%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU553^1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 08:24:29 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU553^1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.17 % Computer : n003.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Sep 29 13:51:43 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.22 Running higher-order theorem proving
% 0.11/0.24 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p
% 0.21/0.29 % Version: 3.5.1-ho
% 0.21/0.29 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.21/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.29 % Starting new_ho_10 with 1500s (5) cores
% 0.21/0.29 % Starting sh5l with 300s (1) cores
% 0.21/0.29 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.29 % Starting new_bool_2 with 300s (1) cores
% 0.21/0.29 % new_bool_2 with pid 2534383 completed with status 0
% 0.21/0.29 % Result found by new_bool_2
% 0.21/0.29 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.21/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.29 % Starting new_ho_10 with 1500s (5) cores
% 0.21/0.29 % Starting sh5l with 300s (1) cores
% 0.21/0.29 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.29 % Starting new_bool_2 with 300s (1) cores
% 0.21/0.29 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.21/0.29 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.29 % Search class: HGHSM-FSLM31-SHFMMMBN
% 0.21/0.29 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.29 % Starting SubtermCWHack with 28s (1) cores
% 0.21/0.29 % SubtermCWHack with pid 2534386 completed with status 0
% 0.21/0.29 % Result found by SubtermCWHack
% 0.21/0.29 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.21/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.29 % Starting new_ho_10 with 1500s (5) cores
% 0.21/0.29 % Starting sh5l with 300s (1) cores
% 0.21/0.29 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.29 % Starting new_bool_2 with 300s (1) cores
% 0.21/0.29 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.21/0.29 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.29 % Search class: HGHSM-FSLM31-SHFMMMBN
% 0.21/0.29 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.29 % Starting SubtermCWHack with 28s (1) cores
% 0.21/0.29 % Preprocessing time : 0.004 s
% 0.21/0.29
% 0.21/0.29 % Proof found!
% 0.21/0.29 % SZS status Theorem
% 0.21/0.29 % SZS output start CNFRefutation
% 0.21/0.29 thf(decl_23, type, in: $i > $i > $o).
% 0.21/0.29 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.21/0.29 thf(decl_25, type, setextAx: $o).
% 0.21/0.29 thf(decl_26, type, emptyset: $i).
% 0.21/0.29 thf(decl_27, type, emptysetAx: $o).
% 0.21/0.29 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.21/0.29 thf(decl_29, type, setadjoinAx: $o).
% 0.21/0.29 thf(decl_30, type, powerset: $i > $i).
% 0.21/0.29 thf(decl_31, type, powersetAx: $o).
% 0.21/0.29 thf(decl_32, type, setunion: $i > $i).
% 0.21/0.29 thf(decl_33, type, setunionAx: $o).
% 0.21/0.29 thf(decl_34, type, omega: $i).
% 0.21/0.29 thf(decl_35, type, omega0Ax: $o).
% 0.21/0.29 thf(decl_36, type, omegaSAx: $o).
% 0.21/0.29 thf(decl_37, type, omegaIndAx: $o).
% 0.21/0.29 thf(decl_38, type, replAx: $o).
% 0.21/0.29 thf(decl_39, type, foundationAx: $o).
% 0.21/0.29 thf(decl_40, type, wellorderingAx: $o).
% 0.21/0.29 thf(decl_42, type, descrp: $o).
% 0.21/0.29 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.21/0.29 thf(decl_44, type, dsetconstrI: $o).
% 0.21/0.29 thf(decl_45, type, dsetconstrEL: $o).
% 0.21/0.29 thf(decl_46, type, dsetconstrER: $o).
% 0.21/0.29 thf(decl_47, type, exuE1: $o).
% 0.21/0.29 thf(decl_48, type, prop2set: $o > $i).
% 0.21/0.29 thf(decl_49, type, prop2setE: $o).
% 0.21/0.29 thf(decl_50, type, emptysetE: $o).
% 0.21/0.29 thf(decl_51, type, emptysetimpfalse: $o).
% 0.21/0.29 thf(decl_52, type, notinemptyset: $o).
% 0.21/0.29 thf(decl_53, type, exuE3e: $o).
% 0.21/0.29 thf(decl_54, type, setext: $o).
% 0.21/0.29 thf(decl_55, type, emptyI: $o).
% 0.21/0.29 thf(decl_56, type, noeltsimpempty: $o).
% 0.21/0.29 thf(decl_57, type, setbeta: $o).
% 0.21/0.29 thf(decl_58, type, nonempty: $i > $o).
% 0.21/0.29 thf(decl_59, type, nonemptyE1: $o).
% 0.21/0.29 thf(decl_60, type, nonemptyI: $o).
% 0.21/0.29 thf(decl_61, type, nonemptyI1: $o).
% 0.21/0.29 thf(decl_62, type, setadjoinIL: $o).
% 0.21/0.29 thf(decl_63, type, emptyinunitempty: $o).
% 0.21/0.29 thf(decl_64, type, setadjoinIR: $o).
% 0.21/0.29 thf(decl_65, type, setadjoinE: $o).
% 0.21/0.29 thf(decl_66, type, setadjoinOr: $o).
% 0.21/0.29 thf(decl_67, type, setoftrueEq: $o).
% 0.21/0.29 thf(decl_68, type, powersetI: $o).
% 0.21/0.29 thf(decl_69, type, emptyinPowerset: $o).
% 0.21/0.29 thf(decl_70, type, emptyInPowerset: $o).
% 0.21/0.29 thf(decl_71, type, powersetE: $o).
% 0.21/0.29 thf(decl_72, type, setunionI: $o).
% 0.21/0.29 thf(decl_73, type, setunionE: $o).
% 0.21/0.29 thf(decl_74, type, subPowSU: $o).
% 0.21/0.29 thf(decl_75, type, exuE2: $o).
% 0.21/0.29 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.21/0.29 thf(decl_77, type, uniqinunit: $o).
% 0.21/0.29 thf(decl_78, type, notinsingleton: $o).
% 0.21/0.29 thf(decl_79, type, eqinunit: $o).
% 0.21/0.29 thf(decl_80, type, singletonsswitch: $o).
% 0.21/0.29 thf(decl_81, type, upairsetE: $o).
% 0.21/0.29 thf(decl_82, type, upairsetIL: $o).
% 0.21/0.29 thf(decl_83, type, upairsetIR: $o).
% 0.21/0.29 thf(decl_84, type, emptyE1: $o).
% 0.21/0.29 thf(decl_85, type, vacuousDall: $o).
% 0.21/0.29 thf(decl_86, type, quantDeMorgan1: $o).
% 0.21/0.29 thf(decl_87, type, quantDeMorgan2: $o).
% 0.21/0.29 thf(decl_88, type, quantDeMorgan3: $o).
% 0.21/0.29 thf(decl_89, type, quantDeMorgan4: $o).
% 0.21/0.29 thf(decl_90, type, prop2setI: $o).
% 0.21/0.29 thf(decl_92, type, prop2set2propI: $o).
% 0.21/0.29 thf(decl_93, type, notdexE: $o).
% 0.21/0.29 thf(decl_94, type, notdallE: $o).
% 0.21/0.29 thf(decl_95, type, exuI1: $o).
% 0.21/0.29 thf(decl_96, type, exuI3: $o).
% 0.21/0.29 thf(decl_97, type, exuI2: $o).
% 0.21/0.29 thf(decl_98, type, inCongP: $o).
% 0.21/0.29 thf(decl_99, type, in__Cong: $o).
% 0.21/0.29 thf(decl_100, type, exuE3u: $o).
% 0.21/0.29 thf(decl_101, type, exu__Cong: $o).
% 0.21/0.29 thf(decl_102, type, emptyset__Cong: $o).
% 0.21/0.29 thf(decl_103, type, setadjoin__Cong: $o).
% 0.21/0.29 thf(decl_104, type, epred1_0: $o).
% 0.21/0.29 thf(decl_105, type, esk1_2: $i > $i > $i).
% 0.21/0.29 thf(decl_106, type, esk2_2: $i > $i > $i).
% 0.21/0.29 thf(decl_107, type, esk3_2: $i > $i > $i).
% 0.21/0.29 thf(decl_108, type, esk4_1: $i > $i).
% 0.21/0.29 thf(decl_109, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.21/0.29 thf(decl_110, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.21/0.29 thf(decl_111, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.21/0.29 thf(decl_112, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.21/0.29 thf(decl_113, type, esk9_1: $i > $i).
% 0.21/0.29 thf(decl_114, type, esk10_2: ($i > $o) > $i > $i).
% 0.21/0.29 thf(decl_115, type, esk11_1: ($i > $o) > $i).
% 0.21/0.29 thf(decl_116, type, esk12_2: ($i > $o) > $i > $i).
% 0.21/0.29 thf(decl_117, type, esk13_1: ($i > $o) > $i).
% 0.21/0.29 thf(decl_118, type, esk14_2: $i > $i > $i).
% 0.21/0.29 thf(decl_119, type, esk15_2: $i > $i > $i).
% 0.21/0.29 thf(decl_120, type, esk16_1: $i > $i).
% 0.21/0.29 thf(decl_121, type, esk17_1: $i > $i).
% 0.21/0.29 thf(decl_122, type, esk18_1: $i > $i).
% 0.21/0.29 thf(decl_123, type, esk19_2: $i > $i > $i).
% 0.21/0.29 thf(decl_124, type, esk20_3: $i > $i > $o > $i).
% 0.21/0.29 thf(decl_125, type, esk21_2: ($i > $o) > $i > $i).
% 0.21/0.29 thf(decl_126, type, esk22_1: ($i > $o) > $i).
% 0.21/0.29 thf(decl_127, type, esk23_1: $i > $i).
% 0.21/0.29 thf(decl_128, type, esk24_2: $i > ($i > $o) > $i).
% 0.21/0.29 thf(decl_129, type, esk25_2: $i > ($i > $o) > $i).
% 0.21/0.29 thf(decl_130, type, esk26_2: $i > ($i > $o) > $i).
% 0.21/0.29 thf(decl_131, type, esk27_2: $i > ($i > $o) > $i).
% 0.21/0.29 thf(decl_132, type, esk28_2: $i > ($i > $o) > $i).
% 0.21/0.29 thf(decl_133, type, esk29_2: $i > ($i > $o) > $i).
% 0.21/0.29 thf(decl_134, type, esk30_2: ($i > $o) > $i > $i).
% 0.21/0.29 thf(decl_135, type, esk31_1: ($i > $o) > $i).
% 0.21/0.29 thf(decl_136, type, esk32_1: ($i > $o) > $i).
% 0.21/0.29 thf(decl_137, type, esk33_1: ($i > $o) > $i).
% 0.21/0.29 thf(decl_138, type, esk34_1: ($i > $o) > $i).
% 0.21/0.29 thf(decl_139, type, esk35_2: ($i > $o) > $i > $i).
% 0.21/0.29 thf(decl_140, type, esk36_1: ($i > $o) > $i).
% 0.21/0.29 thf(decl_141, type, esk37_2: ($i > $o) > $i > $i).
% 0.21/0.29 thf(decl_142, type, esk38_2: ($i > $o) > ($i > $o) > $i).
% 0.21/0.29 thf(decl_143, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 0.21/0.29 thf(decl_144, type, esk40_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.21/0.29 thf(decl_145, type, esk41_2: ($i > $o) > ($i > $o) > $i).
% 0.21/0.29 thf(decl_146, type, esk42_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.21/0.29 thf(decl_147, type, esk43_2: ($i > $o) > ($i > $o) > $i).
% 0.21/0.29 thf(decl_148, type, esk44_0: $i).
% 0.21/0.29 thf(decl_149, type, esk45_0: $i).
% 0.21/0.29 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', exuI1)).
% 0.21/0.29 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', exu)).
% 0.21/0.29 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', exuI3)).
% 0.21/0.29 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', exuI2)).
% 0.21/0.29 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', exuE3u)).
% 0.21/0.29 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', exu__Cong)).
% 0.21/0.29 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', exuE1)).
% 0.21/0.29 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', nonempty)).
% 0.21/0.29 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', replAx)).
% 0.21/0.29 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', exuE3e)).
% 0.21/0.29 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', nonemptyI)).
% 0.21/0.29 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', exuE2)).
% 0.21/0.29 thf(powerset__Cong, 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)=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', powerset__Cong)).
% 0.21/0.29 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', dsetconstrI)).
% 0.21/0.29 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', dsetconstrER)).
% 0.21/0.29 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', dsetconstrEL)).
% 0.21/0.29 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', nonemptyI1)).
% 0.21/0.29 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', setbeta)).
% 0.21/0.29 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', nonemptyE1)).
% 0.21/0.29 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', setoftrueEq)).
% 0.21/0.29 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', nonemptyImpWitness)).
% 0.21/0.29 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', emptyE1)).
% 0.21/0.29 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', quantDeMorgan3)).
% 0.21/0.29 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', quantDeMorgan2)).
% 0.21/0.29 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', quantDeMorgan4)).
% 0.21/0.29 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', prop2setI)).
% 0.21/0.29 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', notdexE)).
% 0.21/0.29 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', notdallE)).
% 0.21/0.29 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', inCongP)).
% 0.21/0.29 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', in__Cong)).
% 0.21/0.29 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', emptyset__Cong)).
% 0.21/0.29 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', setadjoin__Cong)).
% 0.21/0.29 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', omegaSAx)).
% 0.21/0.29 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', setadjoinIL)).
% 0.21/0.29 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', wellorderingAx)).
% 0.21/0.29 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', foundationAx)).
% 0.21/0.29 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', prop2setE)).
% 0.21/0.29 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', noeltsimpempty)).
% 0.21/0.29 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', emptyI)).
% 0.21/0.29 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', setext)).
% 0.21/0.29 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', notinemptyset)).
% 0.21/0.29 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', emptysetimpfalse)).
% 0.21/0.29 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', emptysetE)).
% 0.21/0.29 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', setadjoinE)).
% 0.21/0.29 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', setadjoinIR)).
% 0.21/0.29 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', emptyinunitempty)).
% 0.21/0.29 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', setadjoinOr)).
% 0.21/0.29 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', setunionE)).
% 0.21/0.29 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', setunionI)).
% 0.21/0.29 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', powersetE)).
% 0.21/0.29 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', emptyInPowerset)).
% 0.21/0.29 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', emptyinPowerset)).
% 0.21/0.29 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', powersetI)).
% 0.21/0.29 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', subPowSU)).
% 0.21/0.29 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', upairsetE)).
% 0.21/0.29 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', singletonsswitch)).
% 0.21/0.29 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', eqinunit)).
% 0.21/0.29 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', notinsingleton)).
% 0.21/0.29 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', uniqinunit)).
% 0.21/0.29 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', omegaIndAx)).
% 0.21/0.29 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', upairsetIR)).
% 0.21/0.29 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', vacuousDall)).
% 0.21/0.29 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', quantDeMorgan1)).
% 0.21/0.29 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', upairsetIL)).
% 0.21/0.29 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', omega0Ax)).
% 0.21/0.29 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', setunionAx)).
% 0.21/0.29 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', powersetAx)).
% 0.21/0.29 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', setadjoinAx)).
% 0.21/0.29 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', emptysetAx)).
% 0.21/0.29 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.d9DDLYD9ri/E---3.1_2534347.p', setextAx)).
% 0.21/0.29 thf(c_0_70, 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])).
% 0.21/0.29 thf(c_0_71, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.21/0.29 thf(c_0_72, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.21/0.29 thf(c_0_73, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.21/0.29 thf(c_0_74, 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])).
% 0.21/0.29 thf(c_0_75, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.21/0.29 thf(c_0_76, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.21/0.29 thf(c_0_77, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.21/0.29 thf(c_0_78, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.21/0.29 thf(c_0_79, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.21/0.29 thf(c_0_80, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.21/0.29 thf(c_0_81, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.21/0.29 thf(c_0_82, 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)=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[powerset__Cong])).
% 0.21/0.29 thf(c_0_83, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.21/0.29 thf(c_0_84, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X222:$i]:(((((X1 @ X222)))&(![X223:$i]:(((((X1 @ X223)))=>(((X222)=(X223)))))))))))))), inference(apply_def,[status(thm)],[c_0_70, c_0_71])).
% 0.21/0.29 thf(c_0_85, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X224:$i]:(((((X1 @ X224)))&(![X225:$i]:(((((X1 @ X225)))=>(((X224)=(X225)))))))))))))))), inference(apply_def,[status(thm)],[c_0_72, c_0_71])).
% 0.21/0.29 thf(c_0_86, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X226:$i]:(((((X1 @ X226)))&(![X227:$i]:(((((X1 @ X227)))=>(((X226)=(X227)))))))))))))), inference(apply_def,[status(thm)],[c_0_73, c_0_71])).
% 0.21/0.29 thf(c_0_87, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X228:$i]:(((((X1 @ X228)))&(![X229:$i]:(((((X1 @ X229)))=>(((X228)=(X229))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_74, c_0_71])).
% 0.21/0.29 thf(c_0_88, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X230:$i]:(((((X1 @ X230)))&(![X231:$i]:(((((X1 @ X231)))=>(((X230)=(X231))))))))))<=>((?[X232:$i]:(((((X17 @ X232)))&(![X233:$i]:(((((X17 @ X233)))=>(((X232)=(X233)))))))))))))))), inference(apply_def,[status(thm)],[c_0_75, c_0_71])).
% 0.21/0.29 thf(c_0_89, plain, ((exuE1)=(![X1:$i > $o]:((((?[X216:$i]:(((((X1 @ X216)))&(![X217:$i]:(((((X1 @ X217)))=>(((X216)=(X217))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_76, c_0_71])).
% 0.21/0.29 thf(c_0_90, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.21/0.29 thf(c_0_91, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.21/0.29 thf(c_0_92, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_77])).
% 0.21/0.29 thf(c_0_93, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X214:$i]:(((((X6 @ X2 @ X214)))&(![X215:$i]:(((((X6 @ X2 @ X215)))=>(((X214)=(X215)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_78, c_0_71])).
% 0.21/0.29 thf(c_0_94, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X218:$i]:(((((X1 @ X218)))&(![X219:$i]:(((((X1 @ X219)))=>(((X218)=(X219))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_79, c_0_71])).
% 0.21/0.29 thf(c_0_95, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.21/0.29 thf(c_0_96, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_80, c_0_77])).
% 0.21/0.29 thf(c_0_97, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_77])).
% 0.21/0.29 thf(c_0_98, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.21/0.29 thf(c_0_99, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_77])).
% 0.21/0.29 thf(c_0_100, plain, ((emptyE1)<=>![X4:$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])).
% 0.21/0.29 thf(c_0_101, plain, ((exuE2)=(![X1:$i > $o]:((((?[X220:$i]:(((((X1 @ X220)))&(![X221:$i]:(((((X1 @ X221)))=>(((X220)=(X221))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_81, c_0_71])).
% 0.21/0.29 thf(c_0_102, plain, ((epred1_0)<=>![X263:$i]:(?[X264:$i]:((((![X265:$i]:(((in @ X265 @ X264)=>![X266:$i]:(((in @ X266 @ X265)=>(in @ X266 @ X263)))))&![X267:$i, X268:$i]:((((in @ X267 @ X263)&(in @ X268 @ X263))=>(![X269:$i]:(((in @ X269 @ X264)=>((in @ X267 @ X269)<=>(in @ X268 @ X269))))=>((X267)=(X268))))))&![X270:$i, X271:$i]:((((in @ X270 @ X264)&(in @ X271 @ X264))=>(![X272:$i]:(((in @ X272 @ X270)=>(in @ X272 @ X271)))|![X273:$i]:(((in @ X273 @ X271)=>(in @ X273 @ X270)))))))&![X274:$i]:(((![X275:$i]:(((in @ X275 @ X274)=>(in @ X275 @ X263)))&?[X276:$i]:((in @ X276 @ X274)))=>?[X277:$i, X278:$i]:(((((in @ X277 @ X264)&(in @ X278 @ X274))&~(?[X279:$i]:(((in @ X279 @ X277)&(in @ X279 @ X274)))))&![X280:$i]:(((in @ X280 @ X264)=>(![X281:$i]:(((in @ X281 @ X280)=>(in @ X281 @ X277)))|(in @ X278 @ X280)))))))))))), introduced(definition)).
% 0.21/0.29 thf(c_0_103, negated_conjecture, ~((![X234:$i, X235:$i]:((![X236:$i]:(((in @ X236 @ X234)<=>(in @ X236 @ X235)))=>((X234)=(X235))))=>(![X237:$i]:(~(in @ X237 @ emptyset))=>(![X238:$i, X239:$i, X240:$i]:(((in @ X240 @ (setadjoin @ X238 @ X239))<=>(((X240)=(X238))|(in @ X240 @ X239))))=>(![X241:$i, X242:$i]:(((in @ X242 @ (powerset @ X241))<=>![X243:$i]:(((in @ X243 @ X242)=>(in @ X243 @ X241)))))=>(![X244:$i, X245:$i]:(((in @ X245 @ (setunion @ X244))<=>?[X246:$i]:(((in @ X245 @ X246)&(in @ X246 @ X244)))))=>((in @ emptyset @ omega)=>(![X247:$i]:(((in @ X247 @ omega)=>(in @ (setadjoin @ X247 @ X247) @ omega)))=>(![X248:$i]:((((in @ emptyset @ X248)&![X249:$i]:((((in @ X249 @ omega)&(in @ X249 @ X248))=>(in @ (setadjoin @ X249 @ X249) @ X248))))=>![X250:$i]:(((in @ X250 @ omega)=>(in @ X250 @ X248)))))=>(![X251:$i > $i > $o, X252:$i]:((![X253:$i]:(((in @ X253 @ X252)=>?[X254:$i]:(((X251 @ X253 @ X254)&![X255:$i]:(((X251 @ X253 @ X255)=>((X254)=(X255))))))))=>?[X256:$i]:(![X257:$i]:(((in @ X257 @ X256)<=>?[X258:$i]:(((in @ X258 @ X252)&(X251 @ X258 @ X257))))))))=>(![X259:$i]:((?[X260:$i]:((in @ X260 @ X259))=>?[X261:$i]:(((in @ X261 @ X259)&~(?[X262:$i]:(((in @ X262 @ X261)&(in @ X262 @ X259))))))))=>((epred1_0)=>((descrp)=>(![X282:$i, X283:$i > $o, X284:$i]:(((in @ X284 @ X282)=>((X283 @ X284)=>(in @ X284 @ (dsetconstr @ X282 @ (^[Z0:$i]:((X283 @ Z0))))))))=>(![X285:$i, X286:$i > $o, X287:$i]:(((in @ X287 @ (dsetconstr @ X285 @ (^[Z0:$i]:((X286 @ Z0)))))=>(in @ X287 @ X285)))=>(![X288:$i, X289:$i > $o, X290:$i]:(((in @ X290 @ (dsetconstr @ X288 @ (^[Z0:$i]:((X289 @ Z0)))))=>(X289 @ X290)))=>(![X291:$i > $o]:((?[X292:$i]:(((X291 @ X292)&![X293:$i]:(((X291 @ X293)=>((X292)=(X293))))))=>?[X294:$i]:(((X291 @ X294)&![X295:$i]:(((X291 @ X295)=>((X294)=(X295))))))))=>(![X296:$o, X297:$i]:(((in @ X297 @ (prop2set @ ((X296))))=>(X296)))=>(![X298:$i]:(((in @ X298 @ emptyset)=>![X299:$o]:((X299))))=>(![X300:$i]:(~(in @ X300 @ emptyset))=>(![X301:$i]:(~(in @ X301 @ emptyset))=>(![X302:$i > $o]:((?[X303:$i]:(((X302 @ X303)&![X304:$i]:(((X302 @ X304)=>((X303)=(X304))))))=>?[X305:$i]:((X302 @ X305))))=>(![X306:$i, X307:$i]:((![X308:$i]:(((in @ X308 @ X306)=>(in @ X308 @ X307)))=>(![X309:$i]:(((in @ X309 @ X307)=>(in @ X309 @ X306)))=>((X306)=(X307)))))=>(![X310:$i]:((![X311:$i]:(~(in @ X311 @ X310))=>((X310)=(emptyset))))=>(![X312:$i]:((![X313:$i]:(~(in @ X313 @ X312))=>((X312)=(emptyset))))=>(![X314:$i, X315:$i > $o, X316:$i]:(((in @ X316 @ X314)=>((in @ X316 @ (dsetconstr @ X314 @ (^[Z0:$i]:((X315 @ Z0)))))<=>(X315 @ X316))))=>(![X317:$i]:((((X317)!=(emptyset))=>?[X318:$i]:((in @ X318 @ X317))))=>(![X319:$i, X320:$i > $o, X321:$i]:(((in @ X321 @ X319)=>((X320 @ X321)=>((dsetconstr @ X319 @ (^[Z0:$i]:((X320 @ Z0))))!=(emptyset)))))=>(![X322:$i]:((?[X323:$i]:((in @ X323 @ X322))=>((X322)!=(emptyset))))=>(![X324:$i, X325:$i]:((in @ X324 @ (setadjoin @ X324 @ X325)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X326:$i, X327:$i, X328:$i]:(((in @ X328 @ X327)=>(in @ X328 @ (setadjoin @ X326 @ X327))))=>(![X329:$i, X330:$i, X331:$i]:(((in @ X331 @ (setadjoin @ X329 @ X330))=>![X332:$o]:(((((X331)=(X329))=>(X332))=>(((in @ X331 @ X330)=>(X332))=>(X332))))))=>(![X333:$i, X334:$i, X335:$i]:(((in @ X335 @ (setadjoin @ X333 @ X334))=>(((X335)=(X333))|(in @ X335 @ X334))))=>(![X336:$i]:(((dsetconstr @ X336 @ (^[Z0:$i]:(($true))))=(X336)))=>(![X337:$i, X338:$i]:((![X339:$i]:(((in @ X339 @ X338)=>(in @ X339 @ X337)))=>(in @ X338 @ (powerset @ X337))))=>(![X340:$i]:((in @ emptyset @ (powerset @ X340)))=>(![X341:$i]:((in @ emptyset @ (powerset @ X341)))=>(![X342:$i, X343:$i, X344:$i]:(((in @ X343 @ (powerset @ X342))=>((in @ X344 @ X343)=>(in @ X344 @ X342))))=>(![X345:$i, X346:$i, X347:$i]:(((in @ X346 @ X347)=>((in @ X347 @ X345)=>(in @ X346 @ (setunion @ X345)))))=>(![X348:$i, X349:$i]:(((in @ X349 @ (setunion @ X348))=>![X350:$o]:((![X351:$i]:(((in @ X349 @ X351)=>((in @ X351 @ X348)=>(X350))))=>(X350)))))=>(![X352:$i, X353:$i]:(((in @ X353 @ X352)=>(in @ X353 @ (powerset @ (setunion @ X352)))))=>(![X354:$i > $o]:((?[X355:$i]:(((X354 @ X355)&![X356:$i]:(((X354 @ X356)=>((X355)=(X356))))))=>?[X357:$i]:(![X358:$i]:(((X354 @ X358)<=>((X358)=(X357)))))))=>(![X359:$i]:((((X359)!=(emptyset))=>?[X360:$i]:((in @ X360 @ X359))))=>(![X361:$i, X362:$i]:(((in @ X361 @ (setadjoin @ X362 @ emptyset))=>((X361)=(X362))))=>(![X363:$i, X364:$i]:((((X363)!=(X364))=>~(in @ X364 @ (setadjoin @ X363 @ emptyset))))=>(![X365:$i, X366:$i]:((((X365)=(X366))=>(in @ X365 @ (setadjoin @ X366 @ emptyset))))=>(![X367:$i, X368:$i]:(((in @ X367 @ (setadjoin @ X368 @ emptyset))=>(in @ X368 @ (setadjoin @ X367 @ emptyset))))=>(![X369:$i, X370:$i, X371:$i]:(((in @ X371 @ (setadjoin @ X369 @ (setadjoin @ X370 @ emptyset)))=>(((X371)=(X369))|((X371)=(X370)))))=>(![X372:$i, X373:$i]:((in @ X372 @ (setadjoin @ X372 @ (setadjoin @ X373 @ emptyset))))=>(![X374:$i, X375:$i]:((in @ X375 @ (setadjoin @ X374 @ (setadjoin @ X375 @ emptyset))))=>(![X376:$i, X377:$i > $o]:((?[X378:$i]:(((in @ X378 @ X376)&(X377 @ X378)))=>((dsetconstr @ X376 @ (^[Z0:$i]:((X377 @ Z0))))!=(emptyset))))=>(![X379:$i > $o, X380:$i]:(((in @ X380 @ emptyset)=>(X379 @ X380)))=>(![X381:$i, X382:$i > $o]:((~(![X383:$i]:(((in @ X383 @ X381)=>(X382 @ X383))))=>?[X384:$i]:(((in @ X384 @ X381)&~(X382 @ X384)))))=>(![X385:$i, X386:$i > $o]:((![X387:$i]:(((in @ X387 @ X385)=>~(X386 @ X387)))=>~(?[X388:$i]:(((in @ X388 @ X385)&(X386 @ X388))))))=>(![X389:$i, X390:$i > $o]:((~(?[X391:$i]:(((in @ X391 @ X389)&(X390 @ X391))))=>![X392:$i]:(((in @ X392 @ X389)=>~(X390 @ X392)))))=>(![X393:$i, X394:$i > $o]:((?[X395:$i]:(((in @ X395 @ X393)&~(X394 @ X395)))=>~(![X396:$i]:(((in @ X396 @ X393)=>(X394 @ X396))))))=>(![X397:$o]:(((X397)=>(in @ emptyset @ (prop2set @ ((X397))))))=>((prop2set2propI)=>(![X398:$i, X399:$i > $o]:((~(?[X400:$i]:(((in @ X400 @ X398)&(X399 @ X400))))=>![X401:$i]:(((in @ X401 @ X398)=>~(X399 @ X401)))))=>(![X402:$i, X403:$i > $o]:((~(![X404:$i]:(((in @ X404 @ X402)=>(X403 @ X404))))=>?[X405:$i]:(((in @ X405 @ X402)&~(X403 @ X405)))))=>(![X406:$i > $o]:((?[X407:$i]:(((X406 @ X407)&![X408:$i]:(((X406 @ X408)=>((X407)=(X408))))))=>?[X409:$i]:(((X406 @ X409)&![X410:$i]:(((X406 @ X410)=>((X409)=(X410))))))))=>(![X411:$i > $o]:((?[X412:$i]:((X411 @ X412))=>(![X413:$i, X414:$i]:(((X411 @ X413)=>((X411 @ X414)=>((X413)=(X414)))))=>?[X415:$i]:(((X411 @ X415)&![X416:$i]:(((X411 @ X416)=>((X415)=(X416)))))))))=>(![X417:$i > $o]:((?[X418:$i]:(![X419:$i]:(((X417 @ X419)<=>((X419)=(X418)))))=>?[X420:$i]:(((X417 @ X420)&![X421:$i]:(((X417 @ X421)=>((X420)=(X421))))))))=>(![X422:$i, X423:$i]:((((X422)=(X423))=>![X424:$i, X425:$i]:((((X424)=(X425))=>((in @ X424 @ X422)=>(in @ X425 @ X423))))))=>(![X426:$i, X427:$i]:((((X426)=(X427))=>![X428:$i, X429:$i]:((((X428)=(X429))=>((in @ X428 @ X426)<=>(in @ X429 @ X427))))))=>(![X430:$i > $o]:((?[X431:$i]:(((X430 @ X431)&![X432:$i]:(((X430 @ X432)=>((X431)=(X432))))))=>![X433:$i, X434:$i]:(((X430 @ X433)=>((X430 @ X434)=>((X433)=(X434)))))))=>(![X435:$i > $o, X436:$i > $o]:((![X437:$i, X438:$i]:((((X437)=(X438))=>((X435 @ X437)<=>(X436 @ X438))))=>(?[X439:$i]:(((X435 @ X439)&![X440:$i]:(((X435 @ X440)=>((X439)=(X440))))))<=>?[X441:$i]:(((X436 @ X441)&![X442:$i]:(((X436 @ X442)=>((X441)=(X442)))))))))=>(((emptyset)=(emptyset))=>(![X443:$i, X444:$i]:((((X443)=(X444))=>![X445:$i, X446:$i]:((((X445)=(X446))=>((setadjoin @ X443 @ X445)=(setadjoin @ X444 @ X446))))))=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ 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)],[c_0_82, c_0_83]), quantDeMorgan3]), quantDeMorgan2]), quantDeMorgan4]), prop2setI]), notdexE]), notdallE]), c_0_84]), c_0_85]), c_0_86]), inCongP]), in__Cong]), c_0_87]), c_0_88]), emptyset__Cong]), setadjoin__Cong]), omegaSAx]), c_0_89]), c_0_90]), c_0_91]), setadjoinIL]), c_0_92]), wellorderingAx]), foundationAx]), c_0_93]), prop2setE]), noeltsimpempty]), emptyI]), setext]), c_0_94]), notinemptyset]), emptysetimpfalse]), emptysetE]), c_0_95]), setadjoinE]), setadjoinIR]), emptyinunitempty]), c_0_96]), c_0_97]), setadjoinOr]), setunionE]), setunionI]), powersetE]), emptyInPowerset]), emptyinPowerset]), powersetI]), c_0_98]), subPowSU]), upairsetE]), singletonsswitch]), eqinunit]), notinsingleton]), uniqinunit]), c_0_99]), omegaIndAx]), upairsetIR]), c_0_100]), vacuousDall]), quantDeMorgan1]), c_0_101]), upairsetIL]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])]), c_0_102])).
% 0.21/0.29 thf(c_0_104, negated_conjecture, ![X447:$i, X448:$i, X450:$i, X451:$i, X452:$i, X453:$i, X454:$i, X455:$i, X456:$i, X457:$i, X458:$i, X460:$i, X461:$i, X463:$i, X464:$i, X465:$i, X466:$i, X467:$i, X469:$i, X470:$i > $i > $o, X471:$i, X473:$i, X476:$i, X478:$i, X479:$i, X480:$i, X481:$i, X483:$i, X484:$i, X485:$i > $o, X486:$i, X487:$i, X488:$i > $o, X489:$i, X490:$i, X491:$i > $o, X492:$i, X493:$i > $o, X494:$i, X497:$i, X498:$o, X499:$i, X500:$i, X501:$o, X502:$i, X503:$i, X504:$i > $o, X505:$i, X508:$i, X509:$i, X512:$i, X514:$i, X516:$i, X517:$i > $o, X518:$i, X519:$i, X521:$i, X522:$i > $o, X523:$i, X524:$i, X525:$i, X526:$i, X527:$i, X528:$i, X529:$i, X530:$i, X531:$i, X532:$i, X533:$i, X534:$o, X535:$i, X536:$i, X537:$i, X538:$i, X539:$i, X540:$i, X542:$i, X543:$i, X544:$i, X545:$i, X546:$i, X547:$i, X548:$i, X549:$i, X550:$i, X551:$i, X552:$o, X554:$i, X555:$i, X556:$i > $o, X557:$i, X560:$i, X561:$i, X562:$i, X564:$i, X565:$i, X566:$i, X567:$i, X568:$i, X569:$i, X570:$i, X571:$i, X572:$i, X573:$i, X574:$i, X575:$i, X576:$i, X577:$i, X578:$i, X579:$i, X580:$i > $o, X581:$i, X582:$i > $o, X583:$i, X584:$i, X585:$i > $o, X586:$i, X588:$i, X589:$i > $o, X591:$i, X592:$i, X593:$i > $o, X595:$i, X596:$i, X597:$i > $o, X598:$i, X600:$o, X601:$i, X602:$i > $o, X604:$i, X605:$i, X606:$i > $o, X607:$i, X609:$i > $o, X610:$i, X613:$i, X614:$i > $o, X615:$i, X619:$i, X620:$i > $o, X621:$i, X624:$i, X625:$i, X626:$i, X627:$i, X628:$i, X629:$i, X630:$i, X631:$i, X632:$i, X633:$i > $o, X634:$i, X636:$i, X637:$i, X638:$i > $o, X639:$i > $o, X642:$i, X645:$i, X646:$i, X649:$i, X650:$i, X651:$i, X652:$i, X653:$i]:((((~(in @ (esk1_2 @ X447 @ X448) @ X447)|~(in @ (esk1_2 @ X447 @ X448) @ X448)|((X447)=(X448)))&((in @ (esk1_2 @ X447 @ X448) @ X447)|(in @ (esk1_2 @ X447 @ X448) @ X448)|((X447)=(X448))))&(~(in @ X450 @ emptyset)&(((~(in @ X453 @ (setadjoin @ X451 @ X452))|(((X453)=(X451))|(in @ X453 @ X452)))&((((X453)!=(X451))|(in @ X453 @ (setadjoin @ X451 @ X452)))&(~(in @ X453 @ X452)|(in @ X453 @ (setadjoin @ X451 @ X452)))))&(((~(in @ X455 @ (powerset @ X454))|(~(in @ X456 @ X455)|(in @ X456 @ X454)))&(((in @ (esk2_2 @ X457 @ X458) @ X458)|(in @ X458 @ (powerset @ X457)))&(~(in @ (esk2_2 @ X457 @ X458) @ X457)|(in @ X458 @ (powerset @ X457)))))&(((((in @ X461 @ (esk3_2 @ X460 @ X461))|~(in @ X461 @ (setunion @ X460)))&((in @ (esk3_2 @ X460 @ X461) @ X460)|~(in @ X461 @ (setunion @ X460))))&(~(in @ X464 @ X465)|~(in @ X465 @ X463)|(in @ X464 @ (setunion @ X463))))&((in @ emptyset @ omega)&((~(in @ X466 @ omega)|(in @ (setadjoin @ X466 @ X466) @ omega))&(((((in @ (esk4_1 @ X467) @ omega)|~(in @ emptyset @ X467)|(~(in @ X469 @ omega)|(in @ X469 @ X467)))&((in @ (esk4_1 @ X467) @ X467)|~(in @ emptyset @ X467)|(~(in @ X469 @ omega)|(in @ X469 @ X467))))&(~(in @ (setadjoin @ (esk4_1 @ X467) @ (esk4_1 @ X467)) @ X467)|~(in @ emptyset @ X467)|(~(in @ X469 @ omega)|(in @ X469 @ X467))))&((((((in @ (esk8_3 @ X470 @ X471 @ X476) @ X471)|~(in @ X476 @ (esk7_2 @ X470 @ X471))|(in @ (esk5_2 @ X470 @ X471) @ X471))&((X470 @ (esk8_3 @ X470 @ X471 @ X476) @ X476)|~(in @ X476 @ (esk7_2 @ X470 @ X471))|(in @ (esk5_2 @ X470 @ X471) @ X471)))&(~(in @ X479 @ X471)|~(X470 @ X479 @ X478)|(in @ X478 @ (esk7_2 @ X470 @ X471))|(in @ (esk5_2 @ X470 @ X471) @ X471)))&(((((in @ (esk8_3 @ X470 @ X471 @ X476) @ X471)|~(in @ X476 @ (esk7_2 @ X470 @ X471))|((X470 @ (esk5_2 @ X470 @ X471) @ (esk6_3 @ X470 @ X471 @ X473))|~(X470 @ (esk5_2 @ X470 @ X471) @ X473)))&((X470 @ (esk8_3 @ X470 @ X471 @ X476) @ X476)|~(in @ X476 @ (esk7_2 @ X470 @ X471))|((X470 @ (esk5_2 @ X470 @ X471) @ (esk6_3 @ X470 @ X471 @ X473))|~(X470 @ (esk5_2 @ X470 @ X471) @ X473))))&(~(in @ X479 @ X471)|~(X470 @ X479 @ X478)|(in @ X478 @ (esk7_2 @ X470 @ X471))|((X470 @ (esk5_2 @ X470 @ X471) @ (esk6_3 @ X470 @ X471 @ X473))|~(X470 @ (esk5_2 @ X470 @ X471) @ X473))))&((((in @ (esk8_3 @ X470 @ X471 @ X476) @ X471)|~(in @ X476 @ (esk7_2 @ X470 @ X471))|(((X473)!=(esk6_3 @ X470 @ X471 @ X473))|~(X470 @ (esk5_2 @ X470 @ X471) @ X473)))&((X470 @ (esk8_3 @ X470 @ X471 @ X476) @ X476)|~(in @ X476 @ (esk7_2 @ X470 @ X471))|(((X473)!=(esk6_3 @ X470 @ X471 @ X473))|~(X470 @ (esk5_2 @ X470 @ X471) @ X473))))&(~(in @ X479 @ X471)|~(X470 @ X479 @ X478)|(in @ X478 @ (esk7_2 @ X470 @ X471))|(((X473)!=(esk6_3 @ X470 @ X471 @ X473))|~(X470 @ (esk5_2 @ X470 @ X471) @ X473))))))&((((in @ (esk9_1 @ X480) @ X480)|~(in @ X481 @ X480))&(~(in @ X483 @ (esk9_1 @ X480))|~(in @ X483 @ X480)|~(in @ X481 @ X480)))&((epred1_0)&((descrp)&((~(in @ X486 @ X484)|(~(X485 @ X486)|(in @ X486 @ (dsetconstr @ X484 @ (^[Z0:$i]:((X485 @ Z0)))))))&((~(in @ X489 @ (dsetconstr @ X487 @ (^[Z0:$i]:((X488 @ Z0)))))|(in @ X489 @ X487))&((~(in @ X492 @ (dsetconstr @ X490 @ (^[Z0:$i]:((X491 @ Z0)))))|(X491 @ X492))&(((((X493 @ (esk11_1 @ X493))|((X493 @ (esk10_2 @ X493 @ X494))|~(X493 @ X494)))&(~(X493 @ X497)|((esk11_1 @ X493)=(X497))|((X493 @ (esk10_2 @ X493 @ X494))|~(X493 @ X494))))&(((X493 @ (esk11_1 @ X493))|(((X494)!=(esk10_2 @ X493 @ X494))|~(X493 @ X494)))&(~(X493 @ X497)|((esk11_1 @ X493)=(X497))|(((X494)!=(esk10_2 @ X493 @ X494))|~(X493 @ X494)))))&((~(in @ X499 @ (prop2set @ ((X498))))|(X498))&((~(in @ X500 @ emptyset)|(X501))&(~(in @ X502 @ emptyset)&(~(in @ X503 @ emptyset)&((((X504 @ (esk12_2 @ X504 @ X505))|~(X504 @ X505)|(X504 @ (esk13_1 @ X504)))&(((X505)!=(esk12_2 @ X504 @ X505))|~(X504 @ X505)|(X504 @ (esk13_1 @ X504))))&(((((in @ (esk15_2 @ X508 @ X509) @ X509)|((X508)=(X509))|(in @ (esk14_2 @ X508 @ X509) @ X508))&(~(in @ (esk15_2 @ X508 @ X509) @ X508)|((X508)=(X509))|(in @ (esk14_2 @ X508 @ X509) @ X508)))&(((in @ (esk15_2 @ X508 @ X509) @ X509)|((X508)=(X509))|~(in @ (esk14_2 @ X508 @ X509) @ X509))&(~(in @ (esk15_2 @ X508 @ X509) @ X508)|((X508)=(X509))|~(in @ (esk14_2 @ X508 @ X509) @ X509))))&(((in @ (esk16_1 @ X512) @ X512)|((X512)=(emptyset)))&(((in @ (esk17_1 @ X514) @ X514)|((X514)=(emptyset)))&(((~(in @ X518 @ (dsetconstr @ X516 @ (^[Z0:$i]:((X517 @ Z0)))))|(X517 @ X518)|~(in @ X518 @ X516))&(~(X517 @ X518)|(in @ X518 @ (dsetconstr @ X516 @ (^[Z0:$i]:((X517 @ Z0)))))|~(in @ X518 @ X516)))&((((X519)=(emptyset))|(in @ (esk18_1 @ X519) @ X519))&((~(in @ X523 @ X521)|(~(X522 @ X523)|((dsetconstr @ X521 @ (^[Z0:$i]:((X522 @ Z0))))!=(emptyset))))&((~(in @ X525 @ X524)|((X524)!=(emptyset)))&((in @ X526 @ (setadjoin @ X526 @ X527))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X530 @ X529)|(in @ X530 @ (setadjoin @ X528 @ X529)))&(((((in @ X533 @ X532)|(X534)|((X533)=(X531))|~(in @ X533 @ (setadjoin @ X531 @ X532)))&(~(X534)|(X534)|((X533)=(X531))|~(in @ X533 @ (setadjoin @ X531 @ X532))))&(((in @ X533 @ X532)|(X534)|~(X534)|~(in @ X533 @ (setadjoin @ X531 @ X532)))&(~(X534)|(X534)|~(X534)|~(in @ X533 @ (setadjoin @ X531 @ X532)))))&((~(in @ X537 @ (setadjoin @ X535 @ X536))|(((X537)=(X535))|(in @ X537 @ X536)))&(((dsetconstr @ X538 @ (^[Z0:$i]:(($true))))=(X538))&((((in @ (esk19_2 @ X539 @ X540) @ X540)|(in @ X540 @ (powerset @ X539)))&(~(in @ (esk19_2 @ X539 @ X540) @ X539)|(in @ X540 @ (powerset @ X539))))&((in @ emptyset @ (powerset @ X542))&((in @ emptyset @ (powerset @ X543))&((~(in @ X545 @ (powerset @ X544))|(~(in @ X546 @ X545)|(in @ X546 @ X544)))&((~(in @ X548 @ X549)|(~(in @ X549 @ X547)|(in @ X548 @ (setunion @ X547))))&((((in @ X551 @ (esk20_3 @ X550 @ X551 @ X552))|(X552)|~(in @ X551 @ (setunion @ X550)))&(((in @ (esk20_3 @ X550 @ X551 @ X552) @ X550)|(X552)|~(in @ X551 @ (setunion @ X550)))&(~(X552)|(X552)|~(in @ X551 @ (setunion @ X550)))))&((~(in @ X555 @ X554)|(in @ X555 @ (powerset @ (setunion @ X554))))&((((~(X556 @ X560)|((X560)=(esk22_1 @ X556))|((X556 @ (esk21_2 @ X556 @ X557))|~(X556 @ X557)))&(((X561)!=(esk22_1 @ X556))|(X556 @ X561)|((X556 @ (esk21_2 @ X556 @ X557))|~(X556 @ X557))))&((~(X556 @ X560)|((X560)=(esk22_1 @ X556))|(((X557)!=(esk21_2 @ X556 @ X557))|~(X556 @ X557)))&(((X561)!=(esk22_1 @ X556))|(X556 @ X561)|(((X557)!=(esk21_2 @ X556 @ X557))|~(X556 @ X557)))))&((((X562)=(emptyset))|(in @ (esk23_1 @ X562) @ X562))&((~(in @ X564 @ (setadjoin @ X565 @ emptyset))|((X564)=(X565)))&((((X566)=(X567))|~(in @ X567 @ (setadjoin @ X566 @ emptyset)))&((((X568)!=(X569))|(in @ X568 @ (setadjoin @ X569 @ emptyset)))&((~(in @ X570 @ (setadjoin @ X571 @ emptyset))|(in @ X571 @ (setadjoin @ X570 @ emptyset)))&((~(in @ X574 @ (setadjoin @ X572 @ (setadjoin @ X573 @ emptyset)))|(((X574)=(X572))|((X574)=(X573))))&((in @ X575 @ (setadjoin @ X575 @ (setadjoin @ X576 @ emptyset)))&((in @ X578 @ (setadjoin @ X577 @ (setadjoin @ X578 @ emptyset)))&((~(in @ X581 @ X579)|~(X580 @ X581)|((dsetconstr @ X579 @ (^[Z0:$i]:((X580 @ Z0))))!=(emptyset)))&((~(in @ X583 @ emptyset)|(X582 @ X583))&((((in @ (esk24_2 @ X584 @ X585) @ X584)|(~(in @ X586 @ X584)|(X585 @ X586)))&(~(X585 @ (esk24_2 @ X584 @ X585))|(~(in @ X586 @ X584)|(X585 @ X586))))&((((in @ (esk25_2 @ X588 @ X589) @ X588)|(~(in @ X591 @ X588)|~(X589 @ X591)))&((X589 @ (esk25_2 @ X588 @ X589))|(~(in @ X591 @ X588)|~(X589 @ X591))))&((((in @ (esk26_2 @ X592 @ X593) @ X592)|(~(in @ X595 @ X592)|~(X593 @ X595)))&((X593 @ (esk26_2 @ X592 @ X593))|(~(in @ X595 @ X592)|~(X593 @ X595))))&((((in @ (esk27_2 @ X596 @ X597) @ X596)|(~(in @ X598 @ X596)|(X597 @ X598)))&(~(X597 @ (esk27_2 @ X596 @ X597))|(~(in @ X598 @ X596)|(X597 @ X598))))&((~(X600)|(in @ emptyset @ (prop2set @ ((X600)))))&((prop2set2propI)&((((in @ (esk28_2 @ X601 @ X602) @ X601)|(~(in @ X604 @ X601)|~(X602 @ X604)))&((X602 @ (esk28_2 @ X601 @ X602))|(~(in @ X604 @ X601)|~(X602 @ X604))))&((((in @ (esk29_2 @ X605 @ X606) @ X605)|(~(in @ X607 @ X605)|(X606 @ X607)))&(~(X606 @ (esk29_2 @ X605 @ X606))|(~(in @ X607 @ X605)|(X606 @ X607))))&(((((X609 @ (esk31_1 @ X609))|((X609 @ (esk30_2 @ X609 @ X610))|~(X609 @ X610)))&(~(X609 @ X613)|((esk31_1 @ X609)=(X613))|((X609 @ (esk30_2 @ X609 @ X610))|~(X609 @ X610))))&(((X609 @ (esk31_1 @ X609))|(((X610)!=(esk30_2 @ X609 @ X610))|~(X609 @ X610)))&(~(X609 @ X613)|((esk31_1 @ X609)=(X613))|(((X610)!=(esk30_2 @ X609 @ X610))|~(X609 @ X610)))))&(((((X614 @ (esk34_1 @ X614))|(X614 @ (esk32_1 @ X614))|~(X614 @ X615))&(~(X614 @ X619)|((esk34_1 @ X614)=(X619))|(X614 @ (esk32_1 @ X614))|~(X614 @ X615)))&((((X614 @ (esk34_1 @ X614))|(X614 @ (esk33_1 @ X614))|~(X614 @ X615))&(~(X614 @ X619)|((esk34_1 @ X614)=(X619))|(X614 @ (esk33_1 @ X614))|~(X614 @ X615)))&(((X614 @ (esk34_1 @ X614))|((esk32_1 @ X614)!=(esk33_1 @ X614))|~(X614 @ X615))&(~(X614 @ X619)|((esk34_1 @ X614)=(X619))|((esk32_1 @ X614)!=(esk33_1 @ X614))|~(X614 @ X615)))))&(((((X620 @ (esk36_1 @ X620))|(~(X620 @ (esk35_2 @ X620 @ X621))|((esk35_2 @ X620 @ X621)!=(X621))))&(~(X620 @ X624)|((esk36_1 @ X620)=(X624))|(~(X620 @ (esk35_2 @ X620 @ X621))|((esk35_2 @ X620 @ X621)!=(X621)))))&(((X620 @ (esk36_1 @ X620))|((X620 @ (esk35_2 @ X620 @ X621))|((esk35_2 @ X620 @ X621)=(X621))))&(~(X620 @ X624)|((esk36_1 @ X620)=(X624))|((X620 @ (esk35_2 @ X620 @ X621))|((esk35_2 @ X620 @ X621)=(X621))))))&((((X625)!=(X626))|(((X627)!=(X628))|(~(in @ X627 @ X625)|(in @ X628 @ X626))))&(((~(in @ X631 @ X629)|(in @ X632 @ X630)|((X631)!=(X632))|((X629)!=(X630)))&(~(in @ X632 @ X630)|(in @ X631 @ X629)|((X631)!=(X632))|((X629)!=(X630))))&((((X633 @ (esk37_2 @ X633 @ X634))|~(X633 @ X634)|(~(X633 @ X636)|(~(X633 @ X637)|((X636)=(X637)))))&(((X634)!=(esk37_2 @ X633 @ X634))|~(X633 @ X634)|(~(X633 @ X636)|(~(X633 @ X637)|((X636)=(X637))))))&(((((((X639 @ (esk41_2 @ X638 @ X639))|((X638 @ (esk40_3 @ X638 @ X639 @ X642))|~(X638 @ X642))|((esk38_2 @ X638 @ X639)=(esk39_2 @ X638 @ X639)))&(~(X639 @ X645)|((esk41_2 @ X638 @ X639)=(X645))|((X638 @ (esk40_3 @ X638 @ X639 @ X642))|~(X638 @ X642))|((esk38_2 @ X638 @ X639)=(esk39_2 @ X638 @ X639))))&(((X639 @ (esk41_2 @ X638 @ X639))|(((X642)!=(esk40_3 @ X638 @ X639 @ X642))|~(X638 @ X642))|((esk38_2 @ X638 @ X639)=(esk39_2 @ X638 @ X639)))&(~(X639 @ X645)|((esk41_2 @ X638 @ X639)=(X645))|(((X642)!=(esk40_3 @ X638 @ X639 @ X642))|~(X638 @ X642))|((esk38_2 @ X638 @ X639)=(esk39_2 @ X638 @ X639)))))&((((X638 @ (esk43_2 @ X638 @ X639))|((X639 @ (esk42_3 @ X638 @ X639 @ X646))|~(X639 @ X646))|((esk38_2 @ X638 @ X639)=(esk39_2 @ X638 @ X639)))&(~(X638 @ X649)|((esk43_2 @ X638 @ X639)=(X649))|((X639 @ (esk42_3 @ X638 @ X639 @ X646))|~(X639 @ X646))|((esk38_2 @ X638 @ X639)=(esk39_2 @ X638 @ X639))))&(((X638 @ (esk43_2 @ X638 @ X639))|(((X646)!=(esk42_3 @ X638 @ X639 @ X646))|~(X639 @ X646))|((esk38_2 @ X638 @ X639)=(esk39_2 @ X638 @ X639)))&(~(X638 @ X649)|((esk43_2 @ X638 @ X639)=(X649))|(((X646)!=(esk42_3 @ X638 @ X639 @ X646))|~(X639 @ X646))|((esk38_2 @ X638 @ X639)=(esk39_2 @ X638 @ X639))))))&((((((X639 @ (esk41_2 @ X638 @ X639))|((X638 @ (esk40_3 @ X638 @ X639 @ X642))|~(X638 @ X642))|(~(X638 @ (esk38_2 @ X638 @ X639))|~(X639 @ (esk39_2 @ X638 @ X639))))&(~(X639 @ X645)|((esk41_2 @ X638 @ X639)=(X645))|((X638 @ (esk40_3 @ X638 @ X639 @ X642))|~(X638 @ X642))|(~(X638 @ (esk38_2 @ X638 @ X639))|~(X639 @ (esk39_2 @ X638 @ X639)))))&(((X639 @ (esk41_2 @ X638 @ X639))|(((X642)!=(esk40_3 @ X638 @ X639 @ X642))|~(X638 @ X642))|(~(X638 @ (esk38_2 @ X638 @ X639))|~(X639 @ (esk39_2 @ X638 @ X639))))&(~(X639 @ X645)|((esk41_2 @ X638 @ X639)=(X645))|(((X642)!=(esk40_3 @ X638 @ X639 @ X642))|~(X638 @ X642))|(~(X638 @ (esk38_2 @ X638 @ X639))|~(X639 @ (esk39_2 @ X638 @ X639))))))&((((X638 @ (esk43_2 @ X638 @ X639))|((X639 @ (esk42_3 @ X638 @ X639 @ X646))|~(X639 @ X646))|(~(X638 @ (esk38_2 @ X638 @ X639))|~(X639 @ (esk39_2 @ X638 @ X639))))&(~(X638 @ X649)|((esk43_2 @ X638 @ X639)=(X649))|((X639 @ (esk42_3 @ X638 @ X639 @ X646))|~(X639 @ X646))|(~(X638 @ (esk38_2 @ X638 @ X639))|~(X639 @ (esk39_2 @ X638 @ X639)))))&(((X638 @ (esk43_2 @ X638 @ X639))|(((X646)!=(esk42_3 @ X638 @ X639 @ X646))|~(X639 @ X646))|(~(X638 @ (esk38_2 @ X638 @ X639))|~(X639 @ (esk39_2 @ X638 @ X639))))&(~(X638 @ X649)|((esk43_2 @ X638 @ X639)=(X649))|(((X646)!=(esk42_3 @ X638 @ X639 @ X646))|~(X639 @ X646))|(~(X638 @ (esk38_2 @ X638 @ X639))|~(X639 @ (esk39_2 @ X638 @ X639)))))))&(((((X639 @ (esk41_2 @ X638 @ X639))|((X638 @ (esk40_3 @ X638 @ X639 @ X642))|~(X638 @ X642))|((X638 @ (esk38_2 @ X638 @ X639))|(X639 @ (esk39_2 @ X638 @ X639))))&(~(X639 @ X645)|((esk41_2 @ X638 @ X639)=(X645))|((X638 @ (esk40_3 @ X638 @ X639 @ X642))|~(X638 @ X642))|((X638 @ (esk38_2 @ X638 @ X639))|(X639 @ (esk39_2 @ X638 @ X639)))))&(((X639 @ (esk41_2 @ X638 @ X639))|(((X642)!=(esk40_3 @ X638 @ X639 @ X642))|~(X638 @ X642))|((X638 @ (esk38_2 @ X638 @ X639))|(X639 @ (esk39_2 @ X638 @ X639))))&(~(X639 @ X645)|((esk41_2 @ X638 @ X639)=(X645))|(((X642)!=(esk40_3 @ X638 @ X639 @ X642))|~(X638 @ X642))|((X638 @ (esk38_2 @ X638 @ X639))|(X639 @ (esk39_2 @ X638 @ X639))))))&((((X638 @ (esk43_2 @ X638 @ X639))|((X639 @ (esk42_3 @ X638 @ X639 @ X646))|~(X639 @ X646))|((X638 @ (esk38_2 @ X638 @ X639))|(X639 @ (esk39_2 @ X638 @ X639))))&(~(X638 @ X649)|((esk43_2 @ X638 @ X639)=(X649))|((X639 @ (esk42_3 @ X638 @ X639 @ X646))|~(X639 @ X646))|((X638 @ (esk38_2 @ X638 @ X639))|(X639 @ (esk39_2 @ X638 @ X639)))))&(((X638 @ (esk43_2 @ X638 @ X639))|(((X646)!=(esk42_3 @ X638 @ X639 @ X646))|~(X639 @ X646))|((X638 @ (esk38_2 @ X638 @ X639))|(X639 @ (esk39_2 @ X638 @ X639))))&(~(X638 @ X649)|((esk43_2 @ X638 @ X639)=(X649))|(((X646)!=(esk42_3 @ X638 @ X639 @ X646))|~(X639 @ X646))|((X638 @ (esk38_2 @ X638 @ X639))|(X639 @ (esk39_2 @ X638 @ X639)))))))))&(((emptyset)=(emptyset))&((((X650)!=(X651))|(((X652)!=(X653))|((setadjoin @ X650 @ X652)=(setadjoin @ X651 @ X653))))&(((esk44_0)=(esk45_0))&((powerset @ esk44_0)!=(powerset @ esk45_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_103])])])])])])).
% 0.21/0.29 thf(c_0_105, negated_conjecture, ((powerset @ esk44_0)!=(powerset @ esk45_0)), inference(split_conjunct,[status(thm)],[c_0_104])).
% 0.21/0.29 thf(c_0_106, negated_conjecture, ((esk44_0)=(esk45_0)), inference(split_conjunct,[status(thm)],[c_0_104])).
% 0.21/0.29 thf(c_0_107, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_105, c_0_106])]), ['proof']).
% 0.21/0.29 % SZS output end CNFRefutation
% 0.21/0.29 % Parsed axioms : 153
% 0.21/0.29 % Removed by relevancy pruning/SinE : 83
% 0.21/0.29 % Initial clauses : 161
% 0.21/0.29 % Removed in clause preprocessing : 9
% 0.21/0.29 % Initial clauses in saturation : 152
% 0.21/0.29 % Processed clauses : 11
% 0.21/0.29 % ...of these trivial : 0
% 0.21/0.29 % ...subsumed : 3
% 0.21/0.29 % ...remaining for further processing : 7
% 0.21/0.29 % Other redundant clauses eliminated : 0
% 0.21/0.29 % Clauses deleted for lack of memory : 0
% 0.21/0.29 % Backward-subsumed : 0
% 0.21/0.29 % Backward-rewritten : 0
% 0.21/0.29 % Generated clauses : 0
% 0.21/0.29 % ...of the previous two non-redundant : 0
% 0.21/0.29 % ...aggressively subsumed : 0
% 0.21/0.29 % Contextual simplify-reflections : 0
% 0.21/0.29 % Paramodulations : 0
% 0.21/0.29 % Factorizations : 0
% 0.21/0.29 % NegExts : 0
% 0.21/0.29 % Equation resolutions : 0
% 0.21/0.29 % Disequality decompositions : 0
% 0.21/0.29 % Total rewrite steps : 1
% 0.21/0.29 % ...of those cached : 0
% 0.21/0.29 % Propositional unsat checks : 0
% 0.21/0.29 % Propositional check models : 0
% 0.21/0.29 % Propositional check unsatisfiable : 0
% 0.21/0.29 % Propositional clauses : 0
% 0.21/0.29 % Propositional clauses after purity: 0
% 0.21/0.29 % Propositional unsat core size : 0
% 0.21/0.29 % Propositional preprocessing time : 0.000
% 0.21/0.29 % Propositional encoding time : 0.000
% 0.21/0.29 % Propositional solver time : 0.000
% 0.21/0.29 % Success case prop preproc time : 0.000
% 0.21/0.29 % Success case prop encoding time : 0.000
% 0.21/0.29 % Success case prop solver time : 0.000
% 0.21/0.29 % Current number of processed clauses : 7
% 0.21/0.29 % Positive orientable unit clauses : 6
% 0.21/0.29 % Positive unorientable unit clauses: 0
% 0.21/0.29 % Negative unit clauses : 1
% 0.21/0.29 % Non-unit-clauses : 0
% 0.21/0.29 % Current number of unprocessed clauses: 141
% 0.21/0.29 % ...number of literals in the above : 491
% 0.21/0.29 % Current number of archived formulas : 0
% 0.21/0.29 % Current number of archived clauses : 0
% 0.21/0.29 % Clause-clause subsumption calls (NU) : 0
% 0.21/0.29 % Rec. Clause-clause subsumption calls : 0
% 0.21/0.29 % Non-unit clause-clause subsumptions : 0
% 0.21/0.29 % Unit Clause-clause subsumption calls : 0
% 0.21/0.29 % Rewrite failures with RHS unbound : 0
% 0.21/0.29 % BW rewrite match attempts : 0
% 0.21/0.29 % BW rewrite match successes : 0
% 0.21/0.29 % Condensation attempts : 0
% 0.21/0.29 % Condensation successes : 0
% 0.21/0.29 % Termbank termtop insertions : 16715
% 0.21/0.29 % Search garbage collected termcells : 6519
% 0.21/0.29
% 0.21/0.29 % -------------------------------------------------
% 0.21/0.29 % User time : 0.018 s
% 0.21/0.29 % System time : 0.008 s
% 0.21/0.29 % Total time : 0.025 s
% 0.21/0.29 % Maximum resident set size: 5580 pages
% 0.21/0.29
% 0.21/0.29 % -------------------------------------------------
% 0.21/0.29 % User time : 0.021 s
% 0.21/0.29 % System time : 0.013 s
% 0.21/0.29 % Total time : 0.035 s
% 0.21/0.29 % Maximum resident set size: 5120 pages
% 0.21/0.29 % E exiting
%------------------------------------------------------------------------------