%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU568^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:24:32 AM UTC 2026
% Result : Theorem 0.21s 0.30s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU568^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n009.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
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 13:51:00 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.25 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p
% 0.21/0.30 % Version: 3.5.1-ho
% 0.21/0.30 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.21/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.30 % Starting new_ho_10 with 1500s (5) cores
% 0.21/0.30 % Starting sh5l with 300s (1) cores
% 0.21/0.30 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.30 % Starting new_bool_2 with 300s (1) cores
% 0.21/0.30 % sh5l with pid 4028170 completed with status 0
% 0.21/0.30 % Result found by sh5l
% 0.21/0.30 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.21/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.30 % Starting new_ho_10 with 1500s (5) cores
% 0.21/0.30 % Starting sh5l with 300s (1) cores
% 0.21/0.30 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.21/0.30 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.21/0.30 % Search class: HGHSM-FSLM31-SHFMMMBN
% 0.21/0.30 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.30 % Starting SubtermCWHack with 31s (1) cores
% 0.21/0.30 % SubtermCWHack with pid 4028173 completed with status 0
% 0.21/0.30 % Result found by SubtermCWHack
% 0.21/0.30 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.21/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.30 % Starting new_ho_10 with 1500s (5) cores
% 0.21/0.30 % Starting sh5l with 300s (1) cores
% 0.21/0.30 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.21/0.30 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.21/0.30 % Search class: HGHSM-FSLM31-SHFMMMBN
% 0.21/0.30 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.30 % Starting SubtermCWHack with 31s (1) cores
% 0.21/0.30 % Preprocessing time : 0.004 s
% 0.21/0.30
% 0.21/0.30 % Proof found!
% 0.21/0.30 % SZS status Theorem
% 0.21/0.30 % SZS output start CNFRefutation
% 0.21/0.30 thf(decl_23, type, in: $i > $i > $o).
% 0.21/0.30 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.21/0.30 thf(decl_25, type, setextAx: $o).
% 0.21/0.30 thf(decl_26, type, emptyset: $i).
% 0.21/0.30 thf(decl_27, type, emptysetAx: $o).
% 0.21/0.30 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.21/0.30 thf(decl_29, type, setadjoinAx: $o).
% 0.21/0.30 thf(decl_30, type, powerset: $i > $i).
% 0.21/0.30 thf(decl_31, type, powersetAx: $o).
% 0.21/0.30 thf(decl_32, type, setunion: $i > $i).
% 0.21/0.30 thf(decl_33, type, setunionAx: $o).
% 0.21/0.30 thf(decl_34, type, omega: $i).
% 0.21/0.30 thf(decl_35, type, omega0Ax: $o).
% 0.21/0.30 thf(decl_36, type, omegaSAx: $o).
% 0.21/0.30 thf(decl_37, type, omegaIndAx: $o).
% 0.21/0.30 thf(decl_38, type, replAx: $o).
% 0.21/0.30 thf(decl_39, type, foundationAx: $o).
% 0.21/0.30 thf(decl_40, type, wellorderingAx: $o).
% 0.21/0.30 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.21/0.30 thf(decl_42, type, descrp: $o).
% 0.21/0.30 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.21/0.30 thf(decl_44, type, dsetconstrI: $o).
% 0.21/0.30 thf(decl_45, type, dsetconstrEL: $o).
% 0.21/0.30 thf(decl_46, type, dsetconstrER: $o).
% 0.21/0.30 thf(decl_47, type, exuE1: $o).
% 0.21/0.30 thf(decl_48, type, prop2set: $o > $i).
% 0.21/0.30 thf(decl_49, type, prop2setE: $o).
% 0.21/0.30 thf(decl_50, type, emptysetE: $o).
% 0.21/0.30 thf(decl_51, type, emptysetimpfalse: $o).
% 0.21/0.30 thf(decl_52, type, notinemptyset: $o).
% 0.21/0.30 thf(decl_53, type, exuE3e: $o).
% 0.21/0.30 thf(decl_54, type, setext: $o).
% 0.21/0.30 thf(decl_55, type, emptyI: $o).
% 0.21/0.30 thf(decl_56, type, noeltsimpempty: $o).
% 0.21/0.30 thf(decl_57, type, setbeta: $o).
% 0.21/0.30 thf(decl_58, type, nonempty: $i > $o).
% 0.21/0.30 thf(decl_59, type, nonemptyE1: $o).
% 0.21/0.30 thf(decl_60, type, nonemptyI: $o).
% 0.21/0.30 thf(decl_61, type, nonemptyI1: $o).
% 0.21/0.30 thf(decl_62, type, setadjoinIL: $o).
% 0.21/0.30 thf(decl_63, type, emptyinunitempty: $o).
% 0.21/0.30 thf(decl_64, type, setadjoinIR: $o).
% 0.21/0.30 thf(decl_65, type, setadjoinE: $o).
% 0.21/0.30 thf(decl_66, type, setadjoinOr: $o).
% 0.21/0.30 thf(decl_67, type, setoftrueEq: $o).
% 0.21/0.30 thf(decl_68, type, powersetI: $o).
% 0.21/0.30 thf(decl_69, type, emptyinPowerset: $o).
% 0.21/0.30 thf(decl_70, type, emptyInPowerset: $o).
% 0.21/0.30 thf(decl_71, type, powersetE: $o).
% 0.21/0.30 thf(decl_72, type, setunionI: $o).
% 0.21/0.30 thf(decl_73, type, setunionE: $o).
% 0.21/0.30 thf(decl_74, type, subPowSU: $o).
% 0.21/0.30 thf(decl_75, type, exuE2: $o).
% 0.21/0.30 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.21/0.30 thf(decl_77, type, uniqinunit: $o).
% 0.21/0.30 thf(decl_78, type, notinsingleton: $o).
% 0.21/0.30 thf(decl_79, type, eqinunit: $o).
% 0.21/0.30 thf(decl_80, type, singletonsswitch: $o).
% 0.21/0.30 thf(decl_81, type, upairsetE: $o).
% 0.21/0.30 thf(decl_82, type, upairsetIL: $o).
% 0.21/0.30 thf(decl_83, type, upairsetIR: $o).
% 0.21/0.30 thf(decl_84, type, emptyE1: $o).
% 0.21/0.30 thf(decl_85, type, vacuousDall: $o).
% 0.21/0.30 thf(decl_86, type, quantDeMorgan1: $o).
% 0.21/0.30 thf(decl_87, type, quantDeMorgan2: $o).
% 0.21/0.30 thf(decl_88, type, quantDeMorgan3: $o).
% 0.21/0.30 thf(decl_89, type, quantDeMorgan4: $o).
% 0.21/0.30 thf(decl_90, type, prop2setI: $o).
% 0.21/0.30 thf(decl_91, type, set2prop: $i > $o).
% 0.21/0.30 thf(decl_92, type, prop2set2propI: $o).
% 0.21/0.30 thf(decl_93, type, notdexE: $o).
% 0.21/0.30 thf(decl_94, type, notdallE: $o).
% 0.21/0.30 thf(decl_95, type, exuI1: $o).
% 0.21/0.30 thf(decl_96, type, exuI3: $o).
% 0.21/0.30 thf(decl_97, type, exuI2: $o).
% 0.21/0.30 thf(decl_98, type, inCongP: $o).
% 0.21/0.30 thf(decl_99, type, in__Cong: $o).
% 0.21/0.30 thf(decl_100, type, exuE3u: $o).
% 0.21/0.30 thf(decl_101, type, exu__Cong: $o).
% 0.21/0.30 thf(decl_102, type, emptyset__Cong: $o).
% 0.21/0.30 thf(decl_103, type, setadjoin__Cong: $o).
% 0.21/0.30 thf(decl_104, type, powerset__Cong: $o).
% 0.21/0.30 thf(decl_105, type, setunion__Cong: $o).
% 0.21/0.30 thf(decl_106, type, omega__Cong: $o).
% 0.21/0.30 thf(decl_107, type, exuEu: $o).
% 0.21/0.30 thf(decl_108, type, descr__Cong: $o).
% 0.21/0.30 thf(decl_109, type, dsetconstr__Cong: $o).
% 0.21/0.30 thf(decl_110, type, subset: $i > $i > $o).
% 0.21/0.30 thf(decl_113, type, subsetI1: $o).
% 0.21/0.30 thf(decl_114, type, eqimpsubset2: $o).
% 0.21/0.30 thf(decl_115, type, eqimpsubset1: $o).
% 0.21/0.30 thf(decl_116, type, subsetI2: $o).
% 0.21/0.30 thf(decl_117, type, emptysetsubset: $o).
% 0.21/0.30 thf(decl_118, type, subsetE: $o).
% 0.21/0.30 thf(decl_119, type, subsetE2: $o).
% 0.21/0.30 thf(decl_120, type, notsubsetI: $o).
% 0.21/0.30 thf(decl_121, type, notequalI1: $o).
% 0.21/0.30 thf(decl_122, type, epred1_0: $o).
% 0.21/0.30 thf(decl_123, type, esk1_2: $i > $i > $i).
% 0.21/0.30 thf(decl_124, type, esk2_2: $i > $i > $i).
% 0.21/0.30 thf(decl_125, type, esk3_2: $i > $i > $i).
% 0.21/0.30 thf(decl_126, type, esk4_1: $i > $i).
% 0.21/0.30 thf(decl_127, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.21/0.30 thf(decl_128, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.21/0.30 thf(decl_129, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.21/0.30 thf(decl_130, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.21/0.30 thf(decl_131, type, esk9_1: $i > $i).
% 0.21/0.30 thf(decl_132, type, esk10_2: ($i > $o) > $i > $i).
% 0.21/0.30 thf(decl_133, type, esk11_2: ($i > $o) > $i > $i).
% 0.21/0.30 thf(decl_134, type, esk12_1: ($i > $o) > $i).
% 0.21/0.30 thf(decl_135, type, esk13_2: ($i > $o) > $i > $i).
% 0.21/0.30 thf(decl_136, type, esk14_1: ($i > $o) > $i).
% 0.21/0.30 thf(decl_137, type, esk15_2: $i > $i > $i).
% 0.21/0.30 thf(decl_138, type, esk16_2: $i > $i > $i).
% 0.21/0.30 thf(decl_139, type, esk17_1: $i > $i).
% 0.21/0.30 thf(decl_140, type, esk18_1: $i > $i).
% 0.21/0.30 thf(decl_141, type, esk19_1: $i > $i).
% 0.21/0.30 thf(decl_142, type, esk20_2: $i > $i > $i).
% 0.21/0.30 thf(decl_143, type, esk21_3: $i > $i > $o > $i).
% 0.21/0.30 thf(decl_144, type, esk22_2: ($i > $o) > $i > $i).
% 0.21/0.30 thf(decl_145, type, esk23_1: ($i > $o) > $i).
% 0.21/0.30 thf(decl_146, type, esk24_1: $i > $i).
% 0.21/0.30 thf(decl_147, type, esk25_2: $i > ($i > $o) > $i).
% 0.21/0.30 thf(decl_148, type, esk26_2: $i > ($i > $o) > $i).
% 0.21/0.30 thf(decl_149, type, esk27_2: $i > ($i > $o) > $i).
% 0.21/0.30 thf(decl_150, type, esk28_2: $i > ($i > $o) > $i).
% 0.21/0.30 thf(decl_151, type, esk29_2: $i > ($i > $o) > $i).
% 0.21/0.30 thf(decl_152, type, esk30_2: $i > ($i > $o) > $i).
% 0.21/0.30 thf(decl_153, type, esk31_2: ($i > $o) > $i > $i).
% 0.21/0.30 thf(decl_154, type, esk32_1: ($i > $o) > $i).
% 0.21/0.30 thf(decl_155, type, esk33_1: ($i > $o) > $i).
% 0.21/0.30 thf(decl_156, type, esk34_1: ($i > $o) > $i).
% 0.21/0.30 thf(decl_157, type, esk35_1: ($i > $o) > $i).
% 0.21/0.30 thf(decl_158, type, esk36_2: ($i > $o) > $i > $i).
% 0.21/0.30 thf(decl_159, type, esk37_1: ($i > $o) > $i).
% 0.21/0.30 thf(decl_160, type, esk38_2: ($i > $o) > $i > $i).
% 0.21/0.30 thf(decl_161, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 0.21/0.30 thf(decl_162, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 0.21/0.30 thf(decl_163, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.21/0.30 thf(decl_164, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 0.21/0.30 thf(decl_165, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.21/0.30 thf(decl_166, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 0.21/0.30 thf(decl_167, type, esk45_2: ($i > $o) > $i > $i).
% 0.21/0.30 thf(decl_168, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 0.21/0.30 thf(decl_169, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 0.21/0.30 thf(decl_170, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.21/0.30 thf(decl_171, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.21/0.30 thf(decl_172, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.21/0.30 thf(decl_173, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.21/0.30 thf(decl_174, type, esk52_2: $i > $i > $i).
% 0.21/0.30 thf(decl_175, type, esk53_2: $i > $i > $i).
% 0.21/0.30 thf(decl_176, type, esk54_0: $i).
% 0.21/0.30 thf(decl_177, type, esk55_0: $i).
% 0.21/0.30 thf(decl_178, type, esk56_0: $i).
% 0.21/0.30 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', exu__Cong)).
% 0.21/0.30 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', exu)).
% 0.21/0.30 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', exuEu)).
% 0.21/0.30 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', descr__Cong)).
% 0.21/0.30 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', exuE1)).
% 0.21/0.30 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', descrp)).
% 0.21/0.30 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', exuE3e)).
% 0.21/0.30 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', nonempty)).
% 0.21/0.30 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', nonemptyI)).
% 0.21/0.30 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', exuE2)).
% 0.21/0.30 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', exuI2)).
% 0.21/0.30 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', exuI3)).
% 0.21/0.30 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', exuI1)).
% 0.21/0.30 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', exuE3u)).
% 0.21/0.30 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', replAx)).
% 0.21/0.30 thf(notequalI2, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', notequalI2)).
% 0.21/0.30 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', dsetconstr__Cong)).
% 0.21/0.30 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', dsetconstrER)).
% 0.21/0.30 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', dsetconstrEL)).
% 0.21/0.30 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', dsetconstrI)).
% 0.21/0.30 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', setbeta)).
% 0.21/0.30 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', nonemptyE1)).
% 0.21/0.30 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', nonemptyI1)).
% 0.21/0.30 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', setoftrueEq)).
% 0.21/0.30 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', nonemptyImpWitness)).
% 0.21/0.30 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', emptyE1)).
% 0.21/0.30 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', omega__Cong)).
% 0.21/0.30 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', emptyset__Cong)).
% 0.21/0.30 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/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', setadjoin__Cong)).
% 0.21/0.30 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', prop2setE)).
% 0.21/0.30 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', subsetI1)).
% 0.21/0.30 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', eqimpsubset2)).
% 0.21/0.30 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', eqimpsubset1)).
% 0.21/0.30 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', subsetI2)).
% 0.21/0.30 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', emptysetsubset)).
% 0.21/0.30 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', emptysetE)).
% 0.21/0.30 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', subsetE)).
% 0.21/0.30 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', subsetE2)).
% 0.21/0.30 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', notsubsetI)).
% 0.21/0.30 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', notequalI1)).
% 0.21/0.30 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', noeltsimpempty)).
% 0.21/0.30 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', emptyI)).
% 0.21/0.30 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', setext)).
% 0.21/0.30 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', notinemptyset)).
% 0.21/0.30 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', emptysetimpfalse)).
% 0.21/0.30 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', setadjoinOr)).
% 0.21/0.30 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', setadjoinE)).
% 0.21/0.30 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', setadjoinIR)).
% 0.21/0.30 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', emptyinunitempty)).
% 0.21/0.30 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', setadjoinIL)).
% 0.21/0.30 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', subPowSU)).
% 0.21/0.30 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', setunionE)).
% 0.21/0.30 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', setunionI)).
% 0.21/0.30 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', powersetE)).
% 0.21/0.30 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', emptyInPowerset)).
% 0.21/0.30 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', emptyinPowerset)).
% 0.21/0.30 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', powersetI)).
% 0.21/0.30 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', upairsetIL)).
% 0.21/0.30 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', upairsetE)).
% 0.21/0.30 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', singletonsswitch)).
% 0.21/0.30 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', eqinunit)).
% 0.21/0.30 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', notinsingleton)).
% 0.21/0.30 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', uniqinunit)).
% 0.21/0.30 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', upairsetIR)).
% 0.21/0.30 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', prop2setI)).
% 0.21/0.30 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', quantDeMorgan4)).
% 0.21/0.30 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', quantDeMorgan3)).
% 0.21/0.30 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', quantDeMorgan2)).
% 0.21/0.30 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', quantDeMorgan1)).
% 0.21/0.30 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', vacuousDall)).
% 0.21/0.30 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', prop2set2propI)).
% 0.21/0.30 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', in__Cong)).
% 0.21/0.30 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', inCongP)).
% 0.21/0.30 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', notdallE)).
% 0.21/0.30 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', powerset__Cong)).
% 0.21/0.30 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', notdexE)).
% 0.21/0.30 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', setunion__Cong)).
% 0.21/0.30 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', wellorderingAx)).
% 0.21/0.30 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/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', foundationAx)).
% 0.21/0.30 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', omegaIndAx)).
% 0.21/0.30 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', omegaSAx)).
% 0.21/0.30 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', omega0Ax)).
% 0.21/0.30 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', setunionAx)).
% 0.21/0.30 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', powersetAx)).
% 0.21/0.30 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', setadjoinAx)).
% 0.21/0.30 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', emptysetAx)).
% 0.21/0.30 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.or4bl1LETY/E---3.1_4028156.p', setextAx)).
% 0.21/0.30 thf(c_0_87, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.21/0.30 thf(c_0_88, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.21/0.30 thf(c_0_89, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 0.21/0.30 thf(c_0_90, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 0.21/0.30 thf(c_0_91, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.21/0.30 thf(c_0_92, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.21/0.30 thf(c_0_93, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.21/0.30 thf(c_0_94, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.21/0.30 thf(c_0_95, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.21/0.30 thf(c_0_96, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.21/0.30 thf(c_0_97, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.21/0.30 thf(c_0_98, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.21/0.30 thf(c_0_99, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 0.21/0.30 thf(c_0_100, 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])).
% 0.21/0.30 thf(c_0_101, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.21/0.30 thf(c_0_102, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[notequalI2])).
% 0.21/0.30 thf(c_0_103, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X274:$i]:(((((X1 @ X274)))&(![X275:$i]:(((((X1 @ X275)))=>(((X274)=(X275))))))))))<=>((?[X276:$i]:(((((X17 @ X276)))&(![X277:$i]:(((((X17 @ X277)))=>(((X276)=(X277)))))))))))))))), inference(apply_def,[status(thm)],[c_0_87, c_0_88])).
% 0.21/0.30 thf(c_0_104, plain, ((exuEu)=(![X1:$i > $o]:((((?[X278:$i]:(((((X1 @ X278)))&(![X279:$i]:(((((X1 @ X279)))=>(((X278)=(X279))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_89, c_0_88])).
% 0.21/0.30 thf(c_0_105, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X280:$i]:(((((X1 @ X280)))&(![X281:$i]:(((((X1 @ X281)))=>(((X280)=(X281))))))))))=>((((?[X282:$i]:(((((X17 @ X282)))&(![X283:$i]:(((((X17 @ X283)))=>(((X282)=(X283))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_90, c_0_88])).
% 0.21/0.30 thf(c_0_106, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 0.21/0.30 thf(c_0_107, plain, ((exuE1)=(![X1:$i > $o]:((((?[X260:$i]:(((((X1 @ X260)))&(![X261:$i]:(((((X1 @ X261)))=>(((X260)=(X261))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_91, c_0_88])).
% 0.21/0.30 thf(c_0_108, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.21/0.30 thf(c_0_109, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.21/0.30 thf(c_0_110, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.21/0.30 thf(c_0_111, plain, ((descrp)=(![X1:$i > $o]:((((?[X258:$i]:(((((X1 @ X258)))&(![X259:$i]:(((((X1 @ X259)))=>(((X258)=(X259))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_92, c_0_88])).
% 0.21/0.30 thf(c_0_112, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.21/0.30 thf(c_0_113, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X262:$i]:(((((X1 @ X262)))&(![X263:$i]:(((((X1 @ X263)))=>(((X262)=(X263))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_93, c_0_88])).
% 0.21/0.30 thf(c_0_114, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_94])).
% 0.21/0.30 thf(c_0_115, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_94])).
% 0.21/0.30 thf(c_0_116, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_95, c_0_94])).
% 0.21/0.30 thf(c_0_117, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.21/0.30 thf(c_0_118, plain, ((exuE2)=(![X1:$i > $o]:((((?[X264:$i]:(((((X1 @ X264)))&(![X265:$i]:(((((X1 @ X265)))=>(((X264)=(X265))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_96, c_0_88])).
% 0.21/0.30 thf(c_0_119, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_94])).
% 0.21/0.30 thf(c_0_120, 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])).
% 0.21/0.30 thf(c_0_121, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X270:$i]:(((((X1 @ X270)))&(![X271:$i]:(((((X1 @ X271)))=>(((X270)=(X271)))))))))))))), inference(apply_def,[status(thm)],[c_0_97, c_0_88])).
% 0.21/0.30 thf(c_0_122, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X268:$i]:(((((X1 @ X268)))&(![X269:$i]:(((((X1 @ X269)))=>(((X268)=(X269)))))))))))))))), inference(apply_def,[status(thm)],[c_0_98, c_0_88])).
% 0.21/0.30 thf(c_0_123, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X266:$i]:(((((X1 @ X266)))&(![X267:$i]:(((((X1 @ X267)))=>(((X266)=(X267)))))))))))))), inference(apply_def,[status(thm)],[c_0_99, c_0_88])).
% 0.21/0.30 thf(c_0_124, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X272:$i]:(((((X1 @ X272)))&(![X273:$i]:(((((X1 @ X273)))=>(((X272)=(X273))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_100, c_0_88])).
% 0.21/0.30 thf(c_0_125, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X256:$i]:(((((X6 @ X2 @ X256)))&(![X257:$i]:(((((X6 @ X2 @ X257)))=>(((X256)=(X257)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_101, c_0_88])).
% 0.21/0.30 thf(c_0_126, plain, ((epred1_0)<=>![X313:$i]:(?[X314:$i]:((((![X315:$i]:(((in @ X315 @ X314)=>![X316:$i]:(((in @ X316 @ X315)=>(in @ X316 @ X313)))))&![X317:$i, X318:$i]:((((in @ X317 @ X313)&(in @ X318 @ X313))=>(![X319:$i]:(((in @ X319 @ X314)=>((in @ X317 @ X319)<=>(in @ X318 @ X319))))=>((X317)=(X318))))))&![X320:$i, X321:$i]:((((in @ X320 @ X314)&(in @ X321 @ X314))=>(![X322:$i]:(((in @ X322 @ X320)=>(in @ X322 @ X321)))|![X323:$i]:(((in @ X323 @ X321)=>(in @ X323 @ X320)))))))&![X324:$i]:(((![X325:$i]:(((in @ X325 @ X324)=>(in @ X325 @ X313)))&?[X326:$i]:((in @ X326 @ X324)))=>?[X327:$i, X328:$i]:(((((in @ X327 @ X314)&(in @ X328 @ X324))&~(?[X329:$i]:(((in @ X329 @ X327)&(in @ X329 @ X324)))))&![X330:$i]:(((in @ X330 @ X314)=>(![X331:$i]:(((in @ X331 @ X330)=>(in @ X331 @ X327)))|(in @ X328 @ X330)))))))))))), introduced(definition)).
% 0.21/0.30 thf(c_0_127, negated_conjecture, ~((![X284:$i, X285:$i]:((![X286:$i]:(((in @ X286 @ X284)<=>(in @ X286 @ X285)))=>((X284)=(X285))))=>(![X287:$i]:(~(in @ X287 @ emptyset))=>(![X288:$i, X289:$i, X290:$i]:(((in @ X290 @ (setadjoin @ X288 @ X289))<=>(((X290)=(X288))|(in @ X290 @ X289))))=>(![X291:$i, X292:$i]:(((in @ X292 @ (powerset @ X291))<=>![X293:$i]:(((in @ X293 @ X292)=>(in @ X293 @ X291)))))=>(![X294:$i, X295:$i]:(((in @ X295 @ (setunion @ X294))<=>?[X296:$i]:(((in @ X295 @ X296)&(in @ X296 @ X294)))))=>((in @ emptyset @ omega)=>(![X297:$i]:(((in @ X297 @ omega)=>(in @ (setadjoin @ X297 @ X297) @ omega)))=>(![X298:$i]:((((in @ emptyset @ X298)&![X299:$i]:((((in @ X299 @ omega)&(in @ X299 @ X298))=>(in @ (setadjoin @ X299 @ X299) @ X298))))=>![X300:$i]:(((in @ X300 @ omega)=>(in @ X300 @ X298)))))=>(![X301:$i > $i > $o, X302:$i]:((![X303:$i]:(((in @ X303 @ X302)=>?[X304:$i]:(((X301 @ X303 @ X304)&![X305:$i]:(((X301 @ X303 @ X305)=>((X304)=(X305))))))))=>?[X306:$i]:(![X307:$i]:(((in @ X307 @ X306)<=>?[X308:$i]:(((in @ X308 @ X302)&(X301 @ X308 @ X307))))))))=>(![X309:$i]:((?[X310:$i]:((in @ X310 @ X309))=>?[X311:$i]:(((in @ X311 @ X309)&~(?[X312:$i]:(((in @ X312 @ X311)&(in @ X312 @ X309))))))))=>((epred1_0)=>(![X332:$i > $o]:((?[X333:$i]:(((X332 @ X333)&![X334:$i]:(((X332 @ X334)=>((X333)=(X334))))))=>(X332 @ (descr @ (^[Z0:$i]:(X332 @ Z0))))))=>(![X335:$i, X336:$i > $o, X337:$i]:(((in @ X337 @ X335)=>((X336 @ X337)=>(in @ X337 @ (dsetconstr @ X335 @ X336)))))=>(![X338:$i, X339:$i > $o, X340:$i]:(((in @ X340 @ (dsetconstr @ X338 @ X339))=>(in @ X340 @ X338)))=>(![X341:$i, X342:$i > $o, X343:$i]:(((in @ X343 @ (dsetconstr @ X341 @ X342))=>(X342 @ X343)))=>(![X344:$i > $o]:((?[X345:$i]:(((X344 @ X345)&![X346:$i]:(((X344 @ X346)=>((X345)=(X346))))))=>?[X347:$i]:(((X344 @ X347)&![X348:$i]:(((X344 @ X348)=>((X347)=(X348))))))))=>(![X349:$o, X350:$i]:(((in @ X350 @ (prop2set @ ((X349))))=>(X349)))=>(![X351:$i]:(((in @ X351 @ emptyset)=>![X352:$o]:((X352))))=>(![X353:$i]:(((in @ X353 @ emptyset)=>~($true)))=>(![X354:$i]:(~(in @ X354 @ emptyset))=>(![X355:$i > $o]:((?[X356:$i]:(((X355 @ X356)&![X357:$i]:(((X355 @ X357)=>((X356)=(X357))))))=>?[X358:$i]:((X355 @ X358))))=>(![X359:$i, X360:$i]:((![X361:$i]:(((in @ X361 @ X359)=>(in @ X361 @ X360)))=>(![X362:$i]:(((in @ X362 @ X360)=>(in @ X362 @ X359)))=>((X359)=(X360)))))=>(![X363:$i]:((![X364:$i]:(~(in @ X364 @ X363))=>((X363)=(emptyset))))=>(![X365:$i]:((![X366:$i]:(~(in @ X366 @ X365))=>((X365)=(emptyset))))=>(![X367:$i, X368:$i > $o, X369:$i]:(((in @ X369 @ X367)=>((in @ X369 @ (dsetconstr @ X367 @ X368))<=>(X368 @ X369))))=>(![X370:$i]:((((X370)!=(emptyset))=>?[X371:$i]:((in @ X371 @ X370))))=>(![X372:$i, X373:$i > $o, X374:$i]:(((in @ X374 @ X372)=>((X373 @ X374)=>((dsetconstr @ X372 @ X373)!=(emptyset)))))=>(![X375:$i]:((?[X376:$i]:((in @ X376 @ X375))=>((X375)!=(emptyset))))=>(![X377:$i, X378:$i]:((in @ X377 @ (setadjoin @ X377 @ X378)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X379:$i, X380:$i, X381:$i]:(((in @ X381 @ X380)=>(in @ X381 @ (setadjoin @ X379 @ X380))))=>(![X382:$i, X383:$i, X384:$i]:(((in @ X384 @ (setadjoin @ X382 @ X383))=>![X385:$o]:(((((X384)=(X382))=>(X385))=>(((in @ X384 @ X383)=>(X385))=>(X385))))))=>(![X386:$i, X387:$i, X388:$i]:(((in @ X388 @ (setadjoin @ X386 @ X387))=>(((X388)=(X386))|(in @ X388 @ X387))))=>(![X389:$i]:(((dsetconstr @ X389 @ (^[Z0:$i]:($true)))=(X389)))=>(![X390:$i, X391:$i]:((![X392:$i]:(((in @ X392 @ X391)=>(in @ X392 @ X390)))=>(in @ X391 @ (powerset @ X390))))=>(![X393:$i]:((in @ emptyset @ (powerset @ X393)))=>(![X394:$i]:((in @ emptyset @ (powerset @ X394)))=>(![X395:$i, X396:$i, X397:$i]:(((in @ X396 @ (powerset @ X395))=>((in @ X397 @ X396)=>(in @ X397 @ X395))))=>(![X398:$i, X399:$i, X400:$i]:(((in @ X399 @ X400)=>((in @ X400 @ X398)=>(in @ X399 @ (setunion @ X398)))))=>(![X401:$i, X402:$i]:(((in @ X402 @ (setunion @ X401))=>![X403:$o]:((![X404:$i]:(((in @ X402 @ X404)=>((in @ X404 @ X401)=>(X403))))=>(X403)))))=>(![X405:$i, X406:$i]:(((in @ X406 @ X405)=>(in @ X406 @ (powerset @ (setunion @ X405)))))=>(![X407:$i > $o]:((?[X408:$i]:(((X407 @ X408)&![X409:$i]:(((X407 @ X409)=>((X408)=(X409))))))=>?[X410:$i]:(![X411:$i]:(((X407 @ X411)<=>((X411)=(X410)))))))=>(![X412:$i]:((((X412)!=(emptyset))=>?[X413:$i]:(((in @ X413 @ X412)&$true))))=>(![X414:$i, X415:$i]:(((in @ X414 @ (setadjoin @ X415 @ emptyset))=>((X414)=(X415))))=>(![X416:$i, X417:$i]:((((X416)!=(X417))=>~(in @ X417 @ (setadjoin @ X416 @ emptyset))))=>(![X418:$i, X419:$i]:((((X418)=(X419))=>(in @ X418 @ (setadjoin @ X419 @ emptyset))))=>(![X420:$i, X421:$i]:(((in @ X420 @ (setadjoin @ X421 @ emptyset))=>(in @ X421 @ (setadjoin @ X420 @ emptyset))))=>(![X422:$i, X423:$i, X424:$i]:(((in @ X424 @ (setadjoin @ X422 @ (setadjoin @ X423 @ emptyset)))=>(((X424)=(X422))|((X424)=(X423)))))=>(![X425:$i, X426:$i]:((in @ X425 @ (setadjoin @ X425 @ (setadjoin @ X426 @ emptyset))))=>(![X427:$i, X428:$i]:((in @ X428 @ (setadjoin @ X427 @ (setadjoin @ X428 @ emptyset))))=>(![X429:$i, X430:$i > $o]:((?[X431:$i]:(((in @ X431 @ X429)&(X430 @ X431)))=>(((dsetconstr @ X429 @ X430)=(emptyset))=>~($true))))=>(![X432:$i > $o, X433:$i]:(((in @ X433 @ emptyset)=>(X432 @ X433)))=>(![X434:$i, X435:$i > $o]:((~(![X436:$i]:(((in @ X436 @ X434)=>(X435 @ X436))))=>?[X437:$i]:(((in @ X437 @ X434)&~((X435 @ X437))))))=>(![X438:$i, X439:$i > $o]:((![X440:$i]:(((in @ X440 @ X438)=>~((X439 @ X440))))=>~(?[X441:$i]:(((in @ X441 @ X438)&(X439 @ X441))))))=>(![X442:$i, X443:$i > $o]:((~(?[X444:$i]:(((in @ X444 @ X442)&(X443 @ X444))))=>![X445:$i]:(((in @ X445 @ X442)=>~((X443 @ X445))))))=>(![X446:$i, X447:$i > $o]:((?[X448:$i]:(((in @ X448 @ X446)&~((X447 @ X448))))=>~(![X449:$i]:(((in @ X449 @ X446)=>(X447 @ X449))))))=>(![X450:$o]:(((X450)=>(in @ emptyset @ (prop2set @ ((X450))))))=>(![X451:$o]:(((X451)=>(set2prop @ (prop2set @ ((X451))))))=>(![X452:$i, X453:$i > $o]:((~(?[X454:$i]:(((in @ X454 @ X452)&(X453 @ X454))))=>![X455:$i]:(((in @ X455 @ X452)=>~((X453 @ X455))))))=>(![X456:$i, X457:$i > $o]:((~(![X458:$i]:(((in @ X458 @ X456)=>(X457 @ X458))))=>?[X459:$i]:(((in @ X459 @ X456)&~((X457 @ X459))))))=>(![X460:$i > $o]:((?[X461:$i]:(((X460 @ X461)&![X462:$i]:(((X460 @ X462)=>((X461)=(X462))))))=>?[X463:$i]:(((X460 @ X463)&![X464:$i]:(((X460 @ X464)=>((X463)=(X464))))))))=>(![X465:$i > $o]:((?[X466:$i]:((X465 @ X466))=>(![X467:$i, X468:$i]:(((X465 @ X467)=>((X465 @ X468)=>((X467)=(X468)))))=>?[X469:$i]:(((X465 @ X469)&![X470:$i]:(((X465 @ X470)=>((X469)=(X470)))))))))=>(![X471:$i > $o]:((?[X472:$i]:(![X473:$i]:(((X471 @ X473)<=>((X473)=(X472)))))=>?[X474:$i]:(((X471 @ X474)&![X475:$i]:(((X471 @ X475)=>((X474)=(X475))))))))=>(![X476:$i, X477:$i]:((((X476)=(X477))=>![X478:$i, X479:$i]:((((X478)=(X479))=>((in @ X478 @ X476)=>(in @ X479 @ X477))))))=>(![X480:$i, X481:$i]:((((X480)=(X481))=>![X482:$i, X483:$i]:((((X482)=(X483))=>((in @ X482 @ X480)<=>(in @ X483 @ X481))))))=>(![X484:$i > $o]:((?[X485:$i]:(((X484 @ X485)&![X486:$i]:(((X484 @ X486)=>((X485)=(X486))))))=>![X487:$i, X488:$i]:(((X484 @ X487)=>((X484 @ X488)=>((X487)=(X488)))))))=>(![X489:$i > $o, X490:$i > $o]:((![X491:$i, X492:$i]:((((X491)=(X492))=>((X489 @ X491)<=>(X490 @ X492))))=>(?[X493:$i]:(((X489 @ X493)&![X494:$i]:(((X489 @ X494)=>((X493)=(X494))))))<=>?[X495:$i]:(((X490 @ X495)&![X496:$i]:(((X490 @ X496)=>((X495)=(X496)))))))))=>(((emptyset)=(emptyset))=>(![X497:$i, X498:$i]:((((X497)=(X498))=>![X499:$i, X500:$i]:((((X499)=(X500))=>((setadjoin @ X497 @ X499)=(setadjoin @ X498 @ X500))))))=>(![X501:$i, X502:$i]:((((X501)=(X502))=>((powerset @ X501)=(powerset @ X502))))=>(![X503:$i, X504:$i]:((((X503)=(X504))=>((setunion @ X503)=(setunion @ X504))))=>(((omega)=(omega))=>(![X505:$i > $o]:((?[X506:$i]:(((X505 @ X506)&![X507:$i]:(((X505 @ X507)=>((X506)=(X507))))))=>![X508:$i, X509:$i]:(((X505 @ X508)=>((X505 @ X509)=>((X508)=(X509)))))))=>(![X510:$i > $o, X511:$i > $o]:((![X512:$i, X513:$i]:((((X512)=(X513))=>((X510 @ X512)<=>(X511 @ X513))))=>(?[X514:$i]:(((X510 @ X514)&![X515:$i]:(((X510 @ X515)=>((X514)=(X515))))))=>(?[X516:$i]:(((X511 @ X516)&![X517:$i]:(((X511 @ X517)=>((X516)=(X517))))))=>((descr @ X510)=(descr @ X511))))))=>(![X518:$i, X519:$i]:((((X518)=(X519))=>![X520:$i > $o, X521:$i > $o]:((![X522:$i]:(((in @ X522 @ X518)=>![X523:$i]:(((in @ X523 @ X519)=>(((X522)=(X523))=>((X520 @ X522)<=>(X521 @ X523)))))))=>((dsetconstr @ X518 @ X520)=(dsetconstr @ X519 @ X521))))))=>(![X524:$i, X525:$i]:((![X526:$i]:(((in @ X526 @ X524)=>(in @ X526 @ X525)))=>(subset @ X524 @ X525)))=>(![X527:$i, X528:$i]:((((X527)=(X528))=>(subset @ X528 @ X527)))=>(![X529:$i, X530:$i]:((((X529)=(X530))=>(subset @ X529 @ X530)))=>(![X531:$i, X532:$i]:((![X533:$i]:(((in @ X533 @ X531)=>(in @ X533 @ X532)))=>(subset @ X531 @ X532)))=>(![X534:$i]:((subset @ emptyset @ X534))=>(![X535:$i, X536:$i, X537:$i]:(((subset @ X535 @ X536)=>((in @ X537 @ X535)=>(in @ X537 @ X536))))=>(![X538:$i, X539:$i, X540:$i]:(((subset @ X538 @ X539)=>(~(in @ X540 @ X539)=>~(in @ X540 @ X538))))=>(![X541:$i, X542:$i, X543:$i]:(((in @ X543 @ X541)=>(~(in @ X543 @ X542)=>~(subset @ X541 @ X542))))=>(![X544:$i, X545:$i]:((~(subset @ X544 @ X545)=>((X544)!=(X545))))=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~(in @ X2 @ X5)=>((X4)!=(X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_102, omega__Cong]), c_0_103]), emptyset__Cong]), setadjoin__Cong]), c_0_104]), c_0_105]), prop2setE]), c_0_106]), c_0_107]), subsetI1]), c_0_108]), eqimpsubset2]), c_0_109]), eqimpsubset1]), c_0_110]), subsetI2]), c_0_111]), emptysetsubset]), emptysetE]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), c_0_112]), noeltsimpempty]), emptyI]), setext]), c_0_113]), notinemptyset]), emptysetimpfalse]), c_0_114]), setadjoinOr]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), c_0_115]), c_0_116]), c_0_117]), subPowSU]), setunionE]), setunionI]), powersetE]), emptyInPowerset]), emptyinPowerset]), powersetI]), c_0_118]), upairsetIL]), upairsetE]), singletonsswitch]), eqinunit]), notinsingleton]), uniqinunit]), c_0_119]), upairsetIR]), prop2setI]), quantDeMorgan4]), quantDeMorgan3]), quantDeMorgan2]), quantDeMorgan1]), vacuousDall]), c_0_120]), prop2set2propI]), in__Cong]), inCongP]), c_0_121]), c_0_122]), c_0_123]), notdallE]), powerset__Cong]), notdexE]), setunion__Cong]), c_0_124]), wellorderingAx]), foundationAx]), c_0_125]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_126])).
% 0.21/0.30 thf(c_0_128, negated_conjecture, ![X546:$i, X547:$i, X549:$i, X550:$i, X551:$i, X552:$i, X553:$i, X554:$i, X555:$i, X556:$i, X557:$i, X559:$i, X560:$i, X562:$i, X563:$i, X564:$i, X565:$i, X566:$i, X568:$i, X569:$i > $i > $o, X570:$i, X572:$i, X575:$i, X577:$i, X578:$i, X579:$i, X580:$i, X582:$i, X583:$i > $o, X584:$i, X586:$i, X587:$i > $o, X588:$i, X589:$i, X590:$i > $o, X591:$i, X592:$i, X593:$i > $o, X594:$i, X595:$i > $o, X596:$i, X599:$i, X600:$o, X601:$i, X602:$i, X603:$o, X604:$i, X605:$i, X606:$i > $o, X607:$i, X610:$i, X611:$i, X614:$i, X616:$i, X618:$i, X619:$i > $o, X620:$i, X621:$i, X623:$i, X624:$i > $o, X625:$i, X626:$i, X627:$i, X628:$i, X629:$i, X630:$i, X631:$i, X632:$i, X633:$i, X634:$i, X635:$i, X636:$o, X637:$i, X638:$i, X639:$i, X640:$i, X641:$i, X642:$i, X644:$i, X645:$i, X646:$i, X647:$i, X648:$i, X649:$i, X650:$i, X651:$i, X652:$i, X653:$i, X654:$o, X656:$i, X657:$i, X658:$i > $o, X659:$i, X662:$i, X663:$i, X664:$i, X666:$i, X667:$i, X668:$i, X669:$i, X670:$i, X671:$i, X672:$i, X673:$i, X674:$i, X675:$i, X676:$i, X677:$i, X678:$i, X679:$i, X680:$i, X681:$i, X682:$i > $o, X683:$i, X684:$i > $o, X685:$i, X686:$i, X687:$i > $o, X688:$i, X690:$i, X691:$i > $o, X693:$i, X694:$i, X695:$i > $o, X697:$i, X698:$i, X699:$i > $o, X700:$i, X702:$o, X703:$o, X704:$i, X705:$i > $o, X707:$i, X708:$i, X709:$i > $o, X710:$i, X712:$i > $o, X713:$i, X716:$i, X717:$i > $o, X718:$i, X722:$i, X723:$i > $o, X724:$i, X727:$i, X728:$i, X729:$i, X730:$i, X731:$i, X732:$i, X733:$i, X734:$i, X735:$i, X736:$i > $o, X737:$i, X739:$i, X740:$i, X741:$i > $o, X742:$i > $o, X745:$i, X748:$i, X749:$i, X752:$i, X753:$i, X754:$i, X755:$i, X756:$i, X757:$i, X758:$i, X759:$i, X760:$i, X761:$i > $o, X762:$i, X764:$i, X765:$i, X766:$i > $o, X767:$i > $o, X770:$i, X772:$i, X774:$i, X775:$i, X776:$i > $o, X777:$i > $o, X780:$i, X781:$i, X783:$i, X784:$i, X785:$i, X786:$i, X787:$i, X788:$i, X790:$i, X791:$i, X792:$i, X793:$i, X794:$i, X795:$i, X796:$i, X797:$i, X798:$i, X799:$i, X800:$i, X801:$i]:((((~(in @ (esk1_2 @ X546 @ X547) @ X546)|~(in @ (esk1_2 @ X546 @ X547) @ X547)|((X546)=(X547)))&((in @ (esk1_2 @ X546 @ X547) @ X546)|(in @ (esk1_2 @ X546 @ X547) @ X547)|((X546)=(X547))))&(~(in @ X549 @ emptyset)&(((~(in @ X552 @ (setadjoin @ X550 @ X551))|(((X552)=(X550))|(in @ X552 @ X551)))&((((X552)!=(X550))|(in @ X552 @ (setadjoin @ X550 @ X551)))&(~(in @ X552 @ X551)|(in @ X552 @ (setadjoin @ X550 @ X551)))))&(((~(in @ X554 @ (powerset @ X553))|(~(in @ X555 @ X554)|(in @ X555 @ X553)))&(((in @ (esk2_2 @ X556 @ X557) @ X557)|(in @ X557 @ (powerset @ X556)))&(~(in @ (esk2_2 @ X556 @ X557) @ X556)|(in @ X557 @ (powerset @ X556)))))&(((((in @ X560 @ (esk3_2 @ X559 @ X560))|~(in @ X560 @ (setunion @ X559)))&((in @ (esk3_2 @ X559 @ X560) @ X559)|~(in @ X560 @ (setunion @ X559))))&(~(in @ X563 @ X564)|~(in @ X564 @ X562)|(in @ X563 @ (setunion @ X562))))&((in @ emptyset @ omega)&((~(in @ X565 @ omega)|(in @ (setadjoin @ X565 @ X565) @ 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X741 @ X742))))&(~(X742 @ X748)|((esk42_2 @ X741 @ X742)=(X748))|(((X745)!=(esk41_3 @ X741 @ X742 @ X745))|~(X741 @ X745))|((X741 @ (esk39_2 @ X741 @ X742))|(X742 @ (esk40_2 @ X741 @ X742))))))&((((X741 @ (esk44_2 @ X741 @ X742))|((X742 @ (esk43_3 @ X741 @ X742 @ X749))|~(X742 @ X749))|((X741 @ (esk39_2 @ X741 @ X742))|(X742 @ (esk40_2 @ X741 @ X742))))&(~(X741 @ X752)|((esk44_2 @ X741 @ X742)=(X752))|((X742 @ (esk43_3 @ X741 @ X742 @ X749))|~(X742 @ X749))|((X741 @ (esk39_2 @ X741 @ X742))|(X742 @ (esk40_2 @ X741 @ X742)))))&(((X741 @ (esk44_2 @ X741 @ X742))|(((X749)!=(esk43_3 @ X741 @ X742 @ X749))|~(X742 @ X749))|((X741 @ (esk39_2 @ X741 @ X742))|(X742 @ (esk40_2 @ X741 @ X742))))&(~(X741 @ X752)|((esk44_2 @ X741 @ X742)=(X752))|(((X749)!=(esk43_3 @ X741 @ X742 @ X749))|~(X742 @ X749))|((X741 @ (esk39_2 @ X741 @ X742))|(X742 @ (esk40_2 @ X741 @ X742)))))))))&(((emptyset)=(emptyset))&((((X753)!=(X754))|(((X755)!=(X756))|((setadjoin @ X753 @ X755)=(setadjoin @ X754 @ X756))))&((((X757)!=(X758))|((powerset @ X757)=(powerset @ X758)))&((((X759)!=(X760))|((setunion @ X759)=(setunion @ X760)))&(((omega)=(omega))&((((X761 @ (esk45_2 @ X761 @ X762))|~(X761 @ X762)|(~(X761 @ X764)|(~(X761 @ X765)|((X764)=(X765)))))&(((X762)!=(esk45_2 @ X761 @ X762))|~(X761 @ X762)|(~(X761 @ X764)|(~(X761 @ X765)|((X764)=(X765))))))&((((((X767 @ (esk49_3 @ X766 @ X767 @ X772))|~(X767 @ X772)|((descr @ X766)=(descr @ X767))|((X766 @ (esk48_3 @ X766 @ X767 @ X770))|~(X766 @ X770))|((esk46_2 @ X766 @ X767)=(esk47_2 @ X766 @ X767)))&(((X772)!=(esk49_3 @ X766 @ X767 @ X772))|~(X767 @ X772)|((descr @ X766)=(descr @ X767))|((X766 @ (esk48_3 @ X766 @ X767 @ X770))|~(X766 @ X770))|((esk46_2 @ X766 @ X767)=(esk47_2 @ X766 @ X767))))&(((X767 @ (esk49_3 @ X766 @ X767 @ X772))|~(X767 @ X772)|((descr @ X766)=(descr @ X767))|(((X770)!=(esk48_3 @ X766 @ X767 @ X770))|~(X766 @ X770))|((esk46_2 @ X766 @ X767)=(esk47_2 @ X766 @ X767)))&(((X772)!=(esk49_3 @ X766 @ X767 @ X772))|~(X767 @ X772)|((descr @ X766)=(descr @ X767))|(((X770)!=(esk48_3 @ X766 @ X767 @ X770))|~(X766 @ X770))|((esk46_2 @ X766 @ X767)=(esk47_2 @ X766 @ X767)))))&(((((X767 @ (esk49_3 @ X766 @ X767 @ X772))|~(X767 @ X772)|((descr @ X766)=(descr @ X767))|((X766 @ (esk48_3 @ X766 @ X767 @ X770))|~(X766 @ X770))|(~(X766 @ (esk46_2 @ X766 @ X767))|~(X767 @ (esk47_2 @ X766 @ X767))))&(((X772)!=(esk49_3 @ X766 @ X767 @ X772))|~(X767 @ X772)|((descr @ X766)=(descr @ X767))|((X766 @ (esk48_3 @ X766 @ X767 @ X770))|~(X766 @ X770))|(~(X766 @ (esk46_2 @ X766 @ X767))|~(X767 @ (esk47_2 @ X766 @ X767)))))&(((X767 @ (esk49_3 @ X766 @ X767 @ X772))|~(X767 @ X772)|((descr @ X766)=(descr @ X767))|(((X770)!=(esk48_3 @ X766 @ X767 @ X770))|~(X766 @ X770))|(~(X766 @ (esk46_2 @ X766 @ X767))|~(X767 @ (esk47_2 @ X766 @ X767))))&(((X772)!=(esk49_3 @ X766 @ X767 @ X772))|~(X767 @ X772)|((descr @ X766)=(descr @ X767))|(((X770)!=(esk48_3 @ X766 @ X767 @ X770))|~(X766 @ X770))|(~(X766 @ (esk46_2 @ X766 @ X767))|~(X767 @ (esk47_2 @ X766 @ X767))))))&((((X767 @ (esk49_3 @ X766 @ X767 @ X772))|~(X767 @ X772)|((descr @ X766)=(descr @ X767))|((X766 @ (esk48_3 @ X766 @ X767 @ X770))|~(X766 @ X770))|((X766 @ (esk46_2 @ X766 @ X767))|(X767 @ (esk47_2 @ X766 @ X767))))&(((X772)!=(esk49_3 @ X766 @ X767 @ X772))|~(X767 @ X772)|((descr @ X766)=(descr @ X767))|((X766 @ (esk48_3 @ X766 @ X767 @ X770))|~(X766 @ X770))|((X766 @ (esk46_2 @ X766 @ X767))|(X767 @ (esk47_2 @ X766 @ X767)))))&(((X767 @ (esk49_3 @ X766 @ X767 @ X772))|~(X767 @ X772)|((descr @ X766)=(descr @ X767))|(((X770)!=(esk48_3 @ X766 @ X767 @ X770))|~(X766 @ X770))|((X766 @ (esk46_2 @ X766 @ X767))|(X767 @ (esk47_2 @ X766 @ X767))))&(((X772)!=(esk49_3 @ X766 @ X767 @ X772))|~(X767 @ X772)|((descr @ X766)=(descr @ X767))|(((X770)!=(esk48_3 @ X766 @ X767 @ X770))|~(X766 @ X770))|((X766 @ (esk46_2 @ X766 @ X767))|(X767 @ (esk47_2 @ X766 @ X767))))))))&((((in @ (esk50_4 @ X774 @ X775 @ X776 @ X777) @ X774)|((dsetconstr @ X774 @ X776)=(dsetconstr @ X775 @ X777))|((X774)!=(X775)))&(((in @ (esk51_4 @ X774 @ X775 @ X776 @ X777) @ X775)|((dsetconstr @ X774 @ X776)=(dsetconstr @ X775 @ X777))|((X774)!=(X775)))&((((esk50_4 @ X774 @ X775 @ X776 @ X777)=(esk51_4 @ X774 @ X775 @ X776 @ X777))|((dsetconstr @ X774 @ X776)=(dsetconstr @ X775 @ X777))|((X774)!=(X775)))&((~(X776 @ (esk50_4 @ X774 @ X775 @ X776 @ X777))|~(X777 @ (esk51_4 @ X774 @ X775 @ X776 @ X777))|((dsetconstr @ X774 @ X776)=(dsetconstr @ X775 @ X777))|((X774)!=(X775)))&((X776 @ (esk50_4 @ X774 @ X775 @ X776 @ X777))|(X777 @ (esk51_4 @ X774 @ X775 @ X776 @ X777))|((dsetconstr @ X774 @ X776)=(dsetconstr @ X775 @ X777))|((X774)!=(X775)))))))&((((in @ (esk52_2 @ X780 @ X781) @ X780)|(subset @ X780 @ X781))&(~(in @ (esk52_2 @ X780 @ X781) @ X781)|(subset @ X780 @ X781)))&((((X783)!=(X784))|(subset @ X784 @ X783))&((((X785)!=(X786))|(subset @ X785 @ X786))&((((in @ (esk53_2 @ X787 @ X788) @ X787)|(subset @ X787 @ X788))&(~(in @ (esk53_2 @ X787 @ X788) @ X788)|(subset @ X787 @ X788)))&((subset @ emptyset @ X790)&((~(subset @ X791 @ X792)|(~(in @ X793 @ X791)|(in @ X793 @ X792)))&((~(subset @ X794 @ X795)|((in @ X796 @ X795)|~(in @ X796 @ X794)))&((~(in @ X799 @ X797)|((in @ X799 @ X798)|~(subset @ X797 @ X798)))&(((subset @ X800 @ X801)|((X800)!=(X801)))&((in @ esk56_0 @ esk54_0)&(~(in @ esk56_0 @ esk55_0)&((esk54_0)=(esk55_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_127])])])])])])])).
% 0.21/0.30 thf(c_0_129, negated_conjecture, ~((in @ esk56_0 @ esk55_0)), inference(split_conjunct,[status(thm)],[c_0_128])).
% 0.21/0.30 thf(c_0_130, negated_conjecture, ((esk54_0)=(esk55_0)), inference(split_conjunct,[status(thm)],[c_0_128])).
% 0.21/0.30 thf(c_0_131, negated_conjecture, (in @ esk56_0 @ esk54_0), inference(split_conjunct,[status(thm)],[c_0_128])).
% 0.21/0.30 thf(c_0_132, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_129, c_0_130]), c_0_131])]), ['proof']).
% 0.21/0.30 % SZS output end CNFRefutation
% 0.21/0.30 % Parsed axioms : 186
% 0.21/0.30 % Removed by relevancy pruning/SinE : 99
% 0.21/0.30 % Initial clauses : 197
% 0.21/0.30 % Removed in clause preprocessing : 13
% 0.21/0.30 % Initial clauses in saturation : 184
% 0.21/0.30 % Processed clauses : 7
% 0.21/0.30 % ...of these trivial : 0
% 0.21/0.30 % ...subsumed : 0
% 0.21/0.30 % ...remaining for further processing : 6
% 0.21/0.30 % Other redundant clauses eliminated : 0
% 0.21/0.30 % Clauses deleted for lack of memory : 0
% 0.21/0.30 % Backward-subsumed : 0
% 0.21/0.30 % Backward-rewritten : 0
% 0.21/0.30 % Generated clauses : 0
% 0.21/0.30 % ...of the previous two non-redundant : 0
% 0.21/0.30 % ...aggressively subsumed : 0
% 0.21/0.30 % Contextual simplify-reflections : 0
% 0.21/0.30 % Paramodulations : 0
% 0.21/0.30 % Factorizations : 0
% 0.21/0.30 % NegExts : 0
% 0.21/0.30 % Equation resolutions : 0
% 0.21/0.30 % Disequality decompositions : 0
% 0.21/0.30 % Total rewrite steps : 2
% 0.21/0.30 % ...of those cached : 0
% 0.21/0.30 % Propositional unsat checks : 0
% 0.21/0.30 % Propositional check models : 0
% 0.21/0.30 % Propositional check unsatisfiable : 0
% 0.21/0.30 % Propositional clauses : 0
% 0.21/0.30 % Propositional clauses after purity: 0
% 0.21/0.30 % Propositional unsat core size : 0
% 0.21/0.30 % Propositional preprocessing time : 0.000
% 0.21/0.30 % Propositional encoding time : 0.000
% 0.21/0.30 % Propositional solver time : 0.000
% 0.21/0.30 % Success case prop preproc time : 0.000
% 0.21/0.30 % Success case prop encoding time : 0.000
% 0.21/0.30 % Success case prop solver time : 0.000
% 0.21/0.30 % Current number of processed clauses : 6
% 0.21/0.30 % Positive orientable unit clauses : 6
% 0.21/0.30 % Positive unorientable unit clauses: 0
% 0.21/0.30 % Negative unit clauses : 0
% 0.21/0.30 % Non-unit-clauses : 0
% 0.21/0.30 % Current number of unprocessed clauses: 177
% 0.21/0.30 % ...number of literals in the above : 632
% 0.21/0.30 % Current number of archived formulas : 0
% 0.21/0.30 % Current number of archived clauses : 0
% 0.21/0.30 % Clause-clause subsumption calls (NU) : 0
% 0.21/0.30 % Rec. Clause-clause subsumption calls : 0
% 0.21/0.30 % Non-unit clause-clause subsumptions : 0
% 0.21/0.30 % Unit Clause-clause subsumption calls : 0
% 0.21/0.30 % Rewrite failures with RHS unbound : 0
% 0.21/0.30 % BW rewrite match attempts : 0
% 0.21/0.30 % BW rewrite match successes : 0
% 0.21/0.30 % Condensation attempts : 0
% 0.21/0.30 % Condensation successes : 0
% 0.21/0.30 % Termbank termtop insertions : 24011
% 0.21/0.30 % Search garbage collected termcells : 9783
% 0.21/0.30
% 0.21/0.30 % -------------------------------------------------
% 0.21/0.30 % User time : 0.018 s
% 0.21/0.30 % System time : 0.007 s
% 0.21/0.30 % Total time : 0.025 s
% 0.21/0.30 % Maximum resident set size: 6376 pages
% 0.21/0.30
% 0.21/0.30 % -------------------------------------------------
% 0.21/0.30 % User time : 0.022 s
% 0.21/0.30 % System time : 0.013 s
% 0.21/0.30 % Total time : 0.034 s
% 0.21/0.30 % Maximum resident set size: 5120 pages
% 0.21/0.30 % E exiting
%------------------------------------------------------------------------------