%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU547^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 08:26:40 AM UTC 2026
% Result : Theorem 0.23s 0.30s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU547^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n014.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 13:49:15 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.25 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p
% 0.23/0.30 % Version: 3.5.1-ho
% 0.23/0.30 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.23/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.30 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.30 % Starting sh5l with 300s (1) cores
% 0.23/0.30 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.30 % Starting new_bool_2 with 300s (1) cores
% 0.23/0.30 % sh5l with pid 2691741 completed with status 0
% 0.23/0.30 % Result found by sh5l
% 0.23/0.30 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.23/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.30 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.30 % Starting sh5l with 300s (1) cores
% 0.23/0.30 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.23/0.30 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.23/0.30 % Search class: HGHSM-FFMM31-SHFMMSBN
% 0.23/0.30 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.30 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.30 % SubtermCWHack with pid 2691749 completed with status 0
% 0.23/0.30 % Result found by SubtermCWHack
% 0.23/0.30 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.23/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.30 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.30 % Starting sh5l with 300s (1) cores
% 0.23/0.30 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.23/0.30 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.23/0.30 % Search class: HGHSM-FFMM31-SHFMMSBN
% 0.23/0.30 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.30 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.30 % Preprocessing time : 0.002 s
% 0.23/0.30
% 0.23/0.30 % Proof found!
% 0.23/0.30 % SZS status Theorem
% 0.23/0.30 % SZS output start CNFRefutation
% 0.23/0.30 thf(decl_23, type, in: $i > $i > $o).
% 0.23/0.30 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.23/0.30 thf(decl_25, type, setextAx: $o).
% 0.23/0.30 thf(decl_26, type, emptyset: $i).
% 0.23/0.30 thf(decl_27, type, emptysetAx: $o).
% 0.23/0.30 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.23/0.30 thf(decl_29, type, setadjoinAx: $o).
% 0.23/0.30 thf(decl_30, type, powerset: $i > $i).
% 0.23/0.30 thf(decl_31, type, powersetAx: $o).
% 0.23/0.30 thf(decl_32, type, setunion: $i > $i).
% 0.23/0.30 thf(decl_33, type, setunionAx: $o).
% 0.23/0.30 thf(decl_34, type, omega: $i).
% 0.23/0.30 thf(decl_35, type, omega0Ax: $o).
% 0.23/0.30 thf(decl_36, type, omegaSAx: $o).
% 0.23/0.30 thf(decl_37, type, omegaIndAx: $o).
% 0.23/0.30 thf(decl_38, type, replAx: $o).
% 0.23/0.30 thf(decl_39, type, foundationAx: $o).
% 0.23/0.30 thf(decl_40, type, wellorderingAx: $o).
% 0.23/0.30 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.23/0.30 thf(decl_42, type, descrp: $o).
% 0.23/0.30 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.23/0.30 thf(decl_44, type, dsetconstrI: $o).
% 0.23/0.30 thf(decl_45, type, dsetconstrEL: $o).
% 0.23/0.30 thf(decl_46, type, dsetconstrER: $o).
% 0.23/0.30 thf(decl_47, type, exuE1: $o).
% 0.23/0.30 thf(decl_48, type, prop2set: $o > $i).
% 0.23/0.30 thf(decl_49, type, prop2setE: $o).
% 0.23/0.30 thf(decl_50, type, emptysetE: $o).
% 0.23/0.30 thf(decl_51, type, emptysetimpfalse: $o).
% 0.23/0.30 thf(decl_52, type, notinemptyset: $o).
% 0.23/0.30 thf(decl_53, type, exuE3e: $o).
% 0.23/0.30 thf(decl_54, type, setext: $o).
% 0.23/0.30 thf(decl_55, type, emptyI: $o).
% 0.23/0.30 thf(decl_56, type, noeltsimpempty: $o).
% 0.23/0.30 thf(decl_57, type, setbeta: $o).
% 0.23/0.30 thf(decl_58, type, nonempty: $i > $o).
% 0.23/0.30 thf(decl_59, type, nonemptyE1: $o).
% 0.23/0.30 thf(decl_60, type, nonemptyI: $o).
% 0.23/0.30 thf(decl_61, type, nonemptyI1: $o).
% 0.23/0.30 thf(decl_62, type, setadjoinIL: $o).
% 0.23/0.30 thf(decl_63, type, emptyinunitempty: $o).
% 0.23/0.30 thf(decl_64, type, setadjoinIR: $o).
% 0.23/0.30 thf(decl_65, type, setadjoinE: $o).
% 0.23/0.30 thf(decl_66, type, setadjoinOr: $o).
% 0.23/0.30 thf(decl_67, type, setoftrueEq: $o).
% 0.23/0.30 thf(decl_68, type, powersetI: $o).
% 0.23/0.30 thf(decl_69, type, emptyinPowerset: $o).
% 0.23/0.30 thf(decl_70, type, emptyInPowerset: $o).
% 0.23/0.30 thf(decl_71, type, powersetE: $o).
% 0.23/0.30 thf(decl_72, type, setunionI: $o).
% 0.23/0.30 thf(decl_73, type, setunionE: $o).
% 0.23/0.30 thf(decl_74, type, subPowSU: $o).
% 0.23/0.30 thf(decl_75, type, exuE2: $o).
% 0.23/0.30 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.23/0.30 thf(decl_77, type, uniqinunit: $o).
% 0.23/0.30 thf(decl_78, type, notinsingleton: $o).
% 0.23/0.30 thf(decl_79, type, eqinunit: $o).
% 0.23/0.30 thf(decl_80, type, singletonsswitch: $o).
% 0.23/0.30 thf(decl_81, type, upairsetE: $o).
% 0.23/0.30 thf(decl_82, type, upairsetIL: $o).
% 0.23/0.30 thf(decl_83, type, upairsetIR: $o).
% 0.23/0.30 thf(decl_84, type, emptyE1: $o).
% 0.23/0.30 thf(decl_85, type, vacuousDall: $o).
% 0.23/0.30 thf(decl_86, type, quantDeMorgan1: $o).
% 0.23/0.30 thf(decl_87, type, quantDeMorgan2: $o).
% 0.23/0.30 thf(decl_88, type, quantDeMorgan3: $o).
% 0.23/0.30 thf(decl_89, type, quantDeMorgan4: $o).
% 0.23/0.30 thf(decl_90, type, prop2setI: $o).
% 0.23/0.30 thf(decl_91, type, set2prop: $i > $o).
% 0.23/0.30 thf(decl_92, type, prop2set2propI: $o).
% 0.23/0.30 thf(decl_93, type, notdexE: $o).
% 0.23/0.30 thf(decl_94, type, notdallE: $o).
% 0.23/0.30 thf(decl_95, type, exuI1: $o).
% 0.23/0.30 thf(decl_96, type, exuI3: $o).
% 0.23/0.30 thf(decl_97, type, exuI2: $o).
% 0.23/0.30 thf(decl_98, type, epred1_0: $o).
% 0.23/0.30 thf(decl_99, type, esk1_2: $i > $i > $i).
% 0.23/0.30 thf(decl_100, type, esk2_2: $i > $i > $i).
% 0.23/0.30 thf(decl_101, type, esk3_2: $i > $i > $i).
% 0.23/0.30 thf(decl_102, type, esk4_1: $i > $i).
% 0.23/0.30 thf(decl_103, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.23/0.30 thf(decl_104, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.23/0.30 thf(decl_105, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.23/0.30 thf(decl_106, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.23/0.30 thf(decl_107, type, esk9_1: $i > $i).
% 0.23/0.30 thf(decl_108, type, esk10_2: ($i > $o) > $i > $i).
% 0.23/0.30 thf(decl_109, type, esk11_2: ($i > $o) > $i > $i).
% 0.23/0.30 thf(decl_110, type, esk12_1: ($i > $o) > $i).
% 0.23/0.30 thf(decl_111, type, esk13_2: ($i > $o) > $i > $i).
% 0.23/0.30 thf(decl_112, type, esk14_1: ($i > $o) > $i).
% 0.23/0.30 thf(decl_113, type, esk15_2: $i > $i > $i).
% 0.23/0.30 thf(decl_114, type, esk16_2: $i > $i > $i).
% 0.23/0.30 thf(decl_115, type, esk17_1: $i > $i).
% 0.23/0.30 thf(decl_116, type, esk18_1: $i > $i).
% 0.23/0.30 thf(decl_117, type, esk19_1: $i > $i).
% 0.23/0.30 thf(decl_118, type, esk20_2: $i > $i > $i).
% 0.23/0.30 thf(decl_119, type, esk21_3: $i > $i > $o > $i).
% 0.23/0.30 thf(decl_120, type, esk22_2: ($i > $o) > $i > $i).
% 0.23/0.30 thf(decl_121, type, esk23_1: ($i > $o) > $i).
% 0.23/0.30 thf(decl_122, type, esk24_1: $i > $i).
% 0.23/0.30 thf(decl_123, type, esk25_2: $i > ($i > $o) > $i).
% 0.23/0.30 thf(decl_124, type, esk26_2: $i > ($i > $o) > $i).
% 0.23/0.30 thf(decl_125, type, esk27_2: $i > ($i > $o) > $i).
% 0.23/0.30 thf(decl_126, type, esk28_2: $i > ($i > $o) > $i).
% 0.23/0.30 thf(decl_127, type, esk29_2: $i > ($i > $o) > $i).
% 0.23/0.30 thf(decl_128, type, esk30_2: $i > ($i > $o) > $i).
% 0.23/0.30 thf(decl_129, type, esk31_2: ($i > $o) > $i > $i).
% 0.23/0.30 thf(decl_130, type, esk32_1: ($i > $o) > $i).
% 0.23/0.30 thf(decl_131, type, esk33_1: ($i > $o) > $i).
% 0.23/0.30 thf(decl_132, type, esk34_1: ($i > $o) > $i).
% 0.23/0.30 thf(decl_133, type, esk35_1: ($i > $o) > $i).
% 0.23/0.30 thf(decl_134, type, esk36_2: ($i > $o) > $i > $i).
% 0.23/0.30 thf(decl_135, type, esk37_1: ($i > $o) > $i).
% 0.23/0.30 thf(decl_136, type, esk38_0: $i).
% 0.23/0.30 thf(decl_137, type, esk39_0: $i).
% 0.23/0.30 thf(decl_138, type, esk40_0: $i).
% 0.23/0.30 thf(decl_139, type, esk41_0: $i).
% 0.23/0.30 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', replAx)).
% 0.23/0.30 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', exu)).
% 0.23/0.30 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', exuI1)).
% 0.23/0.30 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', exuI3)).
% 0.23/0.30 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', exuI2)).
% 0.23/0.30 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', descrp)).
% 0.23/0.30 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', nonempty)).
% 0.23/0.30 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.vOo34dzm9b/E---3.1_2691704.p', exuE1)).
% 0.23/0.30 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', exuE3e)).
% 0.23/0.30 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', nonemptyI)).
% 0.23/0.30 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', exuE2)).
% 0.23/0.30 thf(inCongP, 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)=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', inCongP)).
% 0.23/0.30 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.vOo34dzm9b/E---3.1_2691704.p', emptyE1)).
% 0.23/0.30 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', dsetconstrER)).
% 0.23/0.30 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', dsetconstrEL)).
% 0.23/0.30 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', dsetconstrI)).
% 0.23/0.30 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', nonemptyE1)).
% 0.23/0.30 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', setbeta)).
% 0.23/0.30 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', nonemptyI1)).
% 0.23/0.30 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', setoftrueEq)).
% 0.23/0.30 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', nonemptyImpWitness)).
% 0.23/0.30 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', quantDeMorgan2)).
% 0.23/0.30 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', upairsetIL)).
% 0.23/0.30 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', upairsetIR)).
% 0.23/0.30 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', quantDeMorgan3)).
% 0.23/0.30 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', quantDeMorgan4)).
% 0.23/0.30 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', prop2setI)).
% 0.23/0.30 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', prop2set2propI)).
% 0.23/0.30 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', notdexE)).
% 0.23/0.30 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', notdallE)).
% 0.23/0.30 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.vOo34dzm9b/E---3.1_2691704.p', wellorderingAx)).
% 0.23/0.30 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.vOo34dzm9b/E---3.1_2691704.p', foundationAx)).
% 0.23/0.30 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', emptyI)).
% 0.23/0.30 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.vOo34dzm9b/E---3.1_2691704.p', setext)).
% 0.23/0.30 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', notinemptyset)).
% 0.23/0.30 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', emptysetimpfalse)).
% 0.23/0.30 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', emptysetE)).
% 0.23/0.30 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', prop2setE)).
% 0.23/0.30 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', noeltsimpempty)).
% 0.23/0.30 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', setadjoinIR)).
% 0.23/0.30 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', emptyinunitempty)).
% 0.23/0.30 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', setadjoinIL)).
% 0.23/0.30 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.vOo34dzm9b/E---3.1_2691704.p', setadjoinE)).
% 0.23/0.30 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', setunionI)).
% 0.23/0.30 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', powersetE)).
% 0.23/0.30 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', emptyInPowerset)).
% 0.23/0.30 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', emptyinPowerset)).
% 0.23/0.30 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', powersetI)).
% 0.23/0.30 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', setadjoinOr)).
% 0.23/0.30 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.vOo34dzm9b/E---3.1_2691704.p', setunionE)).
% 0.23/0.30 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', singletonsswitch)).
% 0.23/0.30 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', eqinunit)).
% 0.23/0.30 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', notinsingleton)).
% 0.23/0.30 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', uniqinunit)).
% 0.23/0.30 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', vacuousDall)).
% 0.23/0.30 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', subPowSU)).
% 0.23/0.30 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', quantDeMorgan1)).
% 0.23/0.30 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', upairsetE)).
% 0.23/0.30 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', omegaIndAx)).
% 0.23/0.30 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', omegaSAx)).
% 0.23/0.30 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', omega0Ax)).
% 0.23/0.30 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', setunionAx)).
% 0.23/0.30 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', powersetAx)).
% 0.23/0.30 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', setadjoinAx)).
% 0.23/0.30 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', emptysetAx)).
% 0.23/0.30 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.vOo34dzm9b/E---3.1_2691704.p', setextAx)).
% 0.23/0.30 thf(c_0_66, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.23/0.30 thf(c_0_67, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.23/0.30 thf(c_0_68, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 0.23/0.30 thf(c_0_69, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.23/0.30 thf(c_0_70, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.23/0.30 thf(c_0_71, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.23/0.30 thf(c_0_72, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.23/0.30 thf(c_0_73, 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])).
% 0.23/0.30 thf(c_0_74, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.23/0.30 thf(c_0_75, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.23/0.30 thf(c_0_76, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.23/0.30 thf(c_0_77, 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)=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[inCongP])).
% 0.23/0.30 thf(c_0_78, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X197:$i]:(((((X6 @ X2 @ X197)))&(![X198:$i]:(((((X6 @ X2 @ X198)))=>(((X197)=(X198)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_66, c_0_67])).
% 0.23/0.30 thf(c_0_79, 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])).
% 0.23/0.30 thf(c_0_80, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X207:$i]:(((((X1 @ X207)))&(![X208:$i]:(((((X1 @ X208)))=>(((X207)=(X208)))))))))))))), inference(apply_def,[status(thm)],[c_0_68, c_0_67])).
% 0.23/0.30 thf(c_0_81, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X209:$i]:(((((X1 @ X209)))&(![X210:$i]:(((((X1 @ X210)))=>(((X209)=(X210)))))))))))))))), inference(apply_def,[status(thm)],[c_0_69, c_0_67])).
% 0.23/0.30 thf(c_0_82, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X211:$i]:(((((X1 @ X211)))&(![X212:$i]:(((((X1 @ X212)))=>(((X211)=(X212)))))))))))))), inference(apply_def,[status(thm)],[c_0_70, c_0_67])).
% 0.23/0.30 thf(c_0_83, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.23/0.30 thf(c_0_84, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.23/0.30 thf(c_0_85, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.23/0.30 thf(c_0_86, plain, ((descrp)=(![X1:$i > $o]:((((?[X199:$i]:(((((X1 @ X199)))&(![X200:$i]:(((((X1 @ X200)))=>(((X199)=(X200))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_71, c_0_67])).
% 0.23/0.30 thf(c_0_87, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_72])).
% 0.23/0.30 thf(c_0_88, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.23/0.30 thf(c_0_89, plain, ((exuE1)=(![X1:$i > $o]:((((?[X201:$i]:(((((X1 @ X201)))&(![X202:$i]:(((((X1 @ X202)))=>(((X201)=(X202))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_73, c_0_67])).
% 0.23/0.30 thf(c_0_90, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X203:$i]:(((((X1 @ X203)))&(![X204:$i]:(((((X1 @ X204)))=>(((X203)=(X204))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_74, c_0_67])).
% 0.23/0.30 thf(c_0_91, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_72])).
% 0.23/0.30 thf(c_0_92, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_75, c_0_72])).
% 0.23/0.30 thf(c_0_93, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.23/0.30 thf(c_0_94, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_72])).
% 0.23/0.30 thf(c_0_95, plain, ((exuE2)=(![X1:$i > $o]:((((?[X205:$i]:(((((X1 @ X205)))&(![X206:$i]:(((((X1 @ X206)))=>(((X205)=(X206))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_76, c_0_67])).
% 0.23/0.30 thf(c_0_96, plain, ((epred1_0)<=>![X242:$i]:(?[X243:$i]:((((![X244:$i]:(((in @ X244 @ X243)=>![X245:$i]:(((in @ X245 @ X244)=>(in @ X245 @ X242)))))&![X246:$i, X247:$i]:((((in @ X246 @ X242)&(in @ X247 @ X242))=>(![X248:$i]:(((in @ X248 @ X243)=>((in @ X246 @ X248)<=>(in @ X247 @ X248))))=>((X246)=(X247))))))&![X249:$i, X250:$i]:((((in @ X249 @ X243)&(in @ X250 @ X243))=>(![X251:$i]:(((in @ X251 @ X249)=>(in @ X251 @ X250)))|![X252:$i]:(((in @ X252 @ X250)=>(in @ X252 @ X249)))))))&![X253:$i]:(((![X254:$i]:(((in @ X254 @ X253)=>(in @ X254 @ X242)))&?[X255:$i]:((in @ X255 @ X253)))=>?[X256:$i, X257:$i]:(((((in @ X256 @ X243)&(in @ X257 @ X253))&~(?[X258:$i]:(((in @ X258 @ X256)&(in @ X258 @ X253)))))&![X259:$i]:(((in @ X259 @ X243)=>(![X260:$i]:(((in @ X260 @ X259)=>(in @ X260 @ X256)))|(in @ X257 @ X259)))))))))))), introduced(definition)).
% 0.23/0.30 thf(c_0_97, negated_conjecture, ~((![X213:$i, X214:$i]:((![X215:$i]:(((in @ X215 @ X213)<=>(in @ X215 @ X214)))=>((X213)=(X214))))=>(![X216:$i]:(~(in @ X216 @ emptyset))=>(![X217:$i, X218:$i, X219:$i]:(((in @ X219 @ (setadjoin @ X217 @ X218))<=>(((X219)=(X217))|(in @ X219 @ X218))))=>(![X220:$i, X221:$i]:(((in @ X221 @ (powerset @ X220))<=>![X222:$i]:(((in @ X222 @ X221)=>(in @ X222 @ X220)))))=>(![X223:$i, X224:$i]:(((in @ X224 @ (setunion @ X223))<=>?[X225:$i]:(((in @ X224 @ X225)&(in @ X225 @ X223)))))=>((in @ emptyset @ omega)=>(![X226:$i]:(((in @ X226 @ omega)=>(in @ (setadjoin @ X226 @ X226) @ omega)))=>(![X227:$i]:((((in @ emptyset @ X227)&![X228:$i]:((((in @ X228 @ omega)&(in @ X228 @ X227))=>(in @ (setadjoin @ X228 @ X228) @ X227))))=>![X229:$i]:(((in @ X229 @ omega)=>(in @ X229 @ X227)))))=>(![X230:$i > $i > $o, X231:$i]:((![X232:$i]:(((in @ X232 @ X231)=>?[X233:$i]:(((X230 @ X232 @ X233)&![X234:$i]:(((X230 @ X232 @ X234)=>((X233)=(X234))))))))=>?[X235:$i]:(![X236:$i]:(((in @ X236 @ X235)<=>?[X237:$i]:(((in @ X237 @ X231)&(X230 @ X237 @ X236))))))))=>(![X238:$i]:((?[X239:$i]:((in @ X239 @ X238))=>?[X240:$i]:(((in @ X240 @ X238)&~(?[X241:$i]:(((in @ X241 @ X240)&(in @ X241 @ X238))))))))=>((epred1_0)=>(![X261:$i > $o]:((?[X262:$i]:(((X261 @ X262)&![X263:$i]:(((X261 @ X263)=>((X262)=(X263))))))=>(X261 @ (descr @ (^[Z0:$i]:(X261 @ Z0))))))=>(![X264:$i, X265:$i > $o, X266:$i]:(((in @ X266 @ X264)=>((X265 @ X266)=>(in @ X266 @ (dsetconstr @ X264 @ X265)))))=>(![X267:$i, X268:$i > $o, X269:$i]:(((in @ X269 @ (dsetconstr @ X267 @ X268))=>(in @ X269 @ X267)))=>(![X270:$i, X271:$i > $o, X272:$i]:(((in @ X272 @ (dsetconstr @ X270 @ X271))=>(X271 @ X272)))=>(![X273:$i > $o]:((?[X274:$i]:(((X273 @ X274)&![X275:$i]:(((X273 @ X275)=>((X274)=(X275))))))=>?[X276:$i]:(((X273 @ X276)&![X277:$i]:(((X273 @ X277)=>((X276)=(X277))))))))=>(![X278:$o, X279:$i]:(((in @ X279 @ (prop2set @ ((X278))))=>(X278)))=>(![X280:$i]:(((in @ X280 @ emptyset)=>![X281:$o]:((X281))))=>(![X282:$i]:(((in @ X282 @ emptyset)=>~($true)))=>(![X283:$i]:(~(in @ X283 @ emptyset))=>(![X284:$i > $o]:((?[X285:$i]:(((X284 @ X285)&![X286:$i]:(((X284 @ X286)=>((X285)=(X286))))))=>?[X287:$i]:((X284 @ X287))))=>(![X288:$i, X289:$i]:((![X290:$i]:(((in @ X290 @ X288)=>(in @ X290 @ X289)))=>(![X291:$i]:(((in @ X291 @ X289)=>(in @ X291 @ X288)))=>((X288)=(X289)))))=>(![X292:$i]:((![X293:$i]:(~(in @ X293 @ X292))=>((X292)=(emptyset))))=>(![X294:$i]:((![X295:$i]:(~(in @ X295 @ X294))=>((X294)=(emptyset))))=>(![X296:$i, X297:$i > $o, X298:$i]:(((in @ X298 @ X296)=>((in @ X298 @ (dsetconstr @ X296 @ X297))<=>(X297 @ X298))))=>(![X299:$i]:((((X299)!=(emptyset))=>?[X300:$i]:((in @ X300 @ X299))))=>(![X301:$i, X302:$i > $o, X303:$i]:(((in @ X303 @ X301)=>((X302 @ X303)=>((dsetconstr @ X301 @ X302)!=(emptyset)))))=>(![X304:$i]:((?[X305:$i]:((in @ X305 @ X304))=>((X304)!=(emptyset))))=>(![X306:$i, X307:$i]:((in @ X306 @ (setadjoin @ X306 @ X307)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X308:$i, X309:$i, X310:$i]:(((in @ X310 @ X309)=>(in @ X310 @ (setadjoin @ X308 @ X309))))=>(![X311:$i, X312:$i, X313:$i]:(((in @ X313 @ (setadjoin @ X311 @ X312))=>![X314:$o]:(((((X313)=(X311))=>(X314))=>(((in @ X313 @ X312)=>(X314))=>(X314))))))=>(![X315:$i, X316:$i, X317:$i]:(((in @ X317 @ (setadjoin @ X315 @ X316))=>(((X317)=(X315))|(in @ X317 @ X316))))=>(![X318:$i]:(((dsetconstr @ X318 @ (^[Z0:$i]:($true)))=(X318)))=>(![X319:$i, X320:$i]:((![X321:$i]:(((in @ X321 @ X320)=>(in @ X321 @ X319)))=>(in @ X320 @ (powerset @ X319))))=>(![X322:$i]:((in @ emptyset @ (powerset @ X322)))=>(![X323:$i]:((in @ emptyset @ (powerset @ X323)))=>(![X324:$i, X325:$i, X326:$i]:(((in @ X325 @ (powerset @ X324))=>((in @ X326 @ X325)=>(in @ X326 @ X324))))=>(![X327:$i, X328:$i, X329:$i]:(((in @ X328 @ X329)=>((in @ X329 @ X327)=>(in @ X328 @ (setunion @ X327)))))=>(![X330:$i, X331:$i]:(((in @ X331 @ (setunion @ X330))=>![X332:$o]:((![X333:$i]:(((in @ X331 @ X333)=>((in @ X333 @ X330)=>(X332))))=>(X332)))))=>(![X334:$i, X335:$i]:(((in @ X335 @ X334)=>(in @ X335 @ (powerset @ (setunion @ X334)))))=>(![X336:$i > $o]:((?[X337:$i]:(((X336 @ X337)&![X338:$i]:(((X336 @ X338)=>((X337)=(X338))))))=>?[X339:$i]:(![X340:$i]:(((X336 @ X340)<=>((X340)=(X339)))))))=>(![X341:$i]:((((X341)!=(emptyset))=>?[X342:$i]:(((in @ X342 @ X341)&$true))))=>(![X343:$i, X344:$i]:(((in @ X343 @ (setadjoin @ X344 @ emptyset))=>((X343)=(X344))))=>(![X345:$i, X346:$i]:((((X345)!=(X346))=>~(in @ X346 @ (setadjoin @ X345 @ emptyset))))=>(![X347:$i, X348:$i]:((((X347)=(X348))=>(in @ X347 @ (setadjoin @ X348 @ emptyset))))=>(![X349:$i, X350:$i]:(((in @ X349 @ (setadjoin @ X350 @ emptyset))=>(in @ X350 @ (setadjoin @ X349 @ emptyset))))=>(![X351:$i, X352:$i, X353:$i]:(((in @ X353 @ (setadjoin @ X351 @ (setadjoin @ X352 @ emptyset)))=>(((X353)=(X351))|((X353)=(X352)))))=>(![X354:$i, X355:$i]:((in @ X354 @ (setadjoin @ X354 @ (setadjoin @ X355 @ emptyset))))=>(![X356:$i, X357:$i]:((in @ X357 @ (setadjoin @ X356 @ (setadjoin @ X357 @ emptyset))))=>(![X358:$i, X359:$i > $o]:((?[X360:$i]:(((in @ X360 @ X358)&(X359 @ X360)))=>(((dsetconstr @ X358 @ X359)=(emptyset))=>~($true))))=>(![X361:$i > $o, X362:$i]:(((in @ X362 @ emptyset)=>(X361 @ X362)))=>(![X363:$i, X364:$i > $o]:((~(![X365:$i]:(((in @ X365 @ X363)=>(X364 @ X365))))=>?[X366:$i]:(((in @ X366 @ X363)&~((X364 @ X366))))))=>(![X367:$i, X368:$i > $o]:((![X369:$i]:(((in @ X369 @ X367)=>~((X368 @ X369))))=>~(?[X370:$i]:(((in @ X370 @ X367)&(X368 @ X370))))))=>(![X371:$i, X372:$i > $o]:((~(?[X373:$i]:(((in @ X373 @ X371)&(X372 @ X373))))=>![X374:$i]:(((in @ X374 @ X371)=>~((X372 @ X374))))))=>(![X375:$i, X376:$i > $o]:((?[X377:$i]:(((in @ X377 @ X375)&~((X376 @ X377))))=>~(![X378:$i]:(((in @ X378 @ X375)=>(X376 @ X378))))))=>(![X379:$o]:(((X379)=>(in @ emptyset @ (prop2set @ ((X379))))))=>(![X380:$o]:(((X380)=>(set2prop @ (prop2set @ ((X380))))))=>(![X381:$i, X382:$i > $o]:((~(?[X383:$i]:(((in @ X383 @ X381)&(X382 @ X383))))=>![X384:$i]:(((in @ X384 @ X381)=>~((X382 @ X384))))))=>(![X385:$i, X386:$i > $o]:((~(![X387:$i]:(((in @ X387 @ X385)=>(X386 @ X387))))=>?[X388:$i]:(((in @ X388 @ X385)&~((X386 @ X388))))))=>(![X389:$i > $o]:((?[X390:$i]:(((X389 @ X390)&![X391:$i]:(((X389 @ X391)=>((X390)=(X391))))))=>?[X392:$i]:(((X389 @ X392)&![X393:$i]:(((X389 @ X393)=>((X392)=(X393))))))))=>(![X394:$i > $o]:((?[X395:$i]:((X394 @ X395))=>(![X396:$i, X397:$i]:(((X394 @ X396)=>((X394 @ X397)=>((X396)=(X397)))))=>?[X398:$i]:(((X394 @ X398)&![X399:$i]:(((X394 @ X399)=>((X398)=(X399)))))))))=>(![X400:$i > $o]:((?[X401:$i]:(![X402:$i]:(((X400 @ X402)<=>((X402)=(X401)))))=>?[X403:$i]:(((X400 @ X403)&![X404:$i]:(((X400 @ X404)=>((X403)=(X404))))))))=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ 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)],[c_0_77, c_0_78]), quantDeMorgan2]), upairsetIL]), c_0_79]), upairsetIR]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_80]), c_0_81]), c_0_82]), c_0_83]), c_0_84]), c_0_85]), c_0_86]), wellorderingAx]), foundationAx]), c_0_87]), c_0_88]), c_0_89]), emptyI]), setext]), c_0_90]), notinemptyset]), emptysetimpfalse]), emptysetE]), prop2setE]), noeltsimpempty]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), c_0_91]), c_0_92]), setadjoinE]), setunionI]), powersetE]), emptyInPowerset]), emptyinPowerset]), powersetI]), c_0_93]), setadjoinOr]), setunionE]), singletonsswitch]), eqinunit]), notinsingleton]), uniqinunit]), c_0_94]), c_0_95]), vacuousDall]), subPowSU]), quantDeMorgan1]), upairsetE]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_96])).
% 0.23/0.30 thf(c_0_98, negated_conjecture, ![X405:$i, X406:$i, X408:$i, X409:$i, X410:$i, X411:$i, X412:$i, X413:$i, X414:$i, X415:$i, X416:$i, X418:$i, X419:$i, X421:$i, X422:$i, X423:$i, X424:$i, X425:$i, X427:$i, X428:$i > $i > $o, X429:$i, X431:$i, X434:$i, X436:$i, X437:$i, X438:$i, X439:$i, X441:$i, X442:$i > $o, X443:$i, X445:$i, X446:$i > $o, X447:$i, X448:$i, X449:$i > $o, X450:$i, X451:$i, X452:$i > $o, X453:$i, X454:$i > $o, X455:$i, X458:$i, X459:$o, X460:$i, X461:$i, X462:$o, X463:$i, X464:$i, X465:$i > $o, X466:$i, X469:$i, X470:$i, X473:$i, X475:$i, X477:$i, X478:$i > $o, X479:$i, X480:$i, X482:$i, X483:$i > $o, X484:$i, X485:$i, X486:$i, X487:$i, X488:$i, X489:$i, X490:$i, X491:$i, X492:$i, X493:$i, X494:$i, X495:$o, X496:$i, X497:$i, X498:$i, X499:$i, X500:$i, X501:$i, X503:$i, X504:$i, X505:$i, X506:$i, X507:$i, X508:$i, X509:$i, X510:$i, X511:$i, X512:$i, X513:$o, X515:$i, X516:$i, X517:$i > $o, X518:$i, X521:$i, X522:$i, X523:$i, X525:$i, X526:$i, X527:$i, X528:$i, X529:$i, X530:$i, X531:$i, X532:$i, X533:$i, X534:$i, X535:$i, X536:$i, X537:$i, X538:$i, X539:$i, X540:$i, X541:$i > $o, X542:$i, X543:$i > $o, X544:$i, X545:$i, X546:$i > $o, X547:$i, X549:$i, X550:$i > $o, X552:$i, X553:$i, X554:$i > $o, X556:$i, X557:$i, X558:$i > $o, X559:$i, X561:$o, X562:$o, X563:$i, X564:$i > $o, X566:$i, X567:$i, X568:$i > $o, X569:$i, X571:$i > $o, X572:$i, X575:$i, X576:$i > $o, X577:$i, X581:$i, X582:$i > $o, X583:$i, X586:$i]:((((~(in @ (esk1_2 @ X405 @ X406) @ X405)|~(in @ (esk1_2 @ X405 @ X406) @ X406)|((X405)=(X406)))&((in @ (esk1_2 @ X405 @ X406) @ X405)|(in @ (esk1_2 @ X405 @ X406) @ X406)|((X405)=(X406))))&(~(in @ X408 @ emptyset)&(((~(in @ X411 @ (setadjoin @ X409 @ X410))|(((X411)=(X409))|(in @ X411 @ X410)))&((((X411)!=(X409))|(in @ X411 @ (setadjoin @ X409 @ X410)))&(~(in @ X411 @ X410)|(in @ X411 @ (setadjoin @ X409 @ X410)))))&(((~(in @ X413 @ (powerset @ X412))|(~(in @ X414 @ X413)|(in @ X414 @ X412)))&(((in @ (esk2_2 @ X415 @ X416) @ X416)|(in @ X416 @ (powerset @ X415)))&(~(in @ (esk2_2 @ X415 @ X416) @ X415)|(in @ X416 @ (powerset @ X415)))))&(((((in @ X419 @ (esk3_2 @ X418 @ X419))|~(in @ X419 @ (setunion @ X418)))&((in @ (esk3_2 @ X418 @ X419) @ X418)|~(in @ X419 @ (setunion @ X418))))&(~(in @ X422 @ X423)|~(in @ X423 @ X421)|(in @ X422 @ (setunion @ X421))))&((in @ emptyset @ omega)&((~(in @ X424 @ omega)|(in @ (setadjoin @ X424 @ X424) @ omega))&(((((in @ (esk4_1 @ X425) @ omega)|~(in @ emptyset @ X425)|(~(in @ X427 @ omega)|(in @ X427 @ X425)))&((in @ (esk4_1 @ X425) @ X425)|~(in @ emptyset @ X425)|(~(in @ X427 @ omega)|(in @ X427 @ X425))))&(~(in @ (setadjoin @ (esk4_1 @ X425) @ (esk4_1 @ X425)) @ X425)|~(in @ emptyset @ X425)|(~(in @ X427 @ omega)|(in @ X427 @ X425))))&((((((in @ (esk8_3 @ X428 @ X429 @ X434) @ X429)|~(in @ X434 @ (esk7_2 @ X428 @ X429))|(in @ (esk5_2 @ X428 @ X429) @ X429))&((X428 @ (esk8_3 @ X428 @ X429 @ X434) @ X434)|~(in @ X434 @ (esk7_2 @ X428 @ X429))|(in @ (esk5_2 @ X428 @ X429) @ X429)))&(~(in @ X437 @ X429)|~(X428 @ X437 @ X436)|(in @ X436 @ (esk7_2 @ X428 @ X429))|(in @ (esk5_2 @ X428 @ X429) @ X429)))&(((((in @ (esk8_3 @ X428 @ X429 @ X434) @ X429)|~(in @ X434 @ (esk7_2 @ X428 @ X429))|((X428 @ (esk5_2 @ X428 @ X429) @ (esk6_3 @ X428 @ X429 @ X431))|~(X428 @ (esk5_2 @ X428 @ X429) @ X431)))&((X428 @ (esk8_3 @ X428 @ X429 @ X434) @ X434)|~(in @ X434 @ (esk7_2 @ X428 @ X429))|((X428 @ (esk5_2 @ X428 @ X429) @ (esk6_3 @ X428 @ X429 @ X431))|~(X428 @ (esk5_2 @ X428 @ X429) @ X431))))&(~(in @ X437 @ X429)|~(X428 @ X437 @ X436)|(in @ X436 @ (esk7_2 @ X428 @ X429))|((X428 @ (esk5_2 @ X428 @ X429) @ (esk6_3 @ X428 @ X429 @ X431))|~(X428 @ (esk5_2 @ X428 @ X429) @ X431))))&((((in @ (esk8_3 @ X428 @ X429 @ X434) @ X429)|~(in @ X434 @ (esk7_2 @ X428 @ X429))|(((X431)!=(esk6_3 @ X428 @ X429 @ X431))|~(X428 @ (esk5_2 @ X428 @ X429) @ X431)))&((X428 @ (esk8_3 @ X428 @ X429 @ X434) @ X434)|~(in @ X434 @ (esk7_2 @ X428 @ X429))|(((X431)!=(esk6_3 @ X428 @ X429 @ X431))|~(X428 @ (esk5_2 @ X428 @ X429) @ X431))))&(~(in @ X437 @ X429)|~(X428 @ X437 @ X436)|(in @ X436 @ (esk7_2 @ X428 @ X429))|(((X431)!=(esk6_3 @ X428 @ X429 @ X431))|~(X428 @ (esk5_2 @ X428 @ X429) @ X431))))))&((((in @ (esk9_1 @ X438) @ X438)|~(in @ X439 @ X438))&(~(in @ X441 @ (esk9_1 @ X438))|~(in @ X441 @ X438)|~(in @ X439 @ X438)))&((epred1_0)&((((X442 @ (esk10_2 @ X442 @ X443))|~(X442 @ X443)|(X442 @ (descr @ X442)))&(((X443)!=(esk10_2 @ X442 @ X443))|~(X442 @ X443)|(X442 @ (descr @ X442))))&((~(in @ X447 @ X445)|(~(X446 @ X447)|(in @ X447 @ (dsetconstr @ X445 @ X446))))&((~(in @ X450 @ (dsetconstr @ X448 @ X449))|(in @ X450 @ X448))&((~(in @ X453 @ (dsetconstr @ X451 @ X452))|(X452 @ X453))&(((((X454 @ (esk12_1 @ X454))|((X454 @ (esk11_2 @ X454 @ X455))|~(X454 @ X455)))&(~(X454 @ X458)|((esk12_1 @ X454)=(X458))|((X454 @ (esk11_2 @ X454 @ X455))|~(X454 @ X455))))&(((X454 @ (esk12_1 @ X454))|(((X455)!=(esk11_2 @ X454 @ X455))|~(X454 @ X455)))&(~(X454 @ X458)|((esk12_1 @ X454)=(X458))|(((X455)!=(esk11_2 @ X454 @ X455))|~(X454 @ X455)))))&((~(in @ X460 @ (prop2set @ ((X459))))|(X459))&((~(in @ X461 @ emptyset)|(X462))&((~(in @ X463 @ emptyset)|~($true))&(~(in @ X464 @ emptyset)&((((X465 @ (esk13_2 @ X465 @ X466))|~(X465 @ X466)|(X465 @ (esk14_1 @ X465)))&(((X466)!=(esk13_2 @ X465 @ X466))|~(X465 @ X466)|(X465 @ (esk14_1 @ X465))))&(((((in @ (esk16_2 @ X469 @ X470) @ X470)|((X469)=(X470))|(in @ (esk15_2 @ X469 @ X470) @ X469))&(~(in @ (esk16_2 @ X469 @ X470) @ X469)|((X469)=(X470))|(in @ (esk15_2 @ X469 @ X470) @ X469)))&(((in @ (esk16_2 @ X469 @ X470) @ X470)|((X469)=(X470))|~(in @ (esk15_2 @ X469 @ X470) @ X470))&(~(in @ (esk16_2 @ X469 @ X470) @ X469)|((X469)=(X470))|~(in @ (esk15_2 @ X469 @ X470) @ X470))))&(((in @ (esk17_1 @ X473) @ X473)|((X473)=(emptyset)))&(((in @ (esk18_1 @ X475) @ X475)|((X475)=(emptyset)))&(((~(in @ X479 @ (dsetconstr @ X477 @ X478))|(X478 @ X479)|~(in @ X479 @ X477))&(~(X478 @ X479)|(in @ X479 @ (dsetconstr @ X477 @ X478))|~(in @ X479 @ X477)))&((((X480)=(emptyset))|(in @ (esk19_1 @ X480) @ X480))&((~(in @ X484 @ X482)|(~(X483 @ X484)|((dsetconstr @ X482 @ X483)!=(emptyset))))&((~(in @ X486 @ X485)|((X485)!=(emptyset)))&((in @ X487 @ (setadjoin @ X487 @ X488))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X491 @ X490)|(in @ X491 @ (setadjoin @ X489 @ X490)))&(((((in @ X494 @ X493)|(X495)|((X494)=(X492))|~(in @ X494 @ (setadjoin @ X492 @ X493)))&(~(X495)|(X495)|((X494)=(X492))|~(in @ X494 @ (setadjoin @ X492 @ X493))))&(((in @ X494 @ X493)|(X495)|~(X495)|~(in @ X494 @ (setadjoin @ X492 @ X493)))&(~(X495)|(X495)|~(X495)|~(in @ X494 @ (setadjoin @ X492 @ X493)))))&((~(in @ X498 @ (setadjoin @ X496 @ X497))|(((X498)=(X496))|(in @ X498 @ X497)))&(((dsetconstr @ X499 @ (^[Z0:$i]:($true)))=(X499))&((((in @ (esk20_2 @ X500 @ X501) @ X501)|(in @ X501 @ (powerset @ X500)))&(~(in @ (esk20_2 @ X500 @ X501) @ X500)|(in @ X501 @ (powerset @ X500))))&((in @ emptyset @ (powerset @ X503))&((in @ emptyset @ (powerset @ X504))&((~(in @ X506 @ (powerset @ X505))|(~(in @ X507 @ X506)|(in @ X507 @ X505)))&((~(in @ X509 @ X510)|(~(in @ X510 @ X508)|(in @ X509 @ (setunion @ X508))))&((((in @ X512 @ (esk21_3 @ X511 @ X512 @ X513))|(X513)|~(in @ X512 @ (setunion @ X511)))&(((in @ (esk21_3 @ X511 @ X512 @ X513) @ X511)|(X513)|~(in @ X512 @ (setunion @ X511)))&(~(X513)|(X513)|~(in @ X512 @ (setunion @ X511)))))&((~(in @ X516 @ X515)|(in @ X516 @ (powerset @ (setunion @ X515))))&((((~(X517 @ X521)|((X521)=(esk23_1 @ X517))|((X517 @ (esk22_2 @ X517 @ X518))|~(X517 @ X518)))&(((X522)!=(esk23_1 @ X517))|(X517 @ X522)|((X517 @ (esk22_2 @ X517 @ X518))|~(X517 @ X518))))&((~(X517 @ X521)|((X521)=(esk23_1 @ X517))|(((X518)!=(esk22_2 @ X517 @ X518))|~(X517 @ X518)))&(((X522)!=(esk23_1 @ X517))|(X517 @ X522)|(((X518)!=(esk22_2 @ X517 @ X518))|~(X517 @ X518)))))&((((in @ (esk24_1 @ X523) @ X523)|((X523)=(emptyset)))&(($true)|((X523)=(emptyset))))&((~(in @ X525 @ (setadjoin @ X526 @ emptyset))|((X525)=(X526)))&((((X527)=(X528))|~(in @ X528 @ (setadjoin @ X527 @ emptyset)))&((((X529)!=(X530))|(in @ X529 @ (setadjoin @ X530 @ emptyset)))&((~(in @ X531 @ (setadjoin @ X532 @ emptyset))|(in @ X532 @ (setadjoin @ X531 @ emptyset)))&((~(in @ X535 @ (setadjoin @ X533 @ (setadjoin @ X534 @ emptyset)))|(((X535)=(X533))|((X535)=(X534))))&((in @ X536 @ (setadjoin @ X536 @ (setadjoin @ X537 @ emptyset)))&((in @ X539 @ (setadjoin @ X538 @ (setadjoin @ X539 @ emptyset)))&((~(in @ X542 @ X540)|~(X541 @ X542)|(((dsetconstr @ X540 @ X541)!=(emptyset))|~($true)))&((~(in @ X544 @ emptyset)|(X543 @ X544))&((((in @ (esk25_2 @ X545 @ X546) @ X545)|(~(in @ X547 @ X545)|(X546 @ X547)))&(~(X546 @ (esk25_2 @ X545 @ X546))|(~(in @ X547 @ X545)|(X546 @ X547))))&((((in @ (esk26_2 @ X549 @ X550) @ X549)|(~(in @ X552 @ X549)|~(X550 @ X552)))&((X550 @ (esk26_2 @ X549 @ X550))|(~(in @ X552 @ X549)|~(X550 @ X552))))&((((in @ (esk27_2 @ X553 @ X554) @ X553)|(~(in @ X556 @ X553)|~(X554 @ X556)))&((X554 @ (esk27_2 @ X553 @ X554))|(~(in @ X556 @ X553)|~(X554 @ X556))))&((((in @ (esk28_2 @ X557 @ X558) @ X557)|(~(in @ X559 @ X557)|(X558 @ X559)))&(~(X558 @ (esk28_2 @ X557 @ X558))|(~(in @ X559 @ X557)|(X558 @ X559))))&((~(X561)|(in @ emptyset @ (prop2set @ ((X561)))))&((~(X562)|(set2prop @ (prop2set @ ((X562)))))&((((in @ (esk29_2 @ X563 @ X564) @ X563)|(~(in @ X566 @ X563)|~(X564 @ X566)))&((X564 @ (esk29_2 @ X563 @ X564))|(~(in @ X566 @ X563)|~(X564 @ X566))))&((((in @ (esk30_2 @ X567 @ X568) @ X567)|(~(in @ X569 @ X567)|(X568 @ X569)))&(~(X568 @ (esk30_2 @ X567 @ X568))|(~(in @ X569 @ X567)|(X568 @ X569))))&(((((X571 @ (esk32_1 @ X571))|((X571 @ (esk31_2 @ X571 @ X572))|~(X571 @ X572)))&(~(X571 @ X575)|((esk32_1 @ X571)=(X575))|((X571 @ (esk31_2 @ X571 @ X572))|~(X571 @ X572))))&(((X571 @ (esk32_1 @ X571))|(((X572)!=(esk31_2 @ X571 @ X572))|~(X571 @ X572)))&(~(X571 @ X575)|((esk32_1 @ X571)=(X575))|(((X572)!=(esk31_2 @ X571 @ X572))|~(X571 @ X572)))))&(((((X576 @ (esk35_1 @ X576))|(X576 @ (esk33_1 @ X576))|~(X576 @ X577))&(~(X576 @ X581)|((esk35_1 @ X576)=(X581))|(X576 @ (esk33_1 @ X576))|~(X576 @ X577)))&((((X576 @ (esk35_1 @ X576))|(X576 @ (esk34_1 @ X576))|~(X576 @ X577))&(~(X576 @ X581)|((esk35_1 @ X576)=(X581))|(X576 @ (esk34_1 @ X576))|~(X576 @ X577)))&(((X576 @ (esk35_1 @ X576))|((esk33_1 @ X576)!=(esk34_1 @ X576))|~(X576 @ X577))&(~(X576 @ X581)|((esk35_1 @ X576)=(X581))|((esk33_1 @ X576)!=(esk34_1 @ X576))|~(X576 @ X577)))))&(((((X582 @ (esk37_1 @ X582))|(~(X582 @ (esk36_2 @ X582 @ X583))|((esk36_2 @ X582 @ X583)!=(X583))))&(~(X582 @ X586)|((esk37_1 @ X582)=(X586))|(~(X582 @ (esk36_2 @ X582 @ X583))|((esk36_2 @ X582 @ X583)!=(X583)))))&(((X582 @ (esk37_1 @ X582))|((X582 @ (esk36_2 @ X582 @ X583))|((esk36_2 @ X582 @ X583)=(X583))))&(~(X582 @ X586)|((esk37_1 @ X582)=(X586))|((X582 @ (esk36_2 @ X582 @ X583))|((esk36_2 @ X582 @ X583)=(X583))))))&(((esk38_0)=(esk39_0))&(((esk40_0)=(esk41_0))&((in @ esk40_0 @ esk38_0)&~(in @ esk41_0 @ esk39_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_97])])])])])])])).
% 0.23/0.30 thf(c_0_99, negated_conjecture, (in @ esk40_0 @ esk38_0), inference(split_conjunct,[status(thm)],[c_0_98])).
% 0.23/0.30 thf(c_0_100, negated_conjecture, ((esk40_0)=(esk41_0)), inference(split_conjunct,[status(thm)],[c_0_98])).
% 0.23/0.30 thf(c_0_101, negated_conjecture, ~((in @ esk41_0 @ esk39_0)), inference(split_conjunct,[status(thm)],[c_0_98])).
% 0.23/0.30 thf(c_0_102, negated_conjecture, ((esk38_0)=(esk39_0)), inference(split_conjunct,[status(thm)],[c_0_98])).
% 0.23/0.30 thf(c_0_103, negated_conjecture, (in @ esk41_0 @ esk38_0), inference(rw,[status(thm)],[c_0_99, c_0_100])).
% 0.23/0.30 thf(c_0_104, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_101, c_0_102]), c_0_103])]), ['proof']).
% 0.23/0.30 % SZS output end CNFRefutation
% 0.23/0.30 % Parsed axioms : 141
% 0.23/0.30 % Removed by relevancy pruning/SinE : 75
% 0.23/0.30 % Initial clauses : 134
% 0.23/0.30 % Removed in clause preprocessing : 5
% 0.23/0.30 % Initial clauses in saturation : 129
% 0.23/0.30 % Processed clauses : 7
% 0.23/0.30 % ...of these trivial : 0
% 0.23/0.30 % ...subsumed : 0
% 0.23/0.30 % ...remaining for further processing : 6
% 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 : 3
% 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 : 6
% 0.23/0.30 % Positive orientable unit clauses : 6
% 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: 122
% 0.23/0.30 % ...number of literals in the above : 368
% 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 : 16962
% 0.23/0.30 % Search garbage collected termcells : 6969
% 0.23/0.30
% 0.23/0.30 % -------------------------------------------------
% 0.23/0.30 % User time : 0.018 s
% 0.23/0.30 % System time : 0.004 s
% 0.23/0.30 % Total time : 0.022 s
% 0.23/0.30 % Maximum resident set size: 5568 pages
% 0.23/0.30
% 0.23/0.30 % -------------------------------------------------
% 0.23/0.30 % User time : 0.024 s
% 0.23/0.30 % System time : 0.008 s
% 0.23/0.30 % Total time : 0.032 s
% 0.23/0.30 % Maximum resident set size: 4864 pages
% 0.23/0.30 % E exiting
%------------------------------------------------------------------------------