%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU564^1 : 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 : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:26:43 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU564^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.18 % Computer : n008.cluster.edu
% 0.12/0.18 % Model : x86_64 x86_64
% 0.12/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.18 % Memory : 8046.5625MB
% 0.12/0.18 % OS : Linux 6.8.0-71-generic
% 0.12/0.18 % CPULimit : 300
% 0.12/0.18 % WCLimit : 300
% 0.12/0.18 % DateTime : Tue Sep 29 13:51:09 UTC 2026
% 0.12/0.18 % CPUTime :
% 0.12/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.22 Running higher-order theorem proving
% 0.12/0.24 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.gCEA14jRBo/E---3.1_3187040.p
% 0.22/0.29 % Version: 3.5.1-ho
% 0.22/0.29 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.22/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.29 % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.29 % Starting sh5l with 300s (1) cores
% 0.22/0.29 % Starting new_bool_1 with 300s (1) cores
% 0.22/0.29 % Starting new_bool_2 with 300s (1) cores
% 0.22/0.29 % sh5l with pid 3187054 completed with status 0
% 0.22/0.29 % Result found by sh5l
% 0.22/0.29 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.22/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.29 % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.29 % Starting sh5l with 300s (1) cores
% 0.22/0.29 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.22/0.29 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.22/0.29 % Search class: HGHSM-FSLM31-SHFMMMBN
% 0.22/0.29 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.29 % Starting SubtermCWHack with 31s (1) cores
% 0.22/0.29 % SubtermCWHack with pid 3187058 completed with status 0
% 0.22/0.29 % Result found by SubtermCWHack
% 0.22/0.29 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.22/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.29 % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.29 % Starting sh5l with 300s (1) cores
% 0.22/0.29 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.22/0.29 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.22/0.29 % Search class: HGHSM-FSLM31-SHFMMMBN
% 0.22/0.29 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.29 % Starting SubtermCWHack with 31s (1) cores
% 0.22/0.29 % Preprocessing time : 0.003 s
% 0.22/0.29
% 0.22/0.29 % Proof found!
% 0.22/0.29 % SZS status Theorem
% 0.22/0.29 % SZS output start CNFRefutation
% 0.22/0.29 thf(decl_23, type, in: $i > $i > $o).
% 0.22/0.29 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.22/0.29 thf(decl_25, type, setextAx: $o).
% 0.22/0.29 thf(decl_26, type, emptyset: $i).
% 0.22/0.29 thf(decl_27, type, emptysetAx: $o).
% 0.22/0.29 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.22/0.29 thf(decl_29, type, setadjoinAx: $o).
% 0.22/0.29 thf(decl_30, type, powerset: $i > $i).
% 0.22/0.29 thf(decl_31, type, powersetAx: $o).
% 0.22/0.29 thf(decl_32, type, setunion: $i > $i).
% 0.22/0.29 thf(decl_33, type, setunionAx: $o).
% 0.22/0.29 thf(decl_34, type, omega: $i).
% 0.22/0.29 thf(decl_35, type, omega0Ax: $o).
% 0.22/0.29 thf(decl_36, type, omegaSAx: $o).
% 0.22/0.29 thf(decl_37, type, omegaIndAx: $o).
% 0.22/0.29 thf(decl_38, type, replAx: $o).
% 0.22/0.29 thf(decl_39, type, foundationAx: $o).
% 0.22/0.29 thf(decl_40, type, wellorderingAx: $o).
% 0.22/0.29 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.22/0.29 thf(decl_42, type, descrp: $o).
% 0.22/0.29 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.22/0.29 thf(decl_44, type, dsetconstrI: $o).
% 0.22/0.29 thf(decl_45, type, dsetconstrEL: $o).
% 0.22/0.29 thf(decl_46, type, dsetconstrER: $o).
% 0.22/0.29 thf(decl_47, type, exuE1: $o).
% 0.22/0.29 thf(decl_48, type, prop2set: $o > $i).
% 0.22/0.29 thf(decl_49, type, prop2setE: $o).
% 0.22/0.29 thf(decl_50, type, emptysetE: $o).
% 0.22/0.29 thf(decl_51, type, emptysetimpfalse: $o).
% 0.22/0.29 thf(decl_52, type, notinemptyset: $o).
% 0.22/0.29 thf(decl_53, type, exuE3e: $o).
% 0.22/0.29 thf(decl_54, type, setext: $o).
% 0.22/0.29 thf(decl_55, type, emptyI: $o).
% 0.22/0.29 thf(decl_56, type, noeltsimpempty: $o).
% 0.22/0.29 thf(decl_57, type, setbeta: $o).
% 0.22/0.29 thf(decl_58, type, nonempty: $i > $o).
% 0.22/0.29 thf(decl_59, type, nonemptyE1: $o).
% 0.22/0.29 thf(decl_60, type, nonemptyI: $o).
% 0.22/0.29 thf(decl_61, type, nonemptyI1: $o).
% 0.22/0.29 thf(decl_62, type, setadjoinIL: $o).
% 0.22/0.29 thf(decl_63, type, emptyinunitempty: $o).
% 0.22/0.29 thf(decl_64, type, setadjoinIR: $o).
% 0.22/0.29 thf(decl_65, type, setadjoinE: $o).
% 0.22/0.29 thf(decl_66, type, setadjoinOr: $o).
% 0.22/0.29 thf(decl_67, type, setoftrueEq: $o).
% 0.22/0.29 thf(decl_68, type, powersetI: $o).
% 0.22/0.29 thf(decl_69, type, emptyinPowerset: $o).
% 0.22/0.29 thf(decl_70, type, emptyInPowerset: $o).
% 0.22/0.29 thf(decl_71, type, powersetE: $o).
% 0.22/0.29 thf(decl_72, type, setunionI: $o).
% 0.22/0.29 thf(decl_73, type, setunionE: $o).
% 0.22/0.29 thf(decl_74, type, subPowSU: $o).
% 0.22/0.29 thf(decl_75, type, exuE2: $o).
% 0.22/0.29 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.22/0.29 thf(decl_77, type, uniqinunit: $o).
% 0.22/0.29 thf(decl_78, type, notinsingleton: $o).
% 0.22/0.29 thf(decl_79, type, eqinunit: $o).
% 0.22/0.29 thf(decl_80, type, singletonsswitch: $o).
% 0.22/0.29 thf(decl_81, type, upairsetE: $o).
% 0.22/0.29 thf(decl_82, type, upairsetIL: $o).
% 0.22/0.29 thf(decl_83, type, upairsetIR: $o).
% 0.22/0.29 thf(decl_84, type, emptyE1: $o).
% 0.22/0.29 thf(decl_85, type, vacuousDall: $o).
% 0.22/0.29 thf(decl_86, type, quantDeMorgan1: $o).
% 0.22/0.29 thf(decl_87, type, quantDeMorgan2: $o).
% 0.22/0.29 thf(decl_88, type, quantDeMorgan3: $o).
% 0.22/0.29 thf(decl_89, type, quantDeMorgan4: $o).
% 0.22/0.29 thf(decl_90, type, prop2setI: $o).
% 0.22/0.29 thf(decl_91, type, set2prop: $i > $o).
% 0.22/0.29 thf(decl_92, type, prop2set2propI: $o).
% 0.22/0.29 thf(decl_93, type, notdexE: $o).
% 0.22/0.29 thf(decl_94, type, notdallE: $o).
% 0.22/0.29 thf(decl_95, type, exuI1: $o).
% 0.22/0.29 thf(decl_96, type, exuI3: $o).
% 0.22/0.29 thf(decl_97, type, exuI2: $o).
% 0.22/0.29 thf(decl_98, type, inCongP: $o).
% 0.22/0.29 thf(decl_99, type, in__Cong: $o).
% 0.22/0.29 thf(decl_100, type, exuE3u: $o).
% 0.22/0.29 thf(decl_101, type, exu__Cong: $o).
% 0.22/0.29 thf(decl_102, type, emptyset__Cong: $o).
% 0.22/0.29 thf(decl_103, type, setadjoin__Cong: $o).
% 0.22/0.29 thf(decl_104, type, powerset__Cong: $o).
% 0.22/0.29 thf(decl_105, type, setunion__Cong: $o).
% 0.22/0.29 thf(decl_106, type, omega__Cong: $o).
% 0.22/0.29 thf(decl_107, type, exuEu: $o).
% 0.22/0.29 thf(decl_108, type, descr__Cong: $o).
% 0.22/0.29 thf(decl_109, type, dsetconstr__Cong: $o).
% 0.22/0.29 thf(decl_110, type, subset: $i > $i > $o).
% 0.22/0.29 thf(decl_113, type, subsetI1: $o).
% 0.22/0.29 thf(decl_114, type, eqimpsubset2: $o).
% 0.22/0.29 thf(decl_115, type, eqimpsubset1: $o).
% 0.22/0.29 thf(decl_116, type, subsetI2: $o).
% 0.22/0.29 thf(decl_117, type, emptysetsubset: $o).
% 0.22/0.29 thf(decl_118, type, epred1_0: $o).
% 0.22/0.29 thf(decl_119, type, esk1_2: $i > $i > $i).
% 0.22/0.29 thf(decl_120, type, esk2_2: $i > $i > $i).
% 0.22/0.29 thf(decl_121, type, esk3_2: $i > $i > $i).
% 0.22/0.29 thf(decl_122, type, esk4_1: $i > $i).
% 0.22/0.29 thf(decl_123, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.22/0.29 thf(decl_124, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.22/0.29 thf(decl_125, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.22/0.29 thf(decl_126, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.22/0.29 thf(decl_127, type, esk9_1: $i > $i).
% 0.22/0.29 thf(decl_128, type, esk10_2: ($i > $o) > $i > $i).
% 0.22/0.29 thf(decl_129, type, esk11_2: ($i > $o) > $i > $i).
% 0.22/0.29 thf(decl_130, type, esk12_1: ($i > $o) > $i).
% 0.22/0.29 thf(decl_131, type, esk13_2: ($i > $o) > $i > $i).
% 0.22/0.29 thf(decl_132, type, esk14_1: ($i > $o) > $i).
% 0.22/0.29 thf(decl_133, type, esk15_2: $i > $i > $i).
% 0.22/0.29 thf(decl_134, type, esk16_2: $i > $i > $i).
% 0.22/0.29 thf(decl_135, type, esk17_1: $i > $i).
% 0.22/0.29 thf(decl_136, type, esk18_1: $i > $i).
% 0.22/0.29 thf(decl_137, type, esk19_1: $i > $i).
% 0.22/0.29 thf(decl_138, type, esk20_2: $i > $i > $i).
% 0.22/0.29 thf(decl_139, type, esk21_3: $i > $i > $o > $i).
% 0.22/0.29 thf(decl_140, type, esk22_2: ($i > $o) > $i > $i).
% 0.22/0.29 thf(decl_141, type, esk23_1: ($i > $o) > $i).
% 0.22/0.29 thf(decl_142, type, esk24_1: $i > $i).
% 0.22/0.29 thf(decl_143, type, esk25_2: $i > ($i > $o) > $i).
% 0.22/0.29 thf(decl_144, type, esk26_2: $i > ($i > $o) > $i).
% 0.22/0.29 thf(decl_145, type, esk27_2: $i > ($i > $o) > $i).
% 0.22/0.29 thf(decl_146, type, esk28_2: $i > ($i > $o) > $i).
% 0.22/0.29 thf(decl_147, type, esk29_2: $i > ($i > $o) > $i).
% 0.22/0.29 thf(decl_148, type, esk30_2: $i > ($i > $o) > $i).
% 0.22/0.29 thf(decl_149, type, esk31_2: ($i > $o) > $i > $i).
% 0.22/0.29 thf(decl_150, type, esk32_1: ($i > $o) > $i).
% 0.22/0.29 thf(decl_151, type, esk33_1: ($i > $o) > $i).
% 0.22/0.29 thf(decl_152, type, esk34_1: ($i > $o) > $i).
% 0.22/0.29 thf(decl_153, type, esk35_1: ($i > $o) > $i).
% 0.22/0.29 thf(decl_154, type, esk36_2: ($i > $o) > $i > $i).
% 0.22/0.29 thf(decl_155, type, esk37_1: ($i > $o) > $i).
% 0.22/0.29 thf(decl_156, type, esk38_2: ($i > $o) > $i > $i).
% 0.22/0.29 thf(decl_157, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.29 thf(decl_158, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.29 thf(decl_159, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.22/0.29 thf(decl_160, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.29 thf(decl_161, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.22/0.29 thf(decl_162, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.29 thf(decl_163, type, esk45_2: ($i > $o) > $i > $i).
% 0.22/0.29 thf(decl_164, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.29 thf(decl_165, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.29 thf(decl_166, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.22/0.29 thf(decl_167, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.22/0.29 thf(decl_168, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.22/0.29 thf(decl_169, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.22/0.29 thf(decl_170, type, esk52_2: $i > $i > $i).
% 0.22/0.29 thf(decl_171, type, esk53_2: $i > $i > $i).
% 0.22/0.29 thf(decl_172, type, esk54_0: $i).
% 0.22/0.29 thf(decl_173, type, esk55_0: $i).
% 0.22/0.29 thf(decl_174, type, esk56_0: $i).
% 0.22/0.29 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', exuE3u)).
% 0.22/0.29 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', exu)).
% 0.22/0.29 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', exu__Cong)).
% 0.22/0.29 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', exuE1)).
% 0.22/0.29 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.gCEA14jRBo/E---3.1_3187040.p', exuEu)).
% 0.22/0.29 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', descr__Cong)).
% 0.22/0.29 thf(subset, axiom, ((subset)=(^[X4:$i, X5:$i]:(![X2:$i]:((((in @ X2 @ X4))=>((in @ X2 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', subset)).
% 0.22/0.29 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', exuE3e)).
% 0.22/0.29 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', nonempty)).
% 0.22/0.29 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', nonemptyI)).
% 0.22/0.29 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', exuE2)).
% 0.22/0.29 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.gCEA14jRBo/E---3.1_3187040.p', exuI2)).
% 0.22/0.29 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', exuI3)).
% 0.22/0.29 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', exuI1)).
% 0.22/0.29 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', descrp)).
% 0.22/0.29 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', replAx)).
% 0.22/0.29 thf(subsetE, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', subsetE)).
% 0.22/0.29 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', dsetconstr__Cong)).
% 0.22/0.29 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', emptysetsubset)).
% 0.22/0.29 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', subsetI2)).
% 0.22/0.29 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', eqimpsubset1)).
% 0.22/0.29 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', eqimpsubset2)).
% 0.22/0.29 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', subsetI1)).
% 0.22/0.29 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', setbeta)).
% 0.22/0.29 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', dsetconstrER)).
% 0.22/0.29 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', nonemptyI1)).
% 0.22/0.29 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', nonemptyE1)).
% 0.22/0.29 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', setoftrueEq)).
% 0.22/0.29 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', nonemptyImpWitness)).
% 0.22/0.29 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.gCEA14jRBo/E---3.1_3187040.p', emptyE1)).
% 0.22/0.29 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', dsetconstrEL)).
% 0.22/0.29 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', dsetconstrI)).
% 0.22/0.29 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', emptyI)).
% 0.22/0.29 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', powerset__Cong)).
% 0.22/0.29 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', emptyset__Cong)).
% 0.22/0.29 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', setunion__Cong)).
% 0.22/0.29 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', omega__Cong)).
% 0.22/0.29 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', prop2setE)).
% 0.22/0.29 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', noeltsimpempty)).
% 0.22/0.29 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', setunionE)).
% 0.22/0.29 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', setunionI)).
% 0.22/0.29 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.gCEA14jRBo/E---3.1_3187040.p', setext)).
% 0.22/0.29 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', notinemptyset)).
% 0.22/0.29 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', emptysetimpfalse)).
% 0.22/0.29 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', emptysetE)).
% 0.22/0.29 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', setadjoinE)).
% 0.22/0.29 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', setadjoinIR)).
% 0.22/0.29 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', emptyinunitempty)).
% 0.22/0.29 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', setadjoinIL)).
% 0.22/0.29 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', setadjoinOr)).
% 0.22/0.29 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', powersetE)).
% 0.22/0.29 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', emptyInPowerset)).
% 0.22/0.29 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', emptyinPowerset)).
% 0.22/0.29 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', powersetI)).
% 0.22/0.29 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', subPowSU)).
% 0.22/0.29 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', upairsetE)).
% 0.22/0.29 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', singletonsswitch)).
% 0.22/0.29 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', eqinunit)).
% 0.22/0.29 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', notinsingleton)).
% 0.22/0.29 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', uniqinunit)).
% 0.22/0.29 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', upairsetIL)).
% 0.22/0.29 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', quantDeMorgan4)).
% 0.22/0.29 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', quantDeMorgan3)).
% 0.22/0.29 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', quantDeMorgan2)).
% 0.22/0.30 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', quantDeMorgan1)).
% 0.22/0.30 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', vacuousDall)).
% 0.22/0.30 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', upairsetIR)).
% 0.22/0.30 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', prop2setI)).
% 0.22/0.30 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', inCongP)).
% 0.22/0.30 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', notdallE)).
% 0.22/0.30 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', notdexE)).
% 0.22/0.30 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', prop2set2propI)).
% 0.22/0.30 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.gCEA14jRBo/E---3.1_3187040.p', setadjoin__Cong)).
% 0.22/0.30 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.gCEA14jRBo/E---3.1_3187040.p', in__Cong)).
% 0.22/0.30 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', wellorderingAx)).
% 0.22/0.30 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', foundationAx)).
% 0.22/0.30 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.gCEA14jRBo/E---3.1_3187040.p', omegaIndAx)).
% 0.22/0.30 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', omegaSAx)).
% 0.22/0.30 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', omega0Ax)).
% 0.22/0.30 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', setunionAx)).
% 0.22/0.30 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', powersetAx)).
% 0.22/0.30 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', setadjoinAx)).
% 0.22/0.30 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', emptysetAx)).
% 0.22/0.30 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.gCEA14jRBo/E---3.1_3187040.p', setextAx)).
% 0.22/0.30 thf(c_0_84, 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])).
% 0.22/0.30 thf(c_0_85, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.22/0.30 thf(c_0_86, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.22/0.30 thf(c_0_87, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.22/0.30 thf(c_0_88, 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])).
% 0.22/0.30 thf(c_0_89, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 0.22/0.30 thf(c_0_90, plain, ((subset)=(^[Z0:$i, Z1:$i]:(![X2:$i]:((((in @ X2 @ Z0))=>((in @ X2 @ Z1))))))), inference(fof_simplification,[status(thm)],[subset])).
% 0.22/0.30 thf(c_0_91, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.22/0.30 thf(c_0_92, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.22/0.30 thf(c_0_93, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.22/0.30 thf(c_0_94, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.22/0.30 thf(c_0_95, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.22/0.30 thf(c_0_96, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.22/0.30 thf(c_0_97, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 0.22/0.30 thf(c_0_98, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.22/0.30 thf(c_0_99, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.22/0.30 thf(c_0_100, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[subsetE])).
% 0.22/0.30 thf(c_0_101, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X261:$i]:(((((X1 @ X261)))&(![X262:$i]:(((((X1 @ X262)))=>(((X261)=(X262))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_84, c_0_85])).
% 0.22/0.30 thf(c_0_102, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X263:$i]:(((((X1 @ X263)))&(![X264:$i]:(((((X1 @ X264)))=>(((X263)=(X264))))))))))<=>((?[X265:$i]:(((((X17 @ X265)))&(![X266:$i]:(((((X17 @ X266)))=>(((X265)=(X266)))))))))))))))), inference(apply_def,[status(thm)],[c_0_86, c_0_85])).
% 0.22/0.30 thf(c_0_103, plain, ((exuE1)=(![X1:$i > $o]:((((?[X249:$i]:(((((X1 @ X249)))&(![X250:$i]:(((((X1 @ X250)))=>(((X249)=(X250))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_87, c_0_85])).
% 0.22/0.30 thf(c_0_104, plain, ((exuEu)=(![X1:$i > $o]:((((?[X267:$i]:(((((X1 @ X267)))&(![X268:$i]:(((((X1 @ X268)))=>(((X267)=(X268))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_88, c_0_85])).
% 0.22/0.30 thf(c_0_105, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X269:$i]:(((((X1 @ X269)))&(![X270:$i]:(((((X1 @ X270)))=>(((X269)=(X270))))))))))=>((((?[X271:$i]:(((((X17 @ X271)))&(![X272:$i]:(((((X17 @ X272)))=>(((X271)=(X272))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_89, c_0_85])).
% 0.22/0.30 thf(c_0_106, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 0.22/0.30 thf(c_0_107, axiom, ((emptysetsubset)=(![X4:$i]:((![X277:$i]:((((in @ X277 @ emptyset))=>((in @ X277 @ X4)))))))), inference(apply_def,[status(thm)],[emptysetsubset, c_0_90])).
% 0.22/0.30 thf(c_0_108, axiom, ((subsetI2)=(![X4:$i, X5:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((in @ X2 @ X5)))))=>((![X276:$i]:((((in @ X276 @ X4))=>((in @ X276 @ X5)))))))))), inference(apply_def,[status(thm)],[subsetI2, c_0_90])).
% 0.22/0.30 thf(c_0_109, axiom, ((eqimpsubset1)=(![X4:$i, X5:$i]:(((((X4)=(X5)))=>((![X275:$i]:((((in @ X275 @ X4))=>((in @ X275 @ X5)))))))))), inference(apply_def,[status(thm)],[eqimpsubset1, c_0_90])).
% 0.22/0.30 thf(c_0_110, axiom, ((eqimpsubset2)=(![X4:$i, X5:$i]:(((((X4)=(X5)))=>((![X274:$i]:((((in @ X274 @ X5))=>((in @ X274 @ X4)))))))))), inference(apply_def,[status(thm)],[eqimpsubset2, c_0_90])).
% 0.22/0.30 thf(c_0_111, axiom, ((subsetI1)=(![X4:$i, X5:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((in @ X2 @ X5)))))=>((![X273:$i]:((((in @ X273 @ X4))=>((in @ X273 @ X5)))))))))), inference(apply_def,[status(thm)],[subsetI1, c_0_90])).
% 0.22/0.30 thf(c_0_112, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X251:$i]:(((((X1 @ X251)))&(![X252:$i]:(((((X1 @ X252)))=>(((X251)=(X252))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_91, c_0_85])).
% 0.22/0.30 thf(c_0_113, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.22/0.30 thf(c_0_114, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.22/0.30 thf(c_0_115, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_92])).
% 0.22/0.30 thf(c_0_116, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_93, c_0_92])).
% 0.22/0.30 thf(c_0_117, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_92])).
% 0.22/0.30 thf(c_0_118, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.22/0.30 thf(c_0_119, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_92])).
% 0.22/0.30 thf(c_0_120, plain, ((exuE2)=(![X1:$i > $o]:((((?[X253:$i]:(((((X1 @ X253)))&(![X254:$i]:(((((X1 @ X254)))=>(((X253)=(X254))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_94, c_0_85])).
% 0.22/0.30 thf(c_0_121, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
% 0.22/0.30 thf(c_0_122, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X259:$i]:(((((X1 @ X259)))&(![X260:$i]:(((((X1 @ X260)))=>(((X259)=(X260)))))))))))))), inference(apply_def,[status(thm)],[c_0_95, c_0_85])).
% 0.22/0.30 thf(c_0_123, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X257:$i]:(((((X1 @ X257)))&(![X258:$i]:(((((X1 @ X258)))=>(((X257)=(X258)))))))))))))))), inference(apply_def,[status(thm)],[c_0_96, c_0_85])).
% 0.22/0.30 thf(c_0_124, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X255:$i]:(((((X1 @ X255)))&(![X256:$i]:(((((X1 @ X256)))=>(((X255)=(X256)))))))))))))), inference(apply_def,[status(thm)],[c_0_97, c_0_85])).
% 0.22/0.30 thf(c_0_125, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.22/0.30 thf(c_0_126, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.22/0.30 thf(c_0_127, plain, ((descrp)=(![X1:$i > $o]:((((?[X247:$i]:(((((X1 @ X247)))&(![X248:$i]:(((((X1 @ X248)))=>(((X247)=(X248))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_98, c_0_85])).
% 0.22/0.30 thf(c_0_128, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X245:$i]:(((((X6 @ X2 @ X245)))&(![X246:$i]:(((((X6 @ X2 @ X246)))=>(((X245)=(X246)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_99, c_0_85])).
% 0.22/0.30 thf(c_0_129, plain, ((epred1_0)<=>![X307:$i]:(?[X308:$i]:((((![X309:$i]:(((in @ X309 @ X308)=>![X310:$i]:(((in @ X310 @ X309)=>(in @ X310 @ X307)))))&![X311:$i, X312:$i]:((((in @ X311 @ X307)&(in @ X312 @ X307))=>(![X313:$i]:(((in @ X313 @ X308)=>((in @ X311 @ X313)<=>(in @ X312 @ X313))))=>((X311)=(X312))))))&![X314:$i, X315:$i]:((((in @ X314 @ X308)&(in @ X315 @ X308))=>(![X316:$i]:(((in @ X316 @ X314)=>(in @ X316 @ X315)))|![X317:$i]:(((in @ X317 @ X315)=>(in @ X317 @ X314)))))))&![X318:$i]:(((![X319:$i]:(((in @ X319 @ X318)=>(in @ X319 @ X307)))&?[X320:$i]:((in @ X320 @ X318)))=>?[X321:$i, X322:$i]:(((((in @ X321 @ X308)&(in @ X322 @ X318))&~(?[X323:$i]:(((in @ X323 @ X321)&(in @ X323 @ X318)))))&![X324:$i]:(((in @ X324 @ X308)=>(![X325:$i]:(((in @ X325 @ X324)=>(in @ X325 @ X321)))|(in @ X322 @ X324)))))))))))), introduced(definition)).
% 0.22/0.30 thf(c_0_130, negated_conjecture, ~((![X278:$i, X279:$i]:((![X280:$i]:(((in @ X280 @ X278)<=>(in @ X280 @ X279)))=>((X278)=(X279))))=>(![X281:$i]:(~(in @ X281 @ emptyset))=>(![X282:$i, X283:$i, X284:$i]:(((in @ X284 @ (setadjoin @ X282 @ X283))<=>(((X284)=(X282))|(in @ X284 @ X283))))=>(![X285:$i, X286:$i]:(((in @ X286 @ (powerset @ X285))<=>![X287:$i]:(((in @ X287 @ X286)=>(in @ X287 @ X285)))))=>(![X288:$i, X289:$i]:(((in @ X289 @ (setunion @ X288))<=>?[X290:$i]:(((in @ X289 @ X290)&(in @ X290 @ X288)))))=>((in @ emptyset @ omega)=>(![X291:$i]:(((in @ X291 @ omega)=>(in @ (setadjoin @ X291 @ X291) @ omega)))=>(![X292:$i]:((((in @ emptyset @ X292)&![X293:$i]:((((in @ X293 @ omega)&(in @ X293 @ X292))=>(in @ (setadjoin @ X293 @ X293) @ X292))))=>![X294:$i]:(((in @ X294 @ omega)=>(in @ X294 @ X292)))))=>(![X295:$i > $i > $o, X296:$i]:((![X297:$i]:(((in @ X297 @ X296)=>?[X298:$i]:(((X295 @ X297 @ X298)&![X299:$i]:(((X295 @ X297 @ X299)=>((X298)=(X299))))))))=>?[X300:$i]:(![X301:$i]:(((in @ X301 @ X300)<=>?[X302:$i]:(((in @ X302 @ X296)&(X295 @ X302 @ X301))))))))=>(![X303:$i]:((?[X304:$i]:((in @ X304 @ X303))=>?[X305:$i]:(((in @ X305 @ X303)&~(?[X306:$i]:(((in @ X306 @ X305)&(in @ X306 @ X303))))))))=>((epred1_0)=>(![X326:$i > $o]:((?[X327:$i]:(((X326 @ X327)&![X328:$i]:(((X326 @ X328)=>((X327)=(X328))))))=>(X326 @ (descr @ (^[Z0:$i]:(X326 @ Z0))))))=>(![X329:$i, X330:$i > $o, X331:$i]:(((in @ X331 @ X329)=>((X330 @ X331)=>(in @ X331 @ (dsetconstr @ X329 @ X330)))))=>(![X332:$i, X333:$i > $o, X334:$i]:(((in @ X334 @ (dsetconstr @ X332 @ X333))=>(in @ X334 @ X332)))=>(![X335:$i, X336:$i > $o, X337:$i]:(((in @ X337 @ (dsetconstr @ X335 @ X336))=>(X336 @ X337)))=>(![X338:$i > $o]:((?[X339:$i]:(((X338 @ X339)&![X340:$i]:(((X338 @ X340)=>((X339)=(X340))))))=>?[X341:$i]:(((X338 @ X341)&![X342:$i]:(((X338 @ X342)=>((X341)=(X342))))))))=>(![X343:$o, X344:$i]:(((in @ X344 @ (prop2set @ ((X343))))=>(X343)))=>(![X345:$i]:(((in @ X345 @ emptyset)=>![X346:$o]:((X346))))=>(![X347:$i]:(((in @ X347 @ emptyset)=>~($true)))=>(![X348:$i]:(~(in @ X348 @ emptyset))=>(![X349:$i > $o]:((?[X350:$i]:(((X349 @ X350)&![X351:$i]:(((X349 @ X351)=>((X350)=(X351))))))=>?[X352:$i]:((X349 @ X352))))=>(![X353:$i, X354:$i]:((![X355:$i]:(((in @ X355 @ X353)=>(in @ X355 @ X354)))=>(![X356:$i]:(((in @ X356 @ X354)=>(in @ X356 @ X353)))=>((X353)=(X354)))))=>(![X357:$i]:((![X358:$i]:(~(in @ X358 @ X357))=>((X357)=(emptyset))))=>(![X359:$i]:((![X360:$i]:(~(in @ X360 @ X359))=>((X359)=(emptyset))))=>(![X361:$i, X362:$i > $o, X363:$i]:(((in @ X363 @ X361)=>((in @ X363 @ (dsetconstr @ X361 @ X362))<=>(X362 @ X363))))=>(![X364:$i]:((((X364)!=(emptyset))=>?[X365:$i]:((in @ X365 @ X364))))=>(![X366:$i, X367:$i > $o, X368:$i]:(((in @ X368 @ X366)=>((X367 @ X368)=>((dsetconstr @ X366 @ X367)!=(emptyset)))))=>(![X369:$i]:((?[X370:$i]:((in @ X370 @ X369))=>((X369)!=(emptyset))))=>(![X371:$i, X372:$i]:((in @ X371 @ (setadjoin @ X371 @ X372)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X373:$i, X374:$i, X375:$i]:(((in @ X375 @ X374)=>(in @ X375 @ (setadjoin @ X373 @ X374))))=>(![X376:$i, X377:$i, X378:$i]:(((in @ X378 @ (setadjoin @ X376 @ X377))=>![X379:$o]:(((((X378)=(X376))=>(X379))=>(((in @ X378 @ X377)=>(X379))=>(X379))))))=>(![X380:$i, X381:$i, X382:$i]:(((in @ X382 @ (setadjoin @ X380 @ X381))=>(((X382)=(X380))|(in @ X382 @ X381))))=>(![X383:$i]:(((dsetconstr @ X383 @ (^[Z0:$i]:($true)))=(X383)))=>(![X384:$i, X385:$i]:((![X386:$i]:(((in @ X386 @ X385)=>(in @ X386 @ X384)))=>(in @ X385 @ (powerset @ X384))))=>(![X387:$i]:((in @ emptyset @ (powerset @ X387)))=>(![X388:$i]:((in @ emptyset @ (powerset @ X388)))=>(![X389:$i, X390:$i, X391:$i]:(((in @ X390 @ (powerset @ X389))=>((in @ X391 @ X390)=>(in @ X391 @ X389))))=>(![X392:$i, X393:$i, X394:$i]:(((in @ X393 @ X394)=>((in @ X394 @ X392)=>(in @ X393 @ (setunion @ X392)))))=>(![X395:$i, X396:$i]:(((in @ X396 @ (setunion @ X395))=>![X397:$o]:((![X398:$i]:(((in @ X396 @ X398)=>((in @ X398 @ X395)=>(X397))))=>(X397)))))=>(![X399:$i, X400:$i]:(((in @ X400 @ X399)=>(in @ X400 @ (powerset @ (setunion @ X399)))))=>(![X401:$i > $o]:((?[X402:$i]:(((X401 @ X402)&![X403:$i]:(((X401 @ X403)=>((X402)=(X403))))))=>?[X404:$i]:(![X405:$i]:(((X401 @ X405)<=>((X405)=(X404)))))))=>(![X406:$i]:((((X406)!=(emptyset))=>?[X407:$i]:(((in @ X407 @ X406)&$true))))=>(![X408:$i, X409:$i]:(((in @ X408 @ (setadjoin @ X409 @ emptyset))=>((X408)=(X409))))=>(![X410:$i, X411:$i]:((((X410)!=(X411))=>~(in @ X411 @ (setadjoin @ X410 @ emptyset))))=>(![X412:$i, X413:$i]:((((X412)=(X413))=>(in @ X412 @ (setadjoin @ X413 @ emptyset))))=>(![X414:$i, X415:$i]:(((in @ X414 @ (setadjoin @ X415 @ emptyset))=>(in @ X415 @ (setadjoin @ X414 @ emptyset))))=>(![X416:$i, X417:$i, X418:$i]:(((in @ X418 @ (setadjoin @ X416 @ (setadjoin @ X417 @ emptyset)))=>(((X418)=(X416))|((X418)=(X417)))))=>(![X419:$i, X420:$i]:((in @ X419 @ (setadjoin @ X419 @ (setadjoin @ X420 @ emptyset))))=>(![X421:$i, X422:$i]:((in @ X422 @ (setadjoin @ X421 @ (setadjoin @ X422 @ emptyset))))=>(![X423:$i, X424:$i > $o]:((?[X425:$i]:(((in @ X425 @ X423)&(X424 @ X425)))=>(((dsetconstr @ X423 @ X424)=(emptyset))=>~($true))))=>(![X426:$i > $o, X427:$i]:(((in @ X427 @ emptyset)=>(X426 @ X427)))=>(![X428:$i, X429:$i > $o]:((~(![X430:$i]:(((in @ X430 @ X428)=>(X429 @ X430))))=>?[X431:$i]:(((in @ X431 @ X428)&~((X429 @ X431))))))=>(![X432:$i, X433:$i > $o]:((![X434:$i]:(((in @ X434 @ X432)=>~((X433 @ X434))))=>~(?[X435:$i]:(((in @ X435 @ X432)&(X433 @ X435))))))=>(![X436:$i, X437:$i > $o]:((~(?[X438:$i]:(((in @ X438 @ X436)&(X437 @ X438))))=>![X439:$i]:(((in @ X439 @ X436)=>~((X437 @ X439))))))=>(![X440:$i, X441:$i > $o]:((?[X442:$i]:(((in @ X442 @ X440)&~((X441 @ X442))))=>~(![X443:$i]:(((in @ X443 @ X440)=>(X441 @ X443))))))=>(![X444:$o]:(((X444)=>(in @ emptyset @ (prop2set @ ((X444))))))=>(![X445:$o]:(((X445)=>(set2prop @ (prop2set @ ((X445))))))=>(![X446:$i, X447:$i > $o]:((~(?[X448:$i]:(((in @ X448 @ X446)&(X447 @ X448))))=>![X449:$i]:(((in @ X449 @ X446)=>~((X447 @ X449))))))=>(![X450:$i, X451:$i > $o]:((~(![X452:$i]:(((in @ X452 @ X450)=>(X451 @ X452))))=>?[X453:$i]:(((in @ X453 @ X450)&~((X451 @ X453))))))=>(![X454:$i > $o]:((?[X455:$i]:(((X454 @ X455)&![X456:$i]:(((X454 @ X456)=>((X455)=(X456))))))=>?[X457:$i]:(((X454 @ X457)&![X458:$i]:(((X454 @ X458)=>((X457)=(X458))))))))=>(![X459:$i > $o]:((?[X460:$i]:((X459 @ X460))=>(![X461:$i, X462:$i]:(((X459 @ X461)=>((X459 @ X462)=>((X461)=(X462)))))=>?[X463:$i]:(((X459 @ X463)&![X464:$i]:(((X459 @ X464)=>((X463)=(X464)))))))))=>(![X465:$i > $o]:((?[X466:$i]:(![X467:$i]:(((X465 @ X467)<=>((X467)=(X466)))))=>?[X468:$i]:(((X465 @ X468)&![X469:$i]:(((X465 @ X469)=>((X468)=(X469))))))))=>(![X470:$i, X471:$i]:((((X470)=(X471))=>![X472:$i, X473:$i]:((((X472)=(X473))=>((in @ X472 @ X470)=>(in @ X473 @ X471))))))=>(![X474:$i, X475:$i]:((((X474)=(X475))=>![X476:$i, X477:$i]:((((X476)=(X477))=>((in @ X476 @ X474)<=>(in @ X477 @ X475))))))=>(![X478:$i > $o]:((?[X479:$i]:(((X478 @ X479)&![X480:$i]:(((X478 @ X480)=>((X479)=(X480))))))=>![X481:$i, X482:$i]:(((X478 @ X481)=>((X478 @ X482)=>((X481)=(X482)))))))=>(![X483:$i > $o, X484:$i > $o]:((![X485:$i, X486:$i]:((((X485)=(X486))=>((X483 @ X485)<=>(X484 @ X486))))=>(?[X487:$i]:(((X483 @ X487)&![X488:$i]:(((X483 @ X488)=>((X487)=(X488))))))<=>?[X489:$i]:(((X484 @ X489)&![X490:$i]:(((X484 @ X490)=>((X489)=(X490)))))))))=>(((emptyset)=(emptyset))=>(![X491:$i, X492:$i]:((((X491)=(X492))=>![X493:$i, X494:$i]:((((X493)=(X494))=>((setadjoin @ X491 @ X493)=(setadjoin @ X492 @ X494))))))=>(![X495:$i, X496:$i]:((((X495)=(X496))=>((powerset @ X495)=(powerset @ X496))))=>(![X497:$i, X498:$i]:((((X497)=(X498))=>((setunion @ X497)=(setunion @ X498))))=>(((omega)=(omega))=>(![X499:$i > $o]:((?[X500:$i]:(((X499 @ X500)&![X501:$i]:(((X499 @ X501)=>((X500)=(X501))))))=>![X502:$i, X503:$i]:(((X499 @ X502)=>((X499 @ X503)=>((X502)=(X503)))))))=>(![X504:$i > $o, X505:$i > $o]:((![X506:$i, X507:$i]:((((X506)=(X507))=>((X504 @ X506)<=>(X505 @ X507))))=>(?[X508:$i]:(((X504 @ X508)&![X509:$i]:(((X504 @ X509)=>((X508)=(X509))))))=>(?[X510:$i]:(((X505 @ X510)&![X511:$i]:(((X505 @ X511)=>((X510)=(X511))))))=>((descr @ X504)=(descr @ X505))))))=>(![X512:$i, X513:$i]:((((X512)=(X513))=>![X514:$i > $o, X515:$i > $o]:((![X516:$i]:(((in @ X516 @ X512)=>![X517:$i]:(((in @ X517 @ X513)=>(((X516)=(X517))=>((X514 @ X516)<=>(X515 @ X517)))))))=>((dsetconstr @ X512 @ X514)=(dsetconstr @ X513 @ X515))))))=>(![X518:$i, X519:$i]:((![X520:$i]:(((in @ X520 @ X518)=>(in @ X520 @ X519)))=>![X521:$i]:(((in @ X521 @ X518)=>(in @ X521 @ X519)))))=>(![X522:$i, X523:$i]:((((X522)=(X523))=>![X524:$i]:(((in @ X524 @ X523)=>(in @ X524 @ X522)))))=>(![X525:$i, X526:$i]:((((X525)=(X526))=>![X527:$i]:(((in @ X527 @ X525)=>(in @ X527 @ X526)))))=>(![X528:$i, X529:$i]:((![X530:$i]:(((in @ X530 @ X528)=>(in @ X530 @ X529)))=>![X531:$i]:(((in @ X531 @ X528)=>(in @ X531 @ X529)))))=>(![X532:$i, X533:$i]:(((in @ X533 @ emptyset)=>(in @ X533 @ X532)))=>![X4:$i, X5:$i, X2:$i]:((![X534:$i]:(((in @ X534 @ X4)=>(in @ X534 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ 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)],[c_0_100, emptyI]), powerset__Cong]), c_0_101]), c_0_102]), emptyset__Cong]), setunion__Cong]), omega__Cong]), c_0_103]), c_0_104]), prop2setE]), c_0_105]), c_0_106]), c_0_107]), c_0_108]), c_0_109]), c_0_110]), c_0_111]), c_0_90]), noeltsimpempty]), setunionE]), setunionI]), setext]), c_0_112]), notinemptyset]), emptysetimpfalse]), emptysetE]), c_0_113]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), c_0_114]), c_0_115]), c_0_116]), c_0_117]), setadjoinOr]), powersetE]), emptyInPowerset]), emptyinPowerset]), powersetI]), c_0_118]), subPowSU]), upairsetE]), singletonsswitch]), eqinunit]), notinsingleton]), uniqinunit]), c_0_119]), c_0_120]), upairsetIL]), quantDeMorgan4]), quantDeMorgan3]), quantDeMorgan2]), quantDeMorgan1]), vacuousDall]), c_0_121]), upairsetIR]), prop2setI]), inCongP]), c_0_122]), c_0_123]), c_0_124]), notdallE]), notdexE]), prop2set2propI]), setadjoin__Cong]), in__Cong]), c_0_125]), c_0_126]), c_0_127]), wellorderingAx]), foundationAx]), c_0_128]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_129])).
% 0.22/0.30 thf(c_0_131, negated_conjecture, ![X535:$i, X536:$i, X538:$i, X539:$i, X540:$i, X541:$i, X542:$i, X543:$i, X544:$i, X545:$i, X546:$i, X548:$i, X549:$i, X551:$i, X552:$i, X553:$i, X554:$i, X555:$i, X557:$i, X558:$i > $i > $o, X559:$i, X561:$i, X564:$i, X566:$i, X567:$i, X568:$i, X569:$i, X571:$i, X572:$i > $o, X573:$i, X575:$i, X576:$i > $o, X577:$i, X578:$i, X579:$i > $o, X580:$i, X581:$i, X582:$i > $o, X583:$i, X584:$i > $o, X585:$i, X588:$i, X589:$o, X590:$i, X591:$i, X592:$o, X593:$i, X594:$i, X595:$i > $o, X596:$i, X599:$i, X600:$i, X603:$i, X605:$i, X607:$i, X608:$i > $o, X609:$i, X610:$i, X612:$i, X613:$i > $o, X614:$i, X615:$i, X616:$i, X617:$i, X618:$i, X619:$i, X620:$i, X621:$i, X622:$i, X623:$i, X624:$i, X625:$o, X626:$i, X627:$i, X628:$i, X629:$i, X630:$i, X631:$i, X633:$i, X634:$i, X635:$i, X636:$i, X637:$i, X638:$i, X639:$i, X640:$i, X641:$i, X642:$i, X643:$o, X645:$i, X646:$i, X647:$i > $o, X648:$i, X651:$i, X652:$i, X653:$i, X655:$i, X656:$i, X657:$i, X658:$i, X659:$i, X660:$i, X661:$i, X662:$i, X663:$i, X664:$i, X665:$i, X666:$i, X667:$i, X668:$i, X669:$i, X670:$i, X671:$i > $o, X672:$i, X673:$i > $o, X674:$i, X675:$i, X676:$i > $o, X677:$i, X679:$i, X680:$i > $o, X682:$i, X683:$i, X684:$i > $o, X686:$i, X687:$i, X688:$i > $o, X689:$i, X691:$o, X692:$o, X693:$i, X694:$i > $o, X696:$i, X697:$i, X698:$i > $o, X699:$i, X701:$i > $o, X702:$i, X705:$i, X706:$i > $o, X707:$i, X711:$i, X712:$i > $o, X713:$i, X716:$i, X717:$i, X718:$i, X719:$i, X720:$i, X721:$i, X722:$i, X723:$i, X724:$i, X725:$i > $o, X726:$i, X728:$i, X729:$i, X730:$i > $o, X731:$i > $o, X734:$i, X737:$i, X738:$i, X741:$i, X742:$i, X743:$i, X744:$i, X745:$i, X746:$i, X747:$i, X748:$i, X749:$i, X750:$i > $o, X751:$i, X753:$i, X754:$i, X755:$i > $o, X756:$i > $o, X759:$i, X761:$i, X763:$i, X764:$i, X765:$i > $o, X766:$i > $o, X769:$i, X770:$i, X772:$i, X773:$i, X774:$i, X775:$i, X776:$i, X777:$i, X778:$i, X779:$i, X780:$i, X782:$i, X783:$i, X784:$i, X788:$i]:((((~(in @ (esk1_2 @ X535 @ X536) @ X535)|~(in @ (esk1_2 @ X535 @ X536) @ X536)|((X535)=(X536)))&((in @ (esk1_2 @ X535 @ X536) @ X535)|(in @ (esk1_2 @ X535 @ X536) @ X536)|((X535)=(X536))))&(~(in @ X538 @ emptyset)&(((~(in @ X541 @ (setadjoin @ X539 @ X540))|(((X541)=(X539))|(in @ X541 @ X540)))&((((X541)!=(X539))|(in @ X541 @ (setadjoin @ X539 @ X540)))&(~(in @ X541 @ X540)|(in @ X541 @ (setadjoin @ X539 @ X540)))))&(((~(in @ X543 @ (powerset @ X542))|(~(in @ X544 @ X543)|(in @ X544 @ X542)))&(((in @ (esk2_2 @ X545 @ X546) @ X546)|(in @ X546 @ (powerset @ X545)))&(~(in @ (esk2_2 @ X545 @ X546) @ X545)|(in @ X546 @ (powerset @ X545)))))&(((((in @ X549 @ (esk3_2 @ X548 @ X549))|~(in @ X549 @ (setunion @ X548)))&((in @ (esk3_2 @ X548 @ X549) @ X548)|~(in @ X549 @ (setunion @ X548))))&(~(in @ X552 @ X553)|~(in @ X553 @ X551)|(in @ X552 @ (setunion @ X551))))&((in @ emptyset @ omega)&((~(in @ X554 @ omega)|(in @ (setadjoin @ X554 @ X554) @ omega))&(((((in @ (esk4_1 @ X555) @ omega)|~(in @ emptyset @ 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@ X756 @ X759))|~(X755 @ X759))|((esk46_2 @ X755 @ X756)=(esk47_2 @ X755 @ X756)))))&(((((X756 @ (esk49_3 @ X755 @ X756 @ X761))|~(X756 @ X761)|((descr @ X755)=(descr @ X756))|((X755 @ (esk48_3 @ X755 @ X756 @ X759))|~(X755 @ X759))|(~(X755 @ (esk46_2 @ X755 @ X756))|~(X756 @ (esk47_2 @ X755 @ X756))))&(((X761)!=(esk49_3 @ X755 @ X756 @ X761))|~(X756 @ X761)|((descr @ X755)=(descr @ X756))|((X755 @ (esk48_3 @ X755 @ X756 @ X759))|~(X755 @ X759))|(~(X755 @ (esk46_2 @ X755 @ X756))|~(X756 @ (esk47_2 @ X755 @ X756)))))&(((X756 @ (esk49_3 @ X755 @ X756 @ X761))|~(X756 @ X761)|((descr @ X755)=(descr @ X756))|(((X759)!=(esk48_3 @ X755 @ X756 @ X759))|~(X755 @ X759))|(~(X755 @ (esk46_2 @ X755 @ X756))|~(X756 @ (esk47_2 @ X755 @ X756))))&(((X761)!=(esk49_3 @ X755 @ X756 @ X761))|~(X756 @ X761)|((descr @ X755)=(descr @ X756))|(((X759)!=(esk48_3 @ X755 @ X756 @ X759))|~(X755 @ X759))|(~(X755 @ (esk46_2 @ X755 @ X756))|~(X756 @ (esk47_2 @ X755 @ X756))))))&((((X756 @ (esk49_3 @ X755 @ X756 @ X761))|~(X756 @ X761)|((descr @ X755)=(descr @ X756))|((X755 @ (esk48_3 @ X755 @ X756 @ X759))|~(X755 @ X759))|((X755 @ (esk46_2 @ X755 @ X756))|(X756 @ (esk47_2 @ X755 @ X756))))&(((X761)!=(esk49_3 @ X755 @ X756 @ X761))|~(X756 @ X761)|((descr @ X755)=(descr @ X756))|((X755 @ (esk48_3 @ X755 @ X756 @ X759))|~(X755 @ X759))|((X755 @ (esk46_2 @ X755 @ X756))|(X756 @ (esk47_2 @ X755 @ X756)))))&(((X756 @ (esk49_3 @ X755 @ X756 @ X761))|~(X756 @ X761)|((descr @ X755)=(descr @ X756))|(((X759)!=(esk48_3 @ X755 @ X756 @ X759))|~(X755 @ X759))|((X755 @ (esk46_2 @ X755 @ X756))|(X756 @ (esk47_2 @ X755 @ X756))))&(((X761)!=(esk49_3 @ X755 @ X756 @ X761))|~(X756 @ X761)|((descr @ X755)=(descr @ X756))|(((X759)!=(esk48_3 @ X755 @ X756 @ X759))|~(X755 @ X759))|((X755 @ (esk46_2 @ X755 @ X756))|(X756 @ (esk47_2 @ X755 @ X756))))))))&((((in @ (esk50_4 @ X763 @ X764 @ X765 @ X766) @ X763)|((dsetconstr @ X763 @ X765)=(dsetconstr @ X764 @ X766))|((X763)!=(X764)))&(((in @ (esk51_4 @ X763 @ X764 @ X765 @ X766) @ X764)|((dsetconstr @ X763 @ X765)=(dsetconstr @ X764 @ X766))|((X763)!=(X764)))&((((esk50_4 @ X763 @ X764 @ X765 @ X766)=(esk51_4 @ X763 @ X764 @ X765 @ X766))|((dsetconstr @ X763 @ X765)=(dsetconstr @ X764 @ X766))|((X763)!=(X764)))&((~(X765 @ (esk50_4 @ X763 @ X764 @ X765 @ X766))|~(X766 @ (esk51_4 @ X763 @ X764 @ X765 @ X766))|((dsetconstr @ X763 @ X765)=(dsetconstr @ X764 @ X766))|((X763)!=(X764)))&((X765 @ (esk50_4 @ X763 @ X764 @ X765 @ X766))|(X766 @ (esk51_4 @ X763 @ X764 @ X765 @ X766))|((dsetconstr @ X763 @ X765)=(dsetconstr @ X764 @ X766))|((X763)!=(X764)))))))&((((in @ (esk52_2 @ X769 @ X770) @ X769)|(~(in @ X772 @ X769)|(in @ X772 @ X770)))&(~(in @ (esk52_2 @ X769 @ X770) @ X770)|(~(in @ X772 @ X769)|(in @ X772 @ X770))))&((((X773)!=(X774))|(~(in @ X775 @ X774)|(in @ X775 @ X773)))&((((X776)!=(X777))|(~(in @ X778 @ X776)|(in @ X778 @ X777)))&((((in @ (esk53_2 @ X779 @ X780) @ X779)|(~(in @ X782 @ X779)|(in @ X782 @ X780)))&(~(in @ (esk53_2 @ X779 @ X780) @ X780)|(~(in @ X782 @ X779)|(in @ X782 @ X780))))&((~(in @ X784 @ emptyset)|(in @ X784 @ X783))&((~(in @ X788 @ esk54_0)|(in @ X788 @ esk55_0))&((in @ esk56_0 @ esk54_0)&~(in @ esk56_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_130])])])])])])])).
% 0.22/0.30 thf(c_0_132, negated_conjecture, ~((in @ esk56_0 @ esk55_0)), inference(split_conjunct,[status(thm)],[c_0_131])).
% 0.22/0.30 thf(c_0_133, negated_conjecture, ![X2:$i]:(((in @ X2 @ esk55_0)|~((in @ X2 @ esk54_0)))), inference(split_conjunct,[status(thm)],[c_0_131])).
% 0.22/0.30 thf(c_0_134, negated_conjecture, (in @ esk56_0 @ esk54_0), inference(split_conjunct,[status(thm)],[c_0_131])).
% 0.22/0.30 thf(c_0_135, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132, c_0_133]), c_0_134])]), ['proof']).
% 0.22/0.30 % SZS output end CNFRefutation
% 0.22/0.30 % Parsed axioms : 179
% 0.22/0.30 % Removed by relevancy pruning/SinE : 95
% 0.22/0.30 % Initial clauses : 193
% 0.22/0.30 % Removed in clause preprocessing : 15
% 0.22/0.30 % Initial clauses in saturation : 178
% 0.22/0.30 % Processed clauses : 20
% 0.22/0.30 % ...of these trivial : 1
% 0.22/0.30 % ...subsumed : 5
% 0.22/0.30 % ...remaining for further processing : 14
% 0.22/0.30 % Other redundant clauses eliminated : 1
% 0.22/0.30 % Clauses deleted for lack of memory : 0
% 0.22/0.30 % Backward-subsumed : 0
% 0.22/0.30 % Backward-rewritten : 1
% 0.22/0.30 % Generated clauses : 2
% 0.22/0.30 % ...of the previous two non-redundant : 1
% 0.22/0.30 % ...aggressively subsumed : 0
% 0.22/0.30 % Contextual simplify-reflections : 0
% 0.22/0.30 % Paramodulations : 1
% 0.22/0.30 % Factorizations : 0
% 0.22/0.30 % NegExts : 0
% 0.22/0.30 % Equation resolutions : 1
% 0.22/0.30 % Disequality decompositions : 0
% 0.22/0.30 % Total rewrite steps : 3
% 0.22/0.30 % ...of those cached : 0
% 0.22/0.30 % Propositional unsat checks : 0
% 0.22/0.30 % Propositional check models : 0
% 0.22/0.30 % Propositional check unsatisfiable : 0
% 0.22/0.30 % Propositional clauses : 0
% 0.22/0.30 % Propositional clauses after purity: 0
% 0.22/0.30 % Propositional unsat core size : 0
% 0.22/0.30 % Propositional preprocessing time : 0.000
% 0.22/0.30 % Propositional encoding time : 0.000
% 0.22/0.30 % Propositional solver time : 0.000
% 0.22/0.30 % Success case prop preproc time : 0.000
% 0.22/0.30 % Success case prop encoding time : 0.000
% 0.22/0.30 % Success case prop solver time : 0.000
% 0.22/0.30 % Current number of processed clauses : 12
% 0.22/0.30 % Positive orientable unit clauses : 8
% 0.22/0.30 % Positive unorientable unit clauses: 0
% 0.22/0.30 % Negative unit clauses : 3
% 0.22/0.30 % Non-unit-clauses : 1
% 0.22/0.30 % Current number of unprocessed clauses: 159
% 0.22/0.30 % ...number of literals in the above : 608
% 0.22/0.30 % Current number of archived formulas : 0
% 0.22/0.30 % Current number of archived clauses : 1
% 0.22/0.30 % Clause-clause subsumption calls (NU) : 0
% 0.22/0.30 % Rec. Clause-clause subsumption calls : 0
% 0.22/0.30 % Non-unit clause-clause subsumptions : 0
% 0.22/0.30 % Unit Clause-clause subsumption calls : 2
% 0.22/0.30 % Rewrite failures with RHS unbound : 0
% 0.22/0.30 % BW rewrite match attempts : 1
% 0.22/0.30 % BW rewrite match successes : 1
% 0.22/0.30 % Condensation attempts : 0
% 0.22/0.30 % Condensation successes : 0
% 0.22/0.30 % Termbank termtop insertions : 23725
% 0.22/0.30 % Search garbage collected termcells : 9627
% 0.22/0.30
% 0.22/0.30 % -------------------------------------------------
% 0.22/0.30 % User time : 0.024 s
% 0.22/0.30 % System time : 0.007 s
% 0.22/0.30 % Total time : 0.031 s
% 0.22/0.30 % Maximum resident set size: 6116 pages
% 0.22/0.30
% 0.22/0.30 % -------------------------------------------------
% 0.22/0.30 % User time : 0.027 s
% 0.22/0.30 % System time : 0.014 s
% 0.22/0.30 % Total time : 0.041 s
% 0.22/0.30 % Maximum resident set size: 5120 pages
% 0.22/0.30 % E exiting
%------------------------------------------------------------------------------