%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU567^1 : 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 : n017.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
% 0.00/0.02 % Problem : SEU567^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n017.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 13:46:07 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.25 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.KhgdTdgaR9/E---3.1_367545.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 % new_bool_2 with pid 367589 completed with status 0
% 0.21/0.30 % Result found by new_bool_2
% 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 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.21/0.30 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.30 % Search class: HGHSM-FSLM31-SHFMMMBN
% 0.21/0.30 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.30 % Starting SubtermCWHack with 28s (1) cores
% 0.21/0.30 % SubtermCWHack with pid 367598 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 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.30 % Starting new_bool_2 with 300s (1) cores
% 0.21/0.30 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.21/0.30 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.30 % Search class: HGHSM-FSLM31-SHFMMMBN
% 0.21/0.30 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.30 % Starting SubtermCWHack with 28s (1) cores
% 0.21/0.30 % Preprocessing time : 0.002 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_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, epred1_0: $o).
% 0.21/0.30 thf(decl_122, type, esk1_2: $i > $i > $i).
% 0.21/0.30 thf(decl_123, type, esk2_2: $i > $i > $i).
% 0.21/0.30 thf(decl_124, type, esk3_2: $i > $i > $i).
% 0.21/0.30 thf(decl_125, type, esk4_1: $i > $i).
% 0.21/0.30 thf(decl_126, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.21/0.30 thf(decl_127, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.21/0.30 thf(decl_128, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.21/0.30 thf(decl_129, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.21/0.30 thf(decl_130, type, esk9_1: $i > $i).
% 0.21/0.30 thf(decl_131, type, esk10_2: ($i > $o) > $i > $i).
% 0.21/0.30 thf(decl_132, type, esk11_2: ($i > $o) > $i > $i).
% 0.21/0.30 thf(decl_133, type, esk12_1: ($i > $o) > $i).
% 0.21/0.30 thf(decl_134, type, esk13_2: ($i > $o) > $i > $i).
% 0.21/0.30 thf(decl_135, type, esk14_1: ($i > $o) > $i).
% 0.21/0.30 thf(decl_136, type, esk15_2: $i > $i > $i).
% 0.21/0.30 thf(decl_137, type, esk16_2: $i > $i > $i).
% 0.21/0.30 thf(decl_138, type, esk17_1: $i > $i).
% 0.21/0.30 thf(decl_139, type, esk18_1: $i > $i).
% 0.21/0.30 thf(decl_140, type, esk19_1: $i > $i).
% 0.21/0.30 thf(decl_141, type, esk20_2: $i > $i > $i).
% 0.21/0.30 thf(decl_142, type, esk21_3: $i > $i > $o > $i).
% 0.21/0.30 thf(decl_143, type, esk22_2: ($i > $o) > $i > $i).
% 0.21/0.30 thf(decl_144, type, esk23_1: ($i > $o) > $i).
% 0.21/0.30 thf(decl_145, type, esk24_1: $i > $i).
% 0.21/0.30 thf(decl_146, type, esk25_2: $i > ($i > $o) > $i).
% 0.21/0.30 thf(decl_147, type, esk26_2: $i > ($i > $o) > $i).
% 0.21/0.30 thf(decl_148, type, esk27_2: $i > ($i > $o) > $i).
% 0.21/0.30 thf(decl_149, type, esk28_2: $i > ($i > $o) > $i).
% 0.21/0.30 thf(decl_150, type, esk29_2: $i > ($i > $o) > $i).
% 0.21/0.30 thf(decl_151, type, esk30_2: $i > ($i > $o) > $i).
% 0.21/0.30 thf(decl_152, type, esk31_2: ($i > $o) > $i > $i).
% 0.21/0.30 thf(decl_153, type, esk32_1: ($i > $o) > $i).
% 0.21/0.30 thf(decl_154, type, esk33_1: ($i > $o) > $i).
% 0.21/0.30 thf(decl_155, type, esk34_1: ($i > $o) > $i).
% 0.21/0.30 thf(decl_156, type, esk35_1: ($i > $o) > $i).
% 0.21/0.30 thf(decl_157, type, esk36_2: ($i > $o) > $i > $i).
% 0.21/0.30 thf(decl_158, type, esk37_1: ($i > $o) > $i).
% 0.21/0.30 thf(decl_159, type, esk38_2: ($i > $o) > $i > $i).
% 0.21/0.30 thf(decl_160, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 0.21/0.30 thf(decl_161, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 0.21/0.30 thf(decl_162, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.21/0.30 thf(decl_163, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 0.21/0.30 thf(decl_164, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.21/0.30 thf(decl_165, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 0.21/0.30 thf(decl_166, type, esk45_2: ($i > $o) > $i > $i).
% 0.21/0.30 thf(decl_167, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 0.21/0.30 thf(decl_168, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 0.21/0.30 thf(decl_169, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.21/0.30 thf(decl_170, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.21/0.30 thf(decl_171, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.21/0.30 thf(decl_172, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.21/0.30 thf(decl_173, type, esk52_2: $i > $i > $i).
% 0.21/0.30 thf(decl_174, type, esk53_2: $i > $i > $i).
% 0.21/0.30 thf(decl_175, type, esk54_0: $i).
% 0.21/0.30 thf(decl_176, type, esk55_0: $i).
% 0.21/0.30 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', exuE1)).
% 0.21/0.30 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', exu)).
% 0.21/0.30 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', descr__Cong)).
% 0.21/0.30 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', exuE3e)).
% 0.21/0.30 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.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:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', nonemptyI)).
% 0.21/0.30 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', exuE2)).
% 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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', exuI3)).
% 0.21/0.30 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.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.KhgdTdgaR9/E---3.1_367545.p', exuE3u)).
% 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', exu__Cong)).
% 0.21/0.30 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', exuI2)).
% 0.21/0.30 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', descrp)).
% 0.21/0.30 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', replAx)).
% 0.21/0.30 thf(notequalI1, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', notequalI1)).
% 0.21/0.30 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', dsetconstr__Cong)).
% 0.21/0.30 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', dsetconstrI)).
% 0.21/0.30 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', dsetconstrER)).
% 0.21/0.30 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', nonemptyI1)).
% 0.21/0.30 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', nonemptyE1)).
% 0.21/0.30 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', setbeta)).
% 0.21/0.30 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', setoftrueEq)).
% 0.21/0.30 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', nonemptyImpWitness)).
% 0.21/0.30 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', dsetconstrEL)).
% 0.21/0.30 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.KhgdTdgaR9/E---3.1_367545.p', emptyE1)).
% 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.KhgdTdgaR9/E---3.1_367545.p', setadjoin__Cong)).
% 0.21/0.30 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', emptyset__Cong)).
% 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.KhgdTdgaR9/E---3.1_367545.p', powerset__Cong)).
% 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.KhgdTdgaR9/E---3.1_367545.p', setunion__Cong)).
% 0.21/0.30 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', omega__Cong)).
% 0.21/0.30 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', subsetI1)).
% 0.21/0.30 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', eqimpsubset2)).
% 0.21/0.30 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', eqimpsubset1)).
% 0.21/0.30 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', subsetI2)).
% 0.21/0.30 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', emptysetsubset)).
% 0.21/0.30 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', subsetE)).
% 0.21/0.30 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', subsetE2)).
% 0.21/0.30 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', notsubsetI)).
% 0.21/0.30 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', notinemptyset)).
% 0.21/0.30 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', emptysetimpfalse)).
% 0.21/0.30 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', emptysetE)).
% 0.21/0.30 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', prop2setE)).
% 0.21/0.30 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.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.KhgdTdgaR9/E---3.1_367545.p', setadjoinE)).
% 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.KhgdTdgaR9/E---3.1_367545.p', setext)).
% 0.21/0.30 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', setadjoinIL)).
% 0.21/0.30 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.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.KhgdTdgaR9/E---3.1_367545.p', emptyI)).
% 0.21/0.30 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', emptyinunitempty)).
% 0.21/0.30 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', emptyInPowerset)).
% 0.21/0.30 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', emptyinPowerset)).
% 0.21/0.30 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', powersetI)).
% 0.21/0.30 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', setadjoinIR)).
% 0.21/0.30 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', powersetE)).
% 0.21/0.30 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', notinsingleton)).
% 0.21/0.30 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', uniqinunit)).
% 0.21/0.30 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', subPowSU)).
% 0.21/0.30 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', setunionE)).
% 0.21/0.30 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', setunionI)).
% 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.KhgdTdgaR9/E---3.1_367545.p', eqinunit)).
% 0.21/0.30 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', quantDeMorgan1)).
% 0.21/0.30 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', vacuousDall)).
% 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.KhgdTdgaR9/E---3.1_367545.p', upairsetIR)).
% 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.KhgdTdgaR9/E---3.1_367545.p', upairsetIL)).
% 0.21/0.30 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', upairsetE)).
% 0.21/0.30 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', singletonsswitch)).
% 0.21/0.30 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', quantDeMorgan2)).
% 0.21/0.30 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', notdallE)).
% 0.21/0.30 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', notdexE)).
% 0.21/0.30 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', prop2setI)).
% 0.21/0.30 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', quantDeMorgan4)).
% 0.21/0.30 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', quantDeMorgan3)).
% 0.21/0.30 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', inCongP)).
% 0.21/0.30 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', in__Cong)).
% 0.21/0.30 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.KhgdTdgaR9/E---3.1_367545.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.KhgdTdgaR9/E---3.1_367545.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:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', omegaIndAx)).
% 0.21/0.30 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', omegaSAx)).
% 0.21/0.30 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', omega0Ax)).
% 0.21/0.30 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', setunionAx)).
% 0.21/0.30 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', powersetAx)).
% 0.21/0.30 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', setadjoinAx)).
% 0.21/0.30 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', emptysetAx)).
% 0.21/0.30 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.KhgdTdgaR9/E---3.1_367545.p', setextAx)).
% 0.21/0.30 thf(c_0_85, plain, ((exuE1)<=>![X1:$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_86, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.21/0.30 thf(c_0_87, plain, ((exuEu)<=>![X1:$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_88, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 0.21/0.30 thf(c_0_89, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.21/0.30 thf(c_0_90, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.21/0.30 thf(c_0_91, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.21/0.30 thf(c_0_92, plain, ((exuE2)<=>![X1:$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_93, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.21/0.30 thf(c_0_94, plain, ((exuI1)<=>![X1:$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_95, 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_96, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.21/0.30 thf(c_0_97, plain, ((exuI2)<=>![X1:$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, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.21/0.30 thf(c_0_99, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.21/0.30 thf(c_0_100, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[notequalI1])).
% 0.21/0.30 thf(c_0_101, plain, ((exuE1)=(![X1:$i > $o]:((((?[X256:$i]:(((((X1 @ X256)))&(![X257:$i]:(((((X1 @ X257)))=>(((X256)=(X257))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_85, c_0_86])).
% 0.21/0.30 thf(c_0_102, plain, ((exuEu)=(![X1:$i > $o]:((((?[X274:$i]:(((((X1 @ X274)))&(![X275:$i]:(((((X1 @ X275)))=>(((X274)=(X275))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_87, c_0_86])).
% 0.21/0.30 thf(c_0_103, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X276:$i]:(((((X1 @ X276)))&(![X277:$i]:(((((X1 @ X277)))=>(((X276)=(X277))))))))))=>((((?[X278:$i]:(((((X17 @ X278)))&(![X279:$i]:(((((X17 @ X279)))=>(((X278)=(X279))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_88, c_0_86])).
% 0.21/0.30 thf(c_0_104, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 0.21/0.30 thf(c_0_105, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X258:$i]:(((((X1 @ X258)))&(![X259:$i]:(((((X1 @ X259)))=>(((X258)=(X259))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_89, c_0_86])).
% 0.21/0.30 thf(c_0_106, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.21/0.30 thf(c_0_107, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.21/0.30 thf(c_0_108, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_90])).
% 0.21/0.30 thf(c_0_109, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_91, c_0_90])).
% 0.21/0.30 thf(c_0_110, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_90])).
% 0.21/0.30 thf(c_0_111, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.21/0.30 thf(c_0_112, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.21/0.30 thf(c_0_113, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_90])).
% 0.21/0.30 thf(c_0_114, plain, ((exuE2)=(![X1:$i > $o]:((((?[X260:$i]:(((((X1 @ X260)))&(![X261:$i]:(((((X1 @ X261)))=>(((X260)=(X261))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_92, c_0_86])).
% 0.21/0.30 thf(c_0_115, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.21/0.30 thf(c_0_116, plain, ((emptyE1)<=>![X4:$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_117, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X264:$i]:(((((X1 @ X264)))&(![X265:$i]:(((((X1 @ X265)))=>(((X264)=(X265)))))))))))))))), inference(apply_def,[status(thm)],[c_0_93, c_0_86])).
% 0.21/0.30 thf(c_0_118, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X262:$i]:(((((X1 @ X262)))&(![X263:$i]:(((((X1 @ X263)))=>(((X262)=(X263)))))))))))))), inference(apply_def,[status(thm)],[c_0_94, c_0_86])).
% 0.21/0.30 thf(c_0_119, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X268:$i]:(((((X1 @ X268)))&(![X269:$i]:(((((X1 @ X269)))=>(((X268)=(X269))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_95, c_0_86])).
% 0.21/0.30 thf(c_0_120, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X270:$i]:(((((X1 @ X270)))&(![X271:$i]:(((((X1 @ X271)))=>(((X270)=(X271))))))))))<=>((?[X272:$i]:(((((X17 @ X272)))&(![X273:$i]:(((((X17 @ X273)))=>(((X272)=(X273)))))))))))))))), inference(apply_def,[status(thm)],[c_0_96, c_0_86])).
% 0.21/0.30 thf(c_0_121, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X266:$i]:(((((X1 @ X266)))&(![X267:$i]:(((((X1 @ X267)))=>(((X266)=(X267)))))))))))))), inference(apply_def,[status(thm)],[c_0_97, c_0_86])).
% 0.21/0.30 thf(c_0_122, plain, ((descrp)=(![X1:$i > $o]:((((?[X254:$i]:(((((X1 @ X254)))&(![X255:$i]:(((((X1 @ X255)))=>(((X254)=(X255))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_98, c_0_86])).
% 0.21/0.30 thf(c_0_123, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X252:$i]:(((((X6 @ X2 @ X252)))&(![X253:$i]:(((((X6 @ X2 @ X253)))=>(((X252)=(X253)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_99, c_0_86])).
% 0.21/0.30 thf(c_0_124, plain, ((epred1_0)<=>![X309:$i]:(?[X310:$i]:((((![X311:$i]:(((in @ X311 @ X310)=>![X312:$i]:(((in @ X312 @ X311)=>(in @ X312 @ X309)))))&![X313:$i, X314:$i]:((((in @ X313 @ X309)&(in @ X314 @ X309))=>(![X315:$i]:(((in @ X315 @ X310)=>((in @ X313 @ X315)<=>(in @ X314 @ X315))))=>((X313)=(X314))))))&![X316:$i, X317:$i]:((((in @ X316 @ X310)&(in @ X317 @ X310))=>(![X318:$i]:(((in @ X318 @ X316)=>(in @ X318 @ X317)))|![X319:$i]:(((in @ X319 @ X317)=>(in @ X319 @ X316)))))))&![X320:$i]:(((![X321:$i]:(((in @ X321 @ X320)=>(in @ X321 @ X309)))&?[X322:$i]:((in @ X322 @ X320)))=>?[X323:$i, X324:$i]:(((((in @ X323 @ X310)&(in @ X324 @ X320))&~(?[X325:$i]:(((in @ X325 @ X323)&(in @ X325 @ X320)))))&![X326:$i]:(((in @ X326 @ X310)=>(![X327:$i]:(((in @ X327 @ X326)=>(in @ X327 @ X323)))|(in @ X324 @ X326)))))))))))), introduced(definition)).
% 0.21/0.30 thf(c_0_125, negated_conjecture, ~((![X280:$i, X281:$i]:((![X282:$i]:(((in @ X282 @ X280)<=>(in @ X282 @ X281)))=>((X280)=(X281))))=>(![X283:$i]:(~(in @ X283 @ emptyset))=>(![X284:$i, X285:$i, X286:$i]:(((in @ X286 @ (setadjoin @ X284 @ X285))<=>(((X286)=(X284))|(in @ X286 @ X285))))=>(![X287:$i, X288:$i]:(((in @ X288 @ (powerset @ X287))<=>![X289:$i]:(((in @ X289 @ X288)=>(in @ X289 @ X287)))))=>(![X290:$i, X291:$i]:(((in @ X291 @ (setunion @ X290))<=>?[X292:$i]:(((in @ X291 @ X292)&(in @ X292 @ X290)))))=>((in @ emptyset @ omega)=>(![X293:$i]:(((in @ X293 @ omega)=>(in @ (setadjoin @ X293 @ X293) @ omega)))=>(![X294:$i]:((((in @ emptyset @ X294)&![X295:$i]:((((in @ X295 @ omega)&(in @ X295 @ X294))=>(in @ (setadjoin @ X295 @ X295) @ X294))))=>![X296:$i]:(((in @ X296 @ omega)=>(in @ X296 @ X294)))))=>(![X297:$i > $i > $o, X298:$i]:((![X299:$i]:(((in @ X299 @ X298)=>?[X300:$i]:(((X297 @ X299 @ X300)&![X301:$i]:(((X297 @ X299 @ X301)=>((X300)=(X301))))))))=>?[X302:$i]:(![X303:$i]:(((in @ X303 @ X302)<=>?[X304:$i]:(((in @ X304 @ X298)&(X297 @ X304 @ X303))))))))=>(![X305:$i]:((?[X306:$i]:((in @ X306 @ X305))=>?[X307:$i]:(((in @ X307 @ X305)&~(?[X308:$i]:(((in @ X308 @ X307)&(in @ X308 @ X305))))))))=>((epred1_0)=>(![X328:$i > $o]:((?[X329:$i]:(((X328 @ X329)&![X330:$i]:(((X328 @ X330)=>((X329)=(X330))))))=>(X328 @ (descr @ (^[Z0:$i]:((X328 @ Z0)))))))=>(![X331:$i, X332:$i > $o, X333:$i]:(((in @ X333 @ X331)=>((X332 @ X333)=>(in @ X333 @ (dsetconstr @ X331 @ (^[Z0:$i]:((X332 @ Z0))))))))=>(![X334:$i, X335:$i > $o, X336:$i]:(((in @ X336 @ (dsetconstr @ X334 @ (^[Z0:$i]:((X335 @ Z0)))))=>(in @ X336 @ X334)))=>(![X337:$i, X338:$i > $o, X339:$i]:(((in @ X339 @ (dsetconstr @ X337 @ (^[Z0:$i]:((X338 @ Z0)))))=>(X338 @ X339)))=>(![X340:$i > $o]:((?[X341:$i]:(((X340 @ X341)&![X342:$i]:(((X340 @ X342)=>((X341)=(X342))))))=>?[X343:$i]:(((X340 @ X343)&![X344:$i]:(((X340 @ X344)=>((X343)=(X344))))))))=>(![X345:$o, X346:$i]:(((in @ X346 @ (prop2set @ ((X345))))=>(X345)))=>(![X347:$i]:(((in @ X347 @ emptyset)=>![X348:$o]:((X348))))=>(![X349:$i]:(~(in @ X349 @ emptyset))=>(![X350:$i]:(~(in @ X350 @ emptyset))=>(![X351:$i > $o]:((?[X352:$i]:(((X351 @ X352)&![X353:$i]:(((X351 @ X353)=>((X352)=(X353))))))=>?[X354:$i]:((X351 @ X354))))=>(![X355:$i, X356:$i]:((![X357:$i]:(((in @ X357 @ X355)=>(in @ X357 @ X356)))=>(![X358:$i]:(((in @ X358 @ X356)=>(in @ X358 @ X355)))=>((X355)=(X356)))))=>(![X359:$i]:((![X360:$i]:(~(in @ X360 @ X359))=>((X359)=(emptyset))))=>(![X361:$i]:((![X362:$i]:(~(in @ X362 @ X361))=>((X361)=(emptyset))))=>(![X363:$i, X364:$i > $o, X365:$i]:(((in @ X365 @ X363)=>((in @ X365 @ (dsetconstr @ X363 @ (^[Z0:$i]:((X364 @ Z0)))))<=>(X364 @ X365))))=>(![X366:$i]:((((X366)!=(emptyset))=>?[X367:$i]:((in @ X367 @ X366))))=>(![X368:$i, X369:$i > $o, X370:$i]:(((in @ X370 @ X368)=>((X369 @ X370)=>((dsetconstr @ X368 @ (^[Z0:$i]:((X369 @ Z0))))!=(emptyset)))))=>(![X371:$i]:((?[X372:$i]:((in @ X372 @ X371))=>((X371)!=(emptyset))))=>(![X373:$i, X374:$i]:((in @ X373 @ (setadjoin @ X373 @ X374)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X375:$i, X376:$i, X377:$i]:(((in @ X377 @ X376)=>(in @ X377 @ (setadjoin @ X375 @ X376))))=>(![X378:$i, X379:$i, X380:$i]:(((in @ X380 @ (setadjoin @ X378 @ X379))=>![X381:$o]:(((((X380)=(X378))=>(X381))=>(((in @ X380 @ X379)=>(X381))=>(X381))))))=>(![X382:$i, X383:$i, X384:$i]:(((in @ X384 @ (setadjoin @ X382 @ X383))=>(((X384)=(X382))|(in @ X384 @ X383))))=>(![X385:$i]:(((dsetconstr @ X385 @ (^[Z0:$i]:(($true))))=(X385)))=>(![X386:$i, X387:$i]:((![X388:$i]:(((in @ X388 @ X387)=>(in @ X388 @ X386)))=>(in @ X387 @ (powerset @ X386))))=>(![X389:$i]:((in @ emptyset @ (powerset @ X389)))=>(![X390:$i]:((in @ emptyset @ (powerset @ X390)))=>(![X391:$i, X392:$i, X393:$i]:(((in @ X392 @ (powerset @ X391))=>((in @ X393 @ X392)=>(in @ X393 @ X391))))=>(![X394:$i, X395:$i, X396:$i]:(((in @ X395 @ X396)=>((in @ X396 @ X394)=>(in @ X395 @ (setunion @ X394)))))=>(![X397:$i, X398:$i]:(((in @ X398 @ (setunion @ X397))=>![X399:$o]:((![X400:$i]:(((in @ X398 @ X400)=>((in @ X400 @ X397)=>(X399))))=>(X399)))))=>(![X401:$i, X402:$i]:(((in @ X402 @ X401)=>(in @ X402 @ (powerset @ (setunion @ X401)))))=>(![X403:$i > $o]:((?[X404:$i]:(((X403 @ X404)&![X405:$i]:(((X403 @ X405)=>((X404)=(X405))))))=>?[X406:$i]:(![X407:$i]:(((X403 @ X407)<=>((X407)=(X406)))))))=>(![X408:$i]:((((X408)!=(emptyset))=>?[X409:$i]:((in @ X409 @ X408))))=>(![X410:$i, X411:$i]:(((in @ X410 @ (setadjoin @ X411 @ emptyset))=>((X410)=(X411))))=>(![X412:$i, X413:$i]:((((X412)!=(X413))=>~(in @ X413 @ (setadjoin @ X412 @ emptyset))))=>(![X414:$i, X415:$i]:((((X414)=(X415))=>(in @ X414 @ (setadjoin @ X415 @ emptyset))))=>(![X416:$i, X417:$i]:(((in @ X416 @ (setadjoin @ X417 @ emptyset))=>(in @ X417 @ (setadjoin @ X416 @ emptyset))))=>(![X418:$i, X419:$i, X420:$i]:(((in @ X420 @ (setadjoin @ X418 @ (setadjoin @ X419 @ emptyset)))=>(((X420)=(X418))|((X420)=(X419)))))=>(![X421:$i, X422:$i]:((in @ X421 @ (setadjoin @ X421 @ (setadjoin @ X422 @ emptyset))))=>(![X423:$i, X424:$i]:((in @ X424 @ (setadjoin @ X423 @ (setadjoin @ X424 @ emptyset))))=>(![X425:$i, X426:$i > $o]:((?[X427:$i]:(((in @ X427 @ X425)&(X426 @ X427)))=>((dsetconstr @ X425 @ (^[Z0:$i]:((X426 @ Z0))))!=(emptyset))))=>(![X428:$i > $o, X429:$i]:(((in @ X429 @ emptyset)=>(X428 @ X429)))=>(![X430:$i, X431:$i > $o]:((~(![X432:$i]:(((in @ X432 @ X430)=>(X431 @ X432))))=>?[X433:$i]:(((in @ X433 @ X430)&~(X431 @ X433)))))=>(![X434:$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:$i]:(((in @ X445 @ X442)=>(X443 @ X445))))))=>(![X446:$o]:(((X446)=>(in @ emptyset @ (prop2set @ ((X446))))))=>((prop2set2propI)=>(![X447:$i, X448:$i > $o]:((~(?[X449:$i]:(((in @ X449 @ X447)&(X448 @ X449))))=>![X450:$i]:(((in @ X450 @ X447)=>~(X448 @ X450)))))=>(![X451:$i, X452:$i > $o]:((~(![X453:$i]:(((in @ X453 @ X451)=>(X452 @ X453))))=>?[X454:$i]:(((in @ X454 @ X451)&~(X452 @ X454)))))=>(![X455:$i > $o]:((?[X456:$i]:(((X455 @ X456)&![X457:$i]:(((X455 @ X457)=>((X456)=(X457))))))=>?[X458:$i]:(((X455 @ X458)&![X459:$i]:(((X455 @ X459)=>((X458)=(X459))))))))=>(![X460:$i > $o]:((?[X461:$i]:((X460 @ X461))=>(![X462:$i, X463:$i]:(((X460 @ X462)=>((X460 @ X463)=>((X462)=(X463)))))=>?[X464:$i]:(((X460 @ X464)&![X465:$i]:(((X460 @ X465)=>((X464)=(X465)))))))))=>(![X466:$i > $o]:((?[X467:$i]:(![X468:$i]:(((X466 @ X468)<=>((X468)=(X467)))))=>?[X469:$i]:(((X466 @ X469)&![X470:$i]:(((X466 @ X470)=>((X469)=(X470))))))))=>(![X471:$i, X472:$i]:((((X471)=(X472))=>![X473:$i, X474:$i]:((((X473)=(X474))=>((in @ X473 @ X471)=>(in @ X474 @ X472))))))=>(![X475:$i, X476:$i]:((((X475)=(X476))=>![X477:$i, X478:$i]:((((X477)=(X478))=>((in @ X477 @ X475)<=>(in @ X478 @ X476))))))=>(![X479:$i > $o]:((?[X480:$i]:(((X479 @ X480)&![X481:$i]:(((X479 @ X481)=>((X480)=(X481))))))=>![X482:$i, X483:$i]:(((X479 @ X482)=>((X479 @ X483)=>((X482)=(X483)))))))=>(![X484:$i > $o, X485:$i > $o]:((![X486:$i, X487:$i]:((((X486)=(X487))=>((X484 @ X486)<=>(X485 @ X487))))=>(?[X488:$i]:(((X484 @ X488)&![X489:$i]:(((X484 @ X489)=>((X488)=(X489))))))<=>?[X490:$i]:(((X485 @ X490)&![X491:$i]:(((X485 @ X491)=>((X490)=(X491)))))))))=>(((emptyset)=(emptyset))=>(![X492:$i, X493:$i]:((((X492)=(X493))=>![X494:$i, X495:$i]:((((X494)=(X495))=>((setadjoin @ X492 @ X494)=(setadjoin @ X493 @ X495))))))=>(![X496:$i, X497:$i]:((((X496)=(X497))=>((powerset @ X496)=(powerset @ X497))))=>(![X498:$i, X499:$i]:((((X498)=(X499))=>((setunion @ X498)=(setunion @ X499))))=>(((omega)=(omega))=>(![X500:$i > $o]:((?[X501:$i]:(((X500 @ X501)&![X502:$i]:(((X500 @ X502)=>((X501)=(X502))))))=>![X503:$i, X504:$i]:(((X500 @ X503)=>((X500 @ X504)=>((X503)=(X504)))))))=>(![X505:$i > $o, X506:$i > $o]:((![X507:$i, X508:$i]:((((X507)=(X508))=>((X505 @ X507)<=>(X506 @ X508))))=>(?[X509:$i]:(((X505 @ X509)&![X510:$i]:(((X505 @ X510)=>((X509)=(X510))))))=>(?[X511:$i]:(((X506 @ X511)&![X512:$i]:(((X506 @ X512)=>((X511)=(X512))))))=>((descr @ (^[Z0:$i]:((X505 @ Z0))))=(descr @ (^[Z0:$i]:((X506 @ Z0)))))))))=>(![X513:$i, X514:$i]:((((X513)=(X514))=>![X515:$i > $o, X516:$i > $o]:((![X517:$i]:(((in @ X517 @ X513)=>![X518:$i]:(((in @ X518 @ X514)=>(((X517)=(X518))=>((X515 @ X517)<=>(X516 @ X518)))))))=>((dsetconstr @ X513 @ (^[Z0:$i]:((X515 @ Z0))))=(dsetconstr @ X514 @ (^[Z0:$i]:((X516 @ Z0)))))))))=>(![X519:$i, X520:$i]:((![X521:$i]:(((in @ X521 @ X519)=>(in @ X521 @ X520)))=>(subset @ X519 @ X520)))=>(![X522:$i, X523:$i]:((((X522)=(X523))=>(subset @ X523 @ X522)))=>(![X524:$i, X525:$i]:((((X524)=(X525))=>(subset @ X524 @ X525)))=>(![X526:$i, X527:$i]:((![X528:$i]:(((in @ X528 @ X526)=>(in @ X528 @ X527)))=>(subset @ X526 @ X527)))=>(![X529:$i]:((subset @ emptyset @ X529))=>(![X530:$i, X531:$i, X532:$i]:(((subset @ X530 @ X531)=>((in @ X532 @ X530)=>(in @ X532 @ X531))))=>(![X533:$i, X534:$i, X535:$i]:(((subset @ X533 @ X534)=>(~(in @ X535 @ X534)=>~(in @ X535 @ X533))))=>(![X536:$i, X537:$i, X538:$i]:(((in @ X538 @ X536)=>(~(in @ X538 @ X537)=>~(subset @ X536 @ X537))))=>![X4:$i, X5:$i]:((~(subset @ X4 @ X5)=>((X4)!=(X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(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, c_0_101]), setadjoin__Cong]), emptyset__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_102]), c_0_103]), c_0_104]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), c_0_105]), subsetE2]), c_0_106]), notsubsetI]), notinemptyset]), emptysetimpfalse]), emptysetE]), prop2setE]), setadjoinOr]), setadjoinE]), c_0_107]), setext]), setadjoinIL]), c_0_108]), c_0_109]), c_0_110]), c_0_111]), noeltsimpempty]), emptyI]), emptyinunitempty]), emptyInPowerset]), emptyinPowerset]), powersetI]), c_0_112]), setadjoinIR]), powersetE]), notinsingleton]), uniqinunit]), c_0_113]), c_0_114]), subPowSU]), setunionE]), setunionI]), c_0_115]), eqinunit]), quantDeMorgan1]), vacuousDall]), c_0_116]), upairsetIR]), upairsetIL]), upairsetE]), singletonsswitch]), quantDeMorgan2]), c_0_117]), c_0_118]), notdallE]), notdexE]), prop2setI]), quantDeMorgan4]), quantDeMorgan3]), inCongP]), in__Cong]), c_0_119]), c_0_120]), c_0_121]), c_0_122]), wellorderingAx]), foundationAx]), c_0_123]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])]), c_0_124])).
% 0.21/0.30 thf(c_0_126, negated_conjecture, ![X539:$i, X540:$i, X542:$i, X543:$i, X544:$i, X545:$i, X546:$i, X547:$i, X548:$i, X549:$i, X550:$i, X552:$i, X553:$i, X555:$i, X556:$i, X557:$i, X558:$i, X559:$i, X561:$i, X562:$i > $i > $o, X563:$i, X565:$i, X568:$i, X570:$i, X571:$i, X572:$i, X573:$i, X575:$i, X576:$i > $o, X577:$i, X579:$i, X580:$i > $o, X581:$i, X582:$i, X583:$i > $o, X584:$i, X585:$i, X586:$i > $o, X587:$i, X588:$i > $o, X589:$i, X592:$i, X593:$o, X594:$i, X595:$i, X596:$o, X597:$i, X598:$i, X599:$i > $o, X600:$i, X603:$i, X604:$i, X607:$i, X609:$i, X611:$i, X612:$i > $o, X613:$i, X614:$i, X616:$i, X617:$i > $o, X618:$i, X619:$i, X620:$i, X621:$i, X622:$i, X623:$i, X624:$i, X625:$i, X626:$i, X627:$i, X628:$i, X629:$o, X630:$i, X631:$i, X632:$i, X633:$i, X634:$i, X635:$i, X637:$i, X638:$i, X639:$i, X640:$i, X641:$i, X642:$i, X643:$i, X644:$i, X645:$i, X646:$i, X647:$o, X649:$i, X650:$i, X651:$i > $o, X652:$i, X655:$i, X656:$i, X657:$i, X659:$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, X672:$i, X673:$i, X674:$i, X675:$i > $o, X676:$i, X677:$i > $o, X678:$i, X679:$i, X680:$i > $o, X681:$i, X683:$i, X684:$i > $o, X686:$i, X687:$i, X688:$i > $o, X690:$i, X691:$i, X692:$i > $o, X693:$i, X695:$o, X696:$i, X697:$i > $o, X699:$i, X700:$i, X701:$i > $o, X702:$i, X704:$i > $o, X705:$i, X708:$i, X709:$i > $o, X710:$i, X714:$i, X715:$i > $o, X716:$i, X719:$i, X720:$i, X721:$i, X722:$i, X723:$i, X724:$i, X725:$i, X726:$i, X727:$i, X728:$i > $o, X729:$i, X731:$i, X732:$i, X733:$i > $o, X734:$i > $o, X737:$i, X740:$i, X741:$i, X744:$i, X745:$i, X746:$i, X747:$i, X748:$i, X749:$i, X750:$i, X751:$i, X752:$i, X753:$i > $o, X754:$i, X756:$i, X757:$i, X758:$i > $o, X759:$i > $o, X762:$i, X764:$i, X766:$i, X767:$i, X768:$i > $o, X769:$i > $o, X772:$i, X773:$i, X775:$i, X776:$i, X777:$i, X778:$i, X779:$i, X780:$i, X782:$i, X783:$i, X784:$i, X785:$i, X786:$i, X787:$i, X788:$i, X789:$i, X790:$i, X791:$i]:((((~(in @ (esk1_2 @ X539 @ X540) @ X539)|~(in @ (esk1_2 @ X539 @ X540) @ X540)|((X539)=(X540)))&((in @ (esk1_2 @ X539 @ X540) @ X539)|(in @ (esk1_2 @ X539 @ X540) @ X540)|((X539)=(X540))))&(~(in @ X542 @ emptyset)&(((~(in @ X545 @ (setadjoin @ X543 @ X544))|(((X545)=(X543))|(in @ X545 @ X544)))&((((X545)!=(X543))|(in @ X545 @ (setadjoin @ X543 @ X544)))&(~(in @ X545 @ X544)|(in @ X545 @ (setadjoin @ X543 @ X544)))))&(((~(in @ X547 @ (powerset @ X546))|(~(in @ X548 @ X547)|(in @ X548 @ X546)))&(((in @ (esk2_2 @ X549 @ X550) @ X550)|(in @ X550 @ (powerset @ X549)))&(~(in @ (esk2_2 @ X549 @ X550) @ X549)|(in @ X550 @ (powerset @ X549)))))&(((((in @ X553 @ (esk3_2 @ X552 @ X553))|~(in @ X553 @ (setunion @ X552)))&((in @ (esk3_2 @ X552 @ X553) @ X552)|~(in @ X553 @ (setunion @ X552))))&(~(in @ X556 @ X557)|~(in @ X557 @ X555)|(in @ X556 @ (setunion @ X555))))&((in @ emptyset @ omega)&((~(in @ X558 @ omega)|(in @ (setadjoin @ X558 @ X558) @ omega))&(((((in @ (esk4_1 @ X559) @ 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X734)))))))))&(((emptyset)=(emptyset))&((((X745)!=(X746))|(((X747)!=(X748))|((setadjoin @ X745 @ X747)=(setadjoin @ X746 @ X748))))&((((X749)!=(X750))|((powerset @ X749)=(powerset @ X750)))&((((X751)!=(X752))|((setunion @ X751)=(setunion @ X752)))&(((omega)=(omega))&((((X753 @ (esk45_2 @ X753 @ X754))|~(X753 @ X754)|(~(X753 @ X756)|(~(X753 @ X757)|((X756)=(X757)))))&(((X754)!=(esk45_2 @ X753 @ X754))|~(X753 @ X754)|(~(X753 @ X756)|(~(X753 @ X757)|((X756)=(X757))))))&((((((X759 @ (esk49_3 @ X758 @ X759 @ X764))|~(X759 @ X764)|((descr @ (^[Z0:$i]:((X758 @ Z0))))=(descr @ (^[Z0:$i]:((X759 @ Z0)))))|((X758 @ (esk48_3 @ X758 @ X759 @ X762))|~(X758 @ X762))|((esk46_2 @ X758 @ X759)=(esk47_2 @ X758 @ X759)))&(((X764)!=(esk49_3 @ X758 @ X759 @ X764))|~(X759 @ X764)|((descr @ (^[Z0:$i]:((X758 @ Z0))))=(descr @ (^[Z0:$i]:((X759 @ Z0)))))|((X758 @ (esk48_3 @ X758 @ X759 @ X762))|~(X758 @ X762))|((esk46_2 @ X758 @ X759)=(esk47_2 @ X758 @ X759))))&(((X759 @ (esk49_3 @ X758 @ X759 @ X764))|~(X759 @ X764)|((descr @ (^[Z0:$i]:((X758 @ Z0))))=(descr @ (^[Z0:$i]:((X759 @ Z0)))))|(((X762)!=(esk48_3 @ X758 @ X759 @ X762))|~(X758 @ X762))|((esk46_2 @ X758 @ X759)=(esk47_2 @ X758 @ X759)))&(((X764)!=(esk49_3 @ X758 @ X759 @ X764))|~(X759 @ X764)|((descr @ (^[Z0:$i]:((X758 @ Z0))))=(descr @ (^[Z0:$i]:((X759 @ Z0)))))|(((X762)!=(esk48_3 @ X758 @ X759 @ X762))|~(X758 @ X762))|((esk46_2 @ X758 @ X759)=(esk47_2 @ X758 @ X759)))))&(((((X759 @ (esk49_3 @ X758 @ X759 @ X764))|~(X759 @ X764)|((descr @ (^[Z0:$i]:((X758 @ Z0))))=(descr @ (^[Z0:$i]:((X759 @ Z0)))))|((X758 @ (esk48_3 @ X758 @ X759 @ X762))|~(X758 @ X762))|(~(X758 @ (esk46_2 @ X758 @ X759))|~(X759 @ (esk47_2 @ X758 @ X759))))&(((X764)!=(esk49_3 @ X758 @ X759 @ X764))|~(X759 @ X764)|((descr @ (^[Z0:$i]:((X758 @ Z0))))=(descr @ (^[Z0:$i]:((X759 @ Z0)))))|((X758 @ (esk48_3 @ X758 @ X759 @ X762))|~(X758 @ X762))|(~(X758 @ (esk46_2 @ X758 @ X759))|~(X759 @ (esk47_2 @ X758 @ X759)))))&(((X759 @ (esk49_3 @ X758 @ X759 @ X764))|~(X759 @ X764)|((descr @ (^[Z0:$i]:((X758 @ Z0))))=(descr @ (^[Z0:$i]:((X759 @ Z0)))))|(((X762)!=(esk48_3 @ X758 @ X759 @ X762))|~(X758 @ X762))|(~(X758 @ (esk46_2 @ X758 @ X759))|~(X759 @ (esk47_2 @ X758 @ X759))))&(((X764)!=(esk49_3 @ X758 @ X759 @ X764))|~(X759 @ X764)|((descr @ (^[Z0:$i]:((X758 @ Z0))))=(descr @ (^[Z0:$i]:((X759 @ Z0)))))|(((X762)!=(esk48_3 @ X758 @ X759 @ X762))|~(X758 @ X762))|(~(X758 @ (esk46_2 @ X758 @ X759))|~(X759 @ (esk47_2 @ X758 @ X759))))))&((((X759 @ (esk49_3 @ X758 @ X759 @ X764))|~(X759 @ X764)|((descr @ (^[Z0:$i]:((X758 @ Z0))))=(descr @ (^[Z0:$i]:((X759 @ Z0)))))|((X758 @ (esk48_3 @ X758 @ X759 @ X762))|~(X758 @ X762))|((X758 @ (esk46_2 @ X758 @ X759))|(X759 @ (esk47_2 @ X758 @ X759))))&(((X764)!=(esk49_3 @ X758 @ X759 @ X764))|~(X759 @ X764)|((descr @ (^[Z0:$i]:((X758 @ Z0))))=(descr @ (^[Z0:$i]:((X759 @ Z0)))))|((X758 @ (esk48_3 @ X758 @ X759 @ X762))|~(X758 @ X762))|((X758 @ (esk46_2 @ X758 @ X759))|(X759 @ (esk47_2 @ X758 @ X759)))))&(((X759 @ (esk49_3 @ X758 @ X759 @ X764))|~(X759 @ X764)|((descr @ (^[Z0:$i]:((X758 @ Z0))))=(descr @ (^[Z0:$i]:((X759 @ Z0)))))|(((X762)!=(esk48_3 @ X758 @ X759 @ X762))|~(X758 @ X762))|((X758 @ (esk46_2 @ X758 @ X759))|(X759 @ (esk47_2 @ X758 @ X759))))&(((X764)!=(esk49_3 @ X758 @ X759 @ X764))|~(X759 @ X764)|((descr @ (^[Z0:$i]:((X758 @ Z0))))=(descr @ (^[Z0:$i]:((X759 @ Z0)))))|(((X762)!=(esk48_3 @ X758 @ X759 @ X762))|~(X758 @ X762))|((X758 @ (esk46_2 @ X758 @ X759))|(X759 @ (esk47_2 @ X758 @ X759))))))))&((((in @ (esk50_4 @ X766 @ X767 @ X768 @ X769) @ X766)|((dsetconstr @ X766 @ (^[Z0:$i]:((X768 @ Z0))))=(dsetconstr @ X767 @ (^[Z0:$i]:((X769 @ Z0)))))|((X766)!=(X767)))&(((in @ (esk51_4 @ X766 @ X767 @ X768 @ X769) @ X767)|((dsetconstr @ X766 @ (^[Z0:$i]:((X768 @ Z0))))=(dsetconstr @ X767 @ (^[Z0:$i]:((X769 @ Z0)))))|((X766)!=(X767)))&((((esk50_4 @ X766 @ X767 @ X768 @ X769)=(esk51_4 @ X766 @ X767 @ X768 @ X769))|((dsetconstr @ X766 @ (^[Z0:$i]:((X768 @ Z0))))=(dsetconstr @ X767 @ (^[Z0:$i]:((X769 @ Z0)))))|((X766)!=(X767)))&((~(X768 @ (esk50_4 @ X766 @ X767 @ X768 @ X769))|~(X769 @ (esk51_4 @ X766 @ X767 @ X768 @ X769))|((dsetconstr @ X766 @ (^[Z0:$i]:((X768 @ Z0))))=(dsetconstr @ X767 @ (^[Z0:$i]:((X769 @ Z0)))))|((X766)!=(X767)))&((X768 @ (esk50_4 @ X766 @ X767 @ X768 @ X769))|(X769 @ (esk51_4 @ X766 @ X767 @ X768 @ X769))|((dsetconstr @ X766 @ (^[Z0:$i]:((X768 @ Z0))))=(dsetconstr @ X767 @ (^[Z0:$i]:((X769 @ Z0)))))|((X766)!=(X767)))))))&((((in @ (esk52_2 @ X772 @ X773) @ X772)|(subset @ X772 @ X773))&(~(in @ (esk52_2 @ X772 @ X773) @ X773)|(subset @ X772 @ X773)))&((((X775)!=(X776))|(subset @ X776 @ X775))&((((X777)!=(X778))|(subset @ X777 @ X778))&((((in @ (esk53_2 @ X779 @ X780) @ X779)|(subset @ X779 @ X780))&(~(in @ (esk53_2 @ X779 @ X780) @ X780)|(subset @ X779 @ X780)))&((subset @ emptyset @ X782)&((~(subset @ X783 @ X784)|(~(in @ X785 @ X783)|(in @ X785 @ X784)))&((~(subset @ X786 @ X787)|((in @ X788 @ X787)|~(in @ X788 @ X786)))&((~(in @ X791 @ X789)|((in @ X791 @ X790)|~(subset @ X789 @ X790)))&(~(subset @ esk54_0 @ esk55_0)&((esk54_0)=(esk55_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_125])])])])])])).
% 0.21/0.30 thf(c_0_127, negated_conjecture, ~((subset @ esk54_0 @ esk55_0)), inference(split_conjunct,[status(thm)],[c_0_126])).
% 0.21/0.30 thf(c_0_128, negated_conjecture, ((esk54_0)=(esk55_0)), inference(split_conjunct,[status(thm)],[c_0_126])).
% 0.21/0.30 thf(c_0_129, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X3 @ X2)|((X2)!=(X3)))), inference(split_conjunct,[status(thm)],[c_0_126])).
% 0.21/0.30 thf(c_0_130, negated_conjecture, ~((subset @ esk54_0 @ esk54_0)), inference(rw,[status(thm)],[c_0_127, c_0_128])).
% 0.21/0.30 thf(c_0_131, negated_conjecture, ![X2:$i]:((subset @ X2 @ X2)), inference(er,[status(thm)],[c_0_129])).
% 0.21/0.30 thf(c_0_132, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_130, c_0_131])]), ['proof']).
% 0.21/0.30 % SZS output end CNFRefutation
% 0.21/0.30 % Parsed axioms : 184
% 0.21/0.30 % Removed by relevancy pruning/SinE : 99
% 0.21/0.30 % Initial clauses : 194
% 0.21/0.30 % Removed in clause preprocessing : 12
% 0.21/0.30 % Initial clauses in saturation : 182
% 0.21/0.30 % Processed clauses : 20
% 0.21/0.30 % ...of these trivial : 1
% 0.21/0.30 % ...subsumed : 4
% 0.21/0.30 % ...remaining for further processing : 15
% 0.21/0.30 % Other redundant clauses eliminated : 1
% 0.21/0.30 % Clauses deleted for lack of memory : 0
% 0.21/0.30 % Backward-subsumed : 0
% 0.21/0.30 % Backward-rewritten : 2
% 0.21/0.30 % Generated clauses : 1
% 0.21/0.30 % ...of the previous two non-redundant : 1
% 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 : 1
% 0.21/0.30 % Disequality decompositions : 0
% 0.21/0.30 % Total rewrite steps : 4
% 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 : 12
% 0.21/0.30 % Positive orientable unit clauses : 10
% 0.21/0.30 % Positive unorientable unit clauses: 0
% 0.21/0.30 % Negative unit clauses : 2
% 0.21/0.30 % Non-unit-clauses : 0
% 0.21/0.30 % Current number of unprocessed clauses: 163
% 0.21/0.30 % ...number of literals in the above : 615
% 0.21/0.30 % Current number of archived formulas : 0
% 0.21/0.30 % Current number of archived clauses : 2
% 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 : 1
% 0.21/0.30 % Rewrite failures with RHS unbound : 0
% 0.21/0.30 % BW rewrite match attempts : 3
% 0.21/0.30 % BW rewrite match successes : 2
% 0.21/0.30 % Condensation attempts : 0
% 0.21/0.30 % Condensation successes : 0
% 0.21/0.30 % Termbank termtop insertions : 20865
% 0.21/0.30 % Search garbage collected termcells : 8037
% 0.21/0.30
% 0.21/0.30 % -------------------------------------------------
% 0.21/0.30 % User time : 0.019 s
% 0.21/0.30 % System time : 0.009 s
% 0.21/0.30 % Total time : 0.028 s
% 0.21/0.30 % Maximum resident set size: 5864 pages
% 0.21/0.30
% 0.21/0.30 % -------------------------------------------------
% 0.21/0.30 % User time : 0.022 s
% 0.21/0.30 % System time : 0.016 s
% 0.21/0.30 % Total time : 0.038 s
% 0.21/0.30 % Maximum resident set size: 5120 pages
% 0.21/0.30 % E exiting
%------------------------------------------------------------------------------