%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU597^1 : 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 : n026.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 08:26:51 AM UTC 2026
% Result : Theorem 3.87s 0.84s
% Output : CNFRefutation 3.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU597^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n026.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 13:58:57 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.21/0.26 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.rC0Sle01w8/E---3.1_638478.p
% 3.87/0.84 % Version: 3.5.1-ho
% 3.87/0.84 % Preprocessing class: HSLMSLSSLLLCHFA.
% 3.87/0.84 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 3.87/0.84 % Starting ehoh_best5 with 300s (1) cores
% 3.87/0.84 % Starting almost_fo_3_lam with 300s (1) cores
% 3.87/0.84 % Starting new_bool_5 with 300s (1) cores
% 3.87/0.84 % Starting pre_casc_3 with 300s (1) cores
% 3.87/0.84 % Starting ho_unfolding_8 with 300s (1) cores
% 3.87/0.84 % Starting new_ho_10_cnf2 with 300s (1) cores
% 3.87/0.84 % Starting new_bool_3 with 300s (1) cores
% 3.87/0.84 % Starting new_ho_5 with 300s (1) cores
% 3.87/0.84 % new_ho_5 with pid 638517 completed with status 9
% 3.87/0.84 % ho_unfolding_8 with pid 638513 completed with status 0
% 3.87/0.84 % Result found by ho_unfolding_8
% 3.87/0.84 % Preprocessing class: HSLMSLSSLLLCHFA.
% 3.87/0.84 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 3.87/0.84 % Starting ehoh_best5 with 300s (1) cores
% 3.87/0.84 % Starting almost_fo_3_lam with 300s (1) cores
% 3.87/0.84 % Starting new_bool_5 with 300s (1) cores
% 3.87/0.84 % Starting pre_casc_3 with 300s (1) cores
% 3.87/0.84 % Starting ho_unfolding_8 with 300s (1) cores
% 3.87/0.84 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.87/0.84 % No SInE strategy applied
% 3.87/0.84 % Search class: HGHSM-FSLS31-SHFMMSBN
% 3.87/0.84 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 3.87/0.84 % Starting SubtermCWHack with 28s (1) cores
% 3.87/0.84 % SubtermCWHack with pid 638532 completed with status 0
% 3.87/0.84 % Result found by SubtermCWHack
% 3.87/0.84 % Preprocessing class: HSLMSLSSLLLCHFA.
% 3.87/0.84 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 3.87/0.84 % Starting ehoh_best5 with 300s (1) cores
% 3.87/0.84 % Starting almost_fo_3_lam with 300s (1) cores
% 3.87/0.84 % Starting new_bool_5 with 300s (1) cores
% 3.87/0.84 % Starting pre_casc_3 with 300s (1) cores
% 3.87/0.84 % Starting ho_unfolding_8 with 300s (1) cores
% 3.87/0.84 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.87/0.84 % No SInE strategy applied
% 3.87/0.84 % Search class: HGHSM-FSLS31-SHFMMSBN
% 3.87/0.84 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 3.87/0.84 % Starting SubtermCWHack with 28s (1) cores
% 3.87/0.84 % Preprocessing time : 0.004 s
% 3.87/0.84
% 3.87/0.84 % Proof found!
% 3.87/0.84 % SZS status Theorem
% 3.87/0.84 % SZS output start CNFRefutation
% 3.87/0.84 thf(decl_23, type, in: $i > $i > $o).
% 3.87/0.84 thf(decl_24, type, exu: ($i > $o) > $o).
% 3.87/0.84 thf(decl_25, type, setextAx: $o).
% 3.87/0.84 thf(decl_26, type, emptyset: $i).
% 3.87/0.84 thf(decl_27, type, emptysetAx: $o).
% 3.87/0.84 thf(decl_28, type, setadjoin: $i > $i > $i).
% 3.87/0.84 thf(decl_29, type, setadjoinAx: $o).
% 3.87/0.84 thf(decl_30, type, powerset: $i > $i).
% 3.87/0.84 thf(decl_31, type, powersetAx: $o).
% 3.87/0.84 thf(decl_32, type, setunion: $i > $i).
% 3.87/0.84 thf(decl_33, type, setunionAx: $o).
% 3.87/0.84 thf(decl_34, type, omega: $i).
% 3.87/0.84 thf(decl_35, type, omega0Ax: $o).
% 3.87/0.84 thf(decl_36, type, omegaSAx: $o).
% 3.87/0.84 thf(decl_37, type, omegaIndAx: $o).
% 3.87/0.84 thf(decl_38, type, replAx: $o).
% 3.87/0.84 thf(decl_39, type, foundationAx: $o).
% 3.87/0.84 thf(decl_40, type, wellorderingAx: $o).
% 3.87/0.84 thf(decl_41, type, descr: ($i > $o) > $i).
% 3.87/0.84 thf(decl_42, type, descrp: $o).
% 3.87/0.84 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 3.87/0.84 thf(decl_44, type, dsetconstrI: $o).
% 3.87/0.84 thf(decl_45, type, dsetconstrEL: $o).
% 3.87/0.84 thf(decl_46, type, dsetconstrER: $o).
% 3.87/0.84 thf(decl_47, type, exuE1: $o).
% 3.87/0.84 thf(decl_48, type, prop2set: $o > $i).
% 3.87/0.84 thf(decl_49, type, prop2setE: $o).
% 3.87/0.84 thf(decl_50, type, emptysetE: $o).
% 3.87/0.84 thf(decl_51, type, emptysetimpfalse: $o).
% 3.87/0.84 thf(decl_52, type, notinemptyset: $o).
% 3.87/0.84 thf(decl_53, type, exuE3e: $o).
% 3.87/0.84 thf(decl_54, type, setext: $o).
% 3.87/0.84 thf(decl_55, type, emptyI: $o).
% 3.87/0.84 thf(decl_56, type, noeltsimpempty: $o).
% 3.87/0.84 thf(decl_57, type, setbeta: $o).
% 3.87/0.84 thf(decl_58, type, nonempty: $i > $o).
% 3.87/0.84 thf(decl_59, type, nonemptyE1: $o).
% 3.87/0.84 thf(decl_60, type, nonemptyI: $o).
% 3.87/0.84 thf(decl_61, type, nonemptyI1: $o).
% 3.87/0.84 thf(decl_62, type, setadjoinIL: $o).
% 3.87/0.84 thf(decl_63, type, emptyinunitempty: $o).
% 3.87/0.84 thf(decl_64, type, setadjoinIR: $o).
% 3.87/0.84 thf(decl_65, type, setadjoinE: $o).
% 3.87/0.84 thf(decl_66, type, setadjoinOr: $o).
% 3.87/0.84 thf(decl_67, type, setoftrueEq: $o).
% 3.87/0.84 thf(decl_68, type, powersetI: $o).
% 3.87/0.84 thf(decl_69, type, emptyinPowerset: $o).
% 3.87/0.84 thf(decl_70, type, emptyInPowerset: $o).
% 3.87/0.84 thf(decl_71, type, powersetE: $o).
% 3.87/0.84 thf(decl_72, type, setunionI: $o).
% 3.87/0.84 thf(decl_73, type, setunionE: $o).
% 3.87/0.84 thf(decl_74, type, subPowSU: $o).
% 3.87/0.84 thf(decl_75, type, exuE2: $o).
% 3.87/0.84 thf(decl_76, type, nonemptyImpWitness: $o).
% 3.87/0.84 thf(decl_77, type, uniqinunit: $o).
% 3.87/0.84 thf(decl_78, type, notinsingleton: $o).
% 3.87/0.84 thf(decl_79, type, eqinunit: $o).
% 3.87/0.84 thf(decl_80, type, singletonsswitch: $o).
% 3.87/0.84 thf(decl_81, type, upairsetE: $o).
% 3.87/0.84 thf(decl_82, type, upairsetIL: $o).
% 3.87/0.84 thf(decl_83, type, upairsetIR: $o).
% 3.87/0.84 thf(decl_84, type, emptyE1: $o).
% 3.87/0.84 thf(decl_85, type, vacuousDall: $o).
% 3.87/0.84 thf(decl_86, type, quantDeMorgan1: $o).
% 3.87/0.84 thf(decl_87, type, quantDeMorgan2: $o).
% 3.87/0.84 thf(decl_88, type, quantDeMorgan3: $o).
% 3.87/0.84 thf(decl_89, type, quantDeMorgan4: $o).
% 3.87/0.84 thf(decl_90, type, prop2setI: $o).
% 3.87/0.84 thf(decl_91, type, set2prop: $i > $o).
% 3.87/0.84 thf(decl_92, type, prop2set2propI: $o).
% 3.87/0.84 thf(decl_93, type, notdexE: $o).
% 3.87/0.84 thf(decl_94, type, notdallE: $o).
% 3.87/0.84 thf(decl_95, type, exuI1: $o).
% 3.87/0.84 thf(decl_96, type, exuI3: $o).
% 3.87/0.84 thf(decl_97, type, exuI2: $o).
% 3.87/0.84 thf(decl_98, type, inCongP: $o).
% 3.87/0.84 thf(decl_99, type, in__Cong: $o).
% 3.87/0.84 thf(decl_100, type, exuE3u: $o).
% 3.87/0.84 thf(decl_101, type, exu__Cong: $o).
% 3.87/0.84 thf(decl_102, type, emptyset__Cong: $o).
% 3.87/0.84 thf(decl_103, type, setadjoin__Cong: $o).
% 3.87/0.84 thf(decl_104, type, powerset__Cong: $o).
% 3.87/0.84 thf(decl_105, type, setunion__Cong: $o).
% 3.87/0.84 thf(decl_106, type, omega__Cong: $o).
% 3.87/0.84 thf(decl_107, type, exuEu: $o).
% 3.87/0.84 thf(decl_108, type, descr__Cong: $o).
% 3.87/0.84 thf(decl_109, type, dsetconstr__Cong: $o).
% 3.87/0.84 thf(decl_110, type, subset: $i > $i > $o).
% 3.87/0.84 thf(decl_113, type, subsetI1: $o).
% 3.87/0.84 thf(decl_114, type, eqimpsubset2: $o).
% 3.87/0.84 thf(decl_115, type, eqimpsubset1: $o).
% 3.87/0.84 thf(decl_116, type, subsetI2: $o).
% 3.87/0.84 thf(decl_117, type, emptysetsubset: $o).
% 3.87/0.84 thf(decl_118, type, subsetE: $o).
% 3.87/0.84 thf(decl_119, type, subsetE2: $o).
% 3.87/0.84 thf(decl_120, type, notsubsetI: $o).
% 3.87/0.84 thf(decl_121, type, notequalI1: $o).
% 3.87/0.84 thf(decl_122, type, notequalI2: $o).
% 3.87/0.84 thf(decl_123, type, subsetRefl: $o).
% 3.87/0.84 thf(decl_124, type, subsetTrans: $o).
% 3.87/0.84 thf(decl_125, type, setadjoinSub: $o).
% 3.87/0.84 thf(decl_126, type, setadjoinSub2: $o).
% 3.87/0.84 thf(decl_127, type, subset2powerset: $o).
% 3.87/0.84 thf(decl_128, type, setextsub: $o).
% 3.87/0.84 thf(decl_129, type, subsetemptysetimpeq: $o).
% 3.87/0.84 thf(decl_130, type, powersetI1: $o).
% 3.87/0.84 thf(decl_131, type, powersetE1: $o).
% 3.87/0.84 thf(decl_132, type, inPowerset: $o).
% 3.87/0.84 thf(decl_133, type, powersetsubset: $o).
% 3.87/0.84 thf(decl_134, type, sepInPowerset: $o).
% 3.87/0.84 thf(decl_135, type, sepSubset: $o).
% 3.87/0.84 thf(decl_136, type, binunion: $i > $i > $i).
% 3.87/0.84 thf(decl_137, type, binunionIL: $o).
% 3.87/0.84 thf(decl_138, type, upairset2IR: $o).
% 3.87/0.84 thf(decl_139, type, binunionIR: $o).
% 3.87/0.84 thf(decl_140, type, binunionEcases: $o).
% 3.87/0.84 thf(decl_141, type, binunionE: $o).
% 3.87/0.84 thf(decl_142, type, binunionLsub: $o).
% 3.87/0.84 thf(decl_143, type, binunionRsub: $o).
% 3.87/0.84 thf(decl_144, type, binintersect: $i > $i > $i).
% 3.87/0.84 thf(decl_145, type, binintersectI: $o).
% 3.87/0.84 thf(decl_146, type, binintersectSubset5: $o).
% 3.87/0.84 thf(decl_147, type, binintersectEL: $o).
% 3.87/0.84 thf(decl_148, type, binintersectLsub: $o).
% 3.87/0.84 thf(decl_149, type, binintersectSubset2: $o).
% 3.87/0.84 thf(decl_150, type, binintersectSubset3: $o).
% 3.87/0.84 thf(decl_151, type, binintersectER: $o).
% 3.87/0.84 thf(decl_152, type, disjointsetsI1: $o).
% 3.87/0.84 thf(decl_153, type, epred1_0: $o).
% 3.87/0.84 thf(decl_154, type, esk1_2: $i > $i > $i).
% 3.87/0.84 thf(decl_155, type, esk2_2: $i > $i > $i).
% 3.87/0.84 thf(decl_156, type, esk3_2: $i > $i > $i).
% 3.87/0.84 thf(decl_157, type, esk4_1: $i > $i).
% 3.87/0.84 thf(decl_158, type, esk5_2: ($i > $i > $o) > $i > $i).
% 3.87/0.84 thf(decl_159, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 3.87/0.84 thf(decl_160, type, esk7_2: ($i > $i > $o) > $i > $i).
% 3.87/0.84 thf(decl_161, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 3.87/0.84 thf(decl_162, type, esk9_1: $i > $i).
% 3.87/0.84 thf(decl_163, type, esk10_2: ($i > $o) > $i > $i).
% 3.87/0.84 thf(decl_164, type, esk11_2: ($i > $o) > $i > $i).
% 3.87/0.84 thf(decl_165, type, esk12_1: ($i > $o) > $i).
% 3.87/0.84 thf(decl_166, type, esk13_2: ($i > $o) > $i > $i).
% 3.87/0.84 thf(decl_167, type, esk14_1: ($i > $o) > $i).
% 3.87/0.84 thf(decl_168, type, esk15_2: $i > $i > $i).
% 3.87/0.84 thf(decl_169, type, esk16_2: $i > $i > $i).
% 3.87/0.84 thf(decl_170, type, esk17_1: $i > $i).
% 3.87/0.84 thf(decl_171, type, esk18_1: $i > $i).
% 3.87/0.84 thf(decl_172, type, esk19_1: $i > $i).
% 3.87/0.84 thf(decl_173, type, esk20_2: $i > $i > $i).
% 3.87/0.84 thf(decl_174, type, esk21_3: $i > $i > $o > $i).
% 3.87/0.84 thf(decl_175, type, esk22_2: ($i > $o) > $i > $i).
% 3.87/0.84 thf(decl_176, type, esk23_1: ($i > $o) > $i).
% 3.87/0.84 thf(decl_177, type, esk24_1: $i > $i).
% 3.87/0.84 thf(decl_178, type, esk25_2: $i > ($i > $o) > $i).
% 3.87/0.84 thf(decl_179, type, esk26_2: $i > ($i > $o) > $i).
% 3.87/0.84 thf(decl_180, type, esk27_2: $i > ($i > $o) > $i).
% 3.87/0.84 thf(decl_181, type, esk28_2: $i > ($i > $o) > $i).
% 3.87/0.84 thf(decl_182, type, esk29_2: $i > ($i > $o) > $i).
% 3.87/0.84 thf(decl_183, type, esk30_2: $i > ($i > $o) > $i).
% 3.87/0.84 thf(decl_184, type, esk31_2: ($i > $o) > $i > $i).
% 3.87/0.84 thf(decl_185, type, esk32_1: ($i > $o) > $i).
% 3.87/0.84 thf(decl_186, type, esk33_1: ($i > $o) > $i).
% 3.87/0.84 thf(decl_187, type, esk34_1: ($i > $o) > $i).
% 3.87/0.84 thf(decl_188, type, esk35_1: ($i > $o) > $i).
% 3.87/0.84 thf(decl_189, type, esk36_2: ($i > $o) > $i > $i).
% 3.87/0.84 thf(decl_190, type, esk37_1: ($i > $o) > $i).
% 3.87/0.84 thf(decl_191, type, esk38_2: ($i > $o) > $i > $i).
% 3.87/0.84 thf(decl_192, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 3.87/0.84 thf(decl_193, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 3.87/0.84 thf(decl_194, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 3.87/0.84 thf(decl_195, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 3.87/0.84 thf(decl_196, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 3.87/0.84 thf(decl_197, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 3.87/0.84 thf(decl_198, type, esk45_2: ($i > $o) > $i > $i).
% 3.87/0.84 thf(decl_199, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 3.87/0.84 thf(decl_200, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 3.87/0.84 thf(decl_201, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 3.87/0.84 thf(decl_202, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 3.87/0.84 thf(decl_203, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 3.87/0.84 thf(decl_204, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 3.87/0.84 thf(decl_205, type, esk52_2: $i > $i > $i).
% 3.87/0.84 thf(decl_206, type, esk53_2: $i > $i > $i).
% 3.87/0.84 thf(decl_207, type, esk54_2: $i > $i > $i).
% 3.87/0.84 thf(decl_208, type, esk55_0: $i).
% 3.87/0.84 thf(decl_209, type, esk56_0: $i).
% 3.87/0.84 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', replAx)).
% 3.87/0.84 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', exu)).
% 3.87/0.84 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', descrp)).
% 3.87/0.84 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', exuE1)).
% 3.87/0.84 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', exuE3e)).
% 3.87/0.84 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', nonempty)).
% 3.87/0.84 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', nonemptyI)).
% 3.87/0.84 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', exuE2)).
% 3.87/0.84 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.rC0Sle01w8/E---3.1_638478.p', exuI1)).
% 3.87/0.84 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', exuI3)).
% 3.87/0.84 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', exuI2)).
% 3.87/0.84 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.rC0Sle01w8/E---3.1_638478.p', exuE3u)).
% 3.87/0.84 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', exu__Cong)).
% 3.87/0.84 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', exuEu)).
% 3.87/0.84 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', descr__Cong)).
% 3.87/0.84 thf(binintersectRsub, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', binintersectRsub)).
% 3.87/0.84 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', dsetconstrI)).
% 3.87/0.84 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', dsetconstrEL)).
% 3.87/0.84 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', dsetconstrER)).
% 3.87/0.84 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', setbeta)).
% 3.87/0.84 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', nonemptyE1)).
% 3.87/0.84 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', nonemptyI1)).
% 3.87/0.84 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', setoftrueEq)).
% 3.87/0.84 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', nonemptyImpWitness)).
% 3.87/0.84 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.rC0Sle01w8/E---3.1_638478.p', emptyE1)).
% 3.87/0.84 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', dsetconstr__Cong)).
% 3.87/0.84 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', sepInPowerset)).
% 3.87/0.84 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', sepSubset)).
% 3.87/0.84 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', setextAx)).
% 3.87/0.84 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', emptysetAx)).
% 3.87/0.84 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', setadjoinAx)).
% 3.87/0.84 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', powersetAx)).
% 3.87/0.84 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', setunionAx)).
% 3.87/0.84 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', omega0Ax)).
% 3.87/0.84 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', omegaSAx)).
% 3.87/0.84 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', omegaIndAx)).
% 3.87/0.85 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', foundationAx)).
% 3.87/0.85 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.rC0Sle01w8/E---3.1_638478.p', wellorderingAx)).
% 3.87/0.85 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', prop2setE)).
% 3.87/0.85 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', emptysetE)).
% 3.87/0.85 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', emptysetimpfalse)).
% 3.87/0.85 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', notinemptyset)).
% 3.87/0.85 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', setext)).
% 3.87/0.85 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', emptyI)).
% 3.87/0.85 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', noeltsimpempty)).
% 3.87/0.85 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', setadjoinIL)).
% 3.87/0.85 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', emptyinunitempty)).
% 3.87/0.85 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', setadjoinIR)).
% 3.87/0.85 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.rC0Sle01w8/E---3.1_638478.p', setadjoinE)).
% 3.87/0.85 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', setadjoinOr)).
% 3.87/0.85 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', powersetI)).
% 3.87/0.85 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', emptyinPowerset)).
% 3.87/0.85 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', emptyInPowerset)).
% 3.87/0.85 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', powersetE)).
% 3.87/0.85 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', setunionI)).
% 3.87/0.85 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.rC0Sle01w8/E---3.1_638478.p', setunionE)).
% 3.87/0.85 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', subPowSU)).
% 3.87/0.85 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', uniqinunit)).
% 3.87/0.85 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', notinsingleton)).
% 3.87/0.85 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', eqinunit)).
% 3.87/0.85 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', singletonsswitch)).
% 3.87/0.85 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', upairsetE)).
% 3.87/0.85 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', upairsetIL)).
% 3.87/0.85 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', upairsetIR)).
% 3.87/0.85 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', vacuousDall)).
% 3.87/0.85 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', quantDeMorgan1)).
% 3.87/0.85 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', quantDeMorgan2)).
% 3.87/0.85 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', quantDeMorgan3)).
% 3.87/0.85 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', quantDeMorgan4)).
% 3.87/0.85 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', prop2setI)).
% 3.87/0.85 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', prop2set2propI)).
% 3.87/0.85 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', notdexE)).
% 3.87/0.85 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', notdallE)).
% 3.87/0.85 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', inCongP)).
% 3.87/0.85 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', in__Cong)).
% 3.87/0.85 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', emptyset__Cong)).
% 3.87/0.85 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', setadjoin__Cong)).
% 3.87/0.85 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', powerset__Cong)).
% 3.87/0.85 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', setunion__Cong)).
% 3.87/0.85 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', omega__Cong)).
% 3.87/0.85 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', subsetI1)).
% 3.87/0.85 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', eqimpsubset2)).
% 3.87/0.85 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', eqimpsubset1)).
% 3.87/0.85 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', subsetI2)).
% 3.87/0.85 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', emptysetsubset)).
% 3.87/0.85 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', subsetE)).
% 3.87/0.85 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', subsetE2)).
% 3.87/0.85 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', notsubsetI)).
% 3.87/0.85 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', notequalI1)).
% 3.87/0.85 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', notequalI2)).
% 3.87/0.85 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', subsetRefl)).
% 3.87/0.85 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', subsetTrans)).
% 3.87/0.85 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', setadjoinSub)).
% 3.87/0.85 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', setadjoinSub2)).
% 3.87/0.85 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', subset2powerset)).
% 3.87/0.85 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', setextsub)).
% 3.87/0.85 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', subsetemptysetimpeq)).
% 3.87/0.85 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', powersetI1)).
% 3.87/0.85 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', powersetE1)).
% 3.87/0.85 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', inPowerset)).
% 3.87/0.85 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', powersetsubset)).
% 3.87/0.85 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', binunionIL)).
% 3.87/0.85 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', upairset2IR)).
% 3.87/0.85 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', binunionIR)).
% 3.87/0.85 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', binunionEcases)).
% 3.87/0.85 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', binunionE)).
% 3.87/0.85 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', binunionLsub)).
% 3.87/0.85 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', binunionRsub)).
% 3.87/0.85 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', binintersectI)).
% 3.87/0.85 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', binintersectSubset5)).
% 3.87/0.85 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', binintersectEL)).
% 3.87/0.85 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', binintersectLsub)).
% 3.87/0.85 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', binintersectSubset2)).
% 3.87/0.85 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', binintersectSubset3)).
% 3.87/0.85 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', binintersectER)).
% 3.87/0.85 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rC0Sle01w8/E---3.1_638478.p', disjointsetsI1)).
% 3.87/0.85 thf(c_0_116, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 3.87/0.85 thf(c_0_117, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 3.87/0.85 thf(c_0_118, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 3.87/0.85 thf(c_0_119, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 3.87/0.85 thf(c_0_120, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 3.87/0.85 thf(c_0_121, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 3.87/0.85 thf(c_0_122, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 3.87/0.85 thf(c_0_123, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 3.87/0.85 thf(c_0_124, 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])).
% 3.87/0.85 thf(c_0_125, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 3.87/0.85 thf(c_0_126, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 3.87/0.85 thf(c_0_127, 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])).
% 3.87/0.85 thf(c_0_128, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 3.87/0.85 thf(c_0_129, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 3.87/0.85 thf(c_0_130, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 3.87/0.85 thf(c_0_131, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[binintersectRsub])).
% 3.87/0.85 thf(c_0_132, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X324:$i]:(((((X6 @ X2 @ X324)))&(![X325:$i]:(((((X6 @ X2 @ X325)))=>(((X324)=(X325)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_116, c_0_117])).
% 3.87/0.85 thf(c_0_133, plain, ((descrp)=(![X1:$i > $o]:((((?[X326:$i]:(((((X1 @ X326)))&(![X327:$i]:(((((X1 @ X327)))=>(((X326)=(X327))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_118, c_0_117])).
% 3.87/0.85 thf(c_0_134, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 3.87/0.85 thf(c_0_135, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 3.87/0.85 thf(c_0_136, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 3.87/0.85 thf(c_0_137, plain, ((exuE1)=(![X1:$i > $o]:((((?[X328:$i]:(((((X1 @ X328)))&(![X329:$i]:(((((X1 @ X329)))=>(((X328)=(X329))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_119, c_0_117])).
% 3.87/0.85 thf(c_0_138, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X330:$i]:(((((X1 @ X330)))&(![X331:$i]:(((((X1 @ X331)))=>(((X330)=(X331))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_120, c_0_117])).
% 3.87/0.85 thf(c_0_139, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 3.87/0.85 thf(c_0_140, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_121])).
% 3.87/0.85 thf(c_0_141, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_122, c_0_121])).
% 3.87/0.85 thf(c_0_142, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_121])).
% 3.87/0.85 thf(c_0_143, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 3.87/0.85 thf(c_0_144, plain, ((exuE2)=(![X1:$i > $o]:((((?[X332:$i]:(((((X1 @ X332)))&(![X333:$i]:(((((X1 @ X333)))=>(((X332)=(X333))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_123, c_0_117])).
% 3.87/0.85 thf(c_0_145, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_121])).
% 3.87/0.85 thf(c_0_146, 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])).
% 3.87/0.85 thf(c_0_147, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X334:$i]:(((((X1 @ X334)))&(![X335:$i]:(((((X1 @ X335)))=>(((X334)=(X335)))))))))))))), inference(apply_def,[status(thm)],[c_0_124, c_0_117])).
% 3.87/0.85 thf(c_0_148, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X336:$i]:(((((X1 @ X336)))&(![X337:$i]:(((((X1 @ X337)))=>(((X336)=(X337)))))))))))))))), inference(apply_def,[status(thm)],[c_0_125, c_0_117])).
% 3.87/0.85 thf(c_0_149, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X338:$i]:(((((X1 @ X338)))&(![X339:$i]:(((((X1 @ X339)))=>(((X338)=(X339)))))))))))))), inference(apply_def,[status(thm)],[c_0_126, c_0_117])).
% 3.87/0.85 thf(c_0_150, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X340:$i]:(((((X1 @ X340)))&(![X341:$i]:(((((X1 @ X341)))=>(((X340)=(X341))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_127, c_0_117])).
% 3.87/0.85 thf(c_0_151, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X342:$i]:(((((X1 @ X342)))&(![X343:$i]:(((((X1 @ X343)))=>(((X342)=(X343))))))))))<=>((?[X344:$i]:(((((X17 @ X344)))&(![X345:$i]:(((((X17 @ X345)))=>(((X344)=(X345)))))))))))))))), inference(apply_def,[status(thm)],[c_0_128, c_0_117])).
% 3.87/0.85 thf(c_0_152, plain, ((exuEu)=(![X1:$i > $o]:((((?[X346:$i]:(((((X1 @ X346)))&(![X347:$i]:(((((X1 @ X347)))=>(((X346)=(X347))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_129, c_0_117])).
% 3.87/0.85 thf(c_0_153, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X348:$i]:(((((X1 @ X348)))&(![X349:$i]:(((((X1 @ X349)))=>(((X348)=(X349))))))))))=>((((?[X350:$i]:(((((X17 @ X350)))&(![X351:$i]:(((((X17 @ X351)))=>(((X350)=(X351))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_130, c_0_117])).
% 3.87/0.85 thf(c_0_154, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 3.87/0.85 thf(c_0_155, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 3.87/0.85 thf(c_0_156, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 3.87/0.85 thf(c_0_157, plain, ((epred1_0)<=>![X381:$i]:(?[X382:$i]:((((![X383:$i]:(((in @ X383 @ X382)=>![X384:$i]:(((in @ X384 @ X383)=>(in @ X384 @ X381)))))&![X385:$i, X386:$i]:((((in @ X385 @ X381)&(in @ X386 @ X381))=>(![X387:$i]:(((in @ X387 @ X382)=>((in @ X385 @ X387)<=>(in @ X386 @ X387))))=>((X385)=(X386))))))&![X388:$i, X389:$i]:((((in @ X388 @ X382)&(in @ X389 @ X382))=>(![X390:$i]:(((in @ X390 @ X388)=>(in @ X390 @ X389)))|![X391:$i]:(((in @ X391 @ X389)=>(in @ X391 @ X388)))))))&![X392:$i]:(((![X393:$i]:(((in @ X393 @ X392)=>(in @ X393 @ X381)))&?[X394:$i]:((in @ X394 @ X392)))=>?[X395:$i, X396:$i]:(((((in @ X395 @ X382)&(in @ X396 @ X392))&~(?[X397:$i]:(((in @ X397 @ X395)&(in @ X397 @ X392)))))&![X398:$i]:(((in @ X398 @ X382)=>(![X399:$i]:(((in @ X399 @ X398)=>(in @ X399 @ X395)))|(in @ X396 @ X398)))))))))))), introduced(definition)).
% 3.87/0.85 thf(c_0_158, negated_conjecture, ~((![X352:$i, X353:$i]:((![X354:$i]:(((in @ X354 @ X352)<=>(in @ X354 @ X353)))=>((X352)=(X353))))=>(![X355:$i]:(~(in @ X355 @ emptyset))=>(![X356:$i, X357:$i, X358:$i]:(((in @ X358 @ (setadjoin @ X356 @ X357))<=>(((X358)=(X356))|(in @ X358 @ X357))))=>(![X359:$i, X360:$i]:(((in @ X360 @ (powerset @ X359))<=>![X361:$i]:(((in @ X361 @ X360)=>(in @ X361 @ X359)))))=>(![X362:$i, X363:$i]:(((in @ X363 @ (setunion @ X362))<=>?[X364:$i]:(((in @ X363 @ X364)&(in @ X364 @ X362)))))=>((in @ emptyset @ omega)=>(![X365:$i]:(((in @ X365 @ omega)=>(in @ (setadjoin @ X365 @ X365) @ omega)))=>(![X366:$i]:((((in @ emptyset @ X366)&![X367:$i]:((((in @ X367 @ omega)&(in @ X367 @ X366))=>(in @ (setadjoin @ X367 @ X367) @ X366))))=>![X368:$i]:(((in @ X368 @ omega)=>(in @ X368 @ X366)))))=>(![X369:$i > $i > $o, X370:$i]:((![X371:$i]:(((in @ X371 @ X370)=>?[X372:$i]:(((X369 @ X371 @ X372)&![X373:$i]:(((X369 @ X371 @ X373)=>((X372)=(X373))))))))=>?[X374:$i]:(![X375:$i]:(((in @ X375 @ X374)<=>?[X376:$i]:(((in @ X376 @ X370)&(X369 @ X376 @ X375))))))))=>(![X377:$i]:((?[X378:$i]:((in @ X378 @ X377))=>?[X379:$i]:(((in @ X379 @ X377)&~(?[X380:$i]:(((in @ X380 @ X379)&(in @ X380 @ X377))))))))=>((epred1_0)=>(![X400:$i > $o]:((?[X401:$i]:(((X400 @ X401)&![X402:$i]:(((X400 @ X402)=>((X401)=(X402))))))=>(X400 @ (descr @ (^[Z0:$i]:(X400 @ Z0))))))=>(![X403:$i, X404:$i > $o, X405:$i]:(((in @ X405 @ X403)=>((X404 @ X405)=>(in @ X405 @ (dsetconstr @ X403 @ X404)))))=>(![X406:$i, X407:$i > $o, X408:$i]:(((in @ X408 @ (dsetconstr @ X406 @ X407))=>(in @ X408 @ X406)))=>(![X409:$i, X410:$i > $o, X411:$i]:(((in @ X411 @ (dsetconstr @ X409 @ X410))=>(X410 @ X411)))=>(![X412:$i > $o]:((?[X413:$i]:(((X412 @ X413)&![X414:$i]:(((X412 @ X414)=>((X413)=(X414))))))=>?[X415:$i]:(((X412 @ X415)&![X416:$i]:(((X412 @ X416)=>((X415)=(X416))))))))=>(![X417:$o, X418:$i]:(((in @ X418 @ (prop2set @ ((X417))))=>(X417)))=>(![X419:$i]:(((in @ X419 @ emptyset)=>![X420:$o]:((X420))))=>(![X421:$i]:(((in @ X421 @ emptyset)=>~($true)))=>(![X422:$i]:(~(in @ X422 @ emptyset))=>(![X423:$i > $o]:((?[X424:$i]:(((X423 @ X424)&![X425:$i]:(((X423 @ X425)=>((X424)=(X425))))))=>?[X426:$i]:((X423 @ X426))))=>(![X427:$i, X428:$i]:((![X429:$i]:(((in @ X429 @ X427)=>(in @ X429 @ X428)))=>(![X430:$i]:(((in @ X430 @ X428)=>(in @ X430 @ X427)))=>((X427)=(X428)))))=>(![X431:$i]:((![X432:$i]:(~(in @ X432 @ X431))=>((X431)=(emptyset))))=>(![X433:$i]:((![X434:$i]:(~(in @ X434 @ X433))=>((X433)=(emptyset))))=>(![X435:$i, X436:$i > $o, X437:$i]:(((in @ X437 @ X435)=>((in @ X437 @ (dsetconstr @ X435 @ X436))<=>(X436 @ X437))))=>(![X438:$i]:((((X438)!=(emptyset))=>?[X439:$i]:((in @ X439 @ X438))))=>(![X440:$i, X441:$i > $o, X442:$i]:(((in @ X442 @ X440)=>((X441 @ X442)=>((dsetconstr @ X440 @ X441)!=(emptyset)))))=>(![X443:$i]:((?[X444:$i]:((in @ X444 @ X443))=>((X443)!=(emptyset))))=>(![X445:$i, X446:$i]:((in @ X445 @ (setadjoin @ X445 @ X446)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X447:$i, X448:$i, X449:$i]:(((in @ X449 @ X448)=>(in @ X449 @ (setadjoin @ X447 @ X448))))=>(![X450:$i, X451:$i, X452:$i]:(((in @ X452 @ (setadjoin @ X450 @ X451))=>![X453:$o]:(((((X452)=(X450))=>(X453))=>(((in @ X452 @ X451)=>(X453))=>(X453))))))=>(![X454:$i, X455:$i, X456:$i]:(((in @ X456 @ (setadjoin @ X454 @ X455))=>(((X456)=(X454))|(in @ X456 @ X455))))=>(![X457:$i]:(((dsetconstr @ X457 @ (^[Z0:$i]:($true)))=(X457)))=>(![X458:$i, X459:$i]:((![X460:$i]:(((in @ X460 @ X459)=>(in @ X460 @ X458)))=>(in @ X459 @ (powerset @ X458))))=>(![X461:$i]:((in @ emptyset @ (powerset @ X461)))=>(![X462:$i]:((in @ emptyset @ (powerset @ X462)))=>(![X463:$i, X464:$i, X465:$i]:(((in @ X464 @ (powerset @ X463))=>((in @ X465 @ X464)=>(in @ X465 @ X463))))=>(![X466:$i, X467:$i, X468:$i]:(((in @ X467 @ X468)=>((in @ X468 @ X466)=>(in @ X467 @ (setunion @ X466)))))=>(![X469:$i, X470:$i]:(((in @ X470 @ (setunion @ X469))=>![X471:$o]:((![X472:$i]:(((in @ X470 @ X472)=>((in @ X472 @ X469)=>(X471))))=>(X471)))))=>(![X473:$i, X474:$i]:(((in @ X474 @ X473)=>(in @ X474 @ (powerset @ (setunion @ X473)))))=>(![X475:$i > $o]:((?[X476:$i]:(((X475 @ X476)&![X477:$i]:(((X475 @ X477)=>((X476)=(X477))))))=>?[X478:$i]:(![X479:$i]:(((X475 @ X479)<=>((X479)=(X478)))))))=>(![X480:$i]:((((X480)!=(emptyset))=>?[X481:$i]:(((in @ X481 @ X480)&$true))))=>(![X482:$i, X483:$i]:(((in @ X482 @ (setadjoin @ X483 @ emptyset))=>((X482)=(X483))))=>(![X484:$i, X485:$i]:((((X484)!=(X485))=>~(in @ X485 @ (setadjoin @ X484 @ emptyset))))=>(![X486:$i, X487:$i]:((((X486)=(X487))=>(in @ X486 @ (setadjoin @ X487 @ emptyset))))=>(![X488:$i, X489:$i]:(((in @ X488 @ (setadjoin @ X489 @ emptyset))=>(in @ X489 @ (setadjoin @ X488 @ emptyset))))=>(![X490:$i, X491:$i, X492:$i]:(((in @ X492 @ (setadjoin @ X490 @ (setadjoin @ X491 @ emptyset)))=>(((X492)=(X490))|((X492)=(X491)))))=>(![X493:$i, X494:$i]:((in @ X493 @ (setadjoin @ X493 @ (setadjoin @ X494 @ emptyset))))=>(![X495:$i, X496:$i]:((in @ X496 @ (setadjoin @ X495 @ (setadjoin @ X496 @ emptyset))))=>(![X497:$i, X498:$i > $o]:((?[X499:$i]:(((in @ X499 @ X497)&(X498 @ X499)))=>(((dsetconstr @ X497 @ X498)=(emptyset))=>~($true))))=>(![X500:$i > $o, X501:$i]:(((in @ X501 @ emptyset)=>(X500 @ X501)))=>(![X502:$i, X503:$i > $o]:((~(![X504:$i]:(((in @ X504 @ X502)=>(X503 @ X504))))=>?[X505:$i]:(((in @ X505 @ X502)&~((X503 @ X505))))))=>(![X506:$i, X507:$i > $o]:((![X508:$i]:(((in @ X508 @ X506)=>~((X507 @ X508))))=>~(?[X509:$i]:(((in @ X509 @ X506)&(X507 @ X509))))))=>(![X510:$i, X511:$i > $o]:((~(?[X512:$i]:(((in @ X512 @ X510)&(X511 @ X512))))=>![X513:$i]:(((in @ X513 @ X510)=>~((X511 @ X513))))))=>(![X514:$i, X515:$i > $o]:((?[X516:$i]:(((in @ X516 @ X514)&~((X515 @ X516))))=>~(![X517:$i]:(((in @ X517 @ X514)=>(X515 @ X517))))))=>(![X518:$o]:(((X518)=>(in @ emptyset @ (prop2set @ ((X518))))))=>(![X519:$o]:(((X519)=>(set2prop @ (prop2set @ ((X519))))))=>(![X520:$i, X521:$i > $o]:((~(?[X522:$i]:(((in @ X522 @ X520)&(X521 @ X522))))=>![X523:$i]:(((in @ X523 @ X520)=>~((X521 @ X523))))))=>(![X524:$i, X525:$i > $o]:((~(![X526:$i]:(((in @ X526 @ X524)=>(X525 @ X526))))=>?[X527:$i]:(((in @ X527 @ X524)&~((X525 @ X527))))))=>(![X528:$i > $o]:((?[X529:$i]:(((X528 @ X529)&![X530:$i]:(((X528 @ X530)=>((X529)=(X530))))))=>?[X531:$i]:(((X528 @ X531)&![X532:$i]:(((X528 @ X532)=>((X531)=(X532))))))))=>(![X533:$i > $o]:((?[X534:$i]:((X533 @ X534))=>(![X535:$i, X536:$i]:(((X533 @ X535)=>((X533 @ X536)=>((X535)=(X536)))))=>?[X537:$i]:(((X533 @ X537)&![X538:$i]:(((X533 @ X538)=>((X537)=(X538)))))))))=>(![X539:$i > $o]:((?[X540:$i]:(![X541:$i]:(((X539 @ X541)<=>((X541)=(X540)))))=>?[X542:$i]:(((X539 @ X542)&![X543:$i]:(((X539 @ X543)=>((X542)=(X543))))))))=>(![X544:$i, X545:$i]:((((X544)=(X545))=>![X546:$i, X547:$i]:((((X546)=(X547))=>((in @ X546 @ X544)=>(in @ X547 @ X545))))))=>(![X548:$i, X549:$i]:((((X548)=(X549))=>![X550:$i, X551:$i]:((((X550)=(X551))=>((in @ X550 @ X548)<=>(in @ X551 @ X549))))))=>(![X552:$i > $o]:((?[X553:$i]:(((X552 @ X553)&![X554:$i]:(((X552 @ X554)=>((X553)=(X554))))))=>![X555:$i, X556:$i]:(((X552 @ X555)=>((X552 @ X556)=>((X555)=(X556)))))))=>(![X557:$i > $o, X558:$i > $o]:((![X559:$i, X560:$i]:((((X559)=(X560))=>((X557 @ X559)<=>(X558 @ X560))))=>(?[X561:$i]:(((X557 @ X561)&![X562:$i]:(((X557 @ X562)=>((X561)=(X562))))))<=>?[X563:$i]:(((X558 @ X563)&![X564:$i]:(((X558 @ X564)=>((X563)=(X564)))))))))=>(((emptyset)=(emptyset))=>(![X565:$i, X566:$i]:((((X565)=(X566))=>![X567:$i, X568:$i]:((((X567)=(X568))=>((setadjoin @ X565 @ X567)=(setadjoin @ X566 @ X568))))))=>(![X569:$i, X570:$i]:((((X569)=(X570))=>((powerset @ X569)=(powerset @ X570))))=>(![X571:$i, X572:$i]:((((X571)=(X572))=>((setunion @ X571)=(setunion @ X572))))=>(((omega)=(omega))=>(![X573:$i > $o]:((?[X574:$i]:(((X573 @ X574)&![X575:$i]:(((X573 @ X575)=>((X574)=(X575))))))=>![X576:$i, X577:$i]:(((X573 @ X576)=>((X573 @ X577)=>((X576)=(X577)))))))=>(![X578:$i > $o, X579:$i > $o]:((![X580:$i, X581:$i]:((((X580)=(X581))=>((X578 @ X580)<=>(X579 @ X581))))=>(?[X582:$i]:(((X578 @ X582)&![X583:$i]:(((X578 @ X583)=>((X582)=(X583))))))=>(?[X584:$i]:(((X579 @ X584)&![X585:$i]:(((X579 @ X585)=>((X584)=(X585))))))=>((descr @ X578)=(descr @ X579))))))=>(![X586:$i, X587:$i]:((((X586)=(X587))=>![X588:$i > $o, X589:$i > $o]:((![X590:$i]:(((in @ X590 @ X586)=>![X591:$i]:(((in @ X591 @ X587)=>(((X590)=(X591))=>((X588 @ X590)<=>(X589 @ X591)))))))=>((dsetconstr @ X586 @ X588)=(dsetconstr @ X587 @ X589))))))=>(![X592:$i, X593:$i]:((![X594:$i]:(((in @ X594 @ X592)=>(in @ X594 @ X593)))=>(subset @ X592 @ X593)))=>(![X595:$i, X596:$i]:((((X595)=(X596))=>(subset @ X596 @ X595)))=>(![X597:$i, X598:$i]:((((X597)=(X598))=>(subset @ X597 @ X598)))=>(![X599:$i, X600:$i]:((![X601:$i]:(((in @ X601 @ X599)=>(in @ X601 @ X600)))=>(subset @ X599 @ X600)))=>(![X602:$i]:((subset @ emptyset @ X602))=>(![X603:$i, X604:$i, X605:$i]:(((subset @ X603 @ X604)=>((in @ X605 @ X603)=>(in @ X605 @ X604))))=>(![X606:$i, X607:$i, X608:$i]:(((subset @ X606 @ X607)=>(~(in @ X608 @ X607)=>~(in @ X608 @ X606))))=>(![X609:$i, X610:$i, X611:$i]:(((in @ X611 @ X609)=>(~(in @ X611 @ X610)=>~(subset @ X609 @ X610))))=>(![X612:$i, X613:$i]:((~(subset @ X612 @ X613)=>((X612)!=(X613))))=>(![X614:$i, X615:$i, X616:$i]:(((in @ X616 @ X614)=>(~(in @ X616 @ X615)=>((X614)!=(X615)))))=>(![X617:$i]:((subset @ X617 @ X617))=>(![X618:$i, X619:$i, X620:$i]:(((subset @ X618 @ X619)=>((subset @ X619 @ X620)=>(subset @ X618 @ X620))))=>(![X621:$i, X622:$i]:((subset @ X622 @ (setadjoin @ X621 @ X622)))=>(![X623:$i, X624:$i, X625:$i]:(((subset @ X623 @ X625)=>(subset @ X623 @ (setadjoin @ X624 @ X625))))=>(![X626:$i, X627:$i]:(((subset @ X626 @ X627)=>(in @ X626 @ (powerset @ X627))))=>(![X628:$i, X629:$i]:(((subset @ X628 @ X629)=>((subset @ X629 @ X628)=>((X628)=(X629)))))=>(![X630:$i]:(((subset @ X630 @ emptyset)=>((X630)=(emptyset))))=>(![X631:$i, X632:$i]:(((subset @ X632 @ X631)=>(in @ X632 @ (powerset @ X631))))=>(![X633:$i, X634:$i]:(((in @ X634 @ (powerset @ X633))=>(subset @ X634 @ X633)))=>(![X635:$i]:((in @ X635 @ (powerset @ X635)))=>(![X636:$i, X637:$i]:(((subset @ X636 @ X637)=>(subset @ (powerset @ X636) @ (powerset @ X637))))=>(![X638:$i, X639:$i > $o]:((in @ (dsetconstr @ X638 @ X639) @ (powerset @ X638)))=>(![X640:$i, X641:$i > $o]:((subset @ (dsetconstr @ X640 @ X641) @ X640))=>(![X642:$i, X643:$i, X644:$i]:(((in @ X644 @ X642)=>(in @ X644 @ (binunion @ X642 @ X643))))=>(![X645:$i, X646:$i]:((in @ X646 @ (setadjoin @ X645 @ (setadjoin @ X646 @ emptyset))))=>(![X647:$i, X648:$i, X649:$i]:(((in @ X649 @ X648)=>(in @ X649 @ (binunion @ X647 @ X648))))=>(![X650:$i, X651:$i, X652:$i, X653:$o]:(((in @ X652 @ (binunion @ X650 @ X651))=>(((in @ X652 @ X650)=>(X653))=>(((in @ X652 @ X651)=>(X653))=>(X653)))))=>(![X654:$i, X655:$i, X656:$i]:(((in @ X656 @ (binunion @ X654 @ X655))=>((in @ X656 @ X654)|(in @ X656 @ X655))))=>(![X657:$i, X658:$i]:((subset @ X657 @ (binunion @ X657 @ X658)))=>(![X659:$i, X660:$i]:((subset @ X660 @ (binunion @ X659 @ X660)))=>(![X661:$i, X662:$i, X663:$i]:(((in @ X663 @ X661)=>((in @ X663 @ X662)=>(in @ X663 @ (binintersect @ X661 @ X662)))))=>(![X664:$i, X665:$i, X666:$i]:(((subset @ X666 @ X664)=>((subset @ X666 @ X665)=>(subset @ X666 @ (binintersect @ X664 @ X665)))))=>(![X667:$i, X668:$i, X669:$i]:(((in @ X669 @ (binintersect @ X667 @ X668))=>(in @ X669 @ X667)))=>(![X670:$i, X671:$i]:((subset @ (binintersect @ X670 @ X671) @ X670))=>(![X672:$i, X673:$i]:(((subset @ X672 @ X673)=>((binintersect @ X672 @ X673)=(X672))))=>(![X674:$i, X675:$i]:((((binintersect @ X674 @ X675)=(X675))=>(subset @ X675 @ X674)))=>(![X676:$i, X677:$i, X678:$i]:(((in @ X678 @ (binintersect @ X676 @ X677))=>(in @ X678 @ X677)))=>(![X679:$i, X680:$i]:((~(?[X681:$i]:(((in @ X681 @ X679)&(in @ X681 @ X680))))=>((binintersect @ X679 @ X680)=(emptyset))))=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ 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)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(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_131, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_132]), foundationAx]), wellorderingAx]), c_0_133]), c_0_134]), c_0_135]), c_0_136]), c_0_137]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_138]), setext]), emptyI]), noeltsimpempty]), c_0_139]), c_0_140]), c_0_141]), c_0_142]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_143]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_144]), c_0_145]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_146]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_147]), c_0_148]), c_0_149]), inCongP]), in__Cong]), c_0_150]), c_0_151]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_152]), c_0_153]), c_0_154]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_155]), c_0_156]), binunionIL]), upairset2IR]), binunionIR]), binunionEcases]), binunionE]), binunionLsub]), binunionRsub]), binintersectI]), binintersectSubset5]), binintersectEL]), binintersectLsub]), binintersectSubset2]), binintersectSubset3]), binintersectER]), disjointsetsI1])])]), c_0_157])).
% 3.87/0.85 thf(c_0_159, negated_conjecture, ![X682:$i, X683:$i, X685:$i, X686:$i, X687:$i, X688:$i, X689:$i, X690:$i, X691:$i, X692:$i, X693:$i, X695:$i, X696:$i, X698:$i, X699:$i, X700:$i, X701:$i, X702:$i, X704:$i, X705:$i > $i > $o, X706:$i, X708:$i, X711:$i, X713:$i, X714:$i, X715:$i, X716:$i, X718:$i, X719:$i > $o, X720:$i, X722:$i, X723:$i > $o, X724:$i, X725:$i, X726:$i > $o, X727:$i, X728:$i, X729:$i > $o, X730:$i, X731:$i > $o, X732:$i, X735:$i, X736:$o, X737:$i, X738:$i, X739:$o, X740:$i, X741:$i, X742:$i > $o, X743:$i, X746:$i, X747:$i, X750:$i, X752:$i, X754:$i, X755:$i > $o, X756:$i, X757:$i, X759:$i, X760:$i > $o, X761:$i, X762:$i, X763:$i, X764:$i, X765:$i, X766:$i, X767:$i, X768:$i, X769:$i, X770:$i, X771:$i, X772:$o, X773:$i, X774:$i, X775:$i, X776:$i, X777:$i, X778:$i, X780:$i, X781:$i, X782:$i, X783:$i, X784:$i, X785:$i, X786:$i, X787:$i, X788:$i, X789:$i, X790:$o, X792:$i, X793:$i, X794:$i > $o, X795:$i, X798:$i, X799:$i, X800:$i, X802:$i, X803:$i, X804:$i, X805:$i, X806:$i, X807:$i, X808:$i, X809:$i, X810:$i, X811:$i, X812:$i, X813:$i, X814:$i, X815:$i, X816:$i, X817:$i, X818:$i > $o, X819:$i, X820:$i > $o, X821:$i, X822:$i, X823:$i > $o, X824:$i, X826:$i, X827:$i > $o, X829:$i, X830:$i, X831:$i > $o, X833:$i, X834:$i, X835:$i > $o, X836:$i, X838:$o, X839:$o, X840:$i, X841:$i > $o, X843:$i, X844:$i, X845:$i > $o, X846:$i, X848:$i > $o, X849:$i, X852:$i, X853:$i > $o, X854:$i, X858:$i, X859:$i > $o, X860:$i, X863:$i, X864:$i, X865:$i, X866:$i, X867:$i, X868:$i, X869:$i, X870:$i, X871:$i, X872:$i > $o, X873:$i, X875:$i, X876:$i, X877:$i > $o, X878:$i > $o, X881:$i, X884:$i, X885:$i, X888:$i, X889:$i, X890:$i, X891:$i, X892:$i, X893:$i, X894:$i, X895:$i, X896:$i, X897:$i > $o, X898:$i, X900:$i, X901:$i, X902:$i > $o, X903:$i > $o, X906:$i, X908:$i, X910:$i, X911:$i, X912:$i > $o, X913:$i > $o, X916:$i, X917:$i, X919:$i, X920:$i, X921:$i, X922:$i, X923:$i, X924:$i, X926:$i, X927:$i, X928:$i, X929:$i, X930:$i, X931:$i, X932:$i, X933:$i, X934:$i, X935:$i, X936:$i, X937:$i, X938:$i, X939:$i, X940:$i, X941:$i, X942:$i, X943:$i, X944:$i, X945:$i, X946:$i, X947:$i, X948:$i, X949:$i, X950:$i, X951:$i, X952:$i, X953:$i, X954:$i, X955:$i, X956:$i, X957:$i, X958:$i, X959:$i, X960:$i, X961:$i, X962:$i, X963:$i > $o, X964:$i, X965:$i > $o, X966:$i, X967:$i, X968:$i, X969:$i, X970:$i, X971:$i, X972:$i, X973:$i, X974:$i, X975:$i, X976:$i, X977:$o, X978:$i, X979:$i, X980:$i, X981:$i, X982:$i, X983:$i, X984:$i, X985:$i, X986:$i, X987:$i, X988:$i, X989:$i, X990:$i, X991:$i, X992:$i, X993:$i, X994:$i, X995:$i, X996:$i, X997:$i, X998:$i, X999:$i, X1000:$i, X1001:$i, X1002:$i, X1003:$i, X1004:$i]:((((~(in @ (esk1_2 @ X682 @ X683) @ X682)|~(in @ (esk1_2 @ X682 @ X683) @ X683)|((X682)=(X683)))&((in @ (esk1_2 @ X682 @ X683) @ X682)|(in @ (esk1_2 @ X682 @ X683) @ X683)|((X682)=(X683))))&(~(in @ X685 @ emptyset)&(((~(in @ X688 @ (setadjoin @ X686 @ X687))|(((X688)=(X686))|(in @ X688 @ X687)))&((((X688)!=(X686))|(in @ X688 @ (setadjoin @ X686 @ X687)))&(~(in @ X688 @ X687)|(in @ X688 @ (setadjoin @ X686 @ X687)))))&(((~(in @ X690 @ (powerset @ X689))|(~(in @ X691 @ X690)|(in @ X691 @ X689)))&(((in @ (esk2_2 @ X692 @ X693) @ X693)|(in @ X693 @ (powerset @ X692)))&(~(in @ (esk2_2 @ X692 @ X693) @ X692)|(in @ X693 @ (powerset @ X692)))))&(((((in @ X696 @ (esk3_2 @ X695 @ X696))|~(in @ X696 @ (setunion @ X695)))&((in @ (esk3_2 @ X695 @ X696) @ X695)|~(in @ X696 @ (setunion @ X695))))&(~(in @ X699 @ X700)|~(in @ X700 @ X698)|(in @ X699 @ (setunion @ X698))))&((in @ emptyset @ omega)&((~(in @ X701 @ omega)|(in @ (setadjoin @ X701 @ X701) @ omega))&(((((in @ (esk4_1 @ X702) @ omega)|~(in @ emptyset @ X702)|(~(in @ X704 @ omega)|(in @ X704 @ X702)))&((in @ (esk4_1 @ X702) @ X702)|~(in @ emptyset @ X702)|(~(in @ X704 @ omega)|(in @ X704 @ X702))))&(~(in @ (setadjoin @ (esk4_1 @ X702) @ (esk4_1 @ X702)) @ X702)|~(in @ emptyset @ X702)|(~(in @ X704 @ omega)|(in @ X704 @ X702))))&((((((in @ (esk8_3 @ X705 @ X706 @ X711) @ X706)|~(in @ X711 @ (esk7_2 @ X705 @ X706))|(in @ (esk5_2 @ X705 @ X706) @ X706))&((X705 @ (esk8_3 @ X705 @ X706 @ X711) @ X711)|~(in @ X711 @ (esk7_2 @ X705 @ X706))|(in @ (esk5_2 @ X705 @ X706) @ X706)))&(~(in @ X714 @ X706)|~(X705 @ X714 @ X713)|(in @ X713 @ (esk7_2 @ X705 @ X706))|(in @ (esk5_2 @ X705 @ X706) @ X706)))&(((((in @ (esk8_3 @ X705 @ X706 @ X711) @ X706)|~(in @ X711 @ (esk7_2 @ X705 @ X706))|((X705 @ (esk5_2 @ X705 @ X706) @ (esk6_3 @ X705 @ X706 @ X708))|~(X705 @ (esk5_2 @ X705 @ X706) @ X708)))&((X705 @ (esk8_3 @ X705 @ X706 @ X711) @ X711)|~(in @ X711 @ (esk7_2 @ X705 @ X706))|((X705 @ (esk5_2 @ X705 @ X706) @ (esk6_3 @ X705 @ X706 @ X708))|~(X705 @ (esk5_2 @ X705 @ X706) @ X708))))&(~(in @ X714 @ X706)|~(X705 @ X714 @ X713)|(in @ X713 @ (esk7_2 @ X705 @ X706))|((X705 @ (esk5_2 @ X705 @ X706) @ (esk6_3 @ X705 @ X706 @ X708))|~(X705 @ (esk5_2 @ X705 @ X706) @ X708))))&((((in @ (esk8_3 @ X705 @ X706 @ X711) @ X706)|~(in @ X711 @ (esk7_2 @ X705 @ X706))|(((X708)!=(esk6_3 @ X705 @ 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(esk48_3 @ X902 @ X903 @ X906))|~(X902 @ X906))|((esk46_2 @ X902 @ X903)=(esk47_2 @ X902 @ X903)))&(((X908)!=(esk49_3 @ X902 @ X903 @ X908))|~(X903 @ X908)|((descr @ X902)=(descr @ X903))|((X902 @ (esk48_3 @ X902 @ X903 @ X906))|~(X902 @ X906))|((esk46_2 @ X902 @ X903)=(esk47_2 @ X902 @ X903))))&(((X903 @ (esk49_3 @ X902 @ X903 @ X908))|~(X903 @ X908)|((descr @ X902)=(descr @ X903))|(((X906)!=(esk48_3 @ X902 @ X903 @ X906))|~(X902 @ X906))|((esk46_2 @ X902 @ X903)=(esk47_2 @ X902 @ X903)))&(((X908)!=(esk49_3 @ X902 @ X903 @ X908))|~(X903 @ X908)|((descr @ X902)=(descr @ X903))|(((X906)!=(esk48_3 @ X902 @ X903 @ X906))|~(X902 @ X906))|((esk46_2 @ X902 @ X903)=(esk47_2 @ X902 @ X903)))))&(((((X903 @ (esk49_3 @ X902 @ X903 @ X908))|~(X903 @ X908)|((descr @ X902)=(descr @ X903))|((X902 @ (esk48_3 @ X902 @ X903 @ X906))|~(X902 @ X906))|(~(X902 @ (esk46_2 @ X902 @ X903))|~(X903 @ (esk47_2 @ X902 @ X903))))&(((X908)!=(esk49_3 @ X902 @ X903 @ X908))|~(X903 @ X908)|((descr @ X902)=(descr @ X903))|((X902 @ (esk48_3 @ X902 @ X903 @ X906))|~(X902 @ X906))|(~(X902 @ (esk46_2 @ X902 @ X903))|~(X903 @ (esk47_2 @ X902 @ X903)))))&(((X903 @ (esk49_3 @ X902 @ X903 @ X908))|~(X903 @ X908)|((descr @ X902)=(descr @ X903))|(((X906)!=(esk48_3 @ X902 @ X903 @ X906))|~(X902 @ X906))|(~(X902 @ (esk46_2 @ X902 @ X903))|~(X903 @ (esk47_2 @ X902 @ X903))))&(((X908)!=(esk49_3 @ X902 @ X903 @ X908))|~(X903 @ X908)|((descr @ X902)=(descr @ X903))|(((X906)!=(esk48_3 @ X902 @ X903 @ X906))|~(X902 @ X906))|(~(X902 @ (esk46_2 @ X902 @ X903))|~(X903 @ (esk47_2 @ X902 @ X903))))))&((((X903 @ (esk49_3 @ X902 @ X903 @ X908))|~(X903 @ X908)|((descr @ X902)=(descr @ X903))|((X902 @ (esk48_3 @ X902 @ X903 @ X906))|~(X902 @ X906))|((X902 @ (esk46_2 @ X902 @ X903))|(X903 @ (esk47_2 @ X902 @ X903))))&(((X908)!=(esk49_3 @ X902 @ X903 @ X908))|~(X903 @ X908)|((descr @ X902)=(descr @ X903))|((X902 @ (esk48_3 @ X902 @ X903 @ X906))|~(X902 @ X906))|((X902 @ (esk46_2 @ X902 @ X903))|(X903 @ (esk47_2 @ X902 @ X903)))))&(((X903 @ (esk49_3 @ X902 @ X903 @ X908))|~(X903 @ X908)|((descr @ X902)=(descr @ X903))|(((X906)!=(esk48_3 @ X902 @ X903 @ X906))|~(X902 @ X906))|((X902 @ (esk46_2 @ X902 @ X903))|(X903 @ (esk47_2 @ X902 @ X903))))&(((X908)!=(esk49_3 @ X902 @ X903 @ X908))|~(X903 @ X908)|((descr @ X902)=(descr @ X903))|(((X906)!=(esk48_3 @ X902 @ X903 @ X906))|~(X902 @ X906))|((X902 @ (esk46_2 @ X902 @ X903))|(X903 @ (esk47_2 @ X902 @ X903))))))))&((((in @ (esk50_4 @ X910 @ X911 @ X912 @ X913) @ X910)|((dsetconstr @ X910 @ X912)=(dsetconstr @ X911 @ X913))|((X910)!=(X911)))&(((in @ (esk51_4 @ X910 @ X911 @ X912 @ X913) @ X911)|((dsetconstr @ X910 @ X912)=(dsetconstr @ X911 @ X913))|((X910)!=(X911)))&((((esk50_4 @ X910 @ X911 @ X912 @ X913)=(esk51_4 @ X910 @ X911 @ X912 @ X913))|((dsetconstr @ X910 @ X912)=(dsetconstr @ X911 @ X913))|((X910)!=(X911)))&((~(X912 @ (esk50_4 @ X910 @ X911 @ X912 @ X913))|~(X913 @ (esk51_4 @ X910 @ X911 @ X912 @ X913))|((dsetconstr @ X910 @ X912)=(dsetconstr @ X911 @ X913))|((X910)!=(X911)))&((X912 @ (esk50_4 @ X910 @ X911 @ X912 @ X913))|(X913 @ (esk51_4 @ X910 @ X911 @ X912 @ X913))|((dsetconstr @ X910 @ X912)=(dsetconstr @ X911 @ X913))|((X910)!=(X911)))))))&((((in @ (esk52_2 @ X916 @ X917) @ X916)|(subset @ X916 @ X917))&(~(in @ (esk52_2 @ X916 @ X917) @ X917)|(subset @ X916 @ X917)))&((((X919)!=(X920))|(subset @ X920 @ X919))&((((X921)!=(X922))|(subset @ X921 @ X922))&((((in @ (esk53_2 @ X923 @ X924) @ X923)|(subset @ X923 @ X924))&(~(in @ (esk53_2 @ X923 @ X924) @ X924)|(subset @ X923 @ X924)))&((subset @ emptyset @ X926)&((~(subset @ X927 @ X928)|(~(in @ X929 @ X927)|(in @ X929 @ X928)))&((~(subset @ X930 @ X931)|((in @ X932 @ X931)|~(in @ X932 @ X930)))&((~(in @ X935 @ X933)|((in @ X935 @ X934)|~(subset @ X933 @ X934)))&(((subset @ X936 @ X937)|((X936)!=(X937)))&((~(in @ X940 @ X938)|((in @ X940 @ X939)|((X938)!=(X939))))&((subset @ X941 @ X941)&((~(subset @ X942 @ X943)|(~(subset @ X943 @ X944)|(subset @ X942 @ X944)))&((subset @ X946 @ (setadjoin @ X945 @ X946))&((~(subset @ X947 @ X949)|(subset @ X947 @ (setadjoin @ X948 @ X949)))&((~(subset @ X950 @ X951)|(in @ X950 @ (powerset @ X951)))&((~(subset @ X952 @ X953)|(~(subset @ X953 @ X952)|((X952)=(X953))))&((~(subset @ X954 @ emptyset)|((X954)=(emptyset)))&((~(subset @ X956 @ X955)|(in @ X956 @ (powerset @ X955)))&((~(in @ X958 @ (powerset @ X957))|(subset @ X958 @ X957))&((in @ X959 @ (powerset @ X959))&((~(subset @ X960 @ X961)|(subset @ (powerset @ X960) @ (powerset @ X961)))&((in @ (dsetconstr @ X962 @ X963) @ (powerset @ X962))&((subset @ (dsetconstr @ X964 @ X965) @ X964)&((~(in @ X968 @ X966)|(in @ X968 @ (binunion @ X966 @ X967)))&((in @ X970 @ (setadjoin @ X969 @ (setadjoin @ X970 @ emptyset)))&((~(in @ X973 @ X972)|(in @ X973 @ (binunion @ X971 @ X972)))&(((((in @ X976 @ X975)|(X977)|(in @ X976 @ X974)|~(in @ X976 @ (binunion @ X974 @ X975)))&(~(X977)|(X977)|(in @ X976 @ X974)|~(in @ X976 @ (binunion @ X974 @ X975))))&(((in @ X976 @ X975)|(X977)|~(X977)|~(in @ X976 @ (binunion @ X974 @ X975)))&(~(X977)|(X977)|~(X977)|~(in @ X976 @ (binunion @ X974 @ X975)))))&((~(in @ X980 @ (binunion @ X978 @ X979))|((in @ X980 @ X978)|(in @ X980 @ X979)))&((subset @ X981 @ (binunion @ X981 @ X982))&((subset @ X984 @ (binunion @ X983 @ X984))&((~(in @ X987 @ X985)|(~(in @ X987 @ X986)|(in @ X987 @ (binintersect @ X985 @ X986))))&((~(subset @ X990 @ X988)|(~(subset @ X990 @ X989)|(subset @ X990 @ (binintersect @ X988 @ X989))))&((~(in @ X993 @ (binintersect @ X991 @ X992))|(in @ X993 @ X991))&((subset @ (binintersect @ X994 @ X995) @ X994)&((~(subset @ X996 @ X997)|((binintersect @ X996 @ X997)=(X996)))&((((binintersect @ X998 @ X999)!=(X999))|(subset @ X999 @ X998))&((~(in @ X1002 @ (binintersect @ X1000 @ X1001))|(in @ X1002 @ X1001))&((((in @ (esk54_2 @ X1003 @ X1004) @ X1003)|((binintersect @ X1003 @ X1004)=(emptyset)))&((in @ (esk54_2 @ X1003 @ X1004) @ X1004)|((binintersect @ X1003 @ X1004)=(emptyset))))&~(subset @ (binintersect @ esk55_0 @ esk56_0) @ esk56_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_158])])])])])])])).
% 3.87/0.85 thf(c_0_160, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ X2 @ X4)|~((in @ X2 @ (binintersect @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_159])).
% 3.87/0.85 thf(c_0_161, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (esk53_2 @ X2 @ X3) @ X2)|(subset @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_159])).
% 3.87/0.85 thf(c_0_162, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ X3)|~((in @ (esk53_2 @ X2 @ X3) @ X3)))), inference(split_conjunct,[status(thm)],[c_0_159])).
% 3.87/0.85 thf(c_0_163, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ (esk53_2 @ (binintersect @ X2 @ X3) @ X4) @ X3)|(subset @ (binintersect @ X2 @ X3) @ X4))), inference(spm,[status(thm)],[c_0_160, c_0_161])).
% 3.87/0.85 thf(c_0_164, negated_conjecture, ~((subset @ (binintersect @ esk55_0 @ esk56_0) @ esk56_0)), inference(split_conjunct,[status(thm)],[c_0_159])).
% 3.87/0.85 thf(c_0_165, negated_conjecture, ![X2:$i, X3:$i]:((subset @ (binintersect @ X2 @ X3) @ X3)), inference(spm,[status(thm)],[c_0_162, c_0_163])).
% 3.87/0.85 thf(c_0_166, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_164, c_0_165])]), ['proof']).
% 3.87/0.85 % SZS output end CNFRefutation
% 3.87/0.85 % Parsed axioms : 246
% 3.87/0.85 % Removed by relevancy pruning/SinE : 0
% 3.87/0.85 % Initial clauses : 358
% 3.87/0.85 % Removed in clause preprocessing : 147
% 3.87/0.85 % Initial clauses in saturation : 211
% 3.87/0.85 % Processed clauses : 2366
% 3.87/0.85 % ...of these trivial : 15
% 3.87/0.85 % ...subsumed : 1631
% 3.87/0.85 % ...remaining for further processing : 720
% 3.87/0.85 % Other redundant clauses eliminated : 22
% 3.87/0.85 % Clauses deleted for lack of memory : 0
% 3.87/0.85 % Backward-subsumed : 10
% 3.87/0.85 % Backward-rewritten : 7
% 3.87/0.85 % Generated clauses : 33374
% 3.87/0.85 % ...of the previous two non-redundant : 30947
% 3.87/0.85 % ...aggressively subsumed : 0
% 3.87/0.85 % Contextual simplify-reflections : 1
% 3.87/0.85 % Paramodulations : 33350
% 3.87/0.85 % Factorizations : 2
% 3.87/0.85 % NegExts : 0
% 3.87/0.85 % Equation resolutions : 22
% 3.87/0.85 % Disequality decompositions : 0
% 3.87/0.85 % Total rewrite steps : 4061
% 3.87/0.85 % ...of those cached : 3825
% 3.87/0.85 % Propositional unsat checks : 0
% 3.87/0.85 % Propositional check models : 0
% 3.87/0.85 % Propositional check unsatisfiable : 0
% 3.87/0.85 % Propositional clauses : 0
% 3.87/0.85 % Propositional clauses after purity: 0
% 3.87/0.85 % Propositional unsat core size : 0
% 3.87/0.85 % Propositional preprocessing time : 0.000
% 3.87/0.85 % Propositional encoding time : 0.000
% 3.87/0.85 % Propositional solver time : 0.000
% 3.87/0.85 % Success case prop preproc time : 0.000
% 3.87/0.85 % Success case prop encoding time : 0.000
% 3.87/0.85 % Success case prop solver time : 0.000
% 3.87/0.85 % Current number of processed clauses : 690
% 3.87/0.85 % Positive orientable unit clauses : 109
% 3.87/0.85 % Positive unorientable unit clauses: 0
% 3.87/0.85 % Negative unit clauses : 3
% 3.87/0.85 % Non-unit-clauses : 578
% 3.87/0.85 % Current number of unprocessed clauses: 28688
% 3.87/0.85 % ...number of literals in the above : 92706
% 3.87/0.85 % Current number of archived formulas : 0
% 3.87/0.85 % Current number of archived clauses : 17
% 3.87/0.85 % Clause-clause subsumption calls (NU) : 36860
% 3.87/0.85 % Rec. Clause-clause subsumption calls : 28104
% 3.87/0.85 % Non-unit clause-clause subsumptions : 1415
% 3.87/0.85 % Unit Clause-clause subsumption calls : 649
% 3.87/0.85 % Rewrite failures with RHS unbound : 0
% 3.87/0.85 % BW rewrite match attempts : 176
% 3.87/0.85 % BW rewrite match successes : 5
% 3.87/0.85 % Condensation attempts : 0
% 3.87/0.85 % Condensation successes : 0
% 3.87/0.85 % Termbank termtop insertions : 613919
% 3.87/0.85 % Search garbage collected termcells : 11559
% 3.87/0.85
% 3.87/0.85 % -------------------------------------------------
% 3.87/0.85 % User time : 0.496 s
% 3.87/0.85 % System time : 0.028 s
% 3.87/0.85 % Total time : 0.524 s
% 3.87/0.85 % Maximum resident set size: 6688 pages
% 3.87/0.85
% 3.87/0.85 % -------------------------------------------------
% 3.87/0.85 % User time : 0.576 s
% 3.87/0.85 % System time : 0.068 s
% 3.87/0.85 % Total time : 0.644 s
% 3.87/0.85 % Maximum resident set size: 5120 pages
% 3.87/0.85 % E exiting
%------------------------------------------------------------------------------