%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU547^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 08:24:27 AM UTC 2026
% Result : Theorem 0.10s 0.27s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU547^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.16 % Computer : n001.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Sep 29 13:55:21 UTC 2026
% 0.10/0.16 % CPUTime :
% 0.10/0.16 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running higher-order theorem proving
% 0.10/0.23 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p
% 0.10/0.27 % Version: 3.5.1-ho
% 0.10/0.27 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.10/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.27 % Starting sh5l with 300s (1) cores
% 0.10/0.27 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.27 % Starting new_bool_2 with 300s (1) cores
% 0.10/0.27 % new_bool_2 with pid 1277402 completed with status 0
% 0.10/0.27 % Result found by new_bool_2
% 0.10/0.27 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.10/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.27 % Starting sh5l with 300s (1) cores
% 0.10/0.27 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.27 % Starting new_bool_2 with 300s (1) cores
% 0.10/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.27 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.27 % Search class: HGHSM-FFMM31-SHFMMSBN
% 0.10/0.27 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.27 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.27 % SubtermCWHack with pid 1277403 completed with status 0
% 0.10/0.27 % Result found by SubtermCWHack
% 0.10/0.27 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.10/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.27 % Starting sh5l with 300s (1) cores
% 0.10/0.27 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.27 % Starting new_bool_2 with 300s (1) cores
% 0.10/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.27 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.27 % Search class: HGHSM-FFMM31-SHFMMSBN
% 0.10/0.27 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.27 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.27 % Preprocessing time : 0.003 s
% 0.10/0.27
% 0.10/0.27 % Proof found!
% 0.10/0.27 % SZS status Theorem
% 0.10/0.27 % SZS output start CNFRefutation
% 0.10/0.27 thf(decl_23, type, in: $i > $i > $o).
% 0.10/0.27 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.10/0.27 thf(decl_25, type, setextAx: $o).
% 0.10/0.27 thf(decl_26, type, emptyset: $i).
% 0.10/0.27 thf(decl_27, type, emptysetAx: $o).
% 0.10/0.27 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.10/0.27 thf(decl_29, type, setadjoinAx: $o).
% 0.10/0.27 thf(decl_30, type, powerset: $i > $i).
% 0.10/0.27 thf(decl_31, type, powersetAx: $o).
% 0.10/0.27 thf(decl_32, type, setunion: $i > $i).
% 0.10/0.27 thf(decl_33, type, setunionAx: $o).
% 0.10/0.27 thf(decl_34, type, omega: $i).
% 0.10/0.27 thf(decl_35, type, omega0Ax: $o).
% 0.10/0.27 thf(decl_36, type, omegaSAx: $o).
% 0.10/0.27 thf(decl_37, type, omegaIndAx: $o).
% 0.10/0.27 thf(decl_38, type, replAx: $o).
% 0.10/0.27 thf(decl_39, type, foundationAx: $o).
% 0.10/0.27 thf(decl_40, type, wellorderingAx: $o).
% 0.10/0.27 thf(decl_42, type, descrp: $o).
% 0.10/0.27 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.10/0.27 thf(decl_44, type, dsetconstrI: $o).
% 0.10/0.27 thf(decl_45, type, dsetconstrEL: $o).
% 0.10/0.27 thf(decl_46, type, dsetconstrER: $o).
% 0.10/0.27 thf(decl_47, type, exuE1: $o).
% 0.10/0.27 thf(decl_48, type, prop2set: $o > $i).
% 0.10/0.27 thf(decl_49, type, prop2setE: $o).
% 0.10/0.27 thf(decl_50, type, emptysetE: $o).
% 0.10/0.27 thf(decl_51, type, emptysetimpfalse: $o).
% 0.10/0.27 thf(decl_52, type, notinemptyset: $o).
% 0.10/0.27 thf(decl_53, type, exuE3e: $o).
% 0.10/0.27 thf(decl_54, type, setext: $o).
% 0.10/0.27 thf(decl_55, type, emptyI: $o).
% 0.10/0.27 thf(decl_56, type, noeltsimpempty: $o).
% 0.10/0.27 thf(decl_57, type, setbeta: $o).
% 0.10/0.27 thf(decl_58, type, nonempty: $i > $o).
% 0.10/0.27 thf(decl_59, type, nonemptyE1: $o).
% 0.10/0.27 thf(decl_60, type, nonemptyI: $o).
% 0.10/0.27 thf(decl_61, type, nonemptyI1: $o).
% 0.10/0.27 thf(decl_62, type, setadjoinIL: $o).
% 0.10/0.27 thf(decl_63, type, emptyinunitempty: $o).
% 0.10/0.27 thf(decl_64, type, setadjoinIR: $o).
% 0.10/0.27 thf(decl_65, type, setadjoinE: $o).
% 0.10/0.27 thf(decl_66, type, setadjoinOr: $o).
% 0.10/0.27 thf(decl_67, type, setoftrueEq: $o).
% 0.10/0.27 thf(decl_68, type, powersetI: $o).
% 0.10/0.27 thf(decl_69, type, emptyinPowerset: $o).
% 0.10/0.27 thf(decl_70, type, emptyInPowerset: $o).
% 0.10/0.27 thf(decl_71, type, powersetE: $o).
% 0.10/0.27 thf(decl_72, type, setunionI: $o).
% 0.10/0.27 thf(decl_73, type, setunionE: $o).
% 0.10/0.27 thf(decl_74, type, subPowSU: $o).
% 0.10/0.27 thf(decl_75, type, exuE2: $o).
% 0.10/0.27 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.10/0.27 thf(decl_77, type, uniqinunit: $o).
% 0.10/0.27 thf(decl_78, type, notinsingleton: $o).
% 0.10/0.27 thf(decl_79, type, eqinunit: $o).
% 0.10/0.27 thf(decl_80, type, singletonsswitch: $o).
% 0.10/0.27 thf(decl_81, type, upairsetE: $o).
% 0.10/0.27 thf(decl_82, type, upairsetIL: $o).
% 0.10/0.27 thf(decl_83, type, upairsetIR: $o).
% 0.10/0.27 thf(decl_84, type, emptyE1: $o).
% 0.10/0.27 thf(decl_85, type, vacuousDall: $o).
% 0.10/0.27 thf(decl_86, type, quantDeMorgan1: $o).
% 0.10/0.27 thf(decl_87, type, quantDeMorgan2: $o).
% 0.10/0.27 thf(decl_88, type, quantDeMorgan3: $o).
% 0.10/0.27 thf(decl_89, type, quantDeMorgan4: $o).
% 0.10/0.27 thf(decl_90, type, prop2setI: $o).
% 0.10/0.27 thf(decl_92, type, prop2set2propI: $o).
% 0.10/0.27 thf(decl_93, type, notdexE: $o).
% 0.10/0.27 thf(decl_94, type, notdallE: $o).
% 0.10/0.27 thf(decl_95, type, exuI1: $o).
% 0.10/0.27 thf(decl_96, type, exuI3: $o).
% 0.10/0.27 thf(decl_97, type, exuI2: $o).
% 0.10/0.27 thf(decl_98, type, epred1_0: $o).
% 0.10/0.27 thf(decl_99, type, esk1_2: $i > $i > $i).
% 0.10/0.27 thf(decl_100, type, esk2_2: $i > $i > $i).
% 0.10/0.27 thf(decl_101, type, esk3_2: $i > $i > $i).
% 0.10/0.27 thf(decl_102, type, esk4_1: $i > $i).
% 0.10/0.27 thf(decl_103, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.10/0.27 thf(decl_104, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.10/0.27 thf(decl_105, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.10/0.27 thf(decl_106, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.10/0.27 thf(decl_107, type, esk9_1: $i > $i).
% 0.10/0.27 thf(decl_108, type, esk10_2: ($i > $o) > $i > $i).
% 0.10/0.27 thf(decl_109, type, esk11_1: ($i > $o) > $i).
% 0.10/0.27 thf(decl_110, type, esk12_2: ($i > $o) > $i > $i).
% 0.10/0.27 thf(decl_111, type, esk13_1: ($i > $o) > $i).
% 0.10/0.27 thf(decl_112, type, esk14_2: $i > $i > $i).
% 0.10/0.27 thf(decl_113, type, esk15_2: $i > $i > $i).
% 0.10/0.27 thf(decl_114, type, esk16_1: $i > $i).
% 0.10/0.27 thf(decl_115, type, esk17_1: $i > $i).
% 0.10/0.27 thf(decl_116, type, esk18_1: $i > $i).
% 0.10/0.27 thf(decl_117, type, esk19_2: $i > $i > $i).
% 0.10/0.27 thf(decl_118, type, esk20_3: $i > $i > $o > $i).
% 0.10/0.27 thf(decl_119, type, esk21_2: ($i > $o) > $i > $i).
% 0.10/0.27 thf(decl_120, type, esk22_1: ($i > $o) > $i).
% 0.10/0.27 thf(decl_121, type, esk23_1: $i > $i).
% 0.10/0.27 thf(decl_122, type, esk24_2: $i > ($i > $o) > $i).
% 0.10/0.27 thf(decl_123, type, esk25_2: $i > ($i > $o) > $i).
% 0.10/0.27 thf(decl_124, type, esk26_2: $i > ($i > $o) > $i).
% 0.10/0.27 thf(decl_125, type, esk27_2: $i > ($i > $o) > $i).
% 0.10/0.27 thf(decl_126, type, esk28_2: $i > ($i > $o) > $i).
% 0.10/0.27 thf(decl_127, type, esk29_2: $i > ($i > $o) > $i).
% 0.10/0.27 thf(decl_128, type, esk30_2: ($i > $o) > $i > $i).
% 0.10/0.27 thf(decl_129, type, esk31_1: ($i > $o) > $i).
% 0.10/0.27 thf(decl_130, type, esk32_1: ($i > $o) > $i).
% 0.10/0.27 thf(decl_131, type, esk33_1: ($i > $o) > $i).
% 0.10/0.27 thf(decl_132, type, esk34_1: ($i > $o) > $i).
% 0.10/0.27 thf(decl_133, type, esk35_2: ($i > $o) > $i > $i).
% 0.10/0.27 thf(decl_134, type, esk36_1: ($i > $o) > $i).
% 0.10/0.27 thf(decl_135, type, esk37_0: $i).
% 0.10/0.27 thf(decl_136, type, esk38_0: $i).
% 0.10/0.27 thf(decl_137, type, esk39_0: $i).
% 0.10/0.27 thf(decl_138, type, esk40_0: $i).
% 0.10/0.27 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', replAx)).
% 0.10/0.27 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', exu)).
% 0.10/0.27 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', exuI1)).
% 0.10/0.27 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', exuI3)).
% 0.10/0.27 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', exuI2)).
% 0.10/0.27 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', exuE1)).
% 0.10/0.27 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', nonempty)).
% 0.10/0.27 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', exuE3e)).
% 0.10/0.27 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', nonemptyI)).
% 0.10/0.27 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', exuE2)).
% 0.10/0.27 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/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', inCongP)).
% 0.10/0.27 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', emptyE1)).
% 0.10/0.27 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', dsetconstrER)).
% 0.10/0.27 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', dsetconstrEL)).
% 0.10/0.27 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', dsetconstrI)).
% 0.10/0.27 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', nonemptyE1)).
% 0.10/0.27 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', setbeta)).
% 0.10/0.27 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', setoftrueEq)).
% 0.10/0.27 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', nonemptyI1)).
% 0.10/0.27 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', nonemptyImpWitness)).
% 0.10/0.27 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', upairsetIL)).
% 0.10/0.27 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', upairsetE)).
% 0.10/0.27 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', upairsetIR)).
% 0.10/0.27 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', vacuousDall)).
% 0.10/0.27 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', quantDeMorgan1)).
% 0.10/0.27 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', quantDeMorgan2)).
% 0.10/0.27 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', quantDeMorgan3)).
% 0.10/0.27 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', quantDeMorgan4)).
% 0.10/0.27 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', omegaIndAx)).
% 0.10/0.27 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', prop2setI)).
% 0.10/0.27 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', omegaSAx)).
% 0.10/0.27 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', notdexE)).
% 0.10/0.27 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', omega0Ax)).
% 0.10/0.27 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', notdallE)).
% 0.10/0.27 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', setunionAx)).
% 0.10/0.27 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', powersetAx)).
% 0.10/0.27 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', setadjoinAx)).
% 0.10/0.27 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', foundationAx)).
% 0.10/0.27 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', emptysetE)).
% 0.10/0.27 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', prop2setE)).
% 0.10/0.27 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', wellorderingAx)).
% 0.10/0.27 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', emptysetimpfalse)).
% 0.10/0.27 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', noeltsimpempty)).
% 0.10/0.27 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', emptyI)).
% 0.10/0.27 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', setext)).
% 0.10/0.27 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', notinemptyset)).
% 0.10/0.27 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', setadjoinOr)).
% 0.10/0.27 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', setadjoinE)).
% 0.10/0.27 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', setadjoinIR)).
% 0.10/0.27 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', emptyinunitempty)).
% 0.10/0.27 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', setadjoinIL)).
% 0.10/0.27 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', powersetI)).
% 0.10/0.27 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', subPowSU)).
% 0.10/0.27 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', setunionE)).
% 0.10/0.27 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', setunionI)).
% 0.10/0.27 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', powersetE)).
% 0.10/0.27 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', emptyInPowerset)).
% 0.10/0.27 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', uniqinunit)).
% 0.10/0.27 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', notinsingleton)).
% 0.10/0.27 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', eqinunit)).
% 0.10/0.27 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', singletonsswitch)).
% 0.10/0.27 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', emptyinPowerset)).
% 0.10/0.27 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', emptysetAx)).
% 0.10/0.27 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.DgyC9VKJSj/E---3.1_1277386.p', setextAx)).
% 0.10/0.27 thf(c_0_64, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.10/0.27 thf(c_0_65, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.10/0.27 thf(c_0_66, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 0.10/0.27 thf(c_0_67, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.10/0.27 thf(c_0_68, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.10/0.27 thf(c_0_69, 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])).
% 0.10/0.27 thf(c_0_70, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.10/0.27 thf(c_0_71, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.10/0.27 thf(c_0_72, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.10/0.27 thf(c_0_73, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.10/0.27 thf(c_0_74, 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])).
% 0.10/0.27 thf(c_0_75, 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])).
% 0.10/0.27 thf(c_0_76, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X195:$i]:(((((X6 @ X2 @ X195)))&(![X196:$i]:(((((X6 @ X2 @ X196)))=>(((X195)=(X196)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_64, c_0_65])).
% 0.10/0.27 thf(c_0_77, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X203:$i]:(((((X1 @ X203)))&(![X204:$i]:(((((X1 @ X204)))=>(((X203)=(X204)))))))))))))), inference(apply_def,[status(thm)],[c_0_66, c_0_65])).
% 0.10/0.27 thf(c_0_78, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X205:$i]:(((((X1 @ X205)))&(![X206:$i]:(((((X1 @ X206)))=>(((X205)=(X206)))))))))))))))), inference(apply_def,[status(thm)],[c_0_67, c_0_65])).
% 0.10/0.27 thf(c_0_79, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X207:$i]:(((((X1 @ X207)))&(![X208:$i]:(((((X1 @ X208)))=>(((X207)=(X208)))))))))))))), inference(apply_def,[status(thm)],[c_0_68, c_0_65])).
% 0.10/0.27 thf(c_0_80, plain, ((exuE1)=(![X1:$i > $o]:((((?[X197:$i]:(((((X1 @ X197)))&(![X198:$i]:(((((X1 @ X198)))=>(((X197)=(X198))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_69, c_0_65])).
% 0.10/0.27 thf(c_0_81, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.10/0.27 thf(c_0_82, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.10/0.27 thf(c_0_83, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.10/0.27 thf(c_0_84, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_70])).
% 0.10/0.27 thf(c_0_85, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.10/0.27 thf(c_0_86, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X199:$i]:(((((X1 @ X199)))&(![X200:$i]:(((((X1 @ X200)))=>(((X199)=(X200))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_71, c_0_65])).
% 0.10/0.27 thf(c_0_87, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_72, c_0_70])).
% 0.10/0.27 thf(c_0_88, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.10/0.27 thf(c_0_89, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_70])).
% 0.10/0.27 thf(c_0_90, plain, ((exuE2)=(![X1:$i > $o]:((((?[X201:$i]:(((((X1 @ X201)))&(![X202:$i]:(((((X1 @ X202)))=>(((X201)=(X202))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_73, c_0_65])).
% 0.10/0.27 thf(c_0_91, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_70])).
% 0.10/0.27 thf(c_0_92, plain, ((epred1_0)<=>![X238:$i]:(?[X239:$i]:((((![X240:$i]:(((in @ X240 @ X239)=>![X241:$i]:(((in @ X241 @ X240)=>(in @ X241 @ X238)))))&![X242:$i, X243:$i]:((((in @ X242 @ X238)&(in @ X243 @ X238))=>(![X244:$i]:(((in @ X244 @ X239)=>((in @ X242 @ X244)<=>(in @ X243 @ X244))))=>((X242)=(X243))))))&![X245:$i, X246:$i]:((((in @ X245 @ X239)&(in @ X246 @ X239))=>(![X247:$i]:(((in @ X247 @ X245)=>(in @ X247 @ X246)))|![X248:$i]:(((in @ X248 @ X246)=>(in @ X248 @ X245)))))))&![X249:$i]:(((![X250:$i]:(((in @ X250 @ X249)=>(in @ X250 @ X238)))&?[X251:$i]:((in @ X251 @ X249)))=>?[X252:$i, X253:$i]:(((((in @ X252 @ X239)&(in @ X253 @ X249))&~(?[X254:$i]:(((in @ X254 @ X252)&(in @ X254 @ X249)))))&![X255:$i]:(((in @ X255 @ X239)=>(![X256:$i]:(((in @ X256 @ X255)=>(in @ X256 @ X252)))|(in @ X253 @ X255)))))))))))), introduced(definition)).
% 0.10/0.27 thf(c_0_93, negated_conjecture, ~((![X209:$i, X210:$i]:((![X211:$i]:(((in @ X211 @ X209)<=>(in @ X211 @ X210)))=>((X209)=(X210))))=>(![X212:$i]:(~(in @ X212 @ emptyset))=>(![X213:$i, X214:$i, X215:$i]:(((in @ X215 @ (setadjoin @ X213 @ X214))<=>(((X215)=(X213))|(in @ X215 @ X214))))=>(![X216:$i, X217:$i]:(((in @ X217 @ (powerset @ X216))<=>![X218:$i]:(((in @ X218 @ X217)=>(in @ X218 @ X216)))))=>(![X219:$i, X220:$i]:(((in @ X220 @ (setunion @ X219))<=>?[X221:$i]:(((in @ X220 @ X221)&(in @ X221 @ X219)))))=>((in @ emptyset @ omega)=>(![X222:$i]:(((in @ X222 @ omega)=>(in @ (setadjoin @ X222 @ X222) @ omega)))=>(![X223:$i]:((((in @ emptyset @ X223)&![X224:$i]:((((in @ X224 @ omega)&(in @ X224 @ X223))=>(in @ (setadjoin @ X224 @ X224) @ X223))))=>![X225:$i]:(((in @ X225 @ omega)=>(in @ X225 @ X223)))))=>(![X226:$i > $i > $o, X227:$i]:((![X228:$i]:(((in @ X228 @ X227)=>?[X229:$i]:(((X226 @ X228 @ X229)&![X230:$i]:(((X226 @ X228 @ X230)=>((X229)=(X230))))))))=>?[X231:$i]:(![X232:$i]:(((in @ X232 @ X231)<=>?[X233:$i]:(((in @ X233 @ X227)&(X226 @ X233 @ X232))))))))=>(![X234:$i]:((?[X235:$i]:((in @ X235 @ X234))=>?[X236:$i]:(((in @ X236 @ X234)&~(?[X237:$i]:(((in @ X237 @ X236)&(in @ X237 @ X234))))))))=>((epred1_0)=>((descrp)=>(![X257:$i, X258:$i > $o, X259:$i]:(((in @ X259 @ X257)=>((X258 @ X259)=>(in @ X259 @ (dsetconstr @ X257 @ (^[Z0:$i]:((X258 @ Z0))))))))=>(![X260:$i, X261:$i > $o, X262:$i]:(((in @ X262 @ (dsetconstr @ X260 @ (^[Z0:$i]:((X261 @ Z0)))))=>(in @ X262 @ X260)))=>(![X263:$i, X264:$i > $o, X265:$i]:(((in @ X265 @ (dsetconstr @ X263 @ (^[Z0:$i]:((X264 @ Z0)))))=>(X264 @ X265)))=>(![X266:$i > $o]:((?[X267:$i]:(((X266 @ X267)&![X268:$i]:(((X266 @ X268)=>((X267)=(X268))))))=>?[X269:$i]:(((X266 @ X269)&![X270:$i]:(((X266 @ X270)=>((X269)=(X270))))))))=>(![X271:$o, X272:$i]:(((in @ X272 @ (prop2set @ ((X271))))=>(X271)))=>(![X273:$i]:(((in @ X273 @ emptyset)=>![X274:$o]:((X274))))=>(![X275:$i]:(~(in @ X275 @ emptyset))=>(![X276:$i]:(~(in @ X276 @ emptyset))=>(![X277:$i > $o]:((?[X278:$i]:(((X277 @ X278)&![X279:$i]:(((X277 @ X279)=>((X278)=(X279))))))=>?[X280:$i]:((X277 @ X280))))=>(![X281:$i, X282:$i]:((![X283:$i]:(((in @ X283 @ X281)=>(in @ X283 @ X282)))=>(![X284:$i]:(((in @ X284 @ X282)=>(in @ X284 @ X281)))=>((X281)=(X282)))))=>(![X285:$i]:((![X286:$i]:(~(in @ X286 @ X285))=>((X285)=(emptyset))))=>(![X287:$i]:((![X288:$i]:(~(in @ X288 @ X287))=>((X287)=(emptyset))))=>(![X289:$i, X290:$i > $o, X291:$i]:(((in @ X291 @ X289)=>((in @ X291 @ (dsetconstr @ X289 @ (^[Z0:$i]:((X290 @ Z0)))))<=>(X290 @ X291))))=>(![X292:$i]:((((X292)!=(emptyset))=>?[X293:$i]:((in @ X293 @ X292))))=>(![X294:$i, X295:$i > $o, X296:$i]:(((in @ X296 @ X294)=>((X295 @ X296)=>((dsetconstr @ X294 @ (^[Z0:$i]:((X295 @ Z0))))!=(emptyset)))))=>(![X297:$i]:((?[X298:$i]:((in @ X298 @ X297))=>((X297)!=(emptyset))))=>(![X299:$i, X300:$i]:((in @ X299 @ (setadjoin @ X299 @ X300)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X301:$i, X302:$i, X303:$i]:(((in @ X303 @ X302)=>(in @ X303 @ (setadjoin @ X301 @ X302))))=>(![X304:$i, X305:$i, X306:$i]:(((in @ X306 @ (setadjoin @ X304 @ X305))=>![X307:$o]:(((((X306)=(X304))=>(X307))=>(((in @ X306 @ X305)=>(X307))=>(X307))))))=>(![X308:$i, X309:$i, X310:$i]:(((in @ X310 @ (setadjoin @ X308 @ X309))=>(((X310)=(X308))|(in @ X310 @ X309))))=>(![X311:$i]:(((dsetconstr @ X311 @ (^[Z0:$i]:(($true))))=(X311)))=>(![X312:$i, X313:$i]:((![X314:$i]:(((in @ X314 @ X313)=>(in @ X314 @ X312)))=>(in @ X313 @ (powerset @ X312))))=>(![X315:$i]:((in @ emptyset @ (powerset @ X315)))=>(![X316:$i]:((in @ emptyset @ (powerset @ X316)))=>(![X317:$i, X318:$i, X319:$i]:(((in @ X318 @ (powerset @ X317))=>((in @ X319 @ X318)=>(in @ X319 @ X317))))=>(![X320:$i, X321:$i, X322:$i]:(((in @ X321 @ X322)=>((in @ X322 @ X320)=>(in @ X321 @ (setunion @ X320)))))=>(![X323:$i, X324:$i]:(((in @ X324 @ (setunion @ X323))=>![X325:$o]:((![X326:$i]:(((in @ X324 @ X326)=>((in @ X326 @ X323)=>(X325))))=>(X325)))))=>(![X327:$i, X328:$i]:(((in @ X328 @ X327)=>(in @ X328 @ (powerset @ (setunion @ X327)))))=>(![X329:$i > $o]:((?[X330:$i]:(((X329 @ X330)&![X331:$i]:(((X329 @ X331)=>((X330)=(X331))))))=>?[X332:$i]:(![X333:$i]:(((X329 @ X333)<=>((X333)=(X332)))))))=>(![X334:$i]:((((X334)!=(emptyset))=>?[X335:$i]:((in @ X335 @ X334))))=>(![X336:$i, X337:$i]:(((in @ X336 @ (setadjoin @ X337 @ emptyset))=>((X336)=(X337))))=>(![X338:$i, X339:$i]:((((X338)!=(X339))=>~(in @ X339 @ (setadjoin @ X338 @ emptyset))))=>(![X340:$i, X341:$i]:((((X340)=(X341))=>(in @ X340 @ (setadjoin @ X341 @ emptyset))))=>(![X342:$i, X343:$i]:(((in @ X342 @ (setadjoin @ X343 @ emptyset))=>(in @ X343 @ (setadjoin @ X342 @ emptyset))))=>(![X344:$i, X345:$i, X346:$i]:(((in @ X346 @ (setadjoin @ X344 @ (setadjoin @ X345 @ emptyset)))=>(((X346)=(X344))|((X346)=(X345)))))=>(![X347:$i, X348:$i]:((in @ X347 @ (setadjoin @ X347 @ (setadjoin @ X348 @ emptyset))))=>(![X349:$i, X350:$i]:((in @ X350 @ (setadjoin @ X349 @ (setadjoin @ X350 @ emptyset))))=>(![X351:$i, X352:$i > $o]:((?[X353:$i]:(((in @ X353 @ X351)&(X352 @ X353)))=>((dsetconstr @ X351 @ (^[Z0:$i]:((X352 @ Z0))))!=(emptyset))))=>(![X354:$i > $o, X355:$i]:(((in @ X355 @ emptyset)=>(X354 @ X355)))=>(![X356:$i, X357:$i > $o]:((~(![X358:$i]:(((in @ X358 @ X356)=>(X357 @ X358))))=>?[X359:$i]:(((in @ X359 @ X356)&~(X357 @ X359)))))=>(![X360:$i, X361:$i > $o]:((![X362:$i]:(((in @ X362 @ X360)=>~(X361 @ X362)))=>~(?[X363:$i]:(((in @ X363 @ X360)&(X361 @ X363))))))=>(![X364:$i, X365:$i > $o]:((~(?[X366:$i]:(((in @ X366 @ X364)&(X365 @ X366))))=>![X367:$i]:(((in @ X367 @ X364)=>~(X365 @ X367)))))=>(![X368:$i, X369:$i > $o]:((?[X370:$i]:(((in @ X370 @ X368)&~(X369 @ X370)))=>~(![X371:$i]:(((in @ X371 @ X368)=>(X369 @ X371))))))=>(![X372:$o]:(((X372)=>(in @ emptyset @ (prop2set @ ((X372))))))=>((prop2set2propI)=>(![X373:$i, X374:$i > $o]:((~(?[X375:$i]:(((in @ X375 @ X373)&(X374 @ X375))))=>![X376:$i]:(((in @ X376 @ X373)=>~(X374 @ X376)))))=>(![X377:$i, X378:$i > $o]:((~(![X379:$i]:(((in @ X379 @ X377)=>(X378 @ X379))))=>?[X380:$i]:(((in @ X380 @ X377)&~(X378 @ X380)))))=>(![X381:$i > $o]:((?[X382:$i]:(((X381 @ X382)&![X383:$i]:(((X381 @ X383)=>((X382)=(X383))))))=>?[X384:$i]:(((X381 @ X384)&![X385:$i]:(((X381 @ X385)=>((X384)=(X385))))))))=>(![X386:$i > $o]:((?[X387:$i]:((X386 @ X387))=>(![X388:$i, X389:$i]:(((X386 @ X388)=>((X386 @ X389)=>((X388)=(X389)))))=>?[X390:$i]:(((X386 @ X390)&![X391:$i]:(((X386 @ X391)=>((X390)=(X391)))))))))=>(![X392:$i > $o]:((?[X393:$i]:(![X394:$i]:(((X392 @ X394)<=>((X394)=(X393)))))=>?[X395:$i]:(((X392 @ X395)&![X396:$i]:(((X392 @ X396)=>((X395)=(X396))))))))=>![X4:$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(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(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_74, upairsetIL]), upairsetE]), upairsetIR]), c_0_75]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), c_0_76]), quantDeMorgan4]), omegaIndAx]), prop2setI]), omegaSAx]), notdexE]), omega0Ax]), notdallE]), setunionAx]), c_0_77]), powersetAx]), c_0_78]), setadjoinAx]), c_0_79]), foundationAx]), emptysetE]), prop2setE]), c_0_80]), c_0_81]), c_0_82]), c_0_83]), wellorderingAx]), emptysetimpfalse]), c_0_84]), c_0_85]), noeltsimpempty]), emptyI]), setext]), c_0_86]), notinemptyset]), c_0_87]), c_0_88]), setadjoinOr]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), c_0_89]), powersetI]), c_0_90]), subPowSU]), setunionE]), setunionI]), powersetE]), emptyInPowerset]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), emptyinPowerset]), c_0_91]), emptysetAx]), setextAx])]), c_0_92])).
% 0.10/0.27 thf(c_0_94, negated_conjecture, ![X397:$i, X398:$i, X400:$i, X401:$i, X402:$i, X403:$i, X404:$i, X405:$i, X406:$i, X407:$i, X408:$i, X410:$i, X411:$i, X413:$i, X414:$i, X415:$i, X416:$i, X417:$i, X419:$i, X420:$i > $i > $o, X421:$i, X423:$i, X426:$i, X428:$i, X429:$i, X430:$i, X431:$i, X433:$i, X434:$i, X435:$i > $o, X436:$i, X437:$i, X438:$i > $o, X439:$i, X440:$i, X441:$i > $o, X442:$i, X443:$i > $o, X444:$i, X447:$i, X448:$o, X449:$i, X450:$i, X451:$o, X452:$i, X453:$i, X454:$i > $o, X455:$i, X458:$i, X459:$i, X462:$i, X464:$i, X466:$i, X467:$i > $o, X468:$i, X469:$i, X471:$i, X472:$i > $o, X473:$i, X474:$i, X475:$i, X476:$i, X477:$i, X478:$i, X479:$i, X480:$i, X481:$i, X482:$i, X483:$i, X484:$o, X485:$i, X486:$i, X487:$i, X488:$i, X489:$i, X490:$i, X492:$i, X493:$i, X494:$i, X495:$i, X496:$i, X497:$i, X498:$i, X499:$i, X500:$i, X501:$i, X502:$o, X504:$i, X505:$i, X506:$i > $o, X507:$i, X510:$i, X511:$i, X512:$i, X514:$i, X515:$i, X516:$i, X517:$i, X518:$i, X519:$i, X520:$i, X521:$i, X522:$i, X523:$i, X524:$i, X525:$i, X526:$i, X527:$i, X528:$i, X529:$i, X530:$i > $o, X531:$i, X532:$i > $o, X533:$i, X534:$i, X535:$i > $o, X536:$i, X538:$i, X539:$i > $o, X541:$i, X542:$i, X543:$i > $o, X545:$i, X546:$i, X547:$i > $o, X548:$i, X550:$o, X551:$i, X552:$i > $o, X554:$i, X555:$i, X556:$i > $o, X557:$i, X559:$i > $o, X560:$i, X563:$i, X564:$i > $o, X565:$i, X569:$i, X570:$i > $o, X571:$i, X574:$i]:((((~(in @ (esk1_2 @ X397 @ X398) @ X397)|~(in @ (esk1_2 @ X397 @ X398) @ X398)|((X397)=(X398)))&((in @ (esk1_2 @ X397 @ X398) @ X397)|(in @ (esk1_2 @ X397 @ X398) @ X398)|((X397)=(X398))))&(~(in @ X400 @ emptyset)&(((~(in @ X403 @ (setadjoin @ X401 @ X402))|(((X403)=(X401))|(in @ X403 @ X402)))&((((X403)!=(X401))|(in @ X403 @ (setadjoin @ X401 @ X402)))&(~(in @ X403 @ X402)|(in @ X403 @ (setadjoin @ X401 @ X402)))))&(((~(in @ X405 @ (powerset @ X404))|(~(in @ X406 @ X405)|(in @ X406 @ X404)))&(((in @ (esk2_2 @ X407 @ X408) @ X408)|(in @ X408 @ (powerset @ X407)))&(~(in @ (esk2_2 @ X407 @ X408) @ X407)|(in @ X408 @ (powerset @ X407)))))&(((((in @ X411 @ (esk3_2 @ X410 @ X411))|~(in @ X411 @ (setunion @ X410)))&((in @ (esk3_2 @ X410 @ X411) @ X410)|~(in @ X411 @ (setunion @ X410))))&(~(in @ X414 @ X415)|~(in @ X415 @ X413)|(in @ X414 @ (setunion @ X413))))&((in @ emptyset @ omega)&((~(in @ X416 @ omega)|(in @ (setadjoin @ X416 @ X416) @ omega))&(((((in @ (esk4_1 @ X417) @ omega)|~(in @ emptyset @ X417)|(~(in @ X419 @ omega)|(in @ X419 @ X417)))&((in @ (esk4_1 @ X417) @ X417)|~(in @ emptyset @ X417)|(~(in @ X419 @ omega)|(in @ X419 @ X417))))&(~(in @ (setadjoin @ (esk4_1 @ X417) @ (esk4_1 @ X417)) @ X417)|~(in @ emptyset @ X417)|(~(in @ X419 @ omega)|(in @ X419 @ X417))))&((((((in @ (esk8_3 @ X420 @ X421 @ X426) @ X421)|~(in @ X426 @ (esk7_2 @ X420 @ X421))|(in @ (esk5_2 @ X420 @ X421) @ X421))&((X420 @ (esk8_3 @ X420 @ X421 @ X426) @ X426)|~(in @ X426 @ (esk7_2 @ X420 @ X421))|(in @ (esk5_2 @ X420 @ X421) @ X421)))&(~(in @ X429 @ X421)|~(X420 @ X429 @ X428)|(in @ X428 @ (esk7_2 @ X420 @ X421))|(in @ (esk5_2 @ X420 @ X421) @ X421)))&(((((in @ (esk8_3 @ X420 @ X421 @ X426) @ X421)|~(in @ X426 @ (esk7_2 @ X420 @ X421))|((X420 @ (esk5_2 @ X420 @ X421) @ (esk6_3 @ X420 @ X421 @ X423))|~(X420 @ (esk5_2 @ X420 @ X421) @ X423)))&((X420 @ (esk8_3 @ X420 @ X421 @ X426) @ X426)|~(in @ X426 @ (esk7_2 @ X420 @ X421))|((X420 @ (esk5_2 @ X420 @ X421) @ (esk6_3 @ X420 @ X421 @ X423))|~(X420 @ (esk5_2 @ X420 @ X421) @ X423))))&(~(in @ X429 @ X421)|~(X420 @ X429 @ X428)|(in @ X428 @ (esk7_2 @ X420 @ X421))|((X420 @ (esk5_2 @ X420 @ X421) @ (esk6_3 @ X420 @ X421 @ X423))|~(X420 @ (esk5_2 @ X420 @ X421) @ X423))))&((((in @ (esk8_3 @ X420 @ X421 @ X426) @ X421)|~(in @ X426 @ (esk7_2 @ X420 @ X421))|(((X423)!=(esk6_3 @ X420 @ X421 @ X423))|~(X420 @ (esk5_2 @ X420 @ X421) @ X423)))&((X420 @ (esk8_3 @ X420 @ X421 @ X426) @ X426)|~(in @ X426 @ (esk7_2 @ X420 @ X421))|(((X423)!=(esk6_3 @ X420 @ X421 @ X423))|~(X420 @ (esk5_2 @ X420 @ X421) @ X423))))&(~(in @ X429 @ X421)|~(X420 @ X429 @ X428)|(in @ X428 @ (esk7_2 @ X420 @ X421))|(((X423)!=(esk6_3 @ X420 @ X421 @ X423))|~(X420 @ (esk5_2 @ X420 @ X421) @ X423))))))&((((in @ (esk9_1 @ X430) @ X430)|~(in @ X431 @ X430))&(~(in @ X433 @ (esk9_1 @ X430))|~(in @ X433 @ X430)|~(in @ X431 @ X430)))&((epred1_0)&((descrp)&((~(in @ X436 @ X434)|(~(X435 @ X436)|(in @ X436 @ (dsetconstr @ X434 @ (^[Z0:$i]:((X435 @ Z0)))))))&((~(in @ X439 @ (dsetconstr @ X437 @ (^[Z0:$i]:((X438 @ Z0)))))|(in @ X439 @ X437))&((~(in @ X442 @ (dsetconstr @ X440 @ (^[Z0:$i]:((X441 @ Z0)))))|(X441 @ X442))&(((((X443 @ (esk11_1 @ X443))|((X443 @ (esk10_2 @ X443 @ X444))|~(X443 @ X444)))&(~(X443 @ X447)|((esk11_1 @ X443)=(X447))|((X443 @ (esk10_2 @ X443 @ X444))|~(X443 @ X444))))&(((X443 @ (esk11_1 @ X443))|(((X444)!=(esk10_2 @ X443 @ X444))|~(X443 @ X444)))&(~(X443 @ X447)|((esk11_1 @ X443)=(X447))|(((X444)!=(esk10_2 @ X443 @ X444))|~(X443 @ X444)))))&((~(in @ X449 @ (prop2set @ ((X448))))|(X448))&((~(in @ X450 @ emptyset)|(X451))&(~(in @ X452 @ emptyset)&(~(in @ X453 @ emptyset)&((((X454 @ (esk12_2 @ X454 @ X455))|~(X454 @ X455)|(X454 @ (esk13_1 @ X454)))&(((X455)!=(esk12_2 @ X454 @ X455))|~(X454 @ X455)|(X454 @ (esk13_1 @ X454))))&(((((in @ (esk15_2 @ X458 @ X459) @ X459)|((X458)=(X459))|(in @ (esk14_2 @ X458 @ X459) @ X458))&(~(in @ (esk15_2 @ X458 @ X459) @ X458)|((X458)=(X459))|(in @ (esk14_2 @ X458 @ X459) @ X458)))&(((in @ (esk15_2 @ X458 @ X459) @ X459)|((X458)=(X459))|~(in @ (esk14_2 @ X458 @ X459) @ X459))&(~(in @ (esk15_2 @ X458 @ X459) @ X458)|((X458)=(X459))|~(in @ (esk14_2 @ X458 @ X459) @ X459))))&(((in @ (esk16_1 @ X462) @ X462)|((X462)=(emptyset)))&(((in @ (esk17_1 @ X464) @ X464)|((X464)=(emptyset)))&(((~(in @ X468 @ (dsetconstr @ X466 @ (^[Z0:$i]:((X467 @ Z0)))))|(X467 @ X468)|~(in @ X468 @ X466))&(~(X467 @ X468)|(in @ X468 @ (dsetconstr @ X466 @ (^[Z0:$i]:((X467 @ Z0)))))|~(in @ X468 @ X466)))&((((X469)=(emptyset))|(in @ (esk18_1 @ X469) @ X469))&((~(in @ X473 @ X471)|(~(X472 @ X473)|((dsetconstr @ X471 @ (^[Z0:$i]:((X472 @ Z0))))!=(emptyset))))&((~(in @ X475 @ X474)|((X474)!=(emptyset)))&((in @ X476 @ (setadjoin @ X476 @ X477))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X480 @ X479)|(in @ X480 @ (setadjoin @ X478 @ X479)))&(((((in @ X483 @ X482)|(X484)|((X483)=(X481))|~(in @ X483 @ (setadjoin @ X481 @ X482)))&(~(X484)|(X484)|((X483)=(X481))|~(in @ X483 @ (setadjoin @ X481 @ X482))))&(((in @ X483 @ X482)|(X484)|~(X484)|~(in @ X483 @ (setadjoin @ X481 @ X482)))&(~(X484)|(X484)|~(X484)|~(in @ X483 @ (setadjoin @ X481 @ X482)))))&((~(in @ X487 @ (setadjoin @ X485 @ X486))|(((X487)=(X485))|(in @ X487 @ X486)))&(((dsetconstr @ X488 @ (^[Z0:$i]:(($true))))=(X488))&((((in @ (esk19_2 @ X489 @ X490) @ X490)|(in @ X490 @ (powerset @ X489)))&(~(in @ (esk19_2 @ X489 @ X490) @ X489)|(in @ X490 @ (powerset @ X489))))&((in @ emptyset @ (powerset @ X492))&((in @ emptyset @ (powerset @ X493))&((~(in @ X495 @ (powerset @ X494))|(~(in @ X496 @ X495)|(in @ X496 @ X494)))&((~(in @ X498 @ X499)|(~(in @ X499 @ X497)|(in @ X498 @ (setunion @ X497))))&((((in @ X501 @ (esk20_3 @ X500 @ X501 @ X502))|(X502)|~(in @ X501 @ (setunion @ X500)))&(((in @ (esk20_3 @ X500 @ X501 @ X502) @ X500)|(X502)|~(in @ X501 @ (setunion @ X500)))&(~(X502)|(X502)|~(in @ X501 @ (setunion @ X500)))))&((~(in @ X505 @ X504)|(in @ X505 @ (powerset @ (setunion @ X504))))&((((~(X506 @ X510)|((X510)=(esk22_1 @ X506))|((X506 @ (esk21_2 @ X506 @ X507))|~(X506 @ X507)))&(((X511)!=(esk22_1 @ X506))|(X506 @ X511)|((X506 @ (esk21_2 @ X506 @ X507))|~(X506 @ X507))))&((~(X506 @ X510)|((X510)=(esk22_1 @ X506))|(((X507)!=(esk21_2 @ X506 @ X507))|~(X506 @ X507)))&(((X511)!=(esk22_1 @ X506))|(X506 @ X511)|(((X507)!=(esk21_2 @ X506 @ X507))|~(X506 @ X507)))))&((((X512)=(emptyset))|(in @ (esk23_1 @ X512) @ X512))&((~(in @ X514 @ (setadjoin @ X515 @ emptyset))|((X514)=(X515)))&((((X516)=(X517))|~(in @ X517 @ (setadjoin @ X516 @ emptyset)))&((((X518)!=(X519))|(in @ X518 @ (setadjoin @ X519 @ emptyset)))&((~(in @ X520 @ (setadjoin @ X521 @ emptyset))|(in @ X521 @ (setadjoin @ X520 @ emptyset)))&((~(in @ X524 @ (setadjoin @ X522 @ (setadjoin @ X523 @ emptyset)))|(((X524)=(X522))|((X524)=(X523))))&((in @ X525 @ (setadjoin @ X525 @ (setadjoin @ X526 @ emptyset)))&((in @ X528 @ (setadjoin @ X527 @ (setadjoin @ X528 @ emptyset)))&((~(in @ X531 @ X529)|~(X530 @ X531)|((dsetconstr @ X529 @ (^[Z0:$i]:((X530 @ Z0))))!=(emptyset)))&((~(in @ X533 @ emptyset)|(X532 @ X533))&((((in @ (esk24_2 @ X534 @ X535) @ X534)|(~(in @ X536 @ X534)|(X535 @ X536)))&(~(X535 @ (esk24_2 @ X534 @ X535))|(~(in @ X536 @ X534)|(X535 @ X536))))&((((in @ (esk25_2 @ X538 @ X539) @ X538)|(~(in @ X541 @ X538)|~(X539 @ X541)))&((X539 @ (esk25_2 @ X538 @ X539))|(~(in @ X541 @ X538)|~(X539 @ X541))))&((((in @ (esk26_2 @ X542 @ X543) @ X542)|(~(in @ X545 @ X542)|~(X543 @ X545)))&((X543 @ (esk26_2 @ X542 @ X543))|(~(in @ X545 @ X542)|~(X543 @ X545))))&((((in @ (esk27_2 @ X546 @ X547) @ X546)|(~(in @ X548 @ X546)|(X547 @ X548)))&(~(X547 @ (esk27_2 @ X546 @ X547))|(~(in @ X548 @ X546)|(X547 @ X548))))&((~(X550)|(in @ emptyset @ (prop2set @ ((X550)))))&((prop2set2propI)&((((in @ (esk28_2 @ X551 @ X552) @ X551)|(~(in @ X554 @ X551)|~(X552 @ X554)))&((X552 @ (esk28_2 @ X551 @ X552))|(~(in @ X554 @ X551)|~(X552 @ X554))))&((((in @ (esk29_2 @ X555 @ X556) @ X555)|(~(in @ X557 @ X555)|(X556 @ X557)))&(~(X556 @ (esk29_2 @ X555 @ X556))|(~(in @ X557 @ X555)|(X556 @ X557))))&(((((X559 @ (esk31_1 @ X559))|((X559 @ (esk30_2 @ X559 @ X560))|~(X559 @ X560)))&(~(X559 @ X563)|((esk31_1 @ X559)=(X563))|((X559 @ (esk30_2 @ X559 @ X560))|~(X559 @ X560))))&(((X559 @ (esk31_1 @ X559))|(((X560)!=(esk30_2 @ X559 @ X560))|~(X559 @ X560)))&(~(X559 @ X563)|((esk31_1 @ X559)=(X563))|(((X560)!=(esk30_2 @ X559 @ X560))|~(X559 @ X560)))))&(((((X564 @ (esk34_1 @ X564))|(X564 @ (esk32_1 @ X564))|~(X564 @ X565))&(~(X564 @ X569)|((esk34_1 @ X564)=(X569))|(X564 @ (esk32_1 @ X564))|~(X564 @ X565)))&((((X564 @ (esk34_1 @ X564))|(X564 @ (esk33_1 @ X564))|~(X564 @ X565))&(~(X564 @ X569)|((esk34_1 @ X564)=(X569))|(X564 @ (esk33_1 @ X564))|~(X564 @ X565)))&(((X564 @ (esk34_1 @ X564))|((esk32_1 @ X564)!=(esk33_1 @ X564))|~(X564 @ X565))&(~(X564 @ X569)|((esk34_1 @ X564)=(X569))|((esk32_1 @ X564)!=(esk33_1 @ X564))|~(X564 @ X565)))))&(((((X570 @ (esk36_1 @ X570))|(~(X570 @ (esk35_2 @ X570 @ X571))|((esk35_2 @ X570 @ X571)!=(X571))))&(~(X570 @ X574)|((esk36_1 @ X570)=(X574))|(~(X570 @ (esk35_2 @ X570 @ X571))|((esk35_2 @ X570 @ X571)!=(X571)))))&(((X570 @ (esk36_1 @ X570))|((X570 @ (esk35_2 @ X570 @ X571))|((esk35_2 @ X570 @ X571)=(X571))))&(~(X570 @ X574)|((esk36_1 @ X570)=(X574))|((X570 @ (esk35_2 @ X570 @ X571))|((esk35_2 @ X570 @ X571)=(X571))))))&(((esk37_0)=(esk38_0))&(((esk39_0)=(esk40_0))&((in @ esk39_0 @ esk37_0)&~(in @ esk40_0 @ esk38_0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_93])])])])])])).
% 0.10/0.27 thf(c_0_95, negated_conjecture, (in @ esk39_0 @ esk37_0), inference(split_conjunct,[status(thm)],[c_0_94])).
% 0.10/0.27 thf(c_0_96, negated_conjecture, ((esk39_0)=(esk40_0)), inference(split_conjunct,[status(thm)],[c_0_94])).
% 0.10/0.27 thf(c_0_97, negated_conjecture, ~((in @ esk40_0 @ esk38_0)), inference(split_conjunct,[status(thm)],[c_0_94])).
% 0.10/0.27 thf(c_0_98, negated_conjecture, ((esk37_0)=(esk38_0)), inference(split_conjunct,[status(thm)],[c_0_94])).
% 0.10/0.27 thf(c_0_99, negated_conjecture, (in @ esk40_0 @ esk37_0), inference(rw,[status(thm)],[c_0_95, c_0_96])).
% 0.10/0.27 thf(c_0_100, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_97, c_0_98]), c_0_99])]), ['proof']).
% 0.10/0.27 % SZS output end CNFRefutation
% 0.10/0.27 % Parsed axioms : 141
% 0.10/0.27 % Removed by relevancy pruning/SinE : 77
% 0.10/0.27 % Initial clauses : 132
% 0.10/0.27 % Removed in clause preprocessing : 4
% 0.10/0.27 % Initial clauses in saturation : 128
% 0.10/0.27 % Processed clauses : 8
% 0.10/0.27 % ...of these trivial : 0
% 0.10/0.27 % ...subsumed : 0
% 0.10/0.27 % ...remaining for further processing : 7
% 0.10/0.27 % Other redundant clauses eliminated : 0
% 0.10/0.27 % Clauses deleted for lack of memory : 0
% 0.10/0.27 % Backward-subsumed : 0
% 0.10/0.27 % Backward-rewritten : 0
% 0.10/0.27 % Generated clauses : 0
% 0.10/0.27 % ...of the previous two non-redundant : 0
% 0.10/0.27 % ...aggressively subsumed : 0
% 0.10/0.27 % Contextual simplify-reflections : 0
% 0.10/0.27 % Paramodulations : 0
% 0.10/0.27 % Factorizations : 0
% 0.10/0.27 % NegExts : 0
% 0.10/0.27 % Equation resolutions : 0
% 0.10/0.27 % Disequality decompositions : 0
% 0.10/0.27 % Total rewrite steps : 3
% 0.10/0.27 % ...of those cached : 0
% 0.10/0.27 % Propositional unsat checks : 0
% 0.10/0.27 % Propositional check models : 0
% 0.10/0.27 % Propositional check unsatisfiable : 0
% 0.10/0.27 % Propositional clauses : 0
% 0.10/0.27 % Propositional clauses after purity: 0
% 0.10/0.27 % Propositional unsat core size : 0
% 0.10/0.27 % Propositional preprocessing time : 0.000
% 0.10/0.27 % Propositional encoding time : 0.000
% 0.10/0.27 % Propositional solver time : 0.000
% 0.10/0.27 % Success case prop preproc time : 0.000
% 0.10/0.27 % Success case prop encoding time : 0.000
% 0.10/0.27 % Success case prop solver time : 0.000
% 0.10/0.27 % Current number of processed clauses : 7
% 0.10/0.27 % Positive orientable unit clauses : 7
% 0.10/0.27 % Positive unorientable unit clauses: 0
% 0.10/0.27 % Negative unit clauses : 0
% 0.10/0.27 % Non-unit-clauses : 0
% 0.10/0.27 % Current number of unprocessed clauses: 120
% 0.10/0.27 % ...number of literals in the above : 362
% 0.10/0.27 % Current number of archived formulas : 0
% 0.10/0.27 % Current number of archived clauses : 0
% 0.10/0.27 % Clause-clause subsumption calls (NU) : 0
% 0.10/0.27 % Rec. Clause-clause subsumption calls : 0
% 0.10/0.27 % Non-unit clause-clause subsumptions : 0
% 0.10/0.27 % Unit Clause-clause subsumption calls : 0
% 0.10/0.27 % Rewrite failures with RHS unbound : 0
% 0.10/0.27 % BW rewrite match attempts : 0
% 0.10/0.27 % BW rewrite match successes : 0
% 0.10/0.27 % Condensation attempts : 0
% 0.10/0.27 % Condensation successes : 0
% 0.10/0.27 % Termbank termtop insertions : 14325
% 0.10/0.27 % Search garbage collected termcells : 5680
% 0.10/0.27
% 0.10/0.27 % -------------------------------------------------
% 0.10/0.27 % User time : 0.012 s
% 0.10/0.27 % System time : 0.004 s
% 0.10/0.27 % Total time : 0.016 s
% 0.10/0.27 % Maximum resident set size: 5568 pages
% 0.10/0.27
% 0.10/0.27 % -------------------------------------------------
% 0.10/0.27 % User time : 0.015 s
% 0.10/0.27 % System time : 0.009 s
% 0.10/0.27 % Total time : 0.025 s
% 0.10/0.27 % Maximum resident set size: 5120 pages
% 0.10/0.27 % E exiting
%------------------------------------------------------------------------------