%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU538^1 : 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 : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:26:38 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU538^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n026.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:51:42 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 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.ENsOZL7Wiv/E---3.1_622782.p
% 0.22/0.28 % Version: 3.5.1-ho
% 0.22/0.28 % Preprocessing class: HSMSSLSSMLLCHSA.
% 0.22/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.28 % Starting sh5l with 300s (1) cores
% 0.22/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.22/0.28 % Starting new_bool_2 with 300s (1) cores
% 0.22/0.28 % new_bool_2 with pid 622816 completed with status 0
% 0.22/0.28 % Result found by new_bool_2
% 0.22/0.28 % Preprocessing class: HSMSSLSSMLLCHSA.
% 0.22/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.28 % Starting sh5l with 300s (1) cores
% 0.22/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.22/0.28 % Starting new_bool_2 with 300s (1) cores
% 0.22/0.28 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.22/0.28 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/0.28 % Search class: HGHSM-FFMM31-SHSSMSBN
% 0.22/0.28 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.28 % Starting SubtermCWHack with 31s (1) cores
% 0.22/0.28 % SubtermCWHack with pid 622819 completed with status 0
% 0.22/0.28 % Result found by SubtermCWHack
% 0.22/0.28 % Preprocessing class: HSMSSLSSMLLCHSA.
% 0.22/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.28 % Starting sh5l with 300s (1) cores
% 0.22/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.22/0.28 % Starting new_bool_2 with 300s (1) cores
% 0.22/0.28 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.22/0.28 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/0.28 % Search class: HGHSM-FFMM31-SHSSMSBN
% 0.22/0.28 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.28 % Starting SubtermCWHack with 31s (1) cores
% 0.22/0.28 % Preprocessing time : 0.003 s
% 0.22/0.28
% 0.22/0.28 % Proof found!
% 0.22/0.28 % SZS status Theorem
% 0.22/0.28 % SZS output start CNFRefutation
% 0.22/0.28 thf(decl_23, type, in: $i > $i > $o).
% 0.22/0.28 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.22/0.28 thf(decl_25, type, setextAx: $o).
% 0.22/0.28 thf(decl_26, type, emptyset: $i).
% 0.22/0.28 thf(decl_27, type, emptysetAx: $o).
% 0.22/0.28 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.22/0.28 thf(decl_29, type, setadjoinAx: $o).
% 0.22/0.28 thf(decl_30, type, powerset: $i > $i).
% 0.22/0.28 thf(decl_31, type, powersetAx: $o).
% 0.22/0.28 thf(decl_32, type, setunion: $i > $i).
% 0.22/0.28 thf(decl_33, type, setunionAx: $o).
% 0.22/0.28 thf(decl_34, type, omega: $i).
% 0.22/0.28 thf(decl_35, type, omega0Ax: $o).
% 0.22/0.28 thf(decl_36, type, omegaSAx: $o).
% 0.22/0.28 thf(decl_37, type, omegaIndAx: $o).
% 0.22/0.28 thf(decl_38, type, replAx: $o).
% 0.22/0.28 thf(decl_39, type, foundationAx: $o).
% 0.22/0.28 thf(decl_40, type, wellorderingAx: $o).
% 0.22/0.28 thf(decl_42, type, descrp: $o).
% 0.22/0.28 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.22/0.28 thf(decl_44, type, dsetconstrI: $o).
% 0.22/0.28 thf(decl_45, type, dsetconstrEL: $o).
% 0.22/0.28 thf(decl_46, type, dsetconstrER: $o).
% 0.22/0.28 thf(decl_47, type, exuE1: $o).
% 0.22/0.28 thf(decl_48, type, prop2set: $o > $i).
% 0.22/0.28 thf(decl_49, type, prop2setE: $o).
% 0.22/0.28 thf(decl_50, type, emptysetE: $o).
% 0.22/0.28 thf(decl_51, type, emptysetimpfalse: $o).
% 0.22/0.28 thf(decl_52, type, notinemptyset: $o).
% 0.22/0.28 thf(decl_53, type, exuE3e: $o).
% 0.22/0.28 thf(decl_54, type, setext: $o).
% 0.22/0.28 thf(decl_55, type, emptyI: $o).
% 0.22/0.28 thf(decl_56, type, noeltsimpempty: $o).
% 0.22/0.28 thf(decl_57, type, setbeta: $o).
% 0.22/0.28 thf(decl_58, type, nonempty: $i > $o).
% 0.22/0.28 thf(decl_59, type, nonemptyE1: $o).
% 0.22/0.28 thf(decl_60, type, nonemptyI: $o).
% 0.22/0.28 thf(decl_61, type, nonemptyI1: $o).
% 0.22/0.28 thf(decl_62, type, setadjoinIL: $o).
% 0.22/0.28 thf(decl_63, type, emptyinunitempty: $o).
% 0.22/0.28 thf(decl_64, type, setadjoinIR: $o).
% 0.22/0.28 thf(decl_65, type, setadjoinE: $o).
% 0.22/0.28 thf(decl_66, type, setadjoinOr: $o).
% 0.22/0.28 thf(decl_67, type, setoftrueEq: $o).
% 0.22/0.28 thf(decl_68, type, powersetI: $o).
% 0.22/0.28 thf(decl_69, type, emptyinPowerset: $o).
% 0.22/0.28 thf(decl_70, type, emptyInPowerset: $o).
% 0.22/0.28 thf(decl_71, type, powersetE: $o).
% 0.22/0.28 thf(decl_72, type, setunionI: $o).
% 0.22/0.28 thf(decl_73, type, setunionE: $o).
% 0.22/0.28 thf(decl_74, type, subPowSU: $o).
% 0.22/0.28 thf(decl_75, type, exuE2: $o).
% 0.22/0.28 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.22/0.28 thf(decl_77, type, uniqinunit: $o).
% 0.22/0.28 thf(decl_78, type, notinsingleton: $o).
% 0.22/0.28 thf(decl_79, type, eqinunit: $o).
% 0.22/0.28 thf(decl_80, type, singletonsswitch: $o).
% 0.22/0.28 thf(decl_81, type, upairsetE: $o).
% 0.22/0.28 thf(decl_82, type, upairsetIL: $o).
% 0.22/0.28 thf(decl_83, type, upairsetIR: $o).
% 0.22/0.28 thf(decl_84, type, emptyE1: $o).
% 0.22/0.28 thf(decl_85, type, vacuousDall: $o).
% 0.22/0.28 thf(decl_86, type, quantDeMorgan1: $o).
% 0.22/0.28 thf(decl_87, type, quantDeMorgan2: $o).
% 0.22/0.28 thf(decl_88, type, epred1_0: $o).
% 0.22/0.28 thf(decl_89, type, esk1_2: $i > $i > $i).
% 0.22/0.28 thf(decl_90, type, esk2_2: $i > $i > $i).
% 0.22/0.28 thf(decl_91, type, esk3_2: $i > $i > $i).
% 0.22/0.28 thf(decl_92, type, esk4_1: $i > $i).
% 0.22/0.28 thf(decl_93, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.22/0.28 thf(decl_94, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.22/0.28 thf(decl_95, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.22/0.28 thf(decl_96, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.22/0.28 thf(decl_97, type, esk9_1: $i > $i).
% 0.22/0.28 thf(decl_98, type, esk10_2: ($i > $o) > $i > $i).
% 0.22/0.28 thf(decl_99, type, esk11_1: ($i > $o) > $i).
% 0.22/0.28 thf(decl_100, type, esk12_2: ($i > $o) > $i > $i).
% 0.22/0.28 thf(decl_101, type, esk13_1: ($i > $o) > $i).
% 0.22/0.28 thf(decl_102, type, esk14_2: $i > $i > $i).
% 0.22/0.28 thf(decl_103, type, esk15_2: $i > $i > $i).
% 0.22/0.28 thf(decl_104, type, esk16_1: $i > $i).
% 0.22/0.28 thf(decl_105, type, esk17_1: $i > $i).
% 0.22/0.28 thf(decl_106, type, esk18_1: $i > $i).
% 0.22/0.28 thf(decl_107, type, esk19_2: $i > $i > $i).
% 0.22/0.28 thf(decl_108, type, esk20_3: $i > $i > $o > $i).
% 0.22/0.28 thf(decl_109, type, esk21_2: ($i > $o) > $i > $i).
% 0.22/0.28 thf(decl_110, type, esk22_1: ($i > $o) > $i).
% 0.22/0.28 thf(decl_111, type, esk23_1: $i > $i).
% 0.22/0.28 thf(decl_112, type, esk24_2: $i > ($i > $o) > $i).
% 0.22/0.28 thf(decl_113, type, esk25_2: $i > ($i > $o) > $i).
% 0.22/0.28 thf(decl_114, type, esk26_0: $i).
% 0.22/0.28 thf(decl_115, type, epred2_0: $i > $o).
% 0.22/0.28 thf(decl_116, type, esk27_0: $i).
% 0.22/0.28 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', replAx)).
% 0.22/0.28 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', exu)).
% 0.22/0.28 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', exuE1)).
% 0.22/0.28 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', exuE3e)).
% 0.22/0.28 thf(prop2set, axiom, ((prop2set)=(^[X10:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[X2:$i]:((X10)))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', prop2set)).
% 0.22/0.28 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', nonempty)).
% 0.22/0.28 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', nonemptyI)).
% 0.22/0.28 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', exuE2)).
% 0.22/0.28 thf(quantDeMorgan3, 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)=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', quantDeMorgan3)).
% 0.22/0.28 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.ENsOZL7Wiv/E---3.1_622782.p', emptyE1)).
% 0.22/0.28 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', dsetconstrER)).
% 0.22/0.28 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', dsetconstrEL)).
% 0.22/0.28 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', dsetconstrI)).
% 0.22/0.28 thf(prop2setE, axiom, ((prop2setE)<=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', prop2setE)).
% 0.22/0.28 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', nonemptyI1)).
% 0.22/0.28 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', nonemptyE1)).
% 0.22/0.28 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', setbeta)).
% 0.22/0.28 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', setoftrueEq)).
% 0.22/0.28 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', nonemptyImpWitness)).
% 0.22/0.28 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', foundationAx)).
% 0.22/0.28 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', notinsingleton)).
% 0.22/0.28 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', eqinunit)).
% 0.22/0.28 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', singletonsswitch)).
% 0.22/0.28 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X15:$i]:(((in @ X15 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X15)=(X2))|((X15)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', upairsetE)).
% 0.22/0.28 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', upairsetIL)).
% 0.22/0.28 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', upairsetIR)).
% 0.22/0.28 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', vacuousDall)).
% 0.22/0.28 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', quantDeMorgan1)).
% 0.22/0.28 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', quantDeMorgan2)).
% 0.22/0.28 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.ENsOZL7Wiv/E---3.1_622782.p', wellorderingAx)).
% 0.22/0.28 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', setunionI)).
% 0.22/0.28 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', powersetE)).
% 0.22/0.28 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', omegaIndAx)).
% 0.22/0.28 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', emptyI)).
% 0.22/0.28 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', setext)).
% 0.22/0.28 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', notinemptyset)).
% 0.22/0.28 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', emptysetimpfalse)).
% 0.22/0.28 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', emptysetE)).
% 0.22/0.28 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', noeltsimpempty)).
% 0.22/0.28 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', omegaSAx)).
% 0.22/0.28 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', setadjoinIR)).
% 0.22/0.28 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', emptyinunitempty)).
% 0.22/0.28 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', setadjoinIL)).
% 0.22/0.28 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X13:$o]:(((((X3)=(X2))=>(X13))=>(((in @ X3 @ X4)=>(X13))=>(X13))))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', setadjoinE)).
% 0.22/0.28 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', emptyInPowerset)).
% 0.22/0.28 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', emptyinPowerset)).
% 0.22/0.28 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', powersetI)).
% 0.22/0.28 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', setadjoinOr)).
% 0.22/0.28 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', subPowSU)).
% 0.22/0.28 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', uniqinunit)).
% 0.22/0.28 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X14:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X14))))=>(X14)))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', setunionE)).
% 0.22/0.28 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', omega0Ax)).
% 0.22/0.28 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', setunionAx)).
% 0.22/0.28 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', powersetAx)).
% 0.22/0.28 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', setadjoinAx)).
% 0.22/0.28 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', emptysetAx)).
% 0.22/0.28 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.ENsOZL7Wiv/E---3.1_622782.p', setextAx)).
% 0.22/0.28 thf(c_0_57, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.22/0.28 thf(c_0_58, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.22/0.28 thf(c_0_59, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.22/0.28 thf(c_0_60, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.22/0.28 thf(c_0_61, plain, ((prop2set)=(^[Z0:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[Z1:$i]:((Z0)))))), inference(fof_simplification,[status(thm)],[prop2set])).
% 0.22/0.28 thf(c_0_62, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.22/0.28 thf(c_0_63, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.22/0.28 thf(c_0_64, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.22/0.28 thf(c_0_65, 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)=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[quantDeMorgan3])).
% 0.22/0.28 thf(c_0_66, plain, ((emptyE1)<=>![X4:$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])).
% 0.22/0.28 thf(c_0_67, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.22/0.28 thf(c_0_68, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.22/0.28 thf(c_0_69, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.22/0.28 thf(c_0_70, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X167:$i]:(((((X6 @ X2 @ X167)))&(![X168:$i]:(((((X6 @ X2 @ X168)))=>(((X167)=(X168)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_57, c_0_58])).
% 0.22/0.28 thf(c_0_71, plain, ((exuE1)=(![X1:$i > $o]:((((?[X169:$i]:(((((X1 @ X169)))&(![X170:$i]:(((((X1 @ X170)))=>(((X169)=(X170))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_59, c_0_58])).
% 0.22/0.28 thf(c_0_72, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X171:$i]:(((((X1 @ X171)))&(![X172:$i]:(((((X1 @ X172)))=>(((X171)=(X172))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_60, c_0_58])).
% 0.22/0.28 thf(c_0_73, axiom, ((prop2setE)=(![X11:$o, X2:$i]:((((in @ X2 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:(((X11)))))))=>((X11)))))), inference(apply_def,[status(thm)],[prop2setE, c_0_61])).
% 0.22/0.28 thf(c_0_74, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_62])).
% 0.22/0.28 thf(c_0_75, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_63, c_0_62])).
% 0.22/0.28 thf(c_0_76, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_62])).
% 0.22/0.28 thf(c_0_77, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.22/0.28 thf(c_0_78, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.22/0.28 thf(c_0_79, plain, ((exuE2)=(![X1:$i > $o]:((((?[X173:$i]:(((((X1 @ X173)))&(![X174:$i]:(((((X1 @ X174)))=>(((X173)=(X174))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_64, c_0_58])).
% 0.22/0.28 thf(c_0_80, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_62])).
% 0.22/0.28 thf(c_0_81, plain, ((epred1_0)<=>![X204:$i]:(?[X205:$i]:((((![X206:$i]:(((in @ X206 @ X205)=>![X207:$i]:(((in @ X207 @ X206)=>(in @ X207 @ X204)))))&![X208:$i, X209:$i]:((((in @ X208 @ X204)&(in @ X209 @ X204))=>(![X210:$i]:(((in @ X210 @ X205)=>((in @ X208 @ X210)<=>(in @ X209 @ X210))))=>((X208)=(X209))))))&![X211:$i, X212:$i]:((((in @ X211 @ X205)&(in @ X212 @ X205))=>(![X213:$i]:(((in @ X213 @ X211)=>(in @ X213 @ X212)))|![X214:$i]:(((in @ X214 @ X212)=>(in @ X214 @ X211)))))))&![X215:$i]:(((![X216:$i]:(((in @ X216 @ X215)=>(in @ X216 @ X204)))&?[X217:$i]:((in @ X217 @ X215)))=>?[X218:$i, X219:$i]:(((((in @ X218 @ X205)&(in @ X219 @ X215))&~(?[X220:$i]:(((in @ X220 @ X218)&(in @ X220 @ X215)))))&![X221:$i]:(((in @ X221 @ X205)=>(![X222:$i]:(((in @ X222 @ X221)=>(in @ X222 @ X218)))|(in @ X219 @ X221)))))))))))), introduced(definition)).
% 0.22/0.28 thf(c_0_82, negated_conjecture, ~((![X175:$i, X176:$i]:((![X177:$i]:(((in @ X177 @ X175)<=>(in @ X177 @ X176)))=>((X175)=(X176))))=>(![X178:$i]:(~(in @ X178 @ emptyset))=>(![X179:$i, X180:$i, X181:$i]:(((in @ X181 @ (setadjoin @ X179 @ X180))<=>(((X181)=(X179))|(in @ X181 @ X180))))=>(![X182:$i, X183:$i]:(((in @ X183 @ (powerset @ X182))<=>![X184:$i]:(((in @ X184 @ X183)=>(in @ X184 @ X182)))))=>(![X185:$i, X186:$i]:(((in @ X186 @ (setunion @ X185))<=>?[X187:$i]:(((in @ X186 @ X187)&(in @ X187 @ X185)))))=>((in @ emptyset @ omega)=>(![X188:$i]:(((in @ X188 @ omega)=>(in @ (setadjoin @ X188 @ X188) @ omega)))=>(![X189:$i]:((((in @ emptyset @ X189)&![X190:$i]:((((in @ X190 @ omega)&(in @ X190 @ X189))=>(in @ (setadjoin @ X190 @ X190) @ X189))))=>![X191:$i]:(((in @ X191 @ omega)=>(in @ X191 @ X189)))))=>(![X192:$i > $i > $o, X193:$i]:((![X194:$i]:(((in @ X194 @ X193)=>?[X195:$i]:(((X192 @ X194 @ X195)&![X196:$i]:(((X192 @ X194 @ X196)=>((X195)=(X196))))))))=>?[X197:$i]:(![X198:$i]:(((in @ X198 @ X197)<=>?[X199:$i]:(((in @ X199 @ X193)&(X192 @ X199 @ X198))))))))=>(![X200:$i]:((?[X201:$i]:((in @ X201 @ X200))=>?[X202:$i]:(((in @ X202 @ X200)&~(?[X203:$i]:(((in @ X203 @ X202)&(in @ X203 @ X200))))))))=>((epred1_0)=>((descrp)=>(![X223:$i, X224:$i > $o, X225:$i]:(((in @ X225 @ X223)=>((X224 @ X225)=>(in @ X225 @ (dsetconstr @ X223 @ (^[Z0:$i]:((X224 @ Z0))))))))=>(![X226:$i, X227:$i > $o, X228:$i]:(((in @ X228 @ (dsetconstr @ X226 @ (^[Z0:$i]:((X227 @ Z0)))))=>(in @ X228 @ X226)))=>(![X229:$i, X230:$i > $o, X231:$i]:(((in @ X231 @ (dsetconstr @ X229 @ (^[Z0:$i]:((X230 @ Z0)))))=>(X230 @ X231)))=>(![X232:$i > $o]:((?[X233:$i]:(((X232 @ X233)&![X234:$i]:(((X232 @ X234)=>((X233)=(X234))))))=>?[X235:$i]:(((X232 @ X235)&![X236:$i]:(((X232 @ X236)=>((X235)=(X236))))))))=>(![X237:$o, X238:$i]:(((in @ X238 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X237)))))=>(X237)))=>(![X239:$i]:(((in @ X239 @ emptyset)=>![X240:$o]:((X240))))=>(![X241:$i]:(~(in @ X241 @ emptyset))=>(![X242:$i]:(~(in @ X242 @ emptyset))=>(![X243:$i > $o]:((?[X244:$i]:(((X243 @ X244)&![X245:$i]:(((X243 @ X245)=>((X244)=(X245))))))=>?[X246:$i]:((X243 @ X246))))=>(![X247:$i, X248:$i]:((![X249:$i]:(((in @ X249 @ X247)=>(in @ X249 @ X248)))=>(![X250:$i]:(((in @ X250 @ X248)=>(in @ X250 @ X247)))=>((X247)=(X248)))))=>(![X251:$i]:((![X252:$i]:(~(in @ X252 @ X251))=>((X251)=(emptyset))))=>(![X253:$i]:((![X254:$i]:(~(in @ X254 @ X253))=>((X253)=(emptyset))))=>(![X255:$i, X256:$i > $o, X257:$i]:(((in @ X257 @ X255)=>((in @ X257 @ (dsetconstr @ X255 @ (^[Z0:$i]:((X256 @ Z0)))))<=>(X256 @ X257))))=>(![X258:$i]:((((X258)!=(emptyset))=>?[X259:$i]:((in @ X259 @ X258))))=>(![X260:$i, X261:$i > $o, X262:$i]:(((in @ X262 @ X260)=>((X261 @ X262)=>((dsetconstr @ X260 @ (^[Z0:$i]:((X261 @ Z0))))!=(emptyset)))))=>(![X263:$i]:((?[X264:$i]:((in @ X264 @ X263))=>((X263)!=(emptyset))))=>(![X265:$i, X266:$i]:((in @ X265 @ (setadjoin @ X265 @ X266)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X267:$i, X268:$i, X269:$i]:(((in @ X269 @ X268)=>(in @ X269 @ (setadjoin @ X267 @ X268))))=>(![X270:$i, X271:$i, X272:$i]:(((in @ X272 @ (setadjoin @ X270 @ X271))=>![X273:$o]:(((((X272)=(X270))=>(X273))=>(((in @ X272 @ X271)=>(X273))=>(X273))))))=>(![X274:$i, X275:$i, X276:$i]:(((in @ X276 @ (setadjoin @ X274 @ X275))=>(((X276)=(X274))|(in @ X276 @ X275))))=>(![X277:$i]:(((dsetconstr @ X277 @ (^[Z0:$i]:(($true))))=(X277)))=>(![X278:$i, X279:$i]:((![X280:$i]:(((in @ X280 @ X279)=>(in @ X280 @ X278)))=>(in @ X279 @ (powerset @ X278))))=>(![X281:$i]:((in @ emptyset @ (powerset @ X281)))=>(![X282:$i]:((in @ emptyset @ (powerset @ X282)))=>(![X283:$i, X284:$i, X285:$i]:(((in @ X284 @ (powerset @ X283))=>((in @ X285 @ X284)=>(in @ X285 @ X283))))=>(![X286:$i, X287:$i, X288:$i]:(((in @ X287 @ X288)=>((in @ X288 @ X286)=>(in @ X287 @ (setunion @ X286)))))=>(![X289:$i, X290:$i]:(((in @ X290 @ (setunion @ X289))=>![X291:$o]:((![X292:$i]:(((in @ X290 @ X292)=>((in @ X292 @ X289)=>(X291))))=>(X291)))))=>(![X293:$i, X294:$i]:(((in @ X294 @ X293)=>(in @ X294 @ (powerset @ (setunion @ X293)))))=>(![X295:$i > $o]:((?[X296:$i]:(((X295 @ X296)&![X297:$i]:(((X295 @ X297)=>((X296)=(X297))))))=>?[X298:$i]:(![X299:$i]:(((X295 @ X299)<=>((X299)=(X298)))))))=>(![X300:$i]:((((X300)!=(emptyset))=>?[X301:$i]:((in @ X301 @ X300))))=>(![X302:$i, X303:$i]:(((in @ X302 @ (setadjoin @ X303 @ emptyset))=>((X302)=(X303))))=>(![X304:$i, X305:$i]:((((X304)!=(X305))=>~(in @ X305 @ (setadjoin @ X304 @ emptyset))))=>(![X306:$i, X307:$i]:((((X306)=(X307))=>(in @ X306 @ (setadjoin @ X307 @ emptyset))))=>(![X308:$i, X309:$i]:(((in @ X308 @ (setadjoin @ X309 @ emptyset))=>(in @ X309 @ (setadjoin @ X308 @ emptyset))))=>(![X310:$i, X311:$i, X312:$i]:(((in @ X312 @ (setadjoin @ X310 @ (setadjoin @ X311 @ emptyset)))=>(((X312)=(X310))|((X312)=(X311)))))=>(![X313:$i, X314:$i]:((in @ X313 @ (setadjoin @ X313 @ (setadjoin @ X314 @ emptyset))))=>(![X315:$i, X316:$i]:((in @ X316 @ (setadjoin @ X315 @ (setadjoin @ X316 @ emptyset))))=>(![X317:$i, X318:$i > $o]:((?[X319:$i]:(((in @ X319 @ X317)&(X318 @ X319)))=>((dsetconstr @ X317 @ (^[Z0:$i]:((X318 @ Z0))))!=(emptyset))))=>(![X320:$i > $o, X321:$i]:(((in @ X321 @ emptyset)=>(X320 @ X321)))=>(![X322:$i, X323:$i > $o]:((~(![X324:$i]:(((in @ X324 @ X322)=>(X323 @ X324))))=>?[X325:$i]:(((in @ X325 @ X322)&~(X323 @ X325)))))=>(![X326:$i, X327:$i > $o]:((![X328:$i]:(((in @ X328 @ X326)=>~(X327 @ X328)))=>~(?[X329:$i]:(((in @ X329 @ X326)&(X327 @ X329))))))=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~(X1 @ X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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)],[c_0_65, foundationAx]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_66]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), c_0_67]), c_0_68]), c_0_69]), wellorderingAx]), setunionI]), powersetE]), c_0_70]), omegaIndAx]), c_0_71]), emptyI]), setext]), c_0_72]), notinemptyset]), emptysetimpfalse]), emptysetE]), c_0_73]), noeltsimpempty]), omegaSAx]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), c_0_74]), c_0_75]), c_0_76]), c_0_77]), setadjoinE]), emptyInPowerset]), emptyinPowerset]), powersetI]), c_0_78]), setadjoinOr]), subPowSU]), c_0_79]), c_0_80]), uniqinunit]), setunionE]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])]), c_0_81])).
% 0.22/0.28 thf(c_0_83, negated_conjecture, ![X330:$i, X331:$i, X333:$i, X334:$i, X335:$i, X336:$i, X337:$i, X338:$i, X339:$i, X340:$i, X341:$i, X343:$i, X344:$i, X346:$i, X347:$i, X348:$i, X349:$i, X350:$i, X352:$i, X353:$i > $i > $o, X354:$i, X356:$i, X359:$i, X361:$i, X362:$i, X363:$i, X364:$i, X366:$i, X367:$i, X368:$i > $o, X369:$i, X370:$i, X371:$i > $o, X372:$i, X373:$i, X374:$i > $o, X375:$i, X376:$i > $o, X377:$i, X380:$i, X381:$o, X382:$i, X383:$i, X384:$o, X385:$i, X386:$i, X387:$i > $o, X388:$i, X391:$i, X392:$i, X395:$i, X397:$i, X399:$i, X400:$i > $o, X401:$i, X402:$i, X404:$i, X405:$i > $o, X406:$i, X407:$i, X408:$i, X409:$i, X410:$i, X411:$i, X412:$i, X413:$i, X414:$i, X415:$i, X416:$i, X417:$o, X418:$i, X419:$i, X420:$i, X421:$i, X422:$i, X423:$i, X425:$i, X426:$i, X427:$i, X428:$i, X429:$i, X430:$i, X431:$i, X432:$i, X433:$i, X434:$i, X435:$o, X437:$i, X438:$i, X439:$i > $o, X440:$i, X443:$i, X444:$i, X445:$i, X447:$i, X448:$i, X449:$i, X450:$i, X451:$i, X452:$i, X453:$i, X454:$i, X455:$i, X456:$i, X457:$i, X458:$i, X459:$i, X460:$i, X461:$i, X462:$i, X463:$i > $o, X464:$i, X465:$i > $o, X466:$i, X467:$i, X468:$i > $o, X469:$i, X471:$i, X472:$i > $o, X474:$i, X477:$i]:((((~(in @ (esk1_2 @ X330 @ X331) @ X330)|~(in @ (esk1_2 @ X330 @ X331) @ X331)|((X330)=(X331)))&((in @ (esk1_2 @ X330 @ X331) @ X330)|(in @ (esk1_2 @ X330 @ X331) @ X331)|((X330)=(X331))))&(~(in @ X333 @ emptyset)&(((~(in @ X336 @ (setadjoin @ X334 @ X335))|(((X336)=(X334))|(in @ X336 @ X335)))&((((X336)!=(X334))|(in @ X336 @ (setadjoin @ X334 @ X335)))&(~(in @ X336 @ X335)|(in @ X336 @ (setadjoin @ X334 @ X335)))))&(((~(in @ X338 @ (powerset @ X337))|(~(in @ X339 @ X338)|(in @ X339 @ X337)))&(((in @ (esk2_2 @ X340 @ X341) @ X341)|(in @ X341 @ (powerset @ X340)))&(~(in @ (esk2_2 @ X340 @ X341) @ X340)|(in @ X341 @ (powerset @ X340)))))&(((((in @ X344 @ (esk3_2 @ X343 @ X344))|~(in @ X344 @ (setunion @ X343)))&((in @ (esk3_2 @ X343 @ X344) @ X343)|~(in @ X344 @ (setunion @ X343))))&(~(in @ X347 @ X348)|~(in @ X348 @ X346)|(in @ X347 @ (setunion @ X346))))&((in @ emptyset @ omega)&((~(in @ X349 @ omega)|(in @ (setadjoin @ X349 @ X349) @ omega))&(((((in @ (esk4_1 @ X350) @ omega)|~(in @ emptyset @ X350)|(~(in @ X352 @ omega)|(in @ X352 @ X350)))&((in @ (esk4_1 @ X350) @ X350)|~(in @ emptyset @ X350)|(~(in @ X352 @ omega)|(in @ X352 @ X350))))&(~(in @ (setadjoin @ (esk4_1 @ X350) @ (esk4_1 @ X350)) @ X350)|~(in @ emptyset @ X350)|(~(in @ X352 @ omega)|(in @ X352 @ X350))))&((((((in @ (esk8_3 @ X353 @ X354 @ X359) @ X354)|~(in @ X359 @ (esk7_2 @ X353 @ X354))|(in @ (esk5_2 @ X353 @ X354) @ X354))&((X353 @ (esk8_3 @ X353 @ X354 @ X359) @ X359)|~(in @ X359 @ (esk7_2 @ X353 @ X354))|(in @ (esk5_2 @ X353 @ X354) @ X354)))&(~(in @ X362 @ X354)|~(X353 @ X362 @ X361)|(in @ X361 @ (esk7_2 @ X353 @ X354))|(in @ (esk5_2 @ X353 @ X354) @ X354)))&(((((in @ (esk8_3 @ X353 @ X354 @ X359) @ X354)|~(in @ X359 @ (esk7_2 @ X353 @ X354))|((X353 @ (esk5_2 @ X353 @ X354) @ (esk6_3 @ X353 @ X354 @ X356))|~(X353 @ (esk5_2 @ X353 @ X354) @ X356)))&((X353 @ (esk8_3 @ X353 @ X354 @ X359) @ X359)|~(in @ X359 @ (esk7_2 @ X353 @ X354))|((X353 @ (esk5_2 @ X353 @ X354) @ (esk6_3 @ X353 @ X354 @ X356))|~(X353 @ (esk5_2 @ X353 @ X354) @ X356))))&(~(in @ X362 @ X354)|~(X353 @ X362 @ X361)|(in @ X361 @ (esk7_2 @ X353 @ X354))|((X353 @ (esk5_2 @ X353 @ X354) @ (esk6_3 @ X353 @ X354 @ X356))|~(X353 @ (esk5_2 @ X353 @ X354) @ X356))))&((((in @ (esk8_3 @ X353 @ X354 @ X359) @ X354)|~(in @ X359 @ (esk7_2 @ X353 @ X354))|(((X356)!=(esk6_3 @ X353 @ X354 @ X356))|~(X353 @ (esk5_2 @ X353 @ X354) @ X356)))&((X353 @ (esk8_3 @ X353 @ X354 @ X359) @ X359)|~(in @ X359 @ (esk7_2 @ X353 @ X354))|(((X356)!=(esk6_3 @ X353 @ X354 @ X356))|~(X353 @ (esk5_2 @ X353 @ X354) @ X356))))&(~(in @ X362 @ X354)|~(X353 @ X362 @ X361)|(in @ X361 @ (esk7_2 @ X353 @ X354))|(((X356)!=(esk6_3 @ X353 @ X354 @ X356))|~(X353 @ (esk5_2 @ X353 @ X354) @ X356))))))&((((in @ (esk9_1 @ X363) @ X363)|~(in @ X364 @ X363))&(~(in @ X366 @ (esk9_1 @ X363))|~(in @ X366 @ X363)|~(in @ X364 @ X363)))&((epred1_0)&((descrp)&((~(in @ X369 @ X367)|(~(X368 @ X369)|(in @ X369 @ (dsetconstr @ X367 @ (^[Z0:$i]:((X368 @ Z0)))))))&((~(in @ X372 @ (dsetconstr @ X370 @ (^[Z0:$i]:((X371 @ Z0)))))|(in @ X372 @ X370))&((~(in @ X375 @ (dsetconstr @ X373 @ (^[Z0:$i]:((X374 @ Z0)))))|(X374 @ X375))&(((((X376 @ (esk11_1 @ X376))|((X376 @ (esk10_2 @ X376 @ X377))|~(X376 @ X377)))&(~(X376 @ X380)|((esk11_1 @ X376)=(X380))|((X376 @ (esk10_2 @ X376 @ X377))|~(X376 @ X377))))&(((X376 @ (esk11_1 @ X376))|(((X377)!=(esk10_2 @ X376 @ X377))|~(X376 @ X377)))&(~(X376 @ X380)|((esk11_1 @ X376)=(X380))|(((X377)!=(esk10_2 @ X376 @ X377))|~(X376 @ X377)))))&((~(in @ X382 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X381)))))|(X381))&((~(in @ X383 @ emptyset)|(X384))&(~(in @ X385 @ emptyset)&(~(in @ X386 @ emptyset)&((((X387 @ (esk12_2 @ X387 @ X388))|~(X387 @ X388)|(X387 @ (esk13_1 @ X387)))&(((X388)!=(esk12_2 @ X387 @ X388))|~(X387 @ X388)|(X387 @ (esk13_1 @ X387))))&(((((in @ (esk15_2 @ X391 @ X392) @ X392)|((X391)=(X392))|(in @ (esk14_2 @ X391 @ X392) @ X391))&(~(in @ (esk15_2 @ X391 @ X392) @ X391)|((X391)=(X392))|(in @ (esk14_2 @ X391 @ X392) @ X391)))&(((in @ (esk15_2 @ X391 @ X392) @ X392)|((X391)=(X392))|~(in @ (esk14_2 @ X391 @ X392) @ X392))&(~(in @ (esk15_2 @ X391 @ X392) @ X391)|((X391)=(X392))|~(in @ (esk14_2 @ X391 @ X392) @ X392))))&(((in @ (esk16_1 @ X395) @ X395)|((X395)=(emptyset)))&(((in @ (esk17_1 @ X397) @ X397)|((X397)=(emptyset)))&(((~(in @ X401 @ (dsetconstr @ X399 @ (^[Z0:$i]:((X400 @ Z0)))))|(X400 @ X401)|~(in @ X401 @ X399))&(~(X400 @ X401)|(in @ X401 @ (dsetconstr @ X399 @ (^[Z0:$i]:((X400 @ Z0)))))|~(in @ X401 @ X399)))&((((X402)=(emptyset))|(in @ (esk18_1 @ X402) @ X402))&((~(in @ X406 @ X404)|(~(X405 @ X406)|((dsetconstr @ X404 @ (^[Z0:$i]:((X405 @ Z0))))!=(emptyset))))&((~(in @ X408 @ X407)|((X407)!=(emptyset)))&((in @ X409 @ (setadjoin @ X409 @ X410))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X413 @ X412)|(in @ X413 @ (setadjoin @ X411 @ X412)))&(((((in @ X416 @ X415)|(X417)|((X416)=(X414))|~(in @ X416 @ (setadjoin @ X414 @ X415)))&(~(X417)|(X417)|((X416)=(X414))|~(in @ X416 @ (setadjoin @ X414 @ X415))))&(((in @ X416 @ X415)|(X417)|~(X417)|~(in @ X416 @ (setadjoin @ X414 @ X415)))&(~(X417)|(X417)|~(X417)|~(in @ X416 @ (setadjoin @ X414 @ X415)))))&((~(in @ X420 @ (setadjoin @ X418 @ X419))|(((X420)=(X418))|(in @ X420 @ X419)))&(((dsetconstr @ X421 @ (^[Z0:$i]:(($true))))=(X421))&((((in @ (esk19_2 @ X422 @ X423) @ X423)|(in @ X423 @ (powerset @ X422)))&(~(in @ (esk19_2 @ X422 @ X423) @ X422)|(in @ X423 @ (powerset @ X422))))&((in @ emptyset @ (powerset @ X425))&((in @ emptyset @ (powerset @ X426))&((~(in @ X428 @ (powerset @ X427))|(~(in @ X429 @ X428)|(in @ X429 @ X427)))&((~(in @ X431 @ X432)|(~(in @ X432 @ X430)|(in @ X431 @ (setunion @ X430))))&((((in @ X434 @ (esk20_3 @ X433 @ X434 @ X435))|(X435)|~(in @ X434 @ (setunion @ X433)))&(((in @ (esk20_3 @ X433 @ X434 @ X435) @ X433)|(X435)|~(in @ X434 @ (setunion @ X433)))&(~(X435)|(X435)|~(in @ X434 @ (setunion @ X433)))))&((~(in @ X438 @ X437)|(in @ X438 @ (powerset @ (setunion @ X437))))&((((~(X439 @ X443)|((X443)=(esk22_1 @ X439))|((X439 @ (esk21_2 @ X439 @ X440))|~(X439 @ X440)))&(((X444)!=(esk22_1 @ X439))|(X439 @ X444)|((X439 @ (esk21_2 @ X439 @ X440))|~(X439 @ X440))))&((~(X439 @ X443)|((X443)=(esk22_1 @ X439))|(((X440)!=(esk21_2 @ X439 @ X440))|~(X439 @ X440)))&(((X444)!=(esk22_1 @ X439))|(X439 @ X444)|(((X440)!=(esk21_2 @ X439 @ X440))|~(X439 @ X440)))))&((((X445)=(emptyset))|(in @ (esk23_1 @ X445) @ X445))&((~(in @ X447 @ (setadjoin @ X448 @ emptyset))|((X447)=(X448)))&((((X449)=(X450))|~(in @ X450 @ (setadjoin @ X449 @ emptyset)))&((((X451)!=(X452))|(in @ X451 @ (setadjoin @ X452 @ emptyset)))&((~(in @ X453 @ (setadjoin @ X454 @ emptyset))|(in @ X454 @ (setadjoin @ X453 @ emptyset)))&((~(in @ X457 @ (setadjoin @ X455 @ (setadjoin @ X456 @ emptyset)))|(((X457)=(X455))|((X457)=(X456))))&((in @ X458 @ (setadjoin @ X458 @ (setadjoin @ X459 @ emptyset)))&((in @ X461 @ (setadjoin @ X460 @ (setadjoin @ X461 @ emptyset)))&((~(in @ X464 @ X462)|~(X463 @ X464)|((dsetconstr @ X462 @ (^[Z0:$i]:((X463 @ Z0))))!=(emptyset)))&((~(in @ X466 @ emptyset)|(X465 @ X466))&((((in @ (esk24_2 @ X467 @ X468) @ X467)|(~(in @ X469 @ X467)|(X468 @ X469)))&(~(X468 @ (esk24_2 @ X467 @ X468))|(~(in @ X469 @ X467)|(X468 @ X469))))&((((in @ (esk25_2 @ X471 @ X472) @ X471)|(~(in @ X474 @ X471)|~(X472 @ X474)))&((X472 @ (esk25_2 @ X471 @ X472))|(~(in @ X474 @ X471)|~(X472 @ X474))))&((~(in @ X477 @ esk26_0)|~(epred2_0 @ X477))&((in @ esk27_0 @ esk26_0)&(epred2_0 @ esk27_0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_82])])])])])])).
% 0.22/0.28 thf(c_0_84, negated_conjecture, ![X2:$i]:((~((in @ X2 @ esk26_0))|~((epred2_0 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_83])).
% 0.22/0.28 thf(c_0_85, negated_conjecture, (in @ esk27_0 @ esk26_0), inference(split_conjunct,[status(thm)],[c_0_83])).
% 0.22/0.28 thf(c_0_86, negated_conjecture, (epred2_0 @ esk27_0), inference(split_conjunct,[status(thm)],[c_0_83])).
% 0.22/0.28 thf(c_0_87, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_85]), c_0_86])]), ['proof']).
% 0.22/0.28 % SZS output end CNFRefutation
% 0.22/0.28 % Parsed axioms : 123
% 0.22/0.28 % Removed by relevancy pruning/SinE : 66
% 0.22/0.28 % Initial clauses : 107
% 0.22/0.28 % Removed in clause preprocessing : 4
% 0.22/0.28 % Initial clauses in saturation : 103
% 0.22/0.28 % Processed clauses : 12
% 0.22/0.28 % ...of these trivial : 1
% 0.22/0.28 % ...subsumed : 3
% 0.22/0.28 % ...remaining for further processing : 8
% 0.22/0.28 % Other redundant clauses eliminated : 0
% 0.22/0.28 % Clauses deleted for lack of memory : 0
% 0.22/0.28 % Backward-subsumed : 0
% 0.22/0.28 % Backward-rewritten : 0
% 0.22/0.28 % Generated clauses : 1
% 0.22/0.28 % ...of the previous two non-redundant : 0
% 0.22/0.28 % ...aggressively subsumed : 0
% 0.22/0.28 % Contextual simplify-reflections : 0
% 0.22/0.28 % Paramodulations : 1
% 0.22/0.28 % Factorizations : 0
% 0.22/0.28 % NegExts : 0
% 0.22/0.28 % Equation resolutions : 0
% 0.22/0.28 % Disequality decompositions : 0
% 0.22/0.28 % Total rewrite steps : 2
% 0.22/0.28 % ...of those cached : 0
% 0.22/0.28 % Propositional unsat checks : 0
% 0.22/0.28 % Propositional check models : 0
% 0.22/0.28 % Propositional check unsatisfiable : 0
% 0.22/0.28 % Propositional clauses : 0
% 0.22/0.28 % Propositional clauses after purity: 0
% 0.22/0.28 % Propositional unsat core size : 0
% 0.22/0.28 % Propositional preprocessing time : 0.000
% 0.22/0.28 % Propositional encoding time : 0.000
% 0.22/0.28 % Propositional solver time : 0.000
% 0.22/0.28 % Success case prop preproc time : 0.000
% 0.22/0.28 % Success case prop encoding time : 0.000
% 0.22/0.28 % Success case prop solver time : 0.000
% 0.22/0.28 % Current number of processed clauses : 8
% 0.22/0.28 % Positive orientable unit clauses : 6
% 0.22/0.28 % Positive unorientable unit clauses: 0
% 0.22/0.28 % Negative unit clauses : 1
% 0.22/0.28 % Non-unit-clauses : 1
% 0.22/0.28 % Current number of unprocessed clauses: 91
% 0.22/0.28 % ...number of literals in the above : 282
% 0.22/0.28 % Current number of archived formulas : 0
% 0.22/0.28 % Current number of archived clauses : 0
% 0.22/0.28 % Clause-clause subsumption calls (NU) : 0
% 0.22/0.28 % Rec. Clause-clause subsumption calls : 0
% 0.22/0.28 % Non-unit clause-clause subsumptions : 0
% 0.22/0.28 % Unit Clause-clause subsumption calls : 0
% 0.22/0.28 % Rewrite failures with RHS unbound : 0
% 0.22/0.28 % BW rewrite match attempts : 0
% 0.22/0.28 % BW rewrite match successes : 0
% 0.22/0.28 % Condensation attempts : 0
% 0.22/0.28 % Condensation successes : 0
% 0.22/0.28 % Termbank termtop insertions : 11867
% 0.22/0.28 % Search garbage collected termcells : 4582
% 0.22/0.28
% 0.22/0.28 % -------------------------------------------------
% 0.22/0.28 % User time : 0.006 s
% 0.22/0.28 % System time : 0.008 s
% 0.22/0.28 % Total time : 0.014 s
% 0.22/0.28 % Maximum resident set size: 5300 pages
% 0.22/0.28
% 0.22/0.28 % -------------------------------------------------
% 0.22/0.28 % User time : 0.010 s
% 0.22/0.28 % System time : 0.013 s
% 0.22/0.28 % Total time : 0.023 s
% 0.22/0.28 % Maximum resident set size: 5120 pages
% 0.22/0.28 % E exiting
%------------------------------------------------------------------------------