%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU555^1 : 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 : n026.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 0.23s 0.29s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU555^1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.19 % Computer : n026.cluster.edu
% 0.12/0.19 % Model : x86_64 x86_64
% 0.12/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.19 % Memory : 8046.5625MB
% 0.12/0.19 % OS : Linux 6.8.0-71-generic
% 0.12/0.19 % CPULimit : 300
% 0.12/0.19 % WCLimit : 300
% 0.12/0.19 % DateTime : Tue Sep 29 13:52:42 UTC 2026
% 0.12/0.19 % CPUTime :
% 0.12/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.23 Running higher-order theorem proving
% 0.12/0.25 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p
% 0.23/0.29 % Version: 3.5.1-ho
% 0.23/0.29 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.23/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.29 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.29 % Starting sh5l with 300s (1) cores
% 0.23/0.29 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.29 % Starting new_bool_2 with 300s (1) cores
% 0.23/0.29 % sh5l with pid 625808 completed with status 0
% 0.23/0.29 % Result found by sh5l
% 0.23/0.29 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.23/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.29 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.29 % Starting sh5l with 300s (1) cores
% 0.23/0.29 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.23/0.29 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.23/0.29 % Search class: HGHSM-FSLM31-SHFMMMBN
% 0.23/0.29 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.29 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.29 % SubtermCWHack with pid 625811 completed with status 0
% 0.23/0.29 % Result found by SubtermCWHack
% 0.23/0.29 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.23/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.29 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.29 % Starting sh5l with 300s (1) cores
% 0.23/0.29 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.23/0.29 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.23/0.29 % Search class: HGHSM-FSLM31-SHFMMMBN
% 0.23/0.29 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.29 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.29 % Preprocessing time : 0.004 s
% 0.23/0.29
% 0.23/0.29 % Proof found!
% 0.23/0.29 % SZS status Theorem
% 0.23/0.29 % SZS output start CNFRefutation
% 0.23/0.29 thf(decl_23, type, in: $i > $i > $o).
% 0.23/0.29 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.23/0.29 thf(decl_25, type, setextAx: $o).
% 0.23/0.29 thf(decl_26, type, emptyset: $i).
% 0.23/0.29 thf(decl_27, type, emptysetAx: $o).
% 0.23/0.29 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.23/0.29 thf(decl_29, type, setadjoinAx: $o).
% 0.23/0.29 thf(decl_30, type, powerset: $i > $i).
% 0.23/0.29 thf(decl_31, type, powersetAx: $o).
% 0.23/0.29 thf(decl_32, type, setunion: $i > $i).
% 0.23/0.29 thf(decl_33, type, setunionAx: $o).
% 0.23/0.29 thf(decl_34, type, omega: $i).
% 0.23/0.29 thf(decl_35, type, omega0Ax: $o).
% 0.23/0.29 thf(decl_36, type, omegaSAx: $o).
% 0.23/0.29 thf(decl_37, type, omegaIndAx: $o).
% 0.23/0.29 thf(decl_38, type, replAx: $o).
% 0.23/0.29 thf(decl_39, type, foundationAx: $o).
% 0.23/0.29 thf(decl_40, type, wellorderingAx: $o).
% 0.23/0.29 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.23/0.29 thf(decl_42, type, descrp: $o).
% 0.23/0.29 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.23/0.29 thf(decl_44, type, dsetconstrI: $o).
% 0.23/0.29 thf(decl_45, type, dsetconstrEL: $o).
% 0.23/0.29 thf(decl_46, type, dsetconstrER: $o).
% 0.23/0.29 thf(decl_47, type, exuE1: $o).
% 0.23/0.29 thf(decl_48, type, prop2set: $o > $i).
% 0.23/0.29 thf(decl_49, type, prop2setE: $o).
% 0.23/0.29 thf(decl_50, type, emptysetE: $o).
% 0.23/0.29 thf(decl_51, type, emptysetimpfalse: $o).
% 0.23/0.29 thf(decl_52, type, notinemptyset: $o).
% 0.23/0.29 thf(decl_53, type, exuE3e: $o).
% 0.23/0.29 thf(decl_54, type, setext: $o).
% 0.23/0.29 thf(decl_55, type, emptyI: $o).
% 0.23/0.29 thf(decl_56, type, noeltsimpempty: $o).
% 0.23/0.29 thf(decl_57, type, setbeta: $o).
% 0.23/0.29 thf(decl_58, type, nonempty: $i > $o).
% 0.23/0.29 thf(decl_59, type, nonemptyE1: $o).
% 0.23/0.29 thf(decl_60, type, nonemptyI: $o).
% 0.23/0.29 thf(decl_61, type, nonemptyI1: $o).
% 0.23/0.29 thf(decl_62, type, setadjoinIL: $o).
% 0.23/0.29 thf(decl_63, type, emptyinunitempty: $o).
% 0.23/0.29 thf(decl_64, type, setadjoinIR: $o).
% 0.23/0.29 thf(decl_65, type, setadjoinE: $o).
% 0.23/0.29 thf(decl_66, type, setadjoinOr: $o).
% 0.23/0.29 thf(decl_67, type, setoftrueEq: $o).
% 0.23/0.29 thf(decl_68, type, powersetI: $o).
% 0.23/0.29 thf(decl_69, type, emptyinPowerset: $o).
% 0.23/0.29 thf(decl_70, type, emptyInPowerset: $o).
% 0.23/0.29 thf(decl_71, type, powersetE: $o).
% 0.23/0.29 thf(decl_72, type, setunionI: $o).
% 0.23/0.29 thf(decl_73, type, setunionE: $o).
% 0.23/0.29 thf(decl_74, type, subPowSU: $o).
% 0.23/0.29 thf(decl_75, type, exuE2: $o).
% 0.23/0.29 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.23/0.29 thf(decl_77, type, uniqinunit: $o).
% 0.23/0.29 thf(decl_78, type, notinsingleton: $o).
% 0.23/0.29 thf(decl_79, type, eqinunit: $o).
% 0.23/0.29 thf(decl_80, type, singletonsswitch: $o).
% 0.23/0.29 thf(decl_81, type, upairsetE: $o).
% 0.23/0.29 thf(decl_82, type, upairsetIL: $o).
% 0.23/0.29 thf(decl_83, type, upairsetIR: $o).
% 0.23/0.29 thf(decl_84, type, emptyE1: $o).
% 0.23/0.29 thf(decl_85, type, vacuousDall: $o).
% 0.23/0.29 thf(decl_86, type, quantDeMorgan1: $o).
% 0.23/0.29 thf(decl_87, type, quantDeMorgan2: $o).
% 0.23/0.29 thf(decl_88, type, quantDeMorgan3: $o).
% 0.23/0.29 thf(decl_89, type, quantDeMorgan4: $o).
% 0.23/0.29 thf(decl_90, type, prop2setI: $o).
% 0.23/0.29 thf(decl_91, type, set2prop: $i > $o).
% 0.23/0.29 thf(decl_92, type, prop2set2propI: $o).
% 0.23/0.29 thf(decl_93, type, notdexE: $o).
% 0.23/0.29 thf(decl_94, type, notdallE: $o).
% 0.23/0.29 thf(decl_95, type, exuI1: $o).
% 0.23/0.29 thf(decl_96, type, exuI3: $o).
% 0.23/0.29 thf(decl_97, type, exuI2: $o).
% 0.23/0.29 thf(decl_98, type, inCongP: $o).
% 0.23/0.29 thf(decl_99, type, in__Cong: $o).
% 0.23/0.29 thf(decl_100, type, exuE3u: $o).
% 0.23/0.29 thf(decl_101, type, exu__Cong: $o).
% 0.23/0.29 thf(decl_102, type, emptyset__Cong: $o).
% 0.23/0.29 thf(decl_103, type, setadjoin__Cong: $o).
% 0.23/0.29 thf(decl_104, type, powerset__Cong: $o).
% 0.23/0.29 thf(decl_105, type, setunion__Cong: $o).
% 0.23/0.29 thf(decl_106, type, epred1_0: $o).
% 0.23/0.29 thf(decl_107, type, esk1_2: $i > $i > $i).
% 0.23/0.29 thf(decl_108, type, esk2_2: $i > $i > $i).
% 0.23/0.29 thf(decl_109, type, esk3_2: $i > $i > $i).
% 0.23/0.29 thf(decl_110, type, esk4_1: $i > $i).
% 0.23/0.29 thf(decl_111, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.23/0.29 thf(decl_112, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.23/0.29 thf(decl_113, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.23/0.29 thf(decl_114, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.23/0.29 thf(decl_115, type, esk9_1: $i > $i).
% 0.23/0.29 thf(decl_116, type, esk10_2: ($i > $o) > $i > $i).
% 0.23/0.29 thf(decl_117, type, esk11_2: ($i > $o) > $i > $i).
% 0.23/0.29 thf(decl_118, type, esk12_1: ($i > $o) > $i).
% 0.23/0.29 thf(decl_119, type, esk13_2: ($i > $o) > $i > $i).
% 0.23/0.29 thf(decl_120, type, esk14_1: ($i > $o) > $i).
% 0.23/0.29 thf(decl_121, type, esk15_2: $i > $i > $i).
% 0.23/0.29 thf(decl_122, type, esk16_2: $i > $i > $i).
% 0.23/0.29 thf(decl_123, type, esk17_1: $i > $i).
% 0.23/0.29 thf(decl_124, type, esk18_1: $i > $i).
% 0.23/0.29 thf(decl_125, type, esk19_1: $i > $i).
% 0.23/0.29 thf(decl_126, type, esk20_2: $i > $i > $i).
% 0.23/0.29 thf(decl_127, type, esk21_3: $i > $i > $o > $i).
% 0.23/0.29 thf(decl_128, type, esk22_2: ($i > $o) > $i > $i).
% 0.23/0.29 thf(decl_129, type, esk23_1: ($i > $o) > $i).
% 0.23/0.29 thf(decl_130, type, esk24_1: $i > $i).
% 0.23/0.29 thf(decl_131, type, esk25_2: $i > ($i > $o) > $i).
% 0.23/0.29 thf(decl_132, type, esk26_2: $i > ($i > $o) > $i).
% 0.23/0.29 thf(decl_133, type, esk27_2: $i > ($i > $o) > $i).
% 0.23/0.29 thf(decl_134, type, esk28_2: $i > ($i > $o) > $i).
% 0.23/0.29 thf(decl_135, type, esk29_2: $i > ($i > $o) > $i).
% 0.23/0.29 thf(decl_136, type, esk30_2: $i > ($i > $o) > $i).
% 0.23/0.29 thf(decl_137, type, esk31_2: ($i > $o) > $i > $i).
% 0.23/0.29 thf(decl_138, type, esk32_1: ($i > $o) > $i).
% 0.23/0.29 thf(decl_139, type, esk33_1: ($i > $o) > $i).
% 0.23/0.29 thf(decl_140, type, esk34_1: ($i > $o) > $i).
% 0.23/0.29 thf(decl_141, type, esk35_1: ($i > $o) > $i).
% 0.23/0.29 thf(decl_142, type, esk36_2: ($i > $o) > $i > $i).
% 0.23/0.29 thf(decl_143, type, esk37_1: ($i > $o) > $i).
% 0.23/0.29 thf(decl_144, type, esk38_2: ($i > $o) > $i > $i).
% 0.23/0.29 thf(decl_145, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 0.23/0.29 thf(decl_146, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 0.23/0.29 thf(decl_147, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.23/0.29 thf(decl_148, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 0.23/0.29 thf(decl_149, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.23/0.29 thf(decl_150, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 0.23/0.29 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', exuI1)).
% 0.23/0.29 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', exu)).
% 0.23/0.29 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', exuI3)).
% 0.23/0.29 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', exuE3u)).
% 0.23/0.29 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', exu__Cong)).
% 0.23/0.29 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', nonempty)).
% 0.23/0.29 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', exuE3e)).
% 0.23/0.29 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', nonemptyI)).
% 0.23/0.29 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', exuE2)).
% 0.23/0.29 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', exuI2)).
% 0.23/0.29 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/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', exuE1)).
% 0.23/0.29 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', descrp)).
% 0.23/0.29 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', replAx)).
% 0.23/0.29 thf(omega__Cong, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega)=(omega))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', omega__Cong)).
% 0.23/0.29 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', nonemptyE1)).
% 0.23/0.29 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', setbeta)).
% 0.23/0.29 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', setoftrueEq)).
% 0.23/0.29 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', nonemptyI1)).
% 0.23/0.29 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', nonemptyImpWitness)).
% 0.23/0.29 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', emptyE1)).
% 0.23/0.29 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', dsetconstrER)).
% 0.23/0.29 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', dsetconstrEL)).
% 0.23/0.29 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', dsetconstrI)).
% 0.23/0.29 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', emptyI)).
% 0.23/0.29 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', in__Cong)).
% 0.23/0.29 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', notdallE)).
% 0.23/0.29 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', emptyset__Cong)).
% 0.23/0.29 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', setadjoin__Cong)).
% 0.23/0.29 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', powerset__Cong)).
% 0.23/0.29 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', setunion__Cong)).
% 0.23/0.29 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', omegaIndAx)).
% 0.23/0.29 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', omegaSAx)).
% 0.23/0.29 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', omega0Ax)).
% 0.23/0.29 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', emptysetE)).
% 0.23/0.29 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', noeltsimpempty)).
% 0.23/0.29 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', setunionE)).
% 0.23/0.29 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', setunionI)).
% 0.23/0.29 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/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', setext)).
% 0.23/0.29 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', notinemptyset)).
% 0.23/0.29 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', setadjoinOr)).
% 0.23/0.29 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/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', setadjoinE)).
% 0.23/0.29 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', setadjoinIR)).
% 0.23/0.29 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', emptyinunitempty)).
% 0.23/0.29 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', setadjoinIL)).
% 0.23/0.29 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', powersetI)).
% 0.23/0.29 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', subPowSU)).
% 0.23/0.29 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', powersetE)).
% 0.23/0.29 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', emptyInPowerset)).
% 0.23/0.29 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', emptyinPowerset)).
% 0.23/0.29 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', upairsetIR)).
% 0.23/0.29 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', upairsetIL)).
% 0.23/0.29 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', upairsetE)).
% 0.23/0.29 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', singletonsswitch)).
% 0.23/0.29 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', eqinunit)).
% 0.23/0.29 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', notinsingleton)).
% 0.23/0.29 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', uniqinunit)).
% 0.23/0.29 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', prop2set2propI)).
% 0.23/0.29 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', prop2setI)).
% 0.23/0.29 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', quantDeMorgan4)).
% 0.23/0.29 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', quantDeMorgan3)).
% 0.23/0.29 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', quantDeMorgan2)).
% 0.23/0.29 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', emptysetimpfalse)).
% 0.23/0.29 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', quantDeMorgan1)).
% 0.23/0.29 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', vacuousDall)).
% 0.23/0.29 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', notdexE)).
% 0.23/0.29 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', inCongP)).
% 0.23/0.29 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', prop2setE)).
% 0.23/0.29 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', wellorderingAx)).
% 0.23/0.29 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/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', foundationAx)).
% 0.23/0.29 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', setunionAx)).
% 0.23/0.29 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', powersetAx)).
% 0.23/0.29 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', setadjoinAx)).
% 0.23/0.29 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', emptysetAx)).
% 0.23/0.29 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.0NvkjP08HK/E---3.1_625794.p', setextAx)).
% 0.23/0.29 thf(c_0_74, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 0.23/0.29 thf(c_0_75, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.23/0.29 thf(c_0_76, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.23/0.29 thf(c_0_77, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 0.23/0.29 thf(c_0_78, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.23/0.29 thf(c_0_79, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.23/0.29 thf(c_0_80, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.23/0.29 thf(c_0_81, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.23/0.29 thf(c_0_82, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.23/0.29 thf(c_0_83, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.23/0.29 thf(c_0_84, 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])).
% 0.23/0.29 thf(c_0_85, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.23/0.29 thf(c_0_86, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.23/0.29 thf(c_0_87, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega)=(omega)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[omega__Cong])).
% 0.23/0.29 thf(c_0_88, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X228:$i]:(((((X1 @ X228)))&(![X229:$i]:(((((X1 @ X229)))=>(((X228)=(X229)))))))))))))), inference(apply_def,[status(thm)],[c_0_74, c_0_75])).
% 0.23/0.29 thf(c_0_89, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X230:$i]:(((((X1 @ X230)))&(![X231:$i]:(((((X1 @ X231)))=>(((X230)=(X231)))))))))))))))), inference(apply_def,[status(thm)],[c_0_76, c_0_75])).
% 0.23/0.29 thf(c_0_90, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X234:$i]:(((((X1 @ X234)))&(![X235:$i]:(((((X1 @ X235)))=>(((X234)=(X235))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_77, c_0_75])).
% 0.23/0.29 thf(c_0_91, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X236:$i]:(((((X1 @ X236)))&(![X237:$i]:(((((X1 @ X237)))=>(((X236)=(X237))))))))))<=>((?[X238:$i]:(((((X17 @ X238)))&(![X239:$i]:(((((X17 @ X239)))=>(((X238)=(X239)))))))))))))))), inference(apply_def,[status(thm)],[c_0_78, c_0_75])).
% 0.23/0.29 thf(c_0_92, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_79])).
% 0.23/0.29 thf(c_0_93, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.23/0.29 thf(c_0_94, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X224:$i]:(((((X1 @ X224)))&(![X225:$i]:(((((X1 @ X225)))=>(((X224)=(X225))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_80, c_0_75])).
% 0.23/0.29 thf(c_0_95, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_81, c_0_79])).
% 0.23/0.29 thf(c_0_96, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.23/0.29 thf(c_0_97, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_79])).
% 0.23/0.29 thf(c_0_98, plain, ((exuE2)=(![X1:$i > $o]:((((?[X226:$i]:(((((X1 @ X226)))&(![X227:$i]:(((((X1 @ X227)))=>(((X226)=(X227))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_82, c_0_75])).
% 0.23/0.29 thf(c_0_99, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_79])).
% 0.23/0.29 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])).
% 0.23/0.29 thf(c_0_101, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X232:$i]:(((((X1 @ X232)))&(![X233:$i]:(((((X1 @ X233)))=>(((X232)=(X233)))))))))))))), inference(apply_def,[status(thm)],[c_0_83, c_0_75])).
% 0.23/0.29 thf(c_0_102, plain, ((exuE1)=(![X1:$i > $o]:((((?[X222:$i]:(((((X1 @ X222)))&(![X223:$i]:(((((X1 @ X223)))=>(((X222)=(X223))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_84, c_0_75])).
% 0.23/0.29 thf(c_0_103, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.23/0.29 thf(c_0_104, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.23/0.29 thf(c_0_105, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.23/0.29 thf(c_0_106, plain, ((descrp)=(![X1:$i > $o]:((((?[X220:$i]:(((((X1 @ X220)))&(![X221:$i]:(((((X1 @ X221)))=>(((X220)=(X221))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_85, c_0_75])).
% 0.23/0.29 thf(c_0_107, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X218:$i]:(((((X6 @ X2 @ X218)))&(![X219:$i]:(((((X6 @ X2 @ X219)))=>(((X218)=(X219)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_86, c_0_75])).
% 0.23/0.29 thf(c_0_108, plain, ((epred1_0)<=>![X269:$i]:(?[X270:$i]:((((![X271:$i]:(((in @ X271 @ X270)=>![X272:$i]:(((in @ X272 @ X271)=>(in @ X272 @ X269)))))&![X273:$i, X274:$i]:((((in @ X273 @ X269)&(in @ X274 @ X269))=>(![X275:$i]:(((in @ X275 @ X270)=>((in @ X273 @ X275)<=>(in @ X274 @ X275))))=>((X273)=(X274))))))&![X276:$i, X277:$i]:((((in @ X276 @ X270)&(in @ X277 @ X270))=>(![X278:$i]:(((in @ X278 @ X276)=>(in @ X278 @ X277)))|![X279:$i]:(((in @ X279 @ X277)=>(in @ X279 @ X276)))))))&![X280:$i]:(((![X281:$i]:(((in @ X281 @ X280)=>(in @ X281 @ X269)))&?[X282:$i]:((in @ X282 @ X280)))=>?[X283:$i, X284:$i]:(((((in @ X283 @ X270)&(in @ X284 @ X280))&~(?[X285:$i]:(((in @ X285 @ X283)&(in @ X285 @ X280)))))&![X286:$i]:(((in @ X286 @ X270)=>(![X287:$i]:(((in @ X287 @ X286)=>(in @ X287 @ X283)))|(in @ X284 @ X286)))))))))))), introduced(definition)).
% 0.23/0.29 thf(c_0_109, negated_conjecture, ~((![X240:$i, X241:$i]:((![X242:$i]:(((in @ X242 @ X240)<=>(in @ X242 @ X241)))=>((X240)=(X241))))=>(![X243:$i]:(~(in @ X243 @ emptyset))=>(![X244:$i, X245:$i, X246:$i]:(((in @ X246 @ (setadjoin @ X244 @ X245))<=>(((X246)=(X244))|(in @ X246 @ X245))))=>(![X247:$i, X248:$i]:(((in @ X248 @ (powerset @ X247))<=>![X249:$i]:(((in @ X249 @ X248)=>(in @ X249 @ X247)))))=>(![X250:$i, X251:$i]:(((in @ X251 @ (setunion @ X250))<=>?[X252:$i]:(((in @ X251 @ X252)&(in @ X252 @ X250)))))=>((in @ emptyset @ omega)=>(![X253:$i]:(((in @ X253 @ omega)=>(in @ (setadjoin @ X253 @ X253) @ omega)))=>(![X254:$i]:((((in @ emptyset @ X254)&![X255:$i]:((((in @ X255 @ omega)&(in @ X255 @ X254))=>(in @ (setadjoin @ X255 @ X255) @ X254))))=>![X256:$i]:(((in @ X256 @ omega)=>(in @ X256 @ X254)))))=>(![X257:$i > $i > $o, X258:$i]:((![X259:$i]:(((in @ X259 @ X258)=>?[X260:$i]:(((X257 @ X259 @ X260)&![X261:$i]:(((X257 @ X259 @ X261)=>((X260)=(X261))))))))=>?[X262:$i]:(![X263:$i]:(((in @ X263 @ X262)<=>?[X264:$i]:(((in @ X264 @ X258)&(X257 @ X264 @ X263))))))))=>(![X265:$i]:((?[X266:$i]:((in @ X266 @ X265))=>?[X267:$i]:(((in @ X267 @ X265)&~(?[X268:$i]:(((in @ X268 @ X267)&(in @ X268 @ X265))))))))=>((epred1_0)=>(![X288:$i > $o]:((?[X289:$i]:(((X288 @ X289)&![X290:$i]:(((X288 @ X290)=>((X289)=(X290))))))=>(X288 @ (descr @ (^[Z0:$i]:(X288 @ Z0))))))=>(![X291:$i, X292:$i > $o, X293:$i]:(((in @ X293 @ X291)=>((X292 @ X293)=>(in @ X293 @ (dsetconstr @ X291 @ X292)))))=>(![X294:$i, X295:$i > $o, X296:$i]:(((in @ X296 @ (dsetconstr @ X294 @ X295))=>(in @ X296 @ X294)))=>(![X297:$i, X298:$i > $o, X299:$i]:(((in @ X299 @ (dsetconstr @ X297 @ X298))=>(X298 @ X299)))=>(![X300:$i > $o]:((?[X301:$i]:(((X300 @ X301)&![X302:$i]:(((X300 @ X302)=>((X301)=(X302))))))=>?[X303:$i]:(((X300 @ X303)&![X304:$i]:(((X300 @ X304)=>((X303)=(X304))))))))=>(![X305:$o, X306:$i]:(((in @ X306 @ (prop2set @ ((X305))))=>(X305)))=>(![X307:$i]:(((in @ X307 @ emptyset)=>![X308:$o]:((X308))))=>(![X309:$i]:(((in @ X309 @ emptyset)=>~($true)))=>(![X310:$i]:(~(in @ X310 @ emptyset))=>(![X311:$i > $o]:((?[X312:$i]:(((X311 @ X312)&![X313:$i]:(((X311 @ X313)=>((X312)=(X313))))))=>?[X314:$i]:((X311 @ X314))))=>(![X315:$i, X316:$i]:((![X317:$i]:(((in @ X317 @ X315)=>(in @ X317 @ X316)))=>(![X318:$i]:(((in @ X318 @ X316)=>(in @ X318 @ X315)))=>((X315)=(X316)))))=>(![X319:$i]:((![X320:$i]:(~(in @ X320 @ X319))=>((X319)=(emptyset))))=>(![X321:$i]:((![X322:$i]:(~(in @ X322 @ X321))=>((X321)=(emptyset))))=>(![X323:$i, X324:$i > $o, X325:$i]:(((in @ X325 @ X323)=>((in @ X325 @ (dsetconstr @ X323 @ X324))<=>(X324 @ X325))))=>(![X326:$i]:((((X326)!=(emptyset))=>?[X327:$i]:((in @ X327 @ X326))))=>(![X328:$i, X329:$i > $o, X330:$i]:(((in @ X330 @ X328)=>((X329 @ X330)=>((dsetconstr @ X328 @ X329)!=(emptyset)))))=>(![X331:$i]:((?[X332:$i]:((in @ X332 @ X331))=>((X331)!=(emptyset))))=>(![X333:$i, X334:$i]:((in @ X333 @ (setadjoin @ X333 @ X334)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X335:$i, X336:$i, X337:$i]:(((in @ X337 @ X336)=>(in @ X337 @ (setadjoin @ X335 @ X336))))=>(![X338:$i, X339:$i, X340:$i]:(((in @ X340 @ (setadjoin @ X338 @ X339))=>![X341:$o]:(((((X340)=(X338))=>(X341))=>(((in @ X340 @ X339)=>(X341))=>(X341))))))=>(![X342:$i, X343:$i, X344:$i]:(((in @ X344 @ (setadjoin @ X342 @ X343))=>(((X344)=(X342))|(in @ X344 @ X343))))=>(![X345:$i]:(((dsetconstr @ X345 @ (^[Z0:$i]:($true)))=(X345)))=>(![X346:$i, X347:$i]:((![X348:$i]:(((in @ X348 @ X347)=>(in @ X348 @ X346)))=>(in @ X347 @ (powerset @ X346))))=>(![X349:$i]:((in @ emptyset @ (powerset @ X349)))=>(![X350:$i]:((in @ emptyset @ (powerset @ X350)))=>(![X351:$i, X352:$i, X353:$i]:(((in @ X352 @ (powerset @ X351))=>((in @ X353 @ X352)=>(in @ X353 @ X351))))=>(![X354:$i, X355:$i, X356:$i]:(((in @ X355 @ X356)=>((in @ X356 @ X354)=>(in @ X355 @ (setunion @ X354)))))=>(![X357:$i, X358:$i]:(((in @ X358 @ (setunion @ X357))=>![X359:$o]:((![X360:$i]:(((in @ X358 @ X360)=>((in @ X360 @ X357)=>(X359))))=>(X359)))))=>(![X361:$i, X362:$i]:(((in @ X362 @ X361)=>(in @ X362 @ (powerset @ (setunion @ X361)))))=>(![X363:$i > $o]:((?[X364:$i]:(((X363 @ X364)&![X365:$i]:(((X363 @ X365)=>((X364)=(X365))))))=>?[X366:$i]:(![X367:$i]:(((X363 @ X367)<=>((X367)=(X366)))))))=>(![X368:$i]:((((X368)!=(emptyset))=>?[X369:$i]:(((in @ X369 @ X368)&$true))))=>(![X370:$i, X371:$i]:(((in @ X370 @ (setadjoin @ X371 @ emptyset))=>((X370)=(X371))))=>(![X372:$i, X373:$i]:((((X372)!=(X373))=>~(in @ X373 @ (setadjoin @ X372 @ emptyset))))=>(![X374:$i, X375:$i]:((((X374)=(X375))=>(in @ X374 @ (setadjoin @ X375 @ emptyset))))=>(![X376:$i, X377:$i]:(((in @ X376 @ (setadjoin @ X377 @ emptyset))=>(in @ X377 @ (setadjoin @ X376 @ emptyset))))=>(![X378:$i, X379:$i, X380:$i]:(((in @ X380 @ (setadjoin @ X378 @ (setadjoin @ X379 @ emptyset)))=>(((X380)=(X378))|((X380)=(X379)))))=>(![X381:$i, X382:$i]:((in @ X381 @ (setadjoin @ X381 @ (setadjoin @ X382 @ emptyset))))=>(![X383:$i, X384:$i]:((in @ X384 @ (setadjoin @ X383 @ (setadjoin @ X384 @ emptyset))))=>(![X385:$i, X386:$i > $o]:((?[X387:$i]:(((in @ X387 @ X385)&(X386 @ X387)))=>(((dsetconstr @ X385 @ X386)=(emptyset))=>~($true))))=>(![X388:$i > $o, X389:$i]:(((in @ X389 @ emptyset)=>(X388 @ X389)))=>(![X390:$i, X391:$i > $o]:((~(![X392:$i]:(((in @ X392 @ X390)=>(X391 @ X392))))=>?[X393:$i]:(((in @ X393 @ X390)&~((X391 @ X393))))))=>(![X394:$i, X395:$i > $o]:((![X396:$i]:(((in @ X396 @ X394)=>~((X395 @ X396))))=>~(?[X397:$i]:(((in @ X397 @ X394)&(X395 @ X397))))))=>(![X398:$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:$i]:(((in @ X405 @ X402)=>(X403 @ X405))))))=>(![X406:$o]:(((X406)=>(in @ emptyset @ (prop2set @ ((X406))))))=>(![X407:$o]:(((X407)=>(set2prop @ (prop2set @ ((X407))))))=>(![X408:$i, X409:$i > $o]:((~(?[X410:$i]:(((in @ X410 @ X408)&(X409 @ X410))))=>![X411:$i]:(((in @ X411 @ X408)=>~((X409 @ X411))))))=>(![X412:$i, X413:$i > $o]:((~(![X414:$i]:(((in @ X414 @ X412)=>(X413 @ X414))))=>?[X415:$i]:(((in @ X415 @ X412)&~((X413 @ X415))))))=>(![X416:$i > $o]:((?[X417:$i]:(((X416 @ X417)&![X418:$i]:(((X416 @ X418)=>((X417)=(X418))))))=>?[X419:$i]:(((X416 @ X419)&![X420:$i]:(((X416 @ X420)=>((X419)=(X420))))))))=>(![X421:$i > $o]:((?[X422:$i]:((X421 @ X422))=>(![X423:$i, X424:$i]:(((X421 @ X423)=>((X421 @ X424)=>((X423)=(X424)))))=>?[X425:$i]:(((X421 @ X425)&![X426:$i]:(((X421 @ X426)=>((X425)=(X426)))))))))=>(![X427:$i > $o]:((?[X428:$i]:(![X429:$i]:(((X427 @ X429)<=>((X429)=(X428)))))=>?[X430:$i]:(((X427 @ X430)&![X431:$i]:(((X427 @ X431)=>((X430)=(X431))))))))=>(![X432:$i, X433:$i]:((((X432)=(X433))=>![X434:$i, X435:$i]:((((X434)=(X435))=>((in @ X434 @ X432)=>(in @ X435 @ X433))))))=>(![X436:$i, X437:$i]:((((X436)=(X437))=>![X438:$i, X439:$i]:((((X438)=(X439))=>((in @ X438 @ X436)<=>(in @ X439 @ X437))))))=>(![X440:$i > $o]:((?[X441:$i]:(((X440 @ X441)&![X442:$i]:(((X440 @ X442)=>((X441)=(X442))))))=>![X443:$i, X444:$i]:(((X440 @ X443)=>((X440 @ X444)=>((X443)=(X444)))))))=>(![X445:$i > $o, X446:$i > $o]:((![X447:$i, X448:$i]:((((X447)=(X448))=>((X445 @ X447)<=>(X446 @ X448))))=>(?[X449:$i]:(((X445 @ X449)&![X450:$i]:(((X445 @ X450)=>((X449)=(X450))))))<=>?[X451:$i]:(((X446 @ X451)&![X452:$i]:(((X446 @ X452)=>((X451)=(X452)))))))))=>(((emptyset)=(emptyset))=>(![X453:$i, X454:$i]:((((X453)=(X454))=>![X455:$i, X456:$i]:((((X455)=(X456))=>((setadjoin @ X453 @ X455)=(setadjoin @ X454 @ X456))))))=>(![X457:$i, X458:$i]:((((X457)=(X458))=>((powerset @ X457)=(powerset @ X458))))=>(![X459:$i, X460:$i]:((((X459)=(X460))=>((setunion @ X459)=(setunion @ X460))))=>((omega)=(omega)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_87, emptyI]), in__Cong]), notdallE]), c_0_88]), c_0_89]), c_0_90]), c_0_91]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omegaIndAx]), omegaSAx]), omega0Ax]), emptysetE]), c_0_92]), c_0_93]), noeltsimpempty]), setunionE]), setunionI]), setext]), c_0_94]), notinemptyset]), c_0_95]), c_0_96]), setadjoinOr]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), c_0_97]), powersetI]), c_0_98]), subPowSU]), powersetE]), emptyInPowerset]), emptyinPowerset]), c_0_99]), upairsetIR]), upairsetIL]), upairsetE]), singletonsswitch]), eqinunit]), notinsingleton]), uniqinunit]), c_0_100]), prop2set2propI]), prop2setI]), quantDeMorgan4]), quantDeMorgan3]), quantDeMorgan2]), emptysetimpfalse]), quantDeMorgan1]), vacuousDall]), c_0_101]), notdexE]), inCongP]), prop2setE]), c_0_102]), c_0_103]), c_0_104]), c_0_105]), c_0_106]), wellorderingAx]), foundationAx]), c_0_107]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_108])).
% 0.23/0.30 thf(c_0_110, negated_conjecture, ![X461:$i, X462:$i, X464:$i, X465:$i, X466:$i, X467:$i, X468:$i, X469:$i, X470:$i, X471:$i, X472:$i, X474:$i, X475:$i, X477:$i, X478:$i, X479:$i, X480:$i, X481:$i, X483:$i, X484:$i > $i > $o, X485:$i, X487:$i, X490:$i, X492:$i, X493:$i, X494:$i, X495:$i, X497:$i, X498:$i > $o, X499:$i, X501:$i, X502:$i > $o, X503:$i, X504:$i, X505:$i > $o, X506:$i, X507:$i, X508:$i > $o, X509:$i, X510:$i > $o, X511:$i, X514:$i, X515:$o, X516:$i, X517:$i, X518:$o, X519:$i, X520:$i, X521:$i > $o, X522:$i, X525:$i, X526:$i, X529:$i, X531:$i, X533:$i, X534:$i > $o, X535:$i, X536:$i, X538:$i, X539:$i > $o, X540:$i, X541:$i, X542:$i, X543:$i, X544:$i, X545:$i, X546:$i, X547:$i, X548:$i, X549:$i, X550:$i, X551:$o, X552:$i, X553:$i, X554:$i, X555:$i, X556:$i, X557:$i, X559:$i, X560:$i, X561:$i, X562:$i, X563:$i, X564:$i, X565:$i, X566:$i, X567:$i, X568:$i, X569:$o, X571:$i, X572:$i, X573:$i > $o, X574:$i, X577:$i, X578:$i, X579:$i, X581:$i, X582:$i, X583:$i, X584:$i, X585:$i, X586:$i, X587:$i, X588:$i, X589:$i, X590:$i, X591:$i, X592:$i, X593:$i, X594:$i, X595:$i, X596:$i, X597:$i > $o, X598:$i, X599:$i > $o, X600:$i, X601:$i, X602:$i > $o, X603:$i, X605:$i, X606:$i > $o, X608:$i, X609:$i, X610:$i > $o, X612:$i, X613:$i, X614:$i > $o, X615:$i, X617:$o, X618:$o, X619:$i, X620:$i > $o, X622:$i, X623:$i, X624:$i > $o, X625:$i, X627:$i > $o, X628:$i, X631:$i, X632:$i > $o, X633:$i, X637:$i, X638:$i > $o, X639:$i, X642:$i, X643:$i, X644:$i, X645:$i, X646:$i, X647:$i, X648:$i, X649:$i, X650:$i, X651:$i > $o, X652:$i, X654:$i, X655:$i, X656:$i > $o, X657:$i > $o, X660:$i, X663:$i, X664:$i, X667:$i, X668:$i, X669:$i, X670:$i, X671:$i, X672:$i, X673:$i, X674:$i, X675:$i]:((((~(in @ (esk1_2 @ X461 @ X462) @ X461)|~(in @ (esk1_2 @ X461 @ X462) @ X462)|((X461)=(X462)))&((in @ (esk1_2 @ X461 @ X462) @ X461)|(in @ (esk1_2 @ X461 @ X462) @ X462)|((X461)=(X462))))&(~(in @ X464 @ emptyset)&(((~(in @ X467 @ (setadjoin @ X465 @ X466))|(((X467)=(X465))|(in @ X467 @ X466)))&((((X467)!=(X465))|(in @ X467 @ (setadjoin @ X465 @ X466)))&(~(in @ X467 @ X466)|(in @ X467 @ (setadjoin @ X465 @ X466)))))&(((~(in @ X469 @ (powerset @ X468))|(~(in @ X470 @ X469)|(in @ X470 @ X468)))&(((in @ (esk2_2 @ X471 @ X472) @ X472)|(in @ X472 @ (powerset @ X471)))&(~(in @ (esk2_2 @ X471 @ X472) @ X471)|(in @ X472 @ (powerset @ X471)))))&(((((in @ X475 @ (esk3_2 @ X474 @ X475))|~(in @ X475 @ (setunion @ X474)))&((in @ (esk3_2 @ X474 @ X475) @ X474)|~(in @ X475 @ (setunion @ X474))))&(~(in @ X478 @ X479)|~(in @ X479 @ X477)|(in @ X478 @ (setunion @ X477))))&((in @ emptyset @ omega)&((~(in @ X480 @ omega)|(in @ (setadjoin @ X480 @ X480) @ omega))&(((((in @ (esk4_1 @ X481) @ omega)|~(in @ emptyset @ X481)|(~(in @ X483 @ omega)|(in @ X483 @ X481)))&((in @ (esk4_1 @ X481) @ X481)|~(in @ emptyset @ X481)|(~(in @ X483 @ omega)|(in @ X483 @ X481))))&(~(in @ (setadjoin @ (esk4_1 @ X481) @ (esk4_1 @ X481)) @ X481)|~(in @ emptyset @ X481)|(~(in @ X483 @ omega)|(in @ X483 @ X481))))&((((((in @ (esk8_3 @ X484 @ X485 @ X490) @ X485)|~(in @ X490 @ (esk7_2 @ X484 @ X485))|(in @ (esk5_2 @ X484 @ X485) @ X485))&((X484 @ (esk8_3 @ X484 @ X485 @ X490) @ X490)|~(in @ X490 @ (esk7_2 @ X484 @ X485))|(in @ (esk5_2 @ X484 @ X485) @ X485)))&(~(in @ X493 @ X485)|~(X484 @ X493 @ X492)|(in @ X492 @ (esk7_2 @ X484 @ X485))|(in @ (esk5_2 @ X484 @ X485) @ X485)))&(((((in @ (esk8_3 @ X484 @ X485 @ X490) @ X485)|~(in @ X490 @ (esk7_2 @ X484 @ X485))|((X484 @ (esk5_2 @ X484 @ X485) @ (esk6_3 @ X484 @ X485 @ X487))|~(X484 @ (esk5_2 @ X484 @ X485) @ X487)))&((X484 @ (esk8_3 @ X484 @ X485 @ X490) @ X490)|~(in @ X490 @ (esk7_2 @ X484 @ X485))|((X484 @ (esk5_2 @ X484 @ X485) @ (esk6_3 @ X484 @ X485 @ X487))|~(X484 @ (esk5_2 @ X484 @ X485) @ X487))))&(~(in @ X493 @ X485)|~(X484 @ X493 @ X492)|(in @ X492 @ (esk7_2 @ X484 @ X485))|((X484 @ (esk5_2 @ X484 @ X485) @ (esk6_3 @ X484 @ X485 @ X487))|~(X484 @ (esk5_2 @ X484 @ X485) @ X487))))&((((in @ (esk8_3 @ X484 @ X485 @ X490) @ X485)|~(in @ X490 @ (esk7_2 @ X484 @ X485))|(((X487)!=(esk6_3 @ X484 @ X485 @ X487))|~(X484 @ (esk5_2 @ X484 @ X485) @ X487)))&((X484 @ (esk8_3 @ X484 @ X485 @ X490) @ X490)|~(in @ X490 @ (esk7_2 @ X484 @ X485))|(((X487)!=(esk6_3 @ X484 @ X485 @ X487))|~(X484 @ (esk5_2 @ X484 @ X485) @ X487))))&(~(in @ X493 @ X485)|~(X484 @ X493 @ X492)|(in @ X492 @ (esk7_2 @ X484 @ X485))|(((X487)!=(esk6_3 @ X484 @ X485 @ X487))|~(X484 @ (esk5_2 @ X484 @ X485) @ X487))))))&((((in @ (esk9_1 @ X494) @ X494)|~(in @ X495 @ X494))&(~(in @ X497 @ (esk9_1 @ X494))|~(in @ X497 @ X494)|~(in @ X495 @ X494)))&((epred1_0)&((((X498 @ (esk10_2 @ X498 @ X499))|~(X498 @ X499)|(X498 @ (descr @ X498)))&(((X499)!=(esk10_2 @ X498 @ X499))|~(X498 @ X499)|(X498 @ (descr @ X498))))&((~(in @ X503 @ X501)|(~(X502 @ X503)|(in @ X503 @ (dsetconstr @ X501 @ X502))))&((~(in @ X506 @ (dsetconstr @ X504 @ X505))|(in @ X506 @ X504))&((~(in @ X509 @ (dsetconstr @ X507 @ X508))|(X508 @ X509))&(((((X510 @ (esk12_1 @ X510))|((X510 @ (esk11_2 @ X510 @ X511))|~(X510 @ X511)))&(~(X510 @ X514)|((esk12_1 @ X510)=(X514))|((X510 @ (esk11_2 @ X510 @ X511))|~(X510 @ X511))))&(((X510 @ (esk12_1 @ X510))|(((X511)!=(esk11_2 @ X510 @ X511))|~(X510 @ X511)))&(~(X510 @ X514)|((esk12_1 @ X510)=(X514))|(((X511)!=(esk11_2 @ X510 @ X511))|~(X510 @ X511)))))&((~(in @ X516 @ (prop2set @ ((X515))))|(X515))&((~(in @ X517 @ emptyset)|(X518))&((~(in @ X519 @ emptyset)|~($true))&(~(in @ X520 @ emptyset)&((((X521 @ (esk13_2 @ X521 @ X522))|~(X521 @ X522)|(X521 @ (esk14_1 @ X521)))&(((X522)!=(esk13_2 @ X521 @ X522))|~(X521 @ X522)|(X521 @ (esk14_1 @ X521))))&(((((in @ (esk16_2 @ X525 @ X526) @ X526)|((X525)=(X526))|(in @ (esk15_2 @ X525 @ X526) @ X525))&(~(in @ (esk16_2 @ X525 @ X526) @ X525)|((X525)=(X526))|(in @ (esk15_2 @ X525 @ X526) @ X525)))&(((in @ (esk16_2 @ X525 @ X526) @ X526)|((X525)=(X526))|~(in @ (esk15_2 @ X525 @ X526) @ X526))&(~(in @ (esk16_2 @ X525 @ X526) @ X525)|((X525)=(X526))|~(in @ (esk15_2 @ X525 @ X526) @ X526))))&(((in @ (esk17_1 @ X529) @ X529)|((X529)=(emptyset)))&(((in @ (esk18_1 @ X531) @ X531)|((X531)=(emptyset)))&(((~(in @ X535 @ (dsetconstr @ X533 @ X534))|(X534 @ X535)|~(in @ X535 @ X533))&(~(X534 @ X535)|(in @ X535 @ (dsetconstr @ X533 @ X534))|~(in @ X535 @ X533)))&((((X536)=(emptyset))|(in @ (esk19_1 @ X536) @ X536))&((~(in @ X540 @ X538)|(~(X539 @ X540)|((dsetconstr @ X538 @ X539)!=(emptyset))))&((~(in @ X542 @ X541)|((X541)!=(emptyset)))&((in @ X543 @ (setadjoin @ X543 @ X544))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X547 @ X546)|(in @ X547 @ (setadjoin @ X545 @ X546)))&(((((in @ X550 @ X549)|(X551)|((X550)=(X548))|~(in @ X550 @ (setadjoin @ X548 @ X549)))&(~(X551)|(X551)|((X550)=(X548))|~(in @ X550 @ (setadjoin @ X548 @ X549))))&(((in @ X550 @ X549)|(X551)|~(X551)|~(in @ X550 @ (setadjoin @ X548 @ X549)))&(~(X551)|(X551)|~(X551)|~(in @ X550 @ (setadjoin @ X548 @ X549)))))&((~(in @ X554 @ (setadjoin @ X552 @ X553))|(((X554)=(X552))|(in @ X554 @ X553)))&(((dsetconstr @ X555 @ (^[Z0:$i]:($true)))=(X555))&((((in @ (esk20_2 @ X556 @ X557) @ X557)|(in @ X557 @ (powerset @ X556)))&(~(in @ (esk20_2 @ X556 @ X557) @ X556)|(in @ X557 @ (powerset @ X556))))&((in @ emptyset @ (powerset @ X559))&((in @ emptyset @ (powerset @ X560))&((~(in @ X562 @ (powerset @ X561))|(~(in @ X563 @ X562)|(in @ X563 @ X561)))&((~(in @ X565 @ X566)|(~(in @ X566 @ X564)|(in @ X565 @ (setunion @ X564))))&((((in @ X568 @ (esk21_3 @ X567 @ X568 @ X569))|(X569)|~(in @ X568 @ (setunion @ X567)))&(((in @ (esk21_3 @ X567 @ X568 @ X569) @ X567)|(X569)|~(in @ X568 @ (setunion @ X567)))&(~(X569)|(X569)|~(in @ X568 @ (setunion @ X567)))))&((~(in @ X572 @ X571)|(in @ X572 @ (powerset @ (setunion @ X571))))&((((~(X573 @ X577)|((X577)=(esk23_1 @ X573))|((X573 @ (esk22_2 @ X573 @ X574))|~(X573 @ X574)))&(((X578)!=(esk23_1 @ X573))|(X573 @ X578)|((X573 @ (esk22_2 @ X573 @ X574))|~(X573 @ X574))))&((~(X573 @ X577)|((X577)=(esk23_1 @ X573))|(((X574)!=(esk22_2 @ X573 @ X574))|~(X573 @ X574)))&(((X578)!=(esk23_1 @ X573))|(X573 @ X578)|(((X574)!=(esk22_2 @ X573 @ X574))|~(X573 @ X574)))))&((((in @ (esk24_1 @ X579) @ X579)|((X579)=(emptyset)))&(($true)|((X579)=(emptyset))))&((~(in @ X581 @ (setadjoin @ X582 @ emptyset))|((X581)=(X582)))&((((X583)=(X584))|~(in @ X584 @ (setadjoin @ X583 @ emptyset)))&((((X585)!=(X586))|(in @ X585 @ (setadjoin @ X586 @ emptyset)))&((~(in @ X587 @ (setadjoin @ X588 @ emptyset))|(in @ X588 @ (setadjoin @ X587 @ emptyset)))&((~(in @ X591 @ (setadjoin @ X589 @ (setadjoin @ X590 @ emptyset)))|(((X591)=(X589))|((X591)=(X590))))&((in @ X592 @ (setadjoin @ X592 @ (setadjoin @ X593 @ emptyset)))&((in @ X595 @ (setadjoin @ X594 @ (setadjoin @ X595 @ emptyset)))&((~(in @ X598 @ X596)|~(X597 @ X598)|(((dsetconstr @ X596 @ X597)!=(emptyset))|~($true)))&((~(in @ X600 @ emptyset)|(X599 @ X600))&((((in @ (esk25_2 @ X601 @ X602) @ X601)|(~(in @ X603 @ X601)|(X602 @ X603)))&(~(X602 @ (esk25_2 @ X601 @ X602))|(~(in @ X603 @ X601)|(X602 @ X603))))&((((in @ (esk26_2 @ X605 @ X606) @ X605)|(~(in @ X608 @ X605)|~(X606 @ X608)))&((X606 @ (esk26_2 @ X605 @ X606))|(~(in @ X608 @ X605)|~(X606 @ X608))))&((((in @ (esk27_2 @ X609 @ X610) @ X609)|(~(in @ X612 @ X609)|~(X610 @ X612)))&((X610 @ (esk27_2 @ X609 @ X610))|(~(in @ X612 @ X609)|~(X610 @ X612))))&((((in @ (esk28_2 @ X613 @ X614) @ X613)|(~(in @ X615 @ X613)|(X614 @ X615)))&(~(X614 @ (esk28_2 @ X613 @ X614))|(~(in @ X615 @ X613)|(X614 @ X615))))&((~(X617)|(in @ emptyset @ (prop2set @ ((X617)))))&((~(X618)|(set2prop @ (prop2set @ ((X618)))))&((((in @ (esk29_2 @ X619 @ X620) @ X619)|(~(in @ X622 @ X619)|~(X620 @ X622)))&((X620 @ (esk29_2 @ X619 @ X620))|(~(in @ X622 @ X619)|~(X620 @ X622))))&((((in @ (esk30_2 @ X623 @ X624) @ X623)|(~(in @ X625 @ X623)|(X624 @ X625)))&(~(X624 @ (esk30_2 @ X623 @ X624))|(~(in @ X625 @ X623)|(X624 @ X625))))&(((((X627 @ (esk32_1 @ X627))|((X627 @ (esk31_2 @ X627 @ X628))|~(X627 @ X628)))&(~(X627 @ X631)|((esk32_1 @ X627)=(X631))|((X627 @ (esk31_2 @ X627 @ X628))|~(X627 @ X628))))&(((X627 @ (esk32_1 @ X627))|(((X628)!=(esk31_2 @ X627 @ X628))|~(X627 @ X628)))&(~(X627 @ X631)|((esk32_1 @ X627)=(X631))|(((X628)!=(esk31_2 @ X627 @ X628))|~(X627 @ X628)))))&(((((X632 @ (esk35_1 @ X632))|(X632 @ (esk33_1 @ X632))|~(X632 @ X633))&(~(X632 @ X637)|((esk35_1 @ X632)=(X637))|(X632 @ (esk33_1 @ X632))|~(X632 @ X633)))&((((X632 @ (esk35_1 @ X632))|(X632 @ (esk34_1 @ X632))|~(X632 @ X633))&(~(X632 @ X637)|((esk35_1 @ X632)=(X637))|(X632 @ (esk34_1 @ X632))|~(X632 @ X633)))&(((X632 @ (esk35_1 @ X632))|((esk33_1 @ X632)!=(esk34_1 @ X632))|~(X632 @ X633))&(~(X632 @ X637)|((esk35_1 @ X632)=(X637))|((esk33_1 @ X632)!=(esk34_1 @ X632))|~(X632 @ X633)))))&(((((X638 @ (esk37_1 @ X638))|(~(X638 @ (esk36_2 @ X638 @ X639))|((esk36_2 @ X638 @ X639)!=(X639))))&(~(X638 @ X642)|((esk37_1 @ X638)=(X642))|(~(X638 @ (esk36_2 @ X638 @ X639))|((esk36_2 @ X638 @ X639)!=(X639)))))&(((X638 @ (esk37_1 @ X638))|((X638 @ (esk36_2 @ X638 @ X639))|((esk36_2 @ X638 @ X639)=(X639))))&(~(X638 @ X642)|((esk37_1 @ X638)=(X642))|((X638 @ (esk36_2 @ X638 @ X639))|((esk36_2 @ X638 @ X639)=(X639))))))&((((X643)!=(X644))|(((X645)!=(X646))|(~(in @ X645 @ X643)|(in @ X646 @ X644))))&(((~(in @ X649 @ X647)|(in @ X650 @ X648)|((X649)!=(X650))|((X647)!=(X648)))&(~(in @ X650 @ X648)|(in @ X649 @ X647)|((X649)!=(X650))|((X647)!=(X648))))&((((X651 @ (esk38_2 @ X651 @ X652))|~(X651 @ X652)|(~(X651 @ X654)|(~(X651 @ X655)|((X654)=(X655)))))&(((X652)!=(esk38_2 @ X651 @ X652))|~(X651 @ X652)|(~(X651 @ X654)|(~(X651 @ X655)|((X654)=(X655))))))&(((((((X657 @ (esk42_2 @ X656 @ X657))|((X656 @ (esk41_3 @ X656 @ X657 @ X660))|~(X656 @ X660))|((esk39_2 @ X656 @ X657)=(esk40_2 @ X656 @ X657)))&(~(X657 @ X663)|((esk42_2 @ X656 @ X657)=(X663))|((X656 @ (esk41_3 @ X656 @ X657 @ X660))|~(X656 @ X660))|((esk39_2 @ X656 @ X657)=(esk40_2 @ X656 @ X657))))&(((X657 @ (esk42_2 @ X656 @ X657))|(((X660)!=(esk41_3 @ X656 @ X657 @ X660))|~(X656 @ X660))|((esk39_2 @ X656 @ X657)=(esk40_2 @ X656 @ X657)))&(~(X657 @ X663)|((esk42_2 @ X656 @ X657)=(X663))|(((X660)!=(esk41_3 @ X656 @ X657 @ X660))|~(X656 @ X660))|((esk39_2 @ X656 @ X657)=(esk40_2 @ X656 @ X657)))))&((((X656 @ (esk44_2 @ X656 @ X657))|((X657 @ (esk43_3 @ X656 @ X657 @ X664))|~(X657 @ X664))|((esk39_2 @ X656 @ X657)=(esk40_2 @ X656 @ X657)))&(~(X656 @ X667)|((esk44_2 @ X656 @ X657)=(X667))|((X657 @ (esk43_3 @ X656 @ X657 @ X664))|~(X657 @ X664))|((esk39_2 @ X656 @ X657)=(esk40_2 @ X656 @ X657))))&(((X656 @ (esk44_2 @ X656 @ X657))|(((X664)!=(esk43_3 @ X656 @ X657 @ X664))|~(X657 @ X664))|((esk39_2 @ X656 @ X657)=(esk40_2 @ X656 @ X657)))&(~(X656 @ X667)|((esk44_2 @ X656 @ X657)=(X667))|(((X664)!=(esk43_3 @ X656 @ X657 @ X664))|~(X657 @ X664))|((esk39_2 @ X656 @ X657)=(esk40_2 @ X656 @ X657))))))&((((((X657 @ (esk42_2 @ X656 @ X657))|((X656 @ (esk41_3 @ X656 @ X657 @ X660))|~(X656 @ X660))|(~(X656 @ (esk39_2 @ X656 @ X657))|~(X657 @ (esk40_2 @ X656 @ X657))))&(~(X657 @ X663)|((esk42_2 @ X656 @ X657)=(X663))|((X656 @ (esk41_3 @ X656 @ X657 @ X660))|~(X656 @ X660))|(~(X656 @ (esk39_2 @ X656 @ X657))|~(X657 @ (esk40_2 @ X656 @ X657)))))&(((X657 @ (esk42_2 @ X656 @ X657))|(((X660)!=(esk41_3 @ X656 @ X657 @ X660))|~(X656 @ X660))|(~(X656 @ (esk39_2 @ X656 @ X657))|~(X657 @ (esk40_2 @ X656 @ X657))))&(~(X657 @ X663)|((esk42_2 @ X656 @ X657)=(X663))|(((X660)!=(esk41_3 @ X656 @ X657 @ X660))|~(X656 @ X660))|(~(X656 @ (esk39_2 @ X656 @ X657))|~(X657 @ (esk40_2 @ X656 @ X657))))))&((((X656 @ (esk44_2 @ X656 @ X657))|((X657 @ (esk43_3 @ X656 @ X657 @ X664))|~(X657 @ X664))|(~(X656 @ (esk39_2 @ X656 @ X657))|~(X657 @ (esk40_2 @ X656 @ X657))))&(~(X656 @ X667)|((esk44_2 @ X656 @ X657)=(X667))|((X657 @ (esk43_3 @ X656 @ X657 @ X664))|~(X657 @ X664))|(~(X656 @ (esk39_2 @ X656 @ X657))|~(X657 @ (esk40_2 @ X656 @ X657)))))&(((X656 @ (esk44_2 @ X656 @ X657))|(((X664)!=(esk43_3 @ X656 @ X657 @ X664))|~(X657 @ X664))|(~(X656 @ (esk39_2 @ X656 @ X657))|~(X657 @ (esk40_2 @ X656 @ X657))))&(~(X656 @ X667)|((esk44_2 @ X656 @ X657)=(X667))|(((X664)!=(esk43_3 @ X656 @ X657 @ X664))|~(X657 @ X664))|(~(X656 @ (esk39_2 @ X656 @ X657))|~(X657 @ (esk40_2 @ X656 @ X657)))))))&(((((X657 @ (esk42_2 @ X656 @ X657))|((X656 @ (esk41_3 @ X656 @ X657 @ X660))|~(X656 @ X660))|((X656 @ (esk39_2 @ X656 @ X657))|(X657 @ (esk40_2 @ X656 @ X657))))&(~(X657 @ X663)|((esk42_2 @ X656 @ X657)=(X663))|((X656 @ (esk41_3 @ X656 @ X657 @ X660))|~(X656 @ X660))|((X656 @ (esk39_2 @ X656 @ X657))|(X657 @ (esk40_2 @ X656 @ X657)))))&(((X657 @ (esk42_2 @ X656 @ X657))|(((X660)!=(esk41_3 @ X656 @ X657 @ X660))|~(X656 @ X660))|((X656 @ (esk39_2 @ X656 @ X657))|(X657 @ (esk40_2 @ X656 @ X657))))&(~(X657 @ X663)|((esk42_2 @ X656 @ X657)=(X663))|(((X660)!=(esk41_3 @ X656 @ X657 @ X660))|~(X656 @ X660))|((X656 @ (esk39_2 @ X656 @ X657))|(X657 @ (esk40_2 @ X656 @ X657))))))&((((X656 @ (esk44_2 @ X656 @ X657))|((X657 @ (esk43_3 @ X656 @ X657 @ X664))|~(X657 @ X664))|((X656 @ (esk39_2 @ X656 @ X657))|(X657 @ (esk40_2 @ X656 @ X657))))&(~(X656 @ X667)|((esk44_2 @ X656 @ X657)=(X667))|((X657 @ (esk43_3 @ X656 @ X657 @ X664))|~(X657 @ X664))|((X656 @ (esk39_2 @ X656 @ X657))|(X657 @ (esk40_2 @ X656 @ X657)))))&(((X656 @ (esk44_2 @ X656 @ X657))|(((X664)!=(esk43_3 @ X656 @ X657 @ X664))|~(X657 @ X664))|((X656 @ (esk39_2 @ X656 @ X657))|(X657 @ (esk40_2 @ X656 @ X657))))&(~(X656 @ X667)|((esk44_2 @ X656 @ X657)=(X667))|(((X664)!=(esk43_3 @ X656 @ X657 @ X664))|~(X657 @ X664))|((X656 @ (esk39_2 @ X656 @ X657))|(X657 @ (esk40_2 @ X656 @ X657)))))))))&(((emptyset)=(emptyset))&((((X668)!=(X669))|(((X670)!=(X671))|((setadjoin @ X668 @ X670)=(setadjoin @ X669 @ X671))))&((((X672)!=(X673))|((powerset @ X672)=(powerset @ X673)))&((((X674)!=(X675))|((setunion @ X674)=(setunion @ X675)))&((omega)!=(omega)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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_109])])])])])])])).
% 0.23/0.30 thf(c_0_111, negated_conjecture, ((omega)!=(omega)), inference(split_conjunct,[status(thm)],[c_0_110])).
% 0.23/0.30 thf(c_0_112, negated_conjecture, ($false), inference(cn,[status(thm)],[c_0_111]), ['proof']).
% 0.23/0.30 % SZS output end CNFRefutation
% 0.23/0.30 % Parsed axioms : 157
% 0.23/0.30 % Removed by relevancy pruning/SinE : 83
% 0.23/0.30 % Initial clauses : 164
% 0.23/0.30 % Removed in clause preprocessing : 12
% 0.23/0.30 % Initial clauses in saturation : 152
% 0.23/0.30 % Processed clauses : 1
% 0.23/0.30 % ...of these trivial : 0
% 0.23/0.30 % ...subsumed : 0
% 0.23/0.30 % ...remaining for further processing : 0
% 0.23/0.30 % Other redundant clauses eliminated : 0
% 0.23/0.30 % Clauses deleted for lack of memory : 0
% 0.23/0.30 % Backward-subsumed : 0
% 0.23/0.30 % Backward-rewritten : 0
% 0.23/0.30 % Generated clauses : 0
% 0.23/0.30 % ...of the previous two non-redundant : 0
% 0.23/0.30 % ...aggressively subsumed : 0
% 0.23/0.30 % Contextual simplify-reflections : 0
% 0.23/0.30 % Paramodulations : 0
% 0.23/0.30 % Factorizations : 0
% 0.23/0.30 % NegExts : 0
% 0.23/0.30 % Equation resolutions : 0
% 0.23/0.30 % Disequality decompositions : 0
% 0.23/0.30 % Total rewrite steps : 0
% 0.23/0.30 % ...of those cached : 0
% 0.23/0.30 % Propositional unsat checks : 0
% 0.23/0.30 % Propositional check models : 0
% 0.23/0.30 % Propositional check unsatisfiable : 0
% 0.23/0.30 % Propositional clauses : 0
% 0.23/0.30 % Propositional clauses after purity: 0
% 0.23/0.30 % Propositional unsat core size : 0
% 0.23/0.30 % Propositional preprocessing time : 0.000
% 0.23/0.30 % Propositional encoding time : 0.000
% 0.23/0.30 % Propositional solver time : 0.000
% 0.23/0.30 % Success case prop preproc time : 0.000
% 0.23/0.30 % Success case prop encoding time : 0.000
% 0.23/0.30 % Success case prop solver time : 0.000
% 0.23/0.30 % Current number of processed clauses : 0
% 0.23/0.30 % Positive orientable unit clauses : 0
% 0.23/0.30 % Positive unorientable unit clauses: 0
% 0.23/0.30 % Negative unit clauses : 0
% 0.23/0.30 % Non-unit-clauses : 0
% 0.23/0.30 % Current number of unprocessed clauses: 151
% 0.23/0.30 % ...number of literals in the above : 505
% 0.23/0.30 % Current number of archived formulas : 0
% 0.23/0.30 % Current number of archived clauses : 0
% 0.23/0.30 % Clause-clause subsumption calls (NU) : 0
% 0.23/0.30 % Rec. Clause-clause subsumption calls : 0
% 0.23/0.30 % Non-unit clause-clause subsumptions : 0
% 0.23/0.30 % Unit Clause-clause subsumption calls : 0
% 0.23/0.30 % Rewrite failures with RHS unbound : 0
% 0.23/0.30 % BW rewrite match attempts : 0
% 0.23/0.30 % BW rewrite match successes : 0
% 0.23/0.30 % Condensation attempts : 0
% 0.23/0.30 % Condensation successes : 0
% 0.23/0.30 % Termbank termtop insertions : 19866
% 0.23/0.30 % Search garbage collected termcells : 7972
% 0.23/0.30
% 0.23/0.30 % -------------------------------------------------
% 0.23/0.30 % User time : 0.013 s
% 0.23/0.30 % System time : 0.008 s
% 0.23/0.30 % Total time : 0.021 s
% 0.23/0.30 % Maximum resident set size: 5840 pages
% 0.23/0.30
% 0.23/0.30 % -------------------------------------------------
% 0.23/0.30 % User time : 0.018 s
% 0.23/0.30 % System time : 0.013 s
% 0.23/0.30 % Total time : 0.030 s
% 0.23/0.30 % Maximum resident set size: 5120 pages
% 0.23/0.30 % E exiting
%------------------------------------------------------------------------------