((in @ X596 @ X594)=>(~(in @ X596 @ X595)=>((X594)!=(X595)))))=>(![X597:$i]:((subset @ X597 @ X597))=>(![X598:$i, X599:$i, X600:$i]:(((subset @ X598 @ X599)=>((subset @ X599 @ X600)=>(subset @ X598 @ X600))))=>(![X601:$i, X602:$i]:((subset @ X602 @ (setadjoin @ X601 @ X602)))=>(![X603:$i, X604:$i, X605:$i]:(((subset @ X603 @ X605)=>(subset @ X603 @ (setadjoin @ X604 @ X605))))=>(![X606:$i, X607:$i]:(((subset @ X606 @ X607)=>(in @ X606 @ (powerset @ X607))))=>(![X608:$i, X609:$i]:(((subset @ X608 @ X609)=>((subset @ X609 @ X608)=>((X608)=(X609)))))=>(![X610:$i]:(((subset @ X610 @ emptyset)=>((X610)=(emptyset))))=>(![X611:$i, X612:$i]:(((subset @ X612 @ X611)=>(in @ X612 @ (powerset @ X611))))=>(![X613:$i, X614:$i]:(((in @ X614 @ (powerset @ X613))=>(subset @ X614 @ X613)))=>(![X615:$i]:((in @ X615 @ (powerset @ X615)))=>(![X616:$i, X617:$i]:(((subset @ X616 @ X617)=>(subset @ (powerset @ X616) @ (powerset @ X617))))=>(![X618:$i, X619:$i > $o]:((in @ (dsetconstr @ X618 @ X619) @ (powerset @ X618)))=>(![X620:$i, X621:$i > $o]:((subset @ (dsetconstr @ X620 @ X621) @ X620))=>(![X622:$i, X623:$i, X624:$i]:(((in @ X624 @ X622)=>(in @ X624 @ (binunion @ X622 @ X623))))=>(![X625:$i, X626:$i]:((in @ X626 @ (setadjoin @ X625 @ (setadjoin @ X626 @ emptyset))))=>(![X627:$i, X628:$i, X629:$i]:(((in @ X629 @ X628)=>(in @ X629 @ (binunion @ X627 @ X628))))=>(![X630:$i, X631:$i, X632:$i, X633:$o]:(((in @ X632 @ (binunion @ X630 @ X631))=>(((in @ X632 @ X630)=>(X633))=>(((in @ X632 @ X631)=>(X633))=>(X633)))))=>(![X634:$i, X635:$i, X636:$i]:(((in @ X636 @ (binunion @ X634 @ X635))=>((in @ X636 @ X634)|(in @ X636 @ X635))))=>(![X637:$i, X638:$i]:((subset @ X637 @ (binunion @ X637 @ X638)))=>(![X639:$i, X640:$i]:((subset @ X640 @ (binunion @ X639 @ X640)))=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ 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)],[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_124, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_125]), foundationAx]), wellorderingAx]), c_0_126]), c_0_127]), c_0_128]), c_0_129]), c_0_130]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_131]), setext]), emptyI]), noeltsimpempty]), c_0_132]), c_0_133]), c_0_134]), c_0_135]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_136]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_137]), c_0_138]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_139]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_140]), c_0_141]), c_0_142]), inCongP]), in__Cong]), c_0_143]), c_0_144]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_145]), c_0_146]), c_0_147]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_148]), c_0_149]), binunionIL]), upairset2IR]), binunionIR]), binunionEcases]), binunionE]), binunionLsub]), binunionRsub])])]), c_0_150])).
% 0.67/0.39 thf(c_0_152, plain, ![X641:$i, X642:$i]:(((binintersect @ X641 @ X642)=(dsetconstr @ X641 @ (^[Z0:$i]:((in @ Z0 @ X642)))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[binintersect])])).
% 0.67/0.39 thf(c_0_153, negated_conjecture, ![X645:$i, X646:$i, X648:$i, X649:$i, X650:$i, X651:$i, X652:$i, X653:$i, X654:$i, X655:$i, X656:$i, X658:$i, X659:$i, X661:$i, X662:$i, X663:$i, X664:$i, X665:$i, X667:$i, X668:$i > $i > $o, X669:$i, X671:$i, X674:$i, X676:$i, X677:$i, X678:$i, X679:$i, X681:$i, X682:$i > $o, X683:$i, X685:$i, X686:$i > $o, X687:$i, X688:$i, X689:$i > $o, X690:$i, X691:$i, X692:$i > $o, X693:$i, X694:$i > $o, X695:$i, X698:$i, X699:$o, X700:$i, X701:$i, X702:$o, X703:$i, X704:$i, X705:$i > $o, X706:$i, X709:$i, X710:$i, X713:$i, X715:$i, X717:$i, X718:$i > $o, X719:$i, X720:$i, X722:$i, X723:$i > $o, X724:$i, X725:$i, X726:$i, X727:$i, X728:$i, X729:$i, X730:$i, X731:$i, X732:$i, X733:$i, X734:$i, X735:$o, X736:$i, X737:$i, X738:$i, X739:$i, X740:$i, X741:$i, X743:$i, X744:$i, X745:$i, X746:$i, X747:$i, X748:$i, X749:$i, X750:$i, X751:$i, X752:$i, X753:$o, X755:$i, X756:$i, X757:$i > $o, X758:$i, X761:$i, X762:$i, X763:$i, X765:$i, X766:$i, X767:$i, X768:$i, X769:$i, X770:$i, X771:$i, X772:$i, X773:$i, X774:$i, X775:$i, X776:$i, X777:$i, X778:$i, X779:$i, X780:$i, X781:$i > $o, X782:$i, X783:$i > $o, X784:$i, X785:$i, X786:$i > $o, X787:$i, X789:$i, X790:$i > $o, X792:$i, X793:$i, X794:$i > $o, X796:$i, X797:$i, X798:$i > $o, X799:$i, X801:$o, X802:$o, X803:$i, X804:$i > $o, X806:$i, X807:$i, X808:$i > $o, X809:$i, X811:$i > $o, X812:$i, X815:$i, X816:$i > $o, X817:$i, X821:$i, X822:$i > $o, X823:$i, X826:$i, X827:$i, X828:$i, X829:$i, X830:$i, X831:$i, X832:$i, X833:$i, X834:$i, X835:$i > $o, X836:$i, X838:$i, X839:$i, X840:$i > $o, X841:$i > $o, X844:$i, X847:$i, X848:$i, X851:$i, X852:$i, X853:$i, X854:$i, X855:$i, X856:$i, X857:$i, X858:$i, X859:$i, X860:$i > $o, X861:$i, X863:$i, X864:$i, X865:$i > $o, X866:$i > $o, X869:$i, X871:$i, X873:$i, X874:$i, X875:$i > $o, X876:$i > $o, X879:$i, X880:$i, X882:$i, X883:$i, X884:$i, X885:$i, X886:$i, X887:$i, X889:$i, X890:$i, X891:$i, X892:$i, X893:$i, X894:$i, X895:$i, X896:$i, X897:$i, X898:$i, X899:$i, X900:$i, X901:$i, X902:$i, X903:$i, X904:$i, X905:$i, X906:$i, X907:$i, X908:$i, X909:$i, X910:$i, X911:$i, X912:$i, X913:$i, X914:$i, X915:$i, X916:$i, X917:$i, X918:$i, X919:$i, X920:$i, X921:$i, X922:$i, X923:$i, X924:$i, X925:$i, X926:$i > $o, X927:$i, X928:$i > $o, X929:$i, X930:$i, X931:$i, X932:$i, X933:$i, X934:$i, X935:$i, X936:$i, X937:$i, X938:$i, X939:$i, X940:$o, X941:$i, X942:$i, X943:$i, X944:$i, X945:$i, X946:$i, X947:$i]:((((~(in @ (esk1_2 @ X645 @ X646) @ X645)|~(in @ (esk1_2 @ X645 @ X646) @ X646)|((X645)=(X646)))&((in @ (esk1_2 @ X645 @ X646) @ X645)|(in @ (esk1_2 @ X645 @ X646) @ X646)|((X645)=(X646))))&(~(in @ X648 @ emptyset)&(((~(in @ X651 @ (setadjoin @ X649 @ X650))|(((X651)=(X649))|(in @ X651 @ X650)))&((((X651)!=(X649))|(in @ X651 @ (setadjoin @ X649 @ X650)))&(~(in @ X651 @ X650)|(in @ X651 @ (setadjoin @ X649 @ X650)))))&(((~(in @ X653 @ (powerset @ X652))|(~(in @ X654 @ X653)|(in @ X654 @ X652)))&(((in @ (esk2_2 @ X655 @ X656) @ X656)|(in @ X656 @ (powerset @ X655)))&(~(in @ (esk2_2 @ X655 @ X656) @ X655)|(in @ X656 @ (powerset @ X655)))))&(((((in @ X659 @ (esk3_2 @ X658 @ X659))|~(in @ X659 @ (setunion @ X658)))&((in @ (esk3_2 @ X658 @ X659) @ X658)|~(in @ X659 @ (setunion @ X658))))&(~(in @ X662 @ X663)|~(in @ X663 @ X661)|(in @ X662 @ (setunion @ X661))))&((in @ emptyset @ omega)&((~(in @ X664 @ omega)|(in @ (setadjoin @ X664 @ X664) @ omega))&(((((in @ (esk4_1 @ X665) @ omega)|~(in @ emptyset @ X665)|(~(in @ X667 @ omega)|(in @ X667 @ X665)))&((in @ (esk4_1 @ X665) @ X665)|~(in @ emptyset @ X665)|(~(in @ X667 @ omega)|(in @ X667 @ X665))))&(~(in @ (setadjoin @ (esk4_1 @ X665) @ (esk4_1 @ X665)) @ X665)|~(in @ emptyset @ X665)|(~(in @ X667 @ omega)|(in @ X667 @ X665))))&((((((in @ (esk8_3 @ X668 @ X669 @ X674) @ X669)|~(in @ X674 @ (esk7_2 @ X668 @ X669))|(in @ (esk5_2 @ X668 @ X669) @ X669))&((X668 @ (esk8_3 @ X668 @ X669 @ X674) @ X674)|~(in @ X674 @ (esk7_2 @ X668 @ X669))|(in @ (esk5_2 @ X668 @ X669) @ X669)))&(~(in @ X677 @ X669)|~(X668 @ X677 @ X676)|(in @ X676 @ (esk7_2 @ X668 @ X669))|(in @ (esk5_2 @ X668 @ X669) @ X669)))&(((((in @ (esk8_3 @ X668 @ X669 @ X674) @ X669)|~(in @ X674 @ (esk7_2 @ X668 @ X669))|((X668 @ (esk5_2 @ X668 @ X669) @ (esk6_3 @ X668 @ X669 @ X671))|~(X668 @ (esk5_2 @ X668 @ X669) @ X671)))&((X668 @ (esk8_3 @ X668 @ X669 @ X674) @ X674)|~(in @ X674 @ (esk7_2 @ X668 @ X669))|((X668 @ (esk5_2 @ X668 @ X669) @ (esk6_3 @ X668 @ X669 @ X671))|~(X668 @ (esk5_2 @ X668 @ X669) @ X671))))&(~(in @ X677 @ X669)|~(X668 @ X677 @ X676)|(in @ X676 @ (esk7_2 @ X668 @ X669))|((X668 @ (esk5_2 @ X668 @ X669) @ (esk6_3 @ X668 @ X669 @ X671))|~(X668 @ (esk5_2 @ X668 @ X669) @ X671))))&((((in @ (esk8_3 @ X668 @ X669 @ X674) @ X669)|~(in @ X674 @ (esk7_2 @ X668 @ X669))|(((X671)!=(esk6_3 @ X668 @ X669 @ X671))|~(X668 @ (esk5_2 @ X668 @ X669) @ X671)))&((X668 @ (esk8_3 @ X668 @ X669 @ X674) @ X674)|~(in @ X674 @ (esk7_2 @ X668 @ X669))|(((X671)!=(esk6_3 @ X668 @ X669 @ X671))|~(X668 @ (esk5_2 @ X668 @ X669) @ X671))))&(~(in @ X677 @ X669)|~(X668 @ X677 @ X676)|(in @ X676 @ (esk7_2 @ X668 @ X669))|(((X671)!=(esk6_3 @ X668 @ X669 @ X671))|~(X668 @ (esk5_2 @ X668 @ X669) @ X671))))))&((((in @ (esk9_1 @ X678) @ X678)|~(in @ X679 @ X678))&(~(in @ X681 @ (esk9_1 @ X678))|~(in @ X681 @ X678)|~(in @ X679 @ X678)))&((epred1_0)&((((X682 @ (esk10_2 @ X682 @ X683))|~(X682 @ X683)|(X682 @ (descr @ X682)))&(((X683)!=(esk10_2 @ X682 @ X683))|~(X682 @ X683)|(X682 @ (descr @ X682))))&((~(in @ X687 @ X685)|(~(X686 @ X687)|(in @ X687 @ (dsetconstr @ X685 @ X686))))&((~(in @ X690 @ (dsetconstr @ X688 @ X689))|(in @ X690 @ X688))&((~(in @ X693 @ (dsetconstr @ X691 @ X692))|(X692 @ X693))&(((((X694 @ (esk12_1 @ X694))|((X694 @ (esk11_2 @ X694 @ X695))|~(X694 @ X695)))&(~(X694 @ X698)|((esk12_1 @ X694)=(X698))|((X694 @ (esk11_2 @ X694 @ X695))|~(X694 @ X695))))&(((X694 @ (esk12_1 @ X694))|(((X695)!=(esk11_2 @ X694 @ X695))|~(X694 @ X695)))&(~(X694 @ X698)|((esk12_1 @ X694)=(X698))|(((X695)!=(esk11_2 @ X694 @ X695))|~(X694 @ X695)))))&((~(in @ X700 @ (prop2set @ ((X699))))|(X699))&((~(in @ X701 @ emptyset)|(X702))&((~(in @ X703 @ emptyset)|~($true))&(~(in @ X704 @ emptyset)&((((X705 @ (esk13_2 @ X705 @ X706))|~(X705 @ X706)|(X705 @ (esk14_1 @ X705)))&(((X706)!=(esk13_2 @ X705 @ X706))|~(X705 @ X706)|(X705 @ (esk14_1 @ X705))))&(((((in @ (esk16_2 @ X709 @ X710) @ X710)|((X709)=(X710))|(in @ (esk15_2 @ X709 @ X710) @ X709))&(~(in @ (esk16_2 @ X709 @ X710) @ X709)|((X709)=(X710))|(in @ (esk15_2 @ X709 @ X710) @ X709)))&(((in @ (esk16_2 @ X709 @ X710) @ X710)|((X709)=(X710))|~(in @ (esk15_2 @ X709 @ X710) @ X710))&(~(in @ (esk16_2 @ X709 @ X710) @ X709)|((X709)=(X710))|~(in @ (esk15_2 @ X709 @ X710) @ X710))))&(((in @ (esk17_1 @ X713) @ X713)|((X713)=(emptyset)))&(((in @ (esk18_1 @ X715) @ X715)|((X715)=(emptyset)))&(((~(in @ X719 @ (dsetconstr @ X717 @ X718))|(X718 @ X719)|~(in @ X719 @ X717))&(~(X718 @ X719)|(in @ X719 @ (dsetconstr @ X717 @ X718))|~(in @ X719 @ X717)))&((((X720)=(emptyset))|(in @ (esk19_1 @ X720) @ X720))&((~(in @ X724 @ X722)|(~(X723 @ X724)|((dsetconstr @ X722 @ X723)!=(emptyset))))&((~(in @ X726 @ X725)|((X725)!=(emptyset)))&((in @ X727 @ (setadjoin @ X727 @ X728))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X731 @ X730)|(in @ X731 @ (setadjoin @ X729 @ X730)))&(((((in @ X734 @ X733)|(X735)|((X734)=(X732))|~(in @ X734 @ (setadjoin @ X732 @ X733)))&(~(X735)|(X735)|((X734)=(X732))|~(in @ X734 @ (setadjoin @ X732 @ X733))))&(((in @ X734 @ X733)|(X735)|~(X735)|~(in @ X734 @ (setadjoin @ X732 @ X733)))&(~(X735)|(X735)|~(X735)|~(in @ X734 @ (setadjoin @ X732 @ X733)))))&((~(in @ X738 @ (setadjoin @ X736 @ X737))|(((X738)=(X736))|(in @ X738 @ X737)))&(((dsetconstr @ X739 @ (^[Z0:$i]:($true)))=(X739))&((((in @ (esk20_2 @ X740 @ X741) @ X741)|(in @ X741 @ (powerset @ X740)))&(~(in @ (esk20_2 @ X740 @ X741) @ X740)|(in @ X741 @ (powerset @ X740))))&((in @ emptyset @ (powerset @ X743))&((in @ emptyset @ (powerset @ X744))&((~(in @ X746 @ (powerset @ X745))|(~(in @ X747 @ X746)|(in @ X747 @ X745)))&((~(in @ X749 @ X750)|(~(in @ X750 @ X748)|(in @ X749 @ (setunion @ X748))))&((((in @ X752 @ (esk21_3 @ X751 @ X752 @ X753))|(X753)|~(in @ X752 @ (setunion @ X751)))&(((in @ (esk21_3 @ X751 @ X752 @ X753) @ X751)|(X753)|~(in @ X752 @ (setunion @ X751)))&(~(X753)|(X753)|~(in @ X752 @ (setunion @ X751)))))&((~(in @ X756 @ X755)|(in @ X756 @ (powerset @ (setunion @ X755))))&((((~(X757 @ X761)|((X761)=(esk23_1 @ X757))|((X757 @ (esk22_2 @ X757 @ X758))|~(X757 @ X758)))&(((X762)!=(esk23_1 @ X757))|(X757 @ X762)|((X757 @ (esk22_2 @ X757 @ X758))|~(X757 @ X758))))&((~(X757 @ X761)|((X761)=(esk23_1 @ X757))|(((X758)!=(esk22_2 @ X757 @ X758))|~(X757 @ X758)))&(((X762)!=(esk23_1 @ X757))|(X757 @ X762)|(((X758)!=(esk22_2 @ X757 @ X758))|~(X757 @ X758)))))&((((in @ (esk24_1 @ X763) @ X763)|((X763)=(emptyset)))&(($true)|((X763)=(emptyset))))&((~(in @ X765 @ (setadjoin @ X766 @ 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X866)))))&(((X866 @ (esk49_3 @ X865 @ X866 @ X871))|~(X866 @ X871)|((descr @ X865)=(descr @ X866))|(((X869)!=(esk48_3 @ X865 @ X866 @ X869))|~(X865 @ X869))|(~(X865 @ (esk46_2 @ X865 @ X866))|~(X866 @ (esk47_2 @ X865 @ X866))))&(((X871)!=(esk49_3 @ X865 @ X866 @ X871))|~(X866 @ X871)|((descr @ X865)=(descr @ X866))|(((X869)!=(esk48_3 @ X865 @ X866 @ X869))|~(X865 @ X869))|(~(X865 @ (esk46_2 @ X865 @ X866))|~(X866 @ (esk47_2 @ X865 @ X866))))))&((((X866 @ (esk49_3 @ X865 @ X866 @ X871))|~(X866 @ X871)|((descr @ X865)=(descr @ X866))|((X865 @ (esk48_3 @ X865 @ X866 @ X869))|~(X865 @ X869))|((X865 @ (esk46_2 @ X865 @ X866))|(X866 @ (esk47_2 @ X865 @ X866))))&(((X871)!=(esk49_3 @ X865 @ X866 @ X871))|~(X866 @ X871)|((descr @ X865)=(descr @ X866))|((X865 @ (esk48_3 @ X865 @ X866 @ X869))|~(X865 @ X869))|((X865 @ (esk46_2 @ X865 @ X866))|(X866 @ (esk47_2 @ X865 @ X866)))))&(((X866 @ (esk49_3 @ X865 @ X866 @ X871))|~(X866 @ X871)|((descr @ X865)=(descr @ X866))|(((X869)!=(esk48_3 @ X865 @ X866 @ X869))|~(X865 @ X869))|((X865 @ (esk46_2 @ X865 @ X866))|(X866 @ (esk47_2 @ X865 @ X866))))&(((X871)!=(esk49_3 @ X865 @ X866 @ X871))|~(X866 @ X871)|((descr @ X865)=(descr @ X866))|(((X869)!=(esk48_3 @ X865 @ X866 @ X869))|~(X865 @ X869))|((X865 @ (esk46_2 @ X865 @ X866))|(X866 @ (esk47_2 @ X865 @ X866))))))))&((((in @ (esk50_4 @ X873 @ X874 @ X875 @ X876) @ X873)|((dsetconstr @ X873 @ X875)=(dsetconstr @ X874 @ X876))|((X873)!=(X874)))&(((in @ (esk51_4 @ X873 @ X874 @ X875 @ X876) @ X874)|((dsetconstr @ X873 @ X875)=(dsetconstr @ X874 @ X876))|((X873)!=(X874)))&((((esk50_4 @ X873 @ X874 @ X875 @ X876)=(esk51_4 @ X873 @ X874 @ X875 @ X876))|((dsetconstr @ X873 @ X875)=(dsetconstr @ X874 @ X876))|((X873)!=(X874)))&((~(X875 @ (esk50_4 @ X873 @ X874 @ X875 @ X876))|~(X876 @ (esk51_4 @ X873 @ X874 @ X875 @ X876))|((dsetconstr @ X873 @ X875)=(dsetconstr @ X874 @ X876))|((X873)!=(X874)))&((X875 @ (esk50_4 @ X873 @ X874 @ X875 @ X876))|(X876 @ (esk51_4 @ X873 @ X874 @ X875 @ X876))|((dsetconstr @ X873 @ X875)=(dsetconstr @ X874 @ X876))|((X873)!=(X874)))))))&((((in @ (esk52_2 @ X879 @ X880) @ X879)|(subset @ X879 @ X880))&(~(in @ (esk52_2 @ X879 @ X880) @ X880)|(subset @ X879 @ X880)))&((((X882)!=(X883))|(subset @ X883 @ X882))&((((X884)!=(X885))|(subset @ X884 @ X885))&((((in @ (esk53_2 @ X886 @ X887) @ X886)|(subset @ X886 @ X887))&(~(in @ (esk53_2 @ X886 @ X887) @ X887)|(subset @ X886 @ X887)))&((subset @ emptyset @ X889)&((~(subset @ X890 @ X891)|(~(in @ X892 @ X890)|(in @ X892 @ X891)))&((~(subset @ X893 @ X894)|((in @ X895 @ X894)|~(in @ X895 @ X893)))&((~(in @ X898 @ X896)|((in @ X898 @ X897)|~(subset @ X896 @ X897)))&(((subset @ X899 @ X900)|((X899)!=(X900)))&((~(in @ X903 @ X901)|((in @ X903 @ X902)|((X901)!=(X902))))&((subset @ X904 @ X904)&((~(subset @ X905 @ X906)|(~(subset @ X906 @ X907)|(subset @ X905 @ X907)))&((subset @ X909 @ (setadjoin @ X908 @ X909))&((~(subset @ X910 @ X912)|(subset @ X910 @ (setadjoin @ X911 @ X912)))&((~(subset @ X913 @ X914)|(in @ X913 @ (powerset @ X914)))&((~(subset @ X915 @ X916)|(~(subset @ X916 @ X915)|((X915)=(X916))))&((~(subset @ X917 @ emptyset)|((X917)=(emptyset)))&((~(subset @ X919 @ X918)|(in @ X919 @ (powerset @ X918)))&((~(in @ X921 @ (powerset @ X920))|(subset @ X921 @ X920))&((in @ X922 @ (powerset @ X922))&((~(subset @ X923 @ X924)|(subset @ (powerset @ X923) @ (powerset @ X924)))&((in @ (dsetconstr @ X925 @ X926) @ (powerset @ X925))&((subset @ (dsetconstr @ X927 @ X928) @ X927)&((~(in @ X931 @ X929)|(in @ X931 @ (binunion @ X929 @ X930)))&((in @ X933 @ (setadjoin @ X932 @ (setadjoin @ X933 @ emptyset)))&((~(in @ X936 @ X935)|(in @ X936 @ (binunion @ X934 @ X935)))&(((((in @ X939 @ X938)|(X940)|(in @ X939 @ X937)|~(in @ X939 @ (binunion @ X937 @ X938)))&(~(X940)|(X940)|(in @ X939 @ X937)|~(in @ X939 @ (binunion @ X937 @ X938))))&(((in @ X939 @ X938)|(X940)|~(X940)|~(in @ X939 @ (binunion @ X937 @ X938)))&(~(X940)|(X940)|~(X940)|~(in @ X939 @ (binunion @ X937 @ X938)))))&((~(in @ X943 @ (binunion @ X941 @ X942))|((in @ X943 @ X941)|(in @ X943 @ X942)))&((subset @ X944 @ (binunion @ X944 @ X945))&((subset @ X947 @ (binunion @ X946 @ X947))&((in @ esk56_0 @ esk54_0)&((in @ esk56_0 @ esk55_0)&~(in @ esk56_0 @ (binintersect @ esk54_0 @ 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_151])])])])])])])).
% 0.67/0.39 thf(c_0_154, plain, ![X643:$i, X644:$i]:(((binintersect @ X643 @ X644)=(dsetconstr @ X643 @ (^[Z0:$i]:((in @ Z0 @ X644)))))), inference(variable_rename,[status(thm)],[c_0_152])).
% 0.67/0.39 thf(c_0_155, negated_conjecture, ~((in @ esk56_0 @ (binintersect @ esk54_0 @ esk55_0))), inference(split_conjunct,[status(thm)],[c_0_153])).
% 0.67/0.39 thf(c_0_156, plain, ![X2:$i, X3:$i]:(((binintersect @ X2 @ X3)=(dsetconstr @ X2 @ (^[Z0:$i]:((in @ Z0 @ X3)))))), inference(split_conjunct,[status(thm)],[c_0_154])).
% 0.67/0.39 thf(c_0_157, negated_conjecture, ~((in @ esk56_0 @ (dsetconstr @ esk54_0 @ (^[Z0:$i]:((in @ Z0 @ esk55_0)))))), inference(rw,[status(thm)],[c_0_155, c_0_156])).
% 0.67/0.39 thf(c_0_158, negated_conjecture, ![X1:$i > $o, X2:$i, X3:$i]:(((in @ X2 @ (dsetconstr @ X3 @ X1))|~((X1 @ X2))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_153])).
% 0.67/0.39 thf(c_0_159, negated_conjecture, (in @ esk56_0 @ esk54_0), inference(split_conjunct,[status(thm)],[c_0_153])).
% 0.67/0.39 thf(c_0_160, negated_conjecture, (in @ esk56_0 @ esk55_0), inference(split_conjunct,[status(thm)],[c_0_153])).
% 0.67/0.39 thf(c_0_161, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157, c_0_158]), c_0_159]), c_0_160])]), ['proof']).
% 0.67/0.39 % SZS output end CNFRefutation
% 0.67/0.39 % Parsed axioms : 231
% 0.67/0.39 % Removed by relevancy pruning/SinE : 0
% 0.67/0.39 % Initial clauses : 344
% 0.67/0.39 % Removed in clause preprocessing : 140
% 0.67/0.39 % Initial clauses in saturation : 204
% 0.67/0.39 % Processed clauses : 473
% 0.67/0.39 % ...of these trivial : 7
% 0.67/0.39 % ...subsumed : 212
% 0.67/0.39 % ...remaining for further processing : 254
% 0.67/0.39 % Other redundant clauses eliminated : 8
% 0.67/0.39 % Clauses deleted for lack of memory : 0
% 0.67/0.39 % Backward-subsumed : 0
% 0.67/0.39 % Backward-rewritten : 4
% 0.67/0.39 % Generated clauses : 3301
% 0.67/0.39 % ...of the previous two non-redundant : 3054
% 0.67/0.39 % ...aggressively subsumed : 0
% 0.67/0.39 % Contextual simplify-reflections : 0
% 0.67/0.39 % Paramodulations : 3291
% 0.67/0.39 % Factorizations : 2
% 0.67/0.39 % NegExts : 0
% 0.67/0.39 % Equation resolutions : 8
% 0.67/0.39 % Disequality decompositions : 0
% 0.67/0.39 % Total rewrite steps : 313
% 0.67/0.39 % ...of those cached : 266
% 0.67/0.39 % Propositional unsat checks : 0
% 0.67/0.39 % Propositional check models : 0
% 0.67/0.39 % Propositional check unsatisfiable : 0
% 0.67/0.39 % Propositional clauses : 0
% 0.67/0.39 % Propositional clauses after purity: 0
% 0.67/0.39 % Propositional unsat core size : 0
% 0.67/0.39 % Propositional preprocessing time : 0.000
% 0.67/0.39 % Propositional encoding time : 0.000
% 0.67/0.39 % Propositional solver time : 0.000
% 0.67/0.39 % Success case prop preproc time : 0.000
% 0.67/0.39 % Success case prop encoding time : 0.000
% 0.67/0.39 % Success case prop solver time : 0.000
% 0.67/0.39 % Current number of processed clauses : 243
% 0.67/0.39 % Positive orientable unit clauses : 42
% 0.67/0.39 % Positive unorientable unit clauses: 0
% 0.67/0.39 % Negative unit clauses : 2
% 0.67/0.39 % Non-unit-clauses : 199
% 0.67/0.39 % Current number of unprocessed clauses: 2764
% 0.67/0.39 % ...number of literals in the above : 8428
% 0.67/0.39 % Current number of archived formulas : 0
% 0.67/0.39 % Current number of archived clauses : 5
% 0.67/0.39 % Clause-clause subsumption calls (NU) : 4600
% 0.67/0.39 % Rec. Clause-clause subsumption calls : 3997
% 0.67/0.39 % Non-unit clause-clause subsumptions : 191
% 0.67/0.39 % Unit Clause-clause subsumption calls : 15
% 0.67/0.39 % Rewrite failures with RHS unbound : 0
% 0.67/0.39 % BW rewrite match attempts : 33
% 0.67/0.39 % BW rewrite match successes : 3
% 0.67/0.39 % Condensation attempts : 0
% 0.67/0.39 % Condensation successes : 0
% 0.67/0.39 % Termbank termtop insertions : 75591
% 0.67/0.39 % Search garbage collected termcells : 11078
% 0.67/0.39
% 0.67/0.39 % -------------------------------------------------
% 0.67/0.39 % User time : 0.071 s
% 0.67/0.39 % System time : 0.009 s
% 0.67/0.39 % Total time : 0.080 s
% 0.67/0.39 % Maximum resident set size: 6416 pages
% 0.67/0.39
% 0.67/0.39 % -------------------------------------------------
% 0.67/0.39 % User time : 0.109 s
% 0.67/0.39 % System time : 0.032 s
% 0.67/0.39 % Total time : 0.142 s
% 0.67/0.39 % Maximum resident set size: 5120 pages
% 0.67/0.39 % E exiting
%------------------------------------------------------------------------------