%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU553^1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:26:41 AM UTC 2026
% Result : Theorem 0.24s 0.30s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU553^1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n019.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 13:50:02 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.26 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.B7krAUK1ZE/E---3.1_797600.p
% 0.24/0.30 % Version: 3.5.1-ho
% 0.24/0.30 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.24/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.30 % Starting new_ho_10 with 1500s (5) cores
% 0.24/0.30 % Starting sh5l with 300s (1) cores
% 0.24/0.30 % Starting new_bool_1 with 300s (1) cores
% 0.24/0.30 % Starting new_bool_2 with 300s (1) cores
% 0.24/0.30 % new_ho_10 with pid 797613 completed with status 0
% 0.24/0.30 % Result found by new_ho_10
% 0.24/0.30 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.24/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.30 % Starting new_ho_10 with 1500s (5) cores
% 0.24/0.30 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.30 % No SInE strategy applied
% 0.24/0.30 % Search class: HGHSM-FSLM31-SHFMMMBN
% 0.24/0.30 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/0.30 % Starting SubtermCWHack with 136s (1) cores
% 0.24/0.30 % Starting new_ho_10 with 151s (1) cores
% 0.24/0.30 % Starting sh5l with 136s (1) cores
% 0.24/0.30 % Starting lpo1_def_fix with 136s (1) cores
% 0.24/0.30 % Starting full_lambda_2 with 136s (1) cores
% 0.24/0.30 % SubtermCWHack with pid 797617 completed with status 0
% 0.24/0.30 % Result found by SubtermCWHack
% 0.24/0.30 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.24/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.30 % Starting new_ho_10 with 1500s (5) cores
% 0.24/0.30 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.30 % No SInE strategy applied
% 0.24/0.30 % Search class: HGHSM-FSLM31-SHFMMMBN
% 0.24/0.30 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/0.30 % Starting SubtermCWHack with 136s (1) cores
% 0.24/0.30 % Preprocessing time : 0.004 s
% 0.24/0.30
% 0.24/0.30 % Proof found!
% 0.24/0.30 % SZS status Theorem
% 0.24/0.30 % SZS output start CNFRefutation
% 0.24/0.30 thf(decl_23, type, in: $i > $i > $o).
% 0.24/0.30 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.24/0.30 thf(decl_25, type, setextAx: $o).
% 0.24/0.30 thf(decl_26, type, emptyset: $i).
% 0.24/0.30 thf(decl_27, type, emptysetAx: $o).
% 0.24/0.30 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.24/0.30 thf(decl_29, type, setadjoinAx: $o).
% 0.24/0.30 thf(decl_30, type, powerset: $i > $i).
% 0.24/0.30 thf(decl_31, type, powersetAx: $o).
% 0.24/0.30 thf(decl_32, type, setunion: $i > $i).
% 0.24/0.30 thf(decl_33, type, setunionAx: $o).
% 0.24/0.30 thf(decl_34, type, omega: $i).
% 0.24/0.30 thf(decl_35, type, omega0Ax: $o).
% 0.24/0.30 thf(decl_36, type, omegaSAx: $o).
% 0.24/0.30 thf(decl_37, type, omegaIndAx: $o).
% 0.24/0.30 thf(decl_38, type, replAx: $o).
% 0.24/0.30 thf(decl_39, type, foundationAx: $o).
% 0.24/0.30 thf(decl_40, type, wellorderingAx: $o).
% 0.24/0.30 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.24/0.30 thf(decl_42, type, descrp: $o).
% 0.24/0.30 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.24/0.30 thf(decl_44, type, dsetconstrI: $o).
% 0.24/0.30 thf(decl_45, type, dsetconstrEL: $o).
% 0.24/0.30 thf(decl_46, type, dsetconstrER: $o).
% 0.24/0.30 thf(decl_47, type, exuE1: $o).
% 0.24/0.30 thf(decl_48, type, prop2set: $o > $i).
% 0.24/0.30 thf(decl_49, type, prop2setE: $o).
% 0.24/0.30 thf(decl_50, type, emptysetE: $o).
% 0.24/0.30 thf(decl_51, type, emptysetimpfalse: $o).
% 0.24/0.30 thf(decl_52, type, notinemptyset: $o).
% 0.24/0.30 thf(decl_53, type, exuE3e: $o).
% 0.24/0.30 thf(decl_54, type, setext: $o).
% 0.24/0.30 thf(decl_55, type, emptyI: $o).
% 0.24/0.30 thf(decl_56, type, noeltsimpempty: $o).
% 0.24/0.30 thf(decl_57, type, setbeta: $o).
% 0.24/0.30 thf(decl_58, type, nonempty: $i > $o).
% 0.24/0.30 thf(decl_59, type, nonemptyE1: $o).
% 0.24/0.30 thf(decl_60, type, nonemptyI: $o).
% 0.24/0.30 thf(decl_61, type, nonemptyI1: $o).
% 0.24/0.30 thf(decl_62, type, setadjoinIL: $o).
% 0.24/0.30 thf(decl_63, type, emptyinunitempty: $o).
% 0.24/0.30 thf(decl_64, type, setadjoinIR: $o).
% 0.24/0.30 thf(decl_65, type, setadjoinE: $o).
% 0.24/0.30 thf(decl_66, type, setadjoinOr: $o).
% 0.24/0.30 thf(decl_67, type, setoftrueEq: $o).
% 0.24/0.30 thf(decl_68, type, powersetI: $o).
% 0.24/0.30 thf(decl_69, type, emptyinPowerset: $o).
% 0.24/0.30 thf(decl_70, type, emptyInPowerset: $o).
% 0.24/0.30 thf(decl_71, type, powersetE: $o).
% 0.24/0.30 thf(decl_72, type, setunionI: $o).
% 0.24/0.30 thf(decl_73, type, setunionE: $o).
% 0.24/0.30 thf(decl_74, type, subPowSU: $o).
% 0.24/0.30 thf(decl_75, type, exuE2: $o).
% 0.24/0.30 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.24/0.30 thf(decl_77, type, uniqinunit: $o).
% 0.24/0.30 thf(decl_78, type, notinsingleton: $o).
% 0.24/0.30 thf(decl_79, type, eqinunit: $o).
% 0.24/0.30 thf(decl_80, type, singletonsswitch: $o).
% 0.24/0.30 thf(decl_81, type, upairsetE: $o).
% 0.24/0.30 thf(decl_82, type, upairsetIL: $o).
% 0.24/0.30 thf(decl_83, type, upairsetIR: $o).
% 0.24/0.30 thf(decl_84, type, emptyE1: $o).
% 0.24/0.30 thf(decl_85, type, vacuousDall: $o).
% 0.24/0.30 thf(decl_86, type, quantDeMorgan1: $o).
% 0.24/0.30 thf(decl_87, type, quantDeMorgan2: $o).
% 0.24/0.30 thf(decl_88, type, quantDeMorgan3: $o).
% 0.24/0.30 thf(decl_89, type, quantDeMorgan4: $o).
% 0.24/0.30 thf(decl_90, type, prop2setI: $o).
% 0.24/0.30 thf(decl_91, type, set2prop: $i > $o).
% 0.24/0.30 thf(decl_92, type, prop2set2propI: $o).
% 0.24/0.30 thf(decl_93, type, notdexE: $o).
% 0.24/0.30 thf(decl_94, type, notdallE: $o).
% 0.24/0.30 thf(decl_95, type, exuI1: $o).
% 0.24/0.30 thf(decl_96, type, exuI3: $o).
% 0.24/0.30 thf(decl_97, type, exuI2: $o).
% 0.24/0.30 thf(decl_98, type, inCongP: $o).
% 0.24/0.30 thf(decl_99, type, in__Cong: $o).
% 0.24/0.30 thf(decl_100, type, exuE3u: $o).
% 0.24/0.30 thf(decl_101, type, exu__Cong: $o).
% 0.24/0.30 thf(decl_102, type, emptyset__Cong: $o).
% 0.24/0.30 thf(decl_103, type, setadjoin__Cong: $o).
% 0.24/0.30 thf(decl_104, type, epred1_0: $o).
% 0.24/0.30 thf(decl_105, type, esk1_2: $i > $i > $i).
% 0.24/0.30 thf(decl_106, type, esk2_2: $i > $i > $i).
% 0.24/0.30 thf(decl_107, type, esk3_2: $i > $i > $i).
% 0.24/0.30 thf(decl_108, type, esk4_1: $i > $i).
% 0.24/0.30 thf(decl_109, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.24/0.30 thf(decl_110, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.24/0.30 thf(decl_111, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.24/0.30 thf(decl_112, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.24/0.30 thf(decl_113, type, esk9_1: $i > $i).
% 0.24/0.30 thf(decl_114, type, esk10_2: ($i > $o) > $i > $i).
% 0.24/0.30 thf(decl_115, type, esk11_2: ($i > $o) > $i > $i).
% 0.24/0.30 thf(decl_116, type, esk12_1: ($i > $o) > $i).
% 0.24/0.30 thf(decl_117, type, esk13_2: ($i > $o) > $i > $i).
% 0.24/0.30 thf(decl_118, type, esk14_1: ($i > $o) > $i).
% 0.24/0.30 thf(decl_119, type, esk15_2: $i > $i > $i).
% 0.24/0.30 thf(decl_120, type, esk16_2: $i > $i > $i).
% 0.24/0.30 thf(decl_121, type, esk17_1: $i > $i).
% 0.24/0.30 thf(decl_122, type, esk18_1: $i > $i).
% 0.24/0.30 thf(decl_123, type, esk19_1: $i > $i).
% 0.24/0.30 thf(decl_124, type, esk20_2: $i > $i > $i).
% 0.24/0.30 thf(decl_125, type, esk21_3: $i > $i > $o > $i).
% 0.24/0.30 thf(decl_126, type, esk22_2: ($i > $o) > $i > $i).
% 0.24/0.30 thf(decl_127, type, esk23_1: ($i > $o) > $i).
% 0.24/0.30 thf(decl_128, type, esk24_1: $i > $i).
% 0.24/0.30 thf(decl_129, type, esk25_2: $i > ($i > $o) > $i).
% 0.24/0.30 thf(decl_130, type, esk26_2: $i > ($i > $o) > $i).
% 0.24/0.30 thf(decl_131, type, esk27_2: $i > ($i > $o) > $i).
% 0.24/0.30 thf(decl_132, type, esk28_2: $i > ($i > $o) > $i).
% 0.24/0.30 thf(decl_133, type, esk29_2: $i > ($i > $o) > $i).
% 0.24/0.30 thf(decl_134, type, esk30_2: $i > ($i > $o) > $i).
% 0.24/0.30 thf(decl_135, type, esk31_2: ($i > $o) > $i > $i).
% 0.24/0.30 thf(decl_136, type, esk32_1: ($i > $o) > $i).
% 0.24/0.30 thf(decl_137, type, esk33_1: ($i > $o) > $i).
% 0.24/0.30 thf(decl_138, type, esk34_1: ($i > $o) > $i).
% 0.24/0.30 thf(decl_139, type, esk35_1: ($i > $o) > $i).
% 0.24/0.30 thf(decl_140, type, esk36_2: ($i > $o) > $i > $i).
% 0.24/0.30 thf(decl_141, type, esk37_1: ($i > $o) > $i).
% 0.24/0.30 thf(decl_142, type, esk38_2: ($i > $o) > $i > $i).
% 0.24/0.30 thf(decl_143, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 0.24/0.30 thf(decl_144, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 0.24/0.30 thf(decl_145, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.24/0.30 thf(decl_146, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 0.24/0.30 thf(decl_147, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.24/0.30 thf(decl_148, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 0.24/0.30 thf(decl_149, type, esk45_0: $i).
% 0.24/0.30 thf(decl_150, type, esk46_0: $i).
% 0.24/0.30 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', replAx)).
% 0.24/0.30 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', exu)).
% 0.24/0.30 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', descrp)).
% 0.24/0.30 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', exuE1)).
% 0.24/0.30 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', exuE3e)).
% 0.24/0.30 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', nonempty)).
% 0.24/0.30 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', nonemptyI)).
% 0.24/0.30 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', exuE2)).
% 0.24/0.30 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.B7krAUK1ZE/E---3.1_797600.p', exuI1)).
% 0.24/0.30 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', exuI3)).
% 0.24/0.30 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', exuI2)).
% 0.24/0.30 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.B7krAUK1ZE/E---3.1_797600.p', exuE3u)).
% 0.24/0.30 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', exu__Cong)).
% 0.24/0.30 thf(powerset__Cong, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', powerset__Cong)).
% 0.24/0.30 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', dsetconstrI)).
% 0.24/0.30 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', dsetconstrEL)).
% 0.24/0.30 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', dsetconstrER)).
% 0.24/0.30 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', setbeta)).
% 0.24/0.30 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', nonemptyE1)).
% 0.24/0.30 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', nonemptyI1)).
% 0.24/0.30 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', setoftrueEq)).
% 0.24/0.30 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', nonemptyImpWitness)).
% 0.24/0.30 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.B7krAUK1ZE/E---3.1_797600.p', emptyE1)).
% 0.24/0.30 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', setextAx)).
% 0.24/0.30 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', emptysetAx)).
% 0.24/0.30 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', setadjoinAx)).
% 0.24/0.30 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', powersetAx)).
% 0.24/0.30 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', setunionAx)).
% 0.24/0.30 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', omega0Ax)).
% 0.24/0.30 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', omegaSAx)).
% 0.24/0.30 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', omegaIndAx)).
% 0.24/0.30 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', foundationAx)).
% 0.24/0.30 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.B7krAUK1ZE/E---3.1_797600.p', wellorderingAx)).
% 0.24/0.30 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', prop2setE)).
% 0.24/0.30 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', emptysetE)).
% 0.24/0.30 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', emptysetimpfalse)).
% 0.24/0.30 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', notinemptyset)).
% 0.24/0.30 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', setext)).
% 0.24/0.30 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', emptyI)).
% 0.24/0.30 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', noeltsimpempty)).
% 0.24/0.30 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', setadjoinIL)).
% 0.24/0.30 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', emptyinunitempty)).
% 0.24/0.30 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', setadjoinIR)).
% 0.24/0.30 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.B7krAUK1ZE/E---3.1_797600.p', setadjoinE)).
% 0.24/0.30 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', setadjoinOr)).
% 0.24/0.30 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', powersetI)).
% 0.24/0.30 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', emptyinPowerset)).
% 0.24/0.30 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', emptyInPowerset)).
% 0.24/0.30 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', powersetE)).
% 0.24/0.30 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', setunionI)).
% 0.24/0.30 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.B7krAUK1ZE/E---3.1_797600.p', setunionE)).
% 0.24/0.30 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', subPowSU)).
% 0.24/0.30 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', uniqinunit)).
% 0.24/0.30 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', notinsingleton)).
% 0.24/0.30 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', eqinunit)).
% 0.24/0.30 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', singletonsswitch)).
% 0.24/0.30 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', upairsetE)).
% 0.24/0.30 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', upairsetIL)).
% 0.24/0.30 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', upairsetIR)).
% 0.24/0.30 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', vacuousDall)).
% 0.24/0.30 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', quantDeMorgan1)).
% 0.24/0.30 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', quantDeMorgan2)).
% 0.24/0.30 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', quantDeMorgan3)).
% 0.24/0.30 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', quantDeMorgan4)).
% 0.24/0.30 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', prop2setI)).
% 0.24/0.30 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', prop2set2propI)).
% 0.24/0.30 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', notdexE)).
% 0.24/0.30 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', notdallE)).
% 0.24/0.30 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', inCongP)).
% 0.24/0.30 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', in__Cong)).
% 0.24/0.30 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', emptyset__Cong)).
% 0.24/0.30 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.B7krAUK1ZE/E---3.1_797600.p', setadjoin__Cong)).
% 0.24/0.30 thf(c_0_72, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.24/0.30 thf(c_0_73, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.24/0.30 thf(c_0_74, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.24/0.30 thf(c_0_75, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.24/0.30 thf(c_0_76, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.24/0.30 thf(c_0_77, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.24/0.30 thf(c_0_78, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.24/0.30 thf(c_0_79, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.24/0.30 thf(c_0_80, 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])).
% 0.24/0.30 thf(c_0_81, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.24/0.30 thf(c_0_82, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.24/0.30 thf(c_0_83, 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])).
% 0.24/0.30 thf(c_0_84, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.24/0.30 thf(c_0_85, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[powerset__Cong])).
% 0.24/0.30 thf(c_0_86, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X216:$i]:(((((X6 @ X2 @ X216)))&(![X217:$i]:(((((X6 @ X2 @ X217)))=>(((X216)=(X217)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_72, c_0_73])).
% 0.24/0.30 thf(c_0_87, plain, ((descrp)=(![X1:$i > $o]:((((?[X218:$i]:(((((X1 @ X218)))&(![X219:$i]:(((((X1 @ X219)))=>(((X218)=(X219))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_74, c_0_73])).
% 0.24/0.30 thf(c_0_88, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.24/0.30 thf(c_0_89, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.24/0.30 thf(c_0_90, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.24/0.30 thf(c_0_91, plain, ((exuE1)=(![X1:$i > $o]:((((?[X220:$i]:(((((X1 @ X220)))&(![X221:$i]:(((((X1 @ X221)))=>(((X220)=(X221))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_75, c_0_73])).
% 0.24/0.30 thf(c_0_92, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X222:$i]:(((((X1 @ X222)))&(![X223:$i]:(((((X1 @ X223)))=>(((X222)=(X223))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_76, c_0_73])).
% 0.24/0.30 thf(c_0_93, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.24/0.30 thf(c_0_94, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_77])).
% 0.24/0.30 thf(c_0_95, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_78, c_0_77])).
% 0.24/0.30 thf(c_0_96, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_77])).
% 0.24/0.30 thf(c_0_97, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.24/0.30 thf(c_0_98, plain, ((exuE2)=(![X1:$i > $o]:((((?[X224:$i]:(((((X1 @ X224)))&(![X225:$i]:(((((X1 @ X225)))=>(((X224)=(X225))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_79, c_0_73])).
% 0.24/0.30 thf(c_0_99, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_77])).
% 0.24/0.30 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])).
% 0.24/0.30 thf(c_0_101, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X226:$i]:(((((X1 @ X226)))&(![X227:$i]:(((((X1 @ X227)))=>(((X226)=(X227)))))))))))))), inference(apply_def,[status(thm)],[c_0_80, c_0_73])).
% 0.24/0.30 thf(c_0_102, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X228:$i]:(((((X1 @ X228)))&(![X229:$i]:(((((X1 @ X229)))=>(((X228)=(X229)))))))))))))))), inference(apply_def,[status(thm)],[c_0_81, c_0_73])).
% 0.24/0.30 thf(c_0_103, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X230:$i]:(((((X1 @ X230)))&(![X231:$i]:(((((X1 @ X231)))=>(((X230)=(X231)))))))))))))), inference(apply_def,[status(thm)],[c_0_82, c_0_73])).
% 0.24/0.30 thf(c_0_104, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X232:$i]:(((((X1 @ X232)))&(![X233:$i]:(((((X1 @ X233)))=>(((X232)=(X233))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_83, c_0_73])).
% 0.24/0.30 thf(c_0_105, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X234:$i]:(((((X1 @ X234)))&(![X235:$i]:(((((X1 @ X235)))=>(((X234)=(X235))))))))))<=>((?[X236:$i]:(((((X17 @ X236)))&(![X237:$i]:(((((X17 @ X237)))=>(((X236)=(X237)))))))))))))))), inference(apply_def,[status(thm)],[c_0_84, c_0_73])).
% 0.24/0.30 thf(c_0_106, plain, ((epred1_0)<=>![X267:$i]:(?[X268:$i]:((((![X269:$i]:(((in @ X269 @ X268)=>![X270:$i]:(((in @ X270 @ X269)=>(in @ X270 @ X267)))))&![X271:$i, X272:$i]:((((in @ X271 @ X267)&(in @ X272 @ X267))=>(![X273:$i]:(((in @ X273 @ X268)=>((in @ X271 @ X273)<=>(in @ X272 @ X273))))=>((X271)=(X272))))))&![X274:$i, X275:$i]:((((in @ X274 @ X268)&(in @ X275 @ X268))=>(![X276:$i]:(((in @ X276 @ X274)=>(in @ X276 @ X275)))|![X277:$i]:(((in @ X277 @ X275)=>(in @ X277 @ X274)))))))&![X278:$i]:(((![X279:$i]:(((in @ X279 @ X278)=>(in @ X279 @ X267)))&?[X280:$i]:((in @ X280 @ X278)))=>?[X281:$i, X282:$i]:(((((in @ X281 @ X268)&(in @ X282 @ X278))&~(?[X283:$i]:(((in @ X283 @ X281)&(in @ X283 @ X278)))))&![X284:$i]:(((in @ X284 @ X268)=>(![X285:$i]:(((in @ X285 @ X284)=>(in @ X285 @ X281)))|(in @ X282 @ X284)))))))))))), introduced(definition)).
% 0.24/0.30 thf(c_0_107, negated_conjecture, ~((![X238:$i, X239:$i]:((![X240:$i]:(((in @ X240 @ X238)<=>(in @ X240 @ X239)))=>((X238)=(X239))))=>(![X241:$i]:(~(in @ X241 @ emptyset))=>(![X242:$i, X243:$i, X244:$i]:(((in @ X244 @ (setadjoin @ X242 @ X243))<=>(((X244)=(X242))|(in @ X244 @ X243))))=>(![X245:$i, X246:$i]:(((in @ X246 @ (powerset @ X245))<=>![X247:$i]:(((in @ X247 @ X246)=>(in @ X247 @ X245)))))=>(![X248:$i, X249:$i]:(((in @ X249 @ (setunion @ X248))<=>?[X250:$i]:(((in @ X249 @ X250)&(in @ X250 @ X248)))))=>((in @ emptyset @ omega)=>(![X251:$i]:(((in @ X251 @ omega)=>(in @ (setadjoin @ X251 @ X251) @ omega)))=>(![X252:$i]:((((in @ emptyset @ X252)&![X253:$i]:((((in @ X253 @ omega)&(in @ X253 @ X252))=>(in @ (setadjoin @ X253 @ X253) @ X252))))=>![X254:$i]:(((in @ X254 @ omega)=>(in @ X254 @ X252)))))=>(![X255:$i > $i > $o, X256:$i]:((![X257:$i]:(((in @ X257 @ X256)=>?[X258:$i]:(((X255 @ X257 @ X258)&![X259:$i]:(((X255 @ X257 @ X259)=>((X258)=(X259))))))))=>?[X260:$i]:(![X261:$i]:(((in @ X261 @ X260)<=>?[X262:$i]:(((in @ X262 @ X256)&(X255 @ X262 @ X261))))))))=>(![X263:$i]:((?[X264:$i]:((in @ X264 @ X263))=>?[X265:$i]:(((in @ X265 @ X263)&~(?[X266:$i]:(((in @ X266 @ X265)&(in @ X266 @ X263))))))))=>((epred1_0)=>(![X286:$i > $o]:((?[X287:$i]:(((X286 @ X287)&![X288:$i]:(((X286 @ X288)=>((X287)=(X288))))))=>(X286 @ (descr @ (^[Z0:$i]:(X286 @ Z0))))))=>(![X289:$i, X290:$i > $o, X291:$i]:(((in @ X291 @ X289)=>((X290 @ X291)=>(in @ X291 @ (dsetconstr @ X289 @ X290)))))=>(![X292:$i, X293:$i > $o, X294:$i]:(((in @ X294 @ (dsetconstr @ X292 @ X293))=>(in @ X294 @ X292)))=>(![X295:$i, X296:$i > $o, X297:$i]:(((in @ X297 @ (dsetconstr @ X295 @ X296))=>(X296 @ X297)))=>(![X298:$i > $o]:((?[X299:$i]:(((X298 @ X299)&![X300:$i]:(((X298 @ X300)=>((X299)=(X300))))))=>?[X301:$i]:(((X298 @ X301)&![X302:$i]:(((X298 @ X302)=>((X301)=(X302))))))))=>(![X303:$o, X304:$i]:(((in @ X304 @ (prop2set @ ((X303))))=>(X303)))=>(![X305:$i]:(((in @ X305 @ emptyset)=>![X306:$o]:((X306))))=>(![X307:$i]:(((in @ X307 @ emptyset)=>~($true)))=>(![X308:$i]:(~(in @ X308 @ emptyset))=>(![X309:$i > $o]:((?[X310:$i]:(((X309 @ X310)&![X311:$i]:(((X309 @ X311)=>((X310)=(X311))))))=>?[X312:$i]:((X309 @ X312))))=>(![X313:$i, X314:$i]:((![X315:$i]:(((in @ X315 @ X313)=>(in @ X315 @ X314)))=>(![X316:$i]:(((in @ X316 @ X314)=>(in @ X316 @ X313)))=>((X313)=(X314)))))=>(![X317:$i]:((![X318:$i]:(~(in @ X318 @ X317))=>((X317)=(emptyset))))=>(![X319:$i]:((![X320:$i]:(~(in @ X320 @ X319))=>((X319)=(emptyset))))=>(![X321:$i, X322:$i > $o, X323:$i]:(((in @ X323 @ X321)=>((in @ X323 @ (dsetconstr @ X321 @ X322))<=>(X322 @ X323))))=>(![X324:$i]:((((X324)!=(emptyset))=>?[X325:$i]:((in @ X325 @ X324))))=>(![X326:$i, X327:$i > $o, X328:$i]:(((in @ X328 @ X326)=>((X327 @ X328)=>((dsetconstr @ X326 @ X327)!=(emptyset)))))=>(![X329:$i]:((?[X330:$i]:((in @ X330 @ X329))=>((X329)!=(emptyset))))=>(![X331:$i, X332:$i]:((in @ X331 @ (setadjoin @ X331 @ X332)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X333:$i, X334:$i, X335:$i]:(((in @ X335 @ X334)=>(in @ X335 @ (setadjoin @ X333 @ X334))))=>(![X336:$i, X337:$i, X338:$i]:(((in @ X338 @ (setadjoin @ X336 @ X337))=>![X339:$o]:(((((X338)=(X336))=>(X339))=>(((in @ X338 @ X337)=>(X339))=>(X339))))))=>(![X340:$i, X341:$i, X342:$i]:(((in @ X342 @ (setadjoin @ X340 @ X341))=>(((X342)=(X340))|(in @ X342 @ X341))))=>(![X343:$i]:(((dsetconstr @ X343 @ (^[Z0:$i]:($true)))=(X343)))=>(![X344:$i, X345:$i]:((![X346:$i]:(((in @ X346 @ X345)=>(in @ X346 @ X344)))=>(in @ X345 @ (powerset @ X344))))=>(![X347:$i]:((in @ emptyset @ (powerset @ X347)))=>(![X348:$i]:((in @ emptyset @ (powerset @ X348)))=>(![X349:$i, X350:$i, X351:$i]:(((in @ X350 @ (powerset @ X349))=>((in @ X351 @ X350)=>(in @ X351 @ X349))))=>(![X352:$i, X353:$i, X354:$i]:(((in @ X353 @ X354)=>((in @ X354 @ X352)=>(in @ X353 @ (setunion @ X352)))))=>(![X355:$i, X356:$i]:(((in @ X356 @ (setunion @ X355))=>![X357:$o]:((![X358:$i]:(((in @ X356 @ X358)=>((in @ X358 @ X355)=>(X357))))=>(X357)))))=>(![X359:$i, X360:$i]:(((in @ X360 @ X359)=>(in @ X360 @ (powerset @ (setunion @ X359)))))=>(![X361:$i > $o]:((?[X362:$i]:(((X361 @ X362)&![X363:$i]:(((X361 @ X363)=>((X362)=(X363))))))=>?[X364:$i]:(![X365:$i]:(((X361 @ X365)<=>((X365)=(X364)))))))=>(![X366:$i]:((((X366)!=(emptyset))=>?[X367:$i]:(((in @ X367 @ X366)&$true))))=>(![X368:$i, X369:$i]:(((in @ X368 @ (setadjoin @ X369 @ emptyset))=>((X368)=(X369))))=>(![X370:$i, X371:$i]:((((X370)!=(X371))=>~(in @ X371 @ (setadjoin @ X370 @ emptyset))))=>(![X372:$i, X373:$i]:((((X372)=(X373))=>(in @ X372 @ (setadjoin @ X373 @ emptyset))))=>(![X374:$i, X375:$i]:(((in @ X374 @ (setadjoin @ X375 @ emptyset))=>(in @ X375 @ (setadjoin @ X374 @ emptyset))))=>(![X376:$i, X377:$i, X378:$i]:(((in @ X378 @ (setadjoin @ X376 @ (setadjoin @ X377 @ emptyset)))=>(((X378)=(X376))|((X378)=(X377)))))=>(![X379:$i, X380:$i]:((in @ X379 @ (setadjoin @ X379 @ (setadjoin @ X380 @ emptyset))))=>(![X381:$i, X382:$i]:((in @ X382 @ (setadjoin @ X381 @ (setadjoin @ X382 @ emptyset))))=>(![X383:$i, X384:$i > $o]:((?[X385:$i]:(((in @ X385 @ X383)&(X384 @ X385)))=>(((dsetconstr @ X383 @ X384)=(emptyset))=>~($true))))=>(![X386:$i > $o, X387:$i]:(((in @ X387 @ emptyset)=>(X386 @ X387)))=>(![X388:$i, X389:$i > $o]:((~(![X390:$i]:(((in @ X390 @ X388)=>(X389 @ X390))))=>?[X391:$i]:(((in @ X391 @ X388)&~((X389 @ X391))))))=>(![X392:$i, X393:$i > $o]:((![X394:$i]:(((in @ X394 @ X392)=>~((X393 @ X394))))=>~(?[X395:$i]:(((in @ X395 @ X392)&(X393 @ X395))))))=>(![X396:$i, X397:$i > $o]:((~(?[X398:$i]:(((in @ X398 @ X396)&(X397 @ X398))))=>![X399:$i]:(((in @ X399 @ X396)=>~((X397 @ X399))))))=>(![X400:$i, X401:$i > $o]:((?[X402:$i]:(((in @ X402 @ X400)&~((X401 @ X402))))=>~(![X403:$i]:(((in @ X403 @ X400)=>(X401 @ X403))))))=>(![X404:$o]:(((X404)=>(in @ emptyset @ (prop2set @ ((X404))))))=>(![X405:$o]:(((X405)=>(set2prop @ (prop2set @ ((X405))))))=>(![X406:$i, X407:$i > $o]:((~(?[X408:$i]:(((in @ X408 @ X406)&(X407 @ X408))))=>![X409:$i]:(((in @ X409 @ X406)=>~((X407 @ X409))))))=>(![X410:$i, X411:$i > $o]:((~(![X412:$i]:(((in @ X412 @ X410)=>(X411 @ X412))))=>?[X413:$i]:(((in @ X413 @ X410)&~((X411 @ X413))))))=>(![X414:$i > $o]:((?[X415:$i]:(((X414 @ X415)&![X416:$i]:(((X414 @ X416)=>((X415)=(X416))))))=>?[X417:$i]:(((X414 @ X417)&![X418:$i]:(((X414 @ X418)=>((X417)=(X418))))))))=>(![X419:$i > $o]:((?[X420:$i]:((X419 @ X420))=>(![X421:$i, X422:$i]:(((X419 @ X421)=>((X419 @ X422)=>((X421)=(X422)))))=>?[X423:$i]:(((X419 @ X423)&![X424:$i]:(((X419 @ X424)=>((X423)=(X424)))))))))=>(![X425:$i > $o]:((?[X426:$i]:(![X427:$i]:(((X425 @ X427)<=>((X427)=(X426)))))=>?[X428:$i]:(((X425 @ X428)&![X429:$i]:(((X425 @ X429)=>((X428)=(X429))))))))=>(![X430:$i, X431:$i]:((((X430)=(X431))=>![X432:$i, X433:$i]:((((X432)=(X433))=>((in @ X432 @ X430)=>(in @ X433 @ X431))))))=>(![X434:$i, X435:$i]:((((X434)=(X435))=>![X436:$i, X437:$i]:((((X436)=(X437))=>((in @ X436 @ X434)<=>(in @ X437 @ X435))))))=>(![X438:$i > $o]:((?[X439:$i]:(((X438 @ X439)&![X440:$i]:(((X438 @ X440)=>((X439)=(X440))))))=>![X441:$i, X442:$i]:(((X438 @ X441)=>((X438 @ X442)=>((X441)=(X442)))))))=>(![X443:$i > $o, X444:$i > $o]:((![X445:$i, X446:$i]:((((X445)=(X446))=>((X443 @ X445)<=>(X444 @ X446))))=>(?[X447:$i]:(((X443 @ X447)&![X448:$i]:(((X443 @ X448)=>((X447)=(X448))))))<=>?[X449:$i]:(((X444 @ X449)&![X450:$i]:(((X444 @ X450)=>((X449)=(X450)))))))))=>(((emptyset)=(emptyset))=>(![X451:$i, X452:$i]:((((X451)=(X452))=>![X453:$i, X454:$i]:((((X453)=(X454))=>((setadjoin @ X451 @ X453)=(setadjoin @ X452 @ X454))))))=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_85, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_86]), foundationAx]), wellorderingAx]), c_0_87]), c_0_88]), c_0_89]), c_0_90]), c_0_91]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_92]), setext]), emptyI]), noeltsimpempty]), c_0_93]), c_0_94]), c_0_95]), c_0_96]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_97]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_98]), c_0_99]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_100]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_101]), c_0_102]), c_0_103]), inCongP]), in__Cong]), c_0_104]), c_0_105]), emptyset__Cong]), setadjoin__Cong])])]), c_0_106])).
% 0.24/0.30 thf(c_0_108, negated_conjecture, ![X455:$i, X456:$i, X458:$i, X459:$i, X460:$i, X461:$i, X462:$i, X463:$i, X464:$i, X465:$i, X466:$i, X468:$i, X469:$i, X471:$i, X472:$i, X473:$i, X474:$i, X475:$i, X477:$i, X478:$i > $i > $o, X479:$i, X481:$i, X484:$i, X486:$i, X487:$i, X488:$i, X489:$i, X491:$i, X492:$i > $o, X493:$i, X495:$i, X496:$i > $o, X497:$i, X498:$i, X499:$i > $o, X500:$i, X501:$i, X502:$i > $o, X503:$i, X504:$i > $o, X505:$i, X508:$i, X509:$o, X510:$i, X511:$i, X512:$o, X513:$i, X514:$i, X515:$i > $o, X516:$i, X519:$i, X520:$i, X523:$i, X525:$i, X527:$i, X528:$i > $o, X529:$i, X530:$i, X532:$i, X533:$i > $o, X534:$i, X535:$i, X536:$i, X537:$i, X538:$i, X539:$i, X540:$i, X541:$i, X542:$i, X543:$i, X544:$i, X545:$o, X546:$i, X547:$i, X548:$i, X549:$i, X550:$i, X551:$i, X553:$i, X554:$i, X555:$i, X556:$i, X557:$i, X558:$i, X559:$i, X560:$i, X561:$i, X562:$i, X563:$o, X565:$i, X566:$i, X567:$i > $o, X568:$i, X571:$i, X572:$i, X573:$i, X575:$i, X576:$i, X577:$i, X578:$i, X579:$i, X580:$i, X581:$i, X582:$i, X583:$i, X584:$i, X585:$i, X586:$i, X587:$i, X588:$i, X589:$i, X590:$i, X591:$i > $o, X592:$i, X593:$i > $o, X594:$i, X595:$i, X596:$i > $o, X597:$i, X599:$i, X600:$i > $o, X602:$i, X603:$i, X604:$i > $o, X606:$i, X607:$i, X608:$i > $o, X609:$i, X611:$o, X612:$o, X613:$i, X614:$i > $o, X616:$i, X617:$i, X618:$i > $o, X619:$i, X621:$i > $o, X622:$i, X625:$i, X626:$i > $o, X627:$i, X631:$i, X632:$i > $o, X633:$i, X636:$i, X637:$i, X638:$i, X639:$i, X640:$i, X641:$i, X642:$i, X643:$i, X644:$i, X645:$i > $o, X646:$i, X648:$i, X649:$i, X650:$i > $o, X651:$i > $o, X654:$i, X657:$i, X658:$i, X661:$i, X662:$i, X663:$i, X664:$i, X665:$i]:((((~(in @ (esk1_2 @ X455 @ X456) @ X455)|~(in @ (esk1_2 @ X455 @ X456) @ X456)|((X455)=(X456)))&((in @ (esk1_2 @ X455 @ X456) @ X455)|(in @ (esk1_2 @ X455 @ X456) @ X456)|((X455)=(X456))))&(~(in @ X458 @ emptyset)&(((~(in @ X461 @ (setadjoin @ X459 @ X460))|(((X461)=(X459))|(in @ X461 @ X460)))&((((X461)!=(X459))|(in @ X461 @ (setadjoin @ X459 @ X460)))&(~(in @ X461 @ X460)|(in @ X461 @ (setadjoin @ X459 @ X460)))))&(((~(in @ X463 @ (powerset @ X462))|(~(in @ X464 @ X463)|(in @ X464 @ X462)))&(((in @ (esk2_2 @ X465 @ X466) @ X466)|(in @ X466 @ (powerset @ X465)))&(~(in @ (esk2_2 @ X465 @ X466) @ X465)|(in @ X466 @ (powerset @ X465)))))&(((((in @ X469 @ (esk3_2 @ X468 @ X469))|~(in @ X469 @ (setunion @ X468)))&((in @ (esk3_2 @ X468 @ X469) @ X468)|~(in @ X469 @ (setunion @ X468))))&(~(in @ X472 @ X473)|~(in @ X473 @ X471)|(in @ X472 @ (setunion @ X471))))&((in @ emptyset @ omega)&((~(in @ X474 @ omega)|(in @ (setadjoin @ X474 @ X474) @ omega))&(((((in @ (esk4_1 @ X475) @ omega)|~(in @ emptyset @ X475)|(~(in @ X477 @ omega)|(in @ X477 @ X475)))&((in @ (esk4_1 @ X475) @ X475)|~(in @ emptyset @ X475)|(~(in @ X477 @ omega)|(in @ X477 @ X475))))&(~(in @ (setadjoin @ (esk4_1 @ X475) @ (esk4_1 @ X475)) @ X475)|~(in @ emptyset @ X475)|(~(in @ X477 @ omega)|(in @ X477 @ X475))))&((((((in @ (esk8_3 @ X478 @ X479 @ X484) @ X479)|~(in @ X484 @ (esk7_2 @ X478 @ X479))|(in @ (esk5_2 @ X478 @ X479) @ X479))&((X478 @ (esk8_3 @ X478 @ X479 @ X484) @ X484)|~(in @ X484 @ (esk7_2 @ X478 @ X479))|(in @ (esk5_2 @ X478 @ X479) @ X479)))&(~(in @ X487 @ X479)|~(X478 @ X487 @ X486)|(in @ X486 @ (esk7_2 @ X478 @ X479))|(in @ (esk5_2 @ X478 @ X479) @ X479)))&(((((in @ (esk8_3 @ X478 @ X479 @ X484) @ X479)|~(in @ X484 @ (esk7_2 @ X478 @ X479))|((X478 @ (esk5_2 @ X478 @ X479) @ (esk6_3 @ X478 @ X479 @ X481))|~(X478 @ (esk5_2 @ X478 @ X479) @ X481)))&((X478 @ (esk8_3 @ X478 @ X479 @ X484) @ X484)|~(in @ X484 @ (esk7_2 @ X478 @ X479))|((X478 @ (esk5_2 @ X478 @ X479) @ (esk6_3 @ X478 @ X479 @ X481))|~(X478 @ (esk5_2 @ X478 @ X479) @ X481))))&(~(in @ X487 @ X479)|~(X478 @ X487 @ X486)|(in @ X486 @ (esk7_2 @ X478 @ X479))|((X478 @ (esk5_2 @ X478 @ X479) @ (esk6_3 @ X478 @ X479 @ X481))|~(X478 @ (esk5_2 @ X478 @ X479) @ X481))))&((((in @ (esk8_3 @ X478 @ X479 @ X484) @ X479)|~(in @ X484 @ (esk7_2 @ X478 @ X479))|(((X481)!=(esk6_3 @ X478 @ X479 @ X481))|~(X478 @ (esk5_2 @ X478 @ X479) @ X481)))&((X478 @ (esk8_3 @ X478 @ X479 @ X484) @ X484)|~(in @ X484 @ (esk7_2 @ X478 @ X479))|(((X481)!=(esk6_3 @ X478 @ X479 @ X481))|~(X478 @ (esk5_2 @ X478 @ X479) @ X481))))&(~(in @ X487 @ X479)|~(X478 @ X487 @ X486)|(in @ X486 @ (esk7_2 @ X478 @ X479))|(((X481)!=(esk6_3 @ X478 @ X479 @ X481))|~(X478 @ (esk5_2 @ X478 @ X479) @ X481))))))&((((in @ (esk9_1 @ X488) @ X488)|~(in @ X489 @ X488))&(~(in @ X491 @ (esk9_1 @ X488))|~(in @ X491 @ X488)|~(in @ X489 @ X488)))&((epred1_0)&((((X492 @ (esk10_2 @ X492 @ X493))|~(X492 @ X493)|(X492 @ (descr @ X492)))&(((X493)!=(esk10_2 @ X492 @ X493))|~(X492 @ X493)|(X492 @ (descr @ X492))))&((~(in @ X497 @ X495)|(~(X496 @ X497)|(in @ X497 @ (dsetconstr @ X495 @ X496))))&((~(in @ X500 @ (dsetconstr @ X498 @ X499))|(in @ X500 @ X498))&((~(in @ X503 @ (dsetconstr @ X501 @ X502))|(X502 @ X503))&(((((X504 @ (esk12_1 @ X504))|((X504 @ (esk11_2 @ X504 @ X505))|~(X504 @ X505)))&(~(X504 @ X508)|((esk12_1 @ X504)=(X508))|((X504 @ (esk11_2 @ X504 @ X505))|~(X504 @ X505))))&(((X504 @ (esk12_1 @ X504))|(((X505)!=(esk11_2 @ X504 @ X505))|~(X504 @ X505)))&(~(X504 @ X508)|((esk12_1 @ X504)=(X508))|(((X505)!=(esk11_2 @ X504 @ X505))|~(X504 @ X505)))))&((~(in @ X510 @ (prop2set @ ((X509))))|(X509))&((~(in @ X511 @ emptyset)|(X512))&((~(in @ X513 @ emptyset)|~($true))&(~(in @ X514 @ emptyset)&((((X515 @ (esk13_2 @ X515 @ X516))|~(X515 @ X516)|(X515 @ (esk14_1 @ X515)))&(((X516)!=(esk13_2 @ X515 @ X516))|~(X515 @ X516)|(X515 @ (esk14_1 @ X515))))&(((((in @ (esk16_2 @ X519 @ X520) @ X520)|((X519)=(X520))|(in @ (esk15_2 @ X519 @ X520) @ X519))&(~(in @ (esk16_2 @ X519 @ X520) @ X519)|((X519)=(X520))|(in @ (esk15_2 @ X519 @ X520) @ X519)))&(((in @ (esk16_2 @ X519 @ X520) @ X520)|((X519)=(X520))|~(in @ (esk15_2 @ X519 @ X520) @ X520))&(~(in @ (esk16_2 @ X519 @ X520) @ X519)|((X519)=(X520))|~(in @ (esk15_2 @ X519 @ X520) @ X520))))&(((in @ (esk17_1 @ X523) @ X523)|((X523)=(emptyset)))&(((in @ (esk18_1 @ X525) @ X525)|((X525)=(emptyset)))&(((~(in @ X529 @ (dsetconstr @ X527 @ X528))|(X528 @ X529)|~(in @ X529 @ X527))&(~(X528 @ X529)|(in @ X529 @ (dsetconstr @ X527 @ X528))|~(in @ X529 @ X527)))&((((X530)=(emptyset))|(in @ (esk19_1 @ X530) @ X530))&((~(in @ X534 @ X532)|(~(X533 @ X534)|((dsetconstr @ X532 @ X533)!=(emptyset))))&((~(in @ X536 @ X535)|((X535)!=(emptyset)))&((in @ X537 @ (setadjoin @ X537 @ X538))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X541 @ X540)|(in @ X541 @ (setadjoin @ X539 @ X540)))&(((((in @ X544 @ X543)|(X545)|((X544)=(X542))|~(in @ X544 @ (setadjoin @ X542 @ X543)))&(~(X545)|(X545)|((X544)=(X542))|~(in @ X544 @ (setadjoin @ X542 @ X543))))&(((in @ X544 @ X543)|(X545)|~(X545)|~(in @ X544 @ (setadjoin @ X542 @ X543)))&(~(X545)|(X545)|~(X545)|~(in @ X544 @ (setadjoin @ X542 @ X543)))))&((~(in @ X548 @ (setadjoin @ X546 @ X547))|(((X548)=(X546))|(in @ X548 @ X547)))&(((dsetconstr @ X549 @ (^[Z0:$i]:($true)))=(X549))&((((in @ (esk20_2 @ X550 @ X551) @ X551)|(in @ X551 @ (powerset @ X550)))&(~(in @ (esk20_2 @ X550 @ X551) @ X550)|(in @ X551 @ (powerset @ X550))))&((in @ emptyset @ (powerset @ X553))&((in @ emptyset @ (powerset @ X554))&((~(in @ X556 @ (powerset @ X555))|(~(in @ X557 @ X556)|(in @ X557 @ X555)))&((~(in @ X559 @ X560)|(~(in @ X560 @ X558)|(in @ X559 @ (setunion @ X558))))&((((in @ X562 @ (esk21_3 @ X561 @ X562 @ X563))|(X563)|~(in @ X562 @ (setunion @ X561)))&(((in @ (esk21_3 @ X561 @ X562 @ X563) @ X561)|(X563)|~(in @ X562 @ (setunion @ X561)))&(~(X563)|(X563)|~(in @ X562 @ (setunion @ X561)))))&((~(in @ X566 @ X565)|(in @ X566 @ (powerset @ (setunion @ X565))))&((((~(X567 @ X571)|((X571)=(esk23_1 @ X567))|((X567 @ (esk22_2 @ X567 @ X568))|~(X567 @ X568)))&(((X572)!=(esk23_1 @ X567))|(X567 @ X572)|((X567 @ (esk22_2 @ X567 @ X568))|~(X567 @ X568))))&((~(X567 @ X571)|((X571)=(esk23_1 @ X567))|(((X568)!=(esk22_2 @ X567 @ X568))|~(X567 @ X568)))&(((X572)!=(esk23_1 @ X567))|(X567 @ X572)|(((X568)!=(esk22_2 @ X567 @ X568))|~(X567 @ X568)))))&((((in @ (esk24_1 @ X573) @ X573)|((X573)=(emptyset)))&(($true)|((X573)=(emptyset))))&((~(in @ X575 @ (setadjoin @ X576 @ emptyset))|((X575)=(X576)))&((((X577)=(X578))|~(in @ X578 @ (setadjoin @ X577 @ emptyset)))&((((X579)!=(X580))|(in @ X579 @ (setadjoin @ X580 @ emptyset)))&((~(in @ X581 @ (setadjoin @ X582 @ emptyset))|(in @ X582 @ (setadjoin @ X581 @ emptyset)))&((~(in @ X585 @ (setadjoin @ X583 @ (setadjoin @ X584 @ emptyset)))|(((X585)=(X583))|((X585)=(X584))))&((in @ X586 @ (setadjoin @ X586 @ (setadjoin @ X587 @ emptyset)))&((in @ X589 @ (setadjoin @ X588 @ (setadjoin @ X589 @ emptyset)))&((~(in @ X592 @ X590)|~(X591 @ X592)|(((dsetconstr @ X590 @ X591)!=(emptyset))|~($true)))&((~(in @ X594 @ emptyset)|(X593 @ X594))&((((in @ (esk25_2 @ X595 @ X596) @ X595)|(~(in @ X597 @ X595)|(X596 @ X597)))&(~(X596 @ (esk25_2 @ X595 @ X596))|(~(in @ X597 @ X595)|(X596 @ X597))))&((((in @ (esk26_2 @ X599 @ X600) @ X599)|(~(in @ X602 @ X599)|~(X600 @ X602)))&((X600 @ (esk26_2 @ X599 @ X600))|(~(in @ X602 @ X599)|~(X600 @ X602))))&((((in @ (esk27_2 @ X603 @ X604) @ X603)|(~(in @ X606 @ X603)|~(X604 @ X606)))&((X604 @ (esk27_2 @ X603 @ X604))|(~(in @ X606 @ X603)|~(X604 @ X606))))&((((in @ (esk28_2 @ X607 @ X608) @ X607)|(~(in @ X609 @ X607)|(X608 @ X609)))&(~(X608 @ (esk28_2 @ X607 @ X608))|(~(in @ X609 @ X607)|(X608 @ X609))))&((~(X611)|(in @ emptyset @ (prop2set @ ((X611)))))&((~(X612)|(set2prop @ (prop2set @ ((X612)))))&((((in @ (esk29_2 @ X613 @ X614) @ X613)|(~(in @ X616 @ X613)|~(X614 @ X616)))&((X614 @ (esk29_2 @ X613 @ X614))|(~(in @ X616 @ X613)|~(X614 @ X616))))&((((in @ (esk30_2 @ X617 @ X618) @ X617)|(~(in @ X619 @ X617)|(X618 @ X619)))&(~(X618 @ (esk30_2 @ X617 @ X618))|(~(in @ X619 @ X617)|(X618 @ X619))))&(((((X621 @ (esk32_1 @ X621))|((X621 @ (esk31_2 @ X621 @ X622))|~(X621 @ X622)))&(~(X621 @ X625)|((esk32_1 @ X621)=(X625))|((X621 @ (esk31_2 @ X621 @ X622))|~(X621 @ X622))))&(((X621 @ (esk32_1 @ X621))|(((X622)!=(esk31_2 @ X621 @ X622))|~(X621 @ X622)))&(~(X621 @ X625)|((esk32_1 @ X621)=(X625))|(((X622)!=(esk31_2 @ X621 @ X622))|~(X621 @ X622)))))&(((((X626 @ (esk35_1 @ X626))|(X626 @ (esk33_1 @ X626))|~(X626 @ X627))&(~(X626 @ X631)|((esk35_1 @ X626)=(X631))|(X626 @ (esk33_1 @ X626))|~(X626 @ X627)))&((((X626 @ (esk35_1 @ X626))|(X626 @ (esk34_1 @ X626))|~(X626 @ X627))&(~(X626 @ X631)|((esk35_1 @ X626)=(X631))|(X626 @ (esk34_1 @ X626))|~(X626 @ X627)))&(((X626 @ (esk35_1 @ X626))|((esk33_1 @ X626)!=(esk34_1 @ X626))|~(X626 @ X627))&(~(X626 @ X631)|((esk35_1 @ X626)=(X631))|((esk33_1 @ X626)!=(esk34_1 @ X626))|~(X626 @ X627)))))&(((((X632 @ (esk37_1 @ X632))|(~(X632 @ (esk36_2 @ X632 @ X633))|((esk36_2 @ X632 @ X633)!=(X633))))&(~(X632 @ X636)|((esk37_1 @ X632)=(X636))|(~(X632 @ (esk36_2 @ X632 @ X633))|((esk36_2 @ X632 @ X633)!=(X633)))))&(((X632 @ (esk37_1 @ X632))|((X632 @ (esk36_2 @ X632 @ X633))|((esk36_2 @ X632 @ X633)=(X633))))&(~(X632 @ X636)|((esk37_1 @ X632)=(X636))|((X632 @ (esk36_2 @ X632 @ X633))|((esk36_2 @ X632 @ X633)=(X633))))))&((((X637)!=(X638))|(((X639)!=(X640))|(~(in @ X639 @ X637)|(in @ X640 @ X638))))&(((~(in @ X643 @ X641)|(in @ X644 @ X642)|((X643)!=(X644))|((X641)!=(X642)))&(~(in @ X644 @ X642)|(in @ X643 @ X641)|((X643)!=(X644))|((X641)!=(X642))))&((((X645 @ (esk38_2 @ X645 @ X646))|~(X645 @ X646)|(~(X645 @ X648)|(~(X645 @ X649)|((X648)=(X649)))))&(((X646)!=(esk38_2 @ X645 @ X646))|~(X645 @ X646)|(~(X645 @ X648)|(~(X645 @ X649)|((X648)=(X649))))))&(((((((X651 @ (esk42_2 @ X650 @ X651))|((X650 @ (esk41_3 @ X650 @ X651 @ X654))|~(X650 @ X654))|((esk39_2 @ X650 @ X651)=(esk40_2 @ X650 @ X651)))&(~(X651 @ X657)|((esk42_2 @ X650 @ X651)=(X657))|((X650 @ (esk41_3 @ X650 @ X651 @ X654))|~(X650 @ X654))|((esk39_2 @ X650 @ X651)=(esk40_2 @ X650 @ X651))))&(((X651 @ (esk42_2 @ X650 @ X651))|(((X654)!=(esk41_3 @ X650 @ X651 @ X654))|~(X650 @ X654))|((esk39_2 @ X650 @ X651)=(esk40_2 @ X650 @ X651)))&(~(X651 @ X657)|((esk42_2 @ X650 @ X651)=(X657))|(((X654)!=(esk41_3 @ X650 @ X651 @ X654))|~(X650 @ X654))|((esk39_2 @ X650 @ X651)=(esk40_2 @ X650 @ X651)))))&((((X650 @ (esk44_2 @ X650 @ X651))|((X651 @ (esk43_3 @ X650 @ X651 @ X658))|~(X651 @ X658))|((esk39_2 @ X650 @ X651)=(esk40_2 @ X650 @ X651)))&(~(X650 @ X661)|((esk44_2 @ X650 @ X651)=(X661))|((X651 @ (esk43_3 @ X650 @ X651 @ X658))|~(X651 @ X658))|((esk39_2 @ X650 @ X651)=(esk40_2 @ X650 @ X651))))&(((X650 @ (esk44_2 @ X650 @ X651))|(((X658)!=(esk43_3 @ X650 @ X651 @ X658))|~(X651 @ X658))|((esk39_2 @ X650 @ X651)=(esk40_2 @ X650 @ X651)))&(~(X650 @ X661)|((esk44_2 @ X650 @ X651)=(X661))|(((X658)!=(esk43_3 @ X650 @ X651 @ X658))|~(X651 @ X658))|((esk39_2 @ X650 @ X651)=(esk40_2 @ X650 @ X651))))))&((((((X651 @ (esk42_2 @ X650 @ X651))|((X650 @ (esk41_3 @ X650 @ X651 @ X654))|~(X650 @ X654))|(~(X650 @ (esk39_2 @ X650 @ X651))|~(X651 @ (esk40_2 @ X650 @ X651))))&(~(X651 @ X657)|((esk42_2 @ X650 @ X651)=(X657))|((X650 @ (esk41_3 @ X650 @ X651 @ X654))|~(X650 @ X654))|(~(X650 @ (esk39_2 @ X650 @ X651))|~(X651 @ (esk40_2 @ X650 @ X651)))))&(((X651 @ (esk42_2 @ X650 @ X651))|(((X654)!=(esk41_3 @ X650 @ X651 @ X654))|~(X650 @ X654))|(~(X650 @ (esk39_2 @ X650 @ X651))|~(X651 @ (esk40_2 @ X650 @ X651))))&(~(X651 @ X657)|((esk42_2 @ X650 @ X651)=(X657))|(((X654)!=(esk41_3 @ X650 @ X651 @ X654))|~(X650 @ X654))|(~(X650 @ (esk39_2 @ X650 @ X651))|~(X651 @ (esk40_2 @ X650 @ X651))))))&((((X650 @ (esk44_2 @ X650 @ X651))|((X651 @ (esk43_3 @ X650 @ X651 @ X658))|~(X651 @ X658))|(~(X650 @ (esk39_2 @ X650 @ X651))|~(X651 @ (esk40_2 @ X650 @ X651))))&(~(X650 @ X661)|((esk44_2 @ X650 @ X651)=(X661))|((X651 @ (esk43_3 @ X650 @ X651 @ X658))|~(X651 @ X658))|(~(X650 @ (esk39_2 @ X650 @ X651))|~(X651 @ (esk40_2 @ X650 @ X651)))))&(((X650 @ (esk44_2 @ X650 @ X651))|(((X658)!=(esk43_3 @ X650 @ X651 @ X658))|~(X651 @ X658))|(~(X650 @ (esk39_2 @ X650 @ X651))|~(X651 @ (esk40_2 @ X650 @ X651))))&(~(X650 @ X661)|((esk44_2 @ X650 @ X651)=(X661))|(((X658)!=(esk43_3 @ X650 @ X651 @ X658))|~(X651 @ X658))|(~(X650 @ (esk39_2 @ X650 @ X651))|~(X651 @ (esk40_2 @ X650 @ X651)))))))&(((((X651 @ (esk42_2 @ X650 @ X651))|((X650 @ (esk41_3 @ X650 @ X651 @ X654))|~(X650 @ X654))|((X650 @ (esk39_2 @ X650 @ X651))|(X651 @ (esk40_2 @ X650 @ X651))))&(~(X651 @ X657)|((esk42_2 @ X650 @ X651)=(X657))|((X650 @ (esk41_3 @ X650 @ X651 @ X654))|~(X650 @ X654))|((X650 @ (esk39_2 @ X650 @ X651))|(X651 @ (esk40_2 @ X650 @ X651)))))&(((X651 @ (esk42_2 @ X650 @ X651))|(((X654)!=(esk41_3 @ X650 @ X651 @ X654))|~(X650 @ X654))|((X650 @ (esk39_2 @ X650 @ X651))|(X651 @ (esk40_2 @ X650 @ X651))))&(~(X651 @ X657)|((esk42_2 @ X650 @ X651)=(X657))|(((X654)!=(esk41_3 @ X650 @ X651 @ X654))|~(X650 @ X654))|((X650 @ (esk39_2 @ X650 @ X651))|(X651 @ (esk40_2 @ X650 @ X651))))))&((((X650 @ (esk44_2 @ X650 @ X651))|((X651 @ (esk43_3 @ X650 @ X651 @ X658))|~(X651 @ X658))|((X650 @ (esk39_2 @ X650 @ X651))|(X651 @ (esk40_2 @ X650 @ X651))))&(~(X650 @ X661)|((esk44_2 @ X650 @ X651)=(X661))|((X651 @ (esk43_3 @ X650 @ X651 @ X658))|~(X651 @ X658))|((X650 @ (esk39_2 @ X650 @ X651))|(X651 @ (esk40_2 @ X650 @ X651)))))&(((X650 @ (esk44_2 @ X650 @ X651))|(((X658)!=(esk43_3 @ X650 @ X651 @ X658))|~(X651 @ X658))|((X650 @ (esk39_2 @ X650 @ X651))|(X651 @ (esk40_2 @ X650 @ X651))))&(~(X650 @ X661)|((esk44_2 @ X650 @ X651)=(X661))|(((X658)!=(esk43_3 @ X650 @ X651 @ X658))|~(X651 @ X658))|((X650 @ (esk39_2 @ X650 @ X651))|(X651 @ (esk40_2 @ X650 @ X651)))))))))&(((emptyset)=(emptyset))&((((X662)!=(X663))|(((X664)!=(X665))|((setadjoin @ X662 @ X664)=(setadjoin @ X663 @ X665))))&(((esk45_0)=(esk46_0))&((powerset @ esk45_0)!=(powerset @ esk46_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_107])])])])])])])).
% 0.24/0.30 thf(c_0_109, negated_conjecture, ((powerset @ esk45_0)!=(powerset @ esk46_0)), inference(split_conjunct,[status(thm)],[c_0_108])).
% 0.24/0.30 thf(c_0_110, negated_conjecture, ((esk45_0)=(esk46_0)), inference(split_conjunct,[status(thm)],[c_0_108])).
% 0.24/0.30 thf(c_0_111, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_109, c_0_110])]), ['proof']).
% 0.24/0.30 % SZS output end CNFRefutation
% 0.24/0.30 % Parsed axioms : 153
% 0.24/0.30 % Removed by relevancy pruning/SinE : 0
% 0.24/0.30 % Initial clauses : 246
% 0.24/0.30 % Removed in clause preprocessing : 92
% 0.24/0.30 % Initial clauses in saturation : 154
% 0.24/0.30 % Processed clauses : 11
% 0.24/0.30 % ...of these trivial : 0
% 0.24/0.30 % ...subsumed : 3
% 0.24/0.30 % ...remaining for further processing : 7
% 0.24/0.30 % Other redundant clauses eliminated : 0
% 0.24/0.30 % Clauses deleted for lack of memory : 0
% 0.24/0.30 % Backward-subsumed : 0
% 0.24/0.30 % Backward-rewritten : 0
% 0.24/0.30 % Generated clauses : 0
% 0.24/0.30 % ...of the previous two non-redundant : 0
% 0.24/0.30 % ...aggressively subsumed : 0
% 0.24/0.30 % Contextual simplify-reflections : 0
% 0.24/0.30 % Paramodulations : 0
% 0.24/0.30 % Factorizations : 0
% 0.24/0.30 % NegExts : 0
% 0.24/0.30 % Equation resolutions : 0
% 0.24/0.30 % Disequality decompositions : 0
% 0.24/0.30 % Total rewrite steps : 1
% 0.24/0.30 % ...of those cached : 0
% 0.24/0.30 % Propositional unsat checks : 0
% 0.24/0.30 % Propositional check models : 0
% 0.24/0.30 % Propositional check unsatisfiable : 0
% 0.24/0.30 % Propositional clauses : 0
% 0.24/0.30 % Propositional clauses after purity: 0
% 0.24/0.30 % Propositional unsat core size : 0
% 0.24/0.30 % Propositional preprocessing time : 0.000
% 0.24/0.30 % Propositional encoding time : 0.000
% 0.24/0.30 % Propositional solver time : 0.000
% 0.24/0.30 % Success case prop preproc time : 0.000
% 0.24/0.30 % Success case prop encoding time : 0.000
% 0.24/0.30 % Success case prop solver time : 0.000
% 0.24/0.30 % Current number of processed clauses : 7
% 0.24/0.30 % Positive orientable unit clauses : 6
% 0.24/0.30 % Positive unorientable unit clauses: 0
% 0.24/0.30 % Negative unit clauses : 1
% 0.24/0.30 % Non-unit-clauses : 0
% 0.24/0.30 % Current number of unprocessed clauses: 143
% 0.24/0.30 % ...number of literals in the above : 497
% 0.24/0.30 % Current number of archived formulas : 0
% 0.24/0.30 % Current number of archived clauses : 0
% 0.24/0.30 % Clause-clause subsumption calls (NU) : 0
% 0.24/0.30 % Rec. Clause-clause subsumption calls : 0
% 0.24/0.30 % Non-unit clause-clause subsumptions : 0
% 0.24/0.30 % Unit Clause-clause subsumption calls : 0
% 0.24/0.30 % Rewrite failures with RHS unbound : 0
% 0.24/0.30 % BW rewrite match attempts : 0
% 0.24/0.30 % BW rewrite match successes : 0
% 0.24/0.30 % Condensation attempts : 0
% 0.24/0.30 % Condensation successes : 0
% 0.24/0.30 % Termbank termtop insertions : 20665
% 0.24/0.30 % Search garbage collected termcells : 7996
% 0.24/0.30
% 0.24/0.30 % -------------------------------------------------
% 0.24/0.30 % User time : 0.019 s
% 0.24/0.30 % System time : 0.005 s
% 0.24/0.30 % Total time : 0.024 s
% 0.24/0.30 % Maximum resident set size: 5836 pages
% 0.24/0.30
% 0.24/0.30 % -------------------------------------------------
% 0.24/0.30 % User time : 0.047 s
% 0.24/0.30 % System time : 0.019 s
% 0.24/0.30 % Total time : 0.066 s
% 0.24/0.30 % Maximum resident set size: 5120 pages
% 0.24/0.30 % E exiting
%------------------------------------------------------------------------------